Copyright	(c) Adam Conner-Sax 2019
License	BSD-3-Clause
Maintainer	adam_conner_sax@yahoo.com
Stability	experimental
Safe Haskell	None
Language	Haskell2010

Knit.Report.Input.Visualization.Diagrams

Contents

Add Diagrams Inputs
re-exports

Description

Functions to Diagrams (from the Diagrams library) to the current Pandoc document.

Synopsis

addDiagramAsSVG :: (PandocEffects effs, Member ToPandoc effs, Member UnusedId effs) => Maybe Text -> Maybe Text -> Double -> Double -> QDiagram SVG V2 Double Any -> Sem effs Text
(<$) :: Functor f => a -> f b -> f a
class Functor f => Applicative (f :: Type -> Type) where
- pure :: a -> f a
- (<*>) :: f (a -> b) -> f a -> f b
- liftA2 :: (a -> b -> c) -> f a -> f b -> f c
- (*>) :: f a -> f b -> f b
- (<*) :: f a -> f b -> f a
class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where
- traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
class Semigroup a where
- (<>) :: a -> a -> a
- sconcat :: NonEmpty a -> a
- stimes :: Integral b => b -> a -> a
liftA :: Applicative f => (a -> b) -> f a -> f b
liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
(<$>) :: Functor f => (a -> b) -> f a -> f b
newtype Const a (b :: k) :: forall k. Type -> k -> Type = Const {
- getConst :: a
}
newtype Identity a = Identity {
- runIdentity :: a
}
simulate :: Rational -> Active a -> [a]
discrete :: [a] -> Active a
movie :: [Active a] -> Active a
(|>>) :: Active a -> Active a -> Active a
(->>) :: Semigroup a => Active a -> Active a -> Active a
after :: Active a -> Active a -> Active a
atTime :: Time Rational -> Active a -> Active a
setEra :: Era Rational -> Active a -> Active a
trimAfter :: Monoid a => Active a -> Active a
trimBefore :: Monoid a => Active a -> Active a
trim :: Monoid a => Active a -> Active a
clampAfter :: Active a -> Active a
clampBefore :: Active a -> Active a
clamp :: Active a -> Active a
snapshot :: Time Rational -> Active a -> Active a
backwards :: Active a -> Active a
shift :: Duration Rational -> Active a -> Active a
during :: Active a -> Active a -> Active a
stretchTo :: Duration Rational -> Active a -> Active a
stretch :: Rational -> Active a -> Active a
interval :: Fractional a => Time Rational -> Time Rational -> Active a
ui :: Fractional a => Active a
isDynamic :: Active a -> Bool
isConstant :: Active a -> Bool
activeEra :: Active a -> Maybe (Era Rational)
activeEnd :: Active a -> a
activeStart :: Active a -> a
runActive :: Active a -> Time Rational -> a
modActive :: (a -> b) -> (Dynamic a -> Dynamic b) -> Active a -> Active b
onActive :: (a -> b) -> (Dynamic a -> b) -> Active a -> b
mkActive :: Time Rational -> Time Rational -> (Time Rational -> a) -> Active a
fromDynamic :: Dynamic a -> Active a
shiftDynamic :: Duration Rational -> Dynamic a -> Dynamic a
onDynamic :: (Time Rational -> Time Rational -> (Time Rational -> a) -> b) -> Dynamic a -> b
mkDynamic :: Time Rational -> Time Rational -> (Time Rational -> a) -> Dynamic a
duration :: Num n => Era n -> Duration n
end :: Era n -> Time n
start :: Era n -> Time n
mkEra :: Time n -> Time n -> Era n
fromDuration :: Duration n -> n
toDuration :: n -> Duration n
data Era n
data Dynamic a = Dynamic {
- era :: Era Rational
- runDynamic :: Time Rational -> a
}
data Active a
fromTime :: Time n -> n
toTime :: n -> Time n
data Duration n
data Time n
class Contravariant (f :: Type -> Type) where
- contramap :: (a -> b) -> f b -> f a
- (>$) :: b -> f b -> f a
option :: b -> (a -> b) -> Option a -> b
mtimesDefault :: (Integral b, Monoid a) => b -> a -> a
diff :: Semigroup m => m -> Endo m
cycle1 :: Semigroup m => m -> m
newtype Min a = Min {
- getMin :: a
}
newtype Max a = Max {
- getMax :: a
}
data Arg a b = Arg a b
type ArgMin a b = Min (Arg a b)
type ArgMax a b = Max (Arg a b)
newtype First a = First {
- getFirst :: a
}
newtype Last a = Last {
- getLast :: a
}
newtype WrappedMonoid m = WrapMonoid {
- unwrapMonoid :: m
}
newtype Option a = Option {
- getOption :: Maybe a
}
class Bifunctor (p :: Type -> Type -> Type) where
- bimap :: (a -> b) -> (c -> d) -> p a c -> p b d
stimesMonoid :: (Integral b, Monoid a) => b -> a -> a
stimesIdempotent :: Integral b => b -> a -> a
newtype Dual a = Dual {
- getDual :: a
}
newtype Endo a = Endo {
- appEndo :: a -> a
}
newtype All = All {
- getAll :: Bool
}
newtype Any = Any {
- getAny :: Bool
}
newtype Sum a = Sum {
- getSum :: a
}
newtype Product a = Product {
- getProduct :: a
}
(&) :: a -> (a -> b) -> b
(<&>) :: Functor f => f a -> (a -> b) -> f b
stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a
yellowgreen :: (Ord a, Floating a) => Colour a
yellow :: (Ord a, Floating a) => Colour a
whitesmoke :: (Ord a, Floating a) => Colour a
white :: (Ord a, Floating a) => Colour a
wheat :: (Ord a, Floating a) => Colour a
violet :: (Ord a, Floating a) => Colour a
turquoise :: (Ord a, Floating a) => Colour a
tomato :: (Ord a, Floating a) => Colour a
thistle :: (Ord a, Floating a) => Colour a
teal :: (Ord a, Floating a) => Colour a
steelblue :: (Ord a, Floating a) => Colour a
springgreen :: (Ord a, Floating a) => Colour a
snow :: (Ord a, Floating a) => Colour a
slategrey :: (Ord a, Floating a) => Colour a
slategray :: (Ord a, Floating a) => Colour a
slateblue :: (Ord a, Floating a) => Colour a
skyblue :: (Ord a, Floating a) => Colour a
silver :: (Ord a, Floating a) => Colour a
sienna :: (Ord a, Floating a) => Colour a
seashell :: (Ord a, Floating a) => Colour a
seagreen :: (Ord a, Floating a) => Colour a
sandybrown :: (Ord a, Floating a) => Colour a
salmon :: (Ord a, Floating a) => Colour a
saddlebrown :: (Ord a, Floating a) => Colour a
royalblue :: (Ord a, Floating a) => Colour a
rosybrown :: (Ord a, Floating a) => Colour a
red :: (Ord a, Floating a) => Colour a
purple :: (Ord a, Floating a) => Colour a
powderblue :: (Ord a, Floating a) => Colour a
plum :: (Ord a, Floating a) => Colour a
pink :: (Ord a, Floating a) => Colour a
peru :: (Ord a, Floating a) => Colour a
peachpuff :: (Ord a, Floating a) => Colour a
papayawhip :: (Ord a, Floating a) => Colour a
palevioletred :: (Ord a, Floating a) => Colour a
paleturquoise :: (Ord a, Floating a) => Colour a
palegreen :: (Ord a, Floating a) => Colour a
palegoldenrod :: (Ord a, Floating a) => Colour a
orchid :: (Ord a, Floating a) => Colour a
orangered :: (Ord a, Floating a) => Colour a
orange :: (Ord a, Floating a) => Colour a
olivedrab :: (Ord a, Floating a) => Colour a
olive :: (Ord a, Floating a) => Colour a
oldlace :: (Ord a, Floating a) => Colour a
navy :: (Ord a, Floating a) => Colour a
navajowhite :: (Ord a, Floating a) => Colour a
moccasin :: (Ord a, Floating a) => Colour a
mistyrose :: (Ord a, Floating a) => Colour a
mintcream :: (Ord a, Floating a) => Colour a
midnightblue :: (Ord a, Floating a) => Colour a
mediumvioletred :: (Ord a, Floating a) => Colour a
mediumturquoise :: (Ord a, Floating a) => Colour a
mediumspringgreen :: (Ord a, Floating a) => Colour a
mediumslateblue :: (Ord a, Floating a) => Colour a
mediumseagreen :: (Ord a, Floating a) => Colour a
mediumpurple :: (Ord a, Floating a) => Colour a
mediumorchid :: (Ord a, Floating a) => Colour a
mediumblue :: (Ord a, Floating a) => Colour a
mediumaquamarine :: (Ord a, Floating a) => Colour a
maroon :: (Ord a, Floating a) => Colour a
magenta :: (Ord a, Floating a) => Colour a
linen :: (Ord a, Floating a) => Colour a
limegreen :: (Ord a, Floating a) => Colour a
lime :: (Ord a, Floating a) => Colour a
lightyellow :: (Ord a, Floating a) => Colour a
lightsteelblue :: (Ord a, Floating a) => Colour a
lightslategrey :: (Ord a, Floating a) => Colour a
lightslategray :: (Ord a, Floating a) => Colour a
lightskyblue :: (Ord a, Floating a) => Colour a
lightseagreen :: (Ord a, Floating a) => Colour a
lightsalmon :: (Ord a, Floating a) => Colour a
lightpink :: (Ord a, Floating a) => Colour a
lightgrey :: (Ord a, Floating a) => Colour a
lightgreen :: (Ord a, Floating a) => Colour a
lightgray :: (Ord a, Floating a) => Colour a
lightgoldenrodyellow :: (Ord a, Floating a) => Colour a
lightcyan :: (Ord a, Floating a) => Colour a
lightcoral :: (Ord a, Floating a) => Colour a
lightblue :: (Ord a, Floating a) => Colour a
lemonchiffon :: (Ord a, Floating a) => Colour a
lawngreen :: (Ord a, Floating a) => Colour a
lavenderblush :: (Ord a, Floating a) => Colour a
lavender :: (Ord a, Floating a) => Colour a
khaki :: (Ord a, Floating a) => Colour a
ivory :: (Ord a, Floating a) => Colour a
indigo :: (Ord a, Floating a) => Colour a
indianred :: (Ord a, Floating a) => Colour a
hotpink :: (Ord a, Floating a) => Colour a
honeydew :: (Ord a, Floating a) => Colour a
greenyellow :: (Ord a, Floating a) => Colour a
green :: (Ord a, Floating a) => Colour a
grey :: (Ord a, Floating a) => Colour a
gray :: (Ord a, Floating a) => Colour a
goldenrod :: (Ord a, Floating a) => Colour a
gold :: (Ord a, Floating a) => Colour a
ghostwhite :: (Ord a, Floating a) => Colour a
gainsboro :: (Ord a, Floating a) => Colour a
fuchsia :: (Ord a, Floating a) => Colour a
forestgreen :: (Ord a, Floating a) => Colour a
floralwhite :: (Ord a, Floating a) => Colour a
firebrick :: (Ord a, Floating a) => Colour a
dodgerblue :: (Ord a, Floating a) => Colour a
dimgrey :: (Ord a, Floating a) => Colour a
dimgray :: (Ord a, Floating a) => Colour a
deepskyblue :: (Ord a, Floating a) => Colour a
deeppink :: (Ord a, Floating a) => Colour a
darkviolet :: (Ord a, Floating a) => Colour a
darkturquoise :: (Ord a, Floating a) => Colour a
darkslategrey :: (Ord a, Floating a) => Colour a
darkslategray :: (Ord a, Floating a) => Colour a
darkslateblue :: (Ord a, Floating a) => Colour a
darkseagreen :: (Ord a, Floating a) => Colour a
darksalmon :: (Ord a, Floating a) => Colour a
darkred :: (Ord a, Floating a) => Colour a
darkorchid :: (Ord a, Floating a) => Colour a
darkorange :: (Ord a, Floating a) => Colour a
darkolivegreen :: (Ord a, Floating a) => Colour a
darkmagenta :: (Ord a, Floating a) => Colour a
darkkhaki :: (Ord a, Floating a) => Colour a
darkgrey :: (Ord a, Floating a) => Colour a
darkgreen :: (Ord a, Floating a) => Colour a
darkgray :: (Ord a, Floating a) => Colour a
darkgoldenrod :: (Ord a, Floating a) => Colour a
darkcyan :: (Ord a, Floating a) => Colour a
darkblue :: (Ord a, Floating a) => Colour a
cyan :: (Ord a, Floating a) => Colour a
crimson :: (Ord a, Floating a) => Colour a
cornsilk :: (Ord a, Floating a) => Colour a
cornflowerblue :: (Ord a, Floating a) => Colour a
coral :: (Ord a, Floating a) => Colour a
chocolate :: (Ord a, Floating a) => Colour a
chartreuse :: (Ord a, Floating a) => Colour a
cadetblue :: (Ord a, Floating a) => Colour a
burlywood :: (Ord a, Floating a) => Colour a
brown :: (Ord a, Floating a) => Colour a
blueviolet :: (Ord a, Floating a) => Colour a
blue :: (Ord a, Floating a) => Colour a
blanchedalmond :: (Ord a, Floating a) => Colour a
bisque :: (Ord a, Floating a) => Colour a
beige :: (Ord a, Floating a) => Colour a
azure :: (Ord a, Floating a) => Colour a
aquamarine :: (Ord a, Floating a) => Colour a
aqua :: (Ord a, Floating a) => Colour a
antiquewhite :: (Ord a, Floating a) => Colour a
aliceblue :: (Ord a, Floating a) => Colour a
readColourName :: (MonadFail m, Monad m, Ord a, Floating a) => String -> m (Colour a)
sRGBSpace :: (Ord a, Floating a) => RGBSpace a
sRGB24read :: (Ord b, Floating b) => String -> Colour b
sRGB24reads :: (Ord b, Floating b) => ReadS (Colour b)
sRGB24show :: (RealFrac b, Floating b) => Colour b -> String
sRGB24shows :: (RealFrac b, Floating b) => Colour b -> ShowS
toSRGB24 :: (RealFrac b, Floating b) => Colour b -> RGB Word8
toSRGBBounded :: (RealFrac b, Floating b, Integral a, Bounded a) => Colour b -> RGB a
toSRGB :: (Ord b, Floating b) => Colour b -> RGB b
sRGB24 :: (Ord b, Floating b) => Word8 -> Word8 -> Word8 -> Colour b
sRGBBounded :: (Ord b, Floating b, Integral a, Bounded a) => a -> a -> a -> Colour b
sRGB :: (Ord b, Floating b) => b -> b -> b -> Colour b
data RGB a = RGB {
- channelRed :: !a
- channelGreen :: !a
- channelBlue :: !a
}
alphaChannel :: AlphaColour a -> a
blend :: (Num a, AffineSpace f) => a -> f a -> f a -> f a
withOpacity :: Num a => Colour a -> a -> AlphaColour a
dissolve :: Num a => a -> AlphaColour a -> AlphaColour a
opaque :: Num a => Colour a -> AlphaColour a
alphaColourConvert :: (Fractional b, Real a) => AlphaColour a -> AlphaColour b
transparent :: Num a => AlphaColour a
black :: Num a => Colour a
colourConvert :: (Fractional b, Real a) => Colour a -> Colour b
data Colour a
data AlphaColour a
class ColourOps (f :: Type -> Type) where
- darken :: Num a => a -> f a -> f a
class Default a where
- def :: a
class Functor f => Additive (f :: Type -> Type) where
- zero :: Num a => f a
- (^+^) :: Num a => f a -> f a -> f a
- (^-^) :: Num a => f a -> f a -> f a
- lerp :: Num a => a -> f a -> f a -> f a
- liftU2 :: (a -> a -> a) -> f a -> f a -> f a
- liftI2 :: (a -> b -> c) -> f a -> f b -> f c
renderDia :: (Backend b v n, HasLinearMap v, Metric v, Typeable n, OrderedField n, Monoid' m) => b -> Options b v n -> QDiagram b v n m -> Result b v n
renderDiaT :: (Backend b v n, HasLinearMap v, Metric v, Typeable n, OrderedField n, Monoid' m) => b -> Options b v n -> QDiagram b v n m -> (Transformation v n, Result b v n)
lookupSub :: IsName nm => nm -> SubMap b v n m -> Maybe [Subdiagram b v n m]
rememberAs :: IsName a => a -> QDiagram b v n m -> SubMap b v n m -> SubMap b v n m
fromNames :: IsName a => [(a, Subdiagram b v n m)] -> SubMap b v n m
rawSub :: Subdiagram b v n m -> QDiagram b v n m
getSub :: (Metric v, OrderedField n, Semigroup m) => Subdiagram b v n m -> QDiagram b v n m
location :: (Additive v, Num n) => Subdiagram b v n m -> Point v n
subPoint :: (Metric v, OrderedField n) => Point v n -> Subdiagram b v n m
mkSubdiagram :: QDiagram b v n m -> Subdiagram b v n m
atop :: (OrderedField n, Metric v, Semigroup m) => QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m
mkQD :: Prim b v n -> Envelope v n -> Trace v n -> SubMap b v n m -> Query v n m -> QDiagram b v n m
query :: Monoid m => QDiagram b v n m -> Query v n m
localize :: (Metric v, OrderedField n, Semigroup m) => QDiagram b v n m -> QDiagram b v n m
withNames :: (IsName nm, Metric v, Semigroup m, OrderedField n) => [nm] -> ([Subdiagram b v n m] -> QDiagram b v n m -> QDiagram b v n m) -> QDiagram b v n m -> QDiagram b v n m
withNameAll :: (IsName nm, Metric v, Semigroup m, OrderedField n) => nm -> ([Subdiagram b v n m] -> QDiagram b v n m -> QDiagram b v n m) -> QDiagram b v n m -> QDiagram b v n m
withName :: (IsName nm, Metric v, Semigroup m, OrderedField n) => nm -> (Subdiagram b v n m -> QDiagram b v n m -> QDiagram b v n m) -> QDiagram b v n m -> QDiagram b v n m
lookupName :: (IsName nm, Metric v, Semigroup m, OrderedField n) => nm -> QDiagram b v n m -> Maybe (Subdiagram b v n m)
nameSub :: (IsName nm, Metric v, OrderedField n, Semigroup m) => (QDiagram b v n m -> Subdiagram b v n m) -> nm -> QDiagram b v n m -> QDiagram b v n m
names :: (Metric v, Semigroup m, OrderedField n) => QDiagram b v n m -> [(Name, [Point v n])]
subMap :: (Metric v, Semigroup m, OrderedField n) => Lens' (QDiagram b v n m) (SubMap b v n m)
setTrace :: (OrderedField n, Metric v, Semigroup m) => Trace v n -> QDiagram b v n m -> QDiagram b v n m
setEnvelope :: (OrderedField n, Metric v, Monoid' m) => Envelope v n -> QDiagram b v n m -> QDiagram b v n m
envelope :: (OrderedField n, Metric v, Monoid' m) => Lens' (QDiagram b v n m) (Envelope v n)
pointDiagram :: (Metric v, Fractional n) => Point v n -> QDiagram b v n m
groupOpacity :: (Metric v, OrderedField n, Semigroup m) => Double -> QDiagram b v n m -> QDiagram b v n m
opacityGroup :: (Metric v, OrderedField n, Semigroup m) => Double -> QDiagram b v n m -> QDiagram b v n m
href :: (Metric v, OrderedField n, Semigroup m) => String -> QDiagram b v n m -> QDiagram b v n m
type TypeableFloat n = (Typeable n, RealFloat n)
data QDiagram b (v :: Type -> Type) n m
type Diagram b = QDiagram b (V b) (N b) Any
data Subdiagram b (v :: Type -> Type) n m = Subdiagram (QDiagram b v n m) (DownAnnots v n)
newtype SubMap b (v :: Type -> Type) n m = SubMap (Map Name [Subdiagram b v n m])
data Prim b (v :: Type -> Type) n where
- Prim :: forall b (v :: Type -> Type) n p. (Transformable p, Typeable p, Renderable p b) => p -> Prim b (V p) (N p)
class Backend b (v :: Type -> Type) n where
- data Render b (v :: Type -> Type) n :: Type
- type Result b (v :: Type -> Type) n :: Type
- data Options b (v :: Type -> Type) n :: Type
- adjustDia :: (Additive v, Monoid' m, Num n) => b -> Options b v n -> QDiagram b v n m -> (Options b v n, Transformation v n, QDiagram b v n m)
- renderRTree :: b -> Options b v n -> RTree b v n Annotation -> Result b v n
type D (v :: Type -> Type) n = QDiagram NullBackend v n Any
data NullBackend
class Transformable t => Renderable t b where
- render :: b -> t -> Render b (V t) (N t)
juxtaposeDefault :: (Enveloped a, HasOrigin a) => Vn a -> a -> a -> a
class Juxtaposable a where
- juxtapose :: Vn a -> a -> a -> a
size :: (V a ~ v, N a ~ n, Enveloped a, HasBasis v) => a -> v n
radius :: (V a ~ v, N a ~ n, Enveloped a) => v n -> a -> n
diameter :: (V a ~ v, N a ~ n, Enveloped a) => v n -> a -> n
envelopeP :: (V a ~ v, N a ~ n, Enveloped a) => v n -> a -> Point v n
envelopePMay :: (V a ~ v, N a ~ n, Enveloped a) => v n -> a -> Maybe (Point v n)
envelopeV :: Enveloped a => Vn a -> a -> Vn a
envelopeVMay :: Enveloped a => Vn a -> a -> Maybe (Vn a)
mkEnvelope :: (v n -> n) -> Envelope v n
onEnvelope :: ((v n -> n) -> v n -> n) -> Envelope v n -> Envelope v n
appEnvelope :: Envelope v n -> Maybe (v n -> n)
newtype Envelope (v :: Type -> Type) n = Envelope (Option (v n -> Max n))
type OrderedField s = (Floating s, Ord s)
class (Metric (V a), OrderedField (N a)) => Enveloped a where
- getEnvelope :: a -> Envelope (V a) (N a)
newtype Query (v :: Type -> Type) n m = Query {
- runQuery :: Point v n -> m
}
maxRayTraceP :: (n ~ N a, Traced a, Num n) => Point (V a) n -> V a n -> a -> Maybe (Point (V a) n)
maxRayTraceV :: (n ~ N a, Traced a, Num n) => Point (V a) n -> V a n -> a -> Maybe (V a n)
rayTraceP :: (n ~ N a, Traced a, Num n) => Point (V a) n -> V a n -> a -> Maybe (Point (V a) n)
rayTraceV :: (n ~ N a, Traced a, Num n) => Point (V a) n -> V a n -> a -> Maybe (V a n)
maxTraceP :: (n ~ N a, Num n, Traced a) => Point (V a) n -> V a n -> a -> Maybe (Point (V a) n)
maxTraceV :: (n ~ N a, Num n, Traced a) => Point (V a) n -> V a n -> a -> Maybe (V a n)
traceP :: (n ~ N a, Traced a, Num n) => Point (V a) n -> V a n -> a -> Maybe (Point (V a) n)
traceV :: (n ~ N a, Num n, Traced a) => Point (V a) n -> V a n -> a -> Maybe (V a n)
mkTrace :: (Point v n -> v n -> SortedList n) -> Trace v n
getSortedList :: SortedList a -> [a]
mkSortedList :: Ord a => [a] -> SortedList a
data SortedList a
newtype Trace (v :: Type -> Type) n = Trace {
- appTrace :: Point v n -> v n -> SortedList n
}
class (Additive (V a), Ord (N a)) => Traced a where
- getTrace :: a -> Trace (V a) (N a)
(.>) :: (IsName a1, IsName a2) => a1 -> a2 -> Name
eachName :: (Typeable a, Ord a, Show a) => Traversal' Name a
class (Typeable a, Ord a, Show a) => IsName a where
- toName :: a -> Name
data AName
data Name
class Qualifiable q where
- (.>>) :: IsName a => a -> q -> q
applyTAttr :: (AttributeClass a, Transformable a, V a ~ V d, N a ~ N d, HasStyle d) => a -> d -> d
applyMAttr :: (AttributeClass a, N d ~ n, HasStyle d) => Measured n a -> d -> d
applyAttr :: (AttributeClass a, HasStyle d) => a -> d -> d
atTAttr :: (V a ~ v, N a ~ n, AttributeClass a, Transformable a) => Lens' (Style v n) (Maybe a)
atMAttr :: (AttributeClass a, Typeable n) => Lens' (Style v n) (Maybe (Measured n a))
atAttr :: AttributeClass a => Lens' (Style v n) (Maybe a)
getAttr :: AttributeClass a => Style v n -> Maybe a
class (Typeable a, Semigroup a) => AttributeClass a
data Attribute (v :: Type -> Type) n where
- Attribute :: forall (v :: Type -> Type) n a. AttributeClass a => a -> Attribute v n
- MAttribute :: forall (v :: Type -> Type) n a. AttributeClass a => Measured n a -> Attribute v n
- TAttribute :: forall (v :: Type -> Type) n a. (AttributeClass a, Transformable a, V a ~ v, N a ~ n) => a -> Attribute v n
data Style (v :: Type -> Type) n
class HasStyle a where
- applyStyle :: Style (V a) (N a) -> a -> a
scale :: (InSpace v n a, Eq n, Fractional n, Transformable a) => n -> a -> a
scaling :: (Additive v, Fractional n) => n -> Transformation v n
translate :: Transformable t => Vn t -> t -> t
translation :: v n -> Transformation v n
avgScale :: (Additive v, Traversable v, Floating n) => Transformation v n -> n
isReflection :: (Additive v, Traversable v, Num n, Ord n) => Transformation v n -> Bool
determinant :: (Additive v, Traversable v, Num n) => Transformation v n -> n
dimension :: (Additive (V a), Traversable (V a)) => a -> Int
fromLinear :: (Additive v, Num n) => (v n :-: v n) -> (v n :-: v n) -> Transformation v n
papply :: (Additive v, Num n) => Transformation v n -> Point v n -> Point v n
apply :: Transformation v n -> v n -> v n
dropTransl :: (Additive v, Num n) => Transformation v n -> Transformation v n
transl :: Transformation v n -> v n
transp :: Transformation v n -> v n :-: v n
inv :: (Functor v, Num n) => Transformation v n -> Transformation v n
eye :: (HasBasis v, Num n) => v (v n)
lapp :: (u :-: v) -> u -> v
linv :: (u :-: v) -> v :-: u
(<->) :: (u -> v) -> (v -> u) -> u :-: v
data u :-: v
data Transformation (v :: Type -> Type) n
type HasLinearMap (v :: Type -> Type) = (HasBasis v, Traversable v)
type HasBasis (v :: Type -> Type) = (Additive v, Representable v, Rep v ~ E v)
class Transformable t where
- transform :: Transformation (V t) (N t) -> t -> t
newtype TransInv t = TransInv t
place :: (InSpace v n t, HasOrigin t) => t -> Point v n -> t
moveTo :: (InSpace v n t, HasOrigin t) => Point v n -> t -> t
moveOriginBy :: (V t ~ v, N t ~ n, HasOrigin t) => v n -> t -> t
class HasOrigin t where
- moveOriginTo :: Point (V t) (N t) -> t -> t
atMost :: Ord n => Measure n -> Measure n -> Measure n
atLeast :: Ord n => Measure n -> Measure n -> Measure n
scaleLocal :: Num n => n -> Measured n a -> Measured n a
normalized :: Num n => n -> Measure n
global :: Num n => n -> Measure n
local :: Num n => n -> Measure n
output :: n -> Measure n
fromMeasured :: Num n => n -> n -> Measured n a -> a
data Measured n a
type Measure n = Measured n n
(*.) :: (Functor v, Num n) => n -> Point v n -> Point v n
type family V a :: Type -> Type
type family N a :: Type
type Vn a = V a (N a)
type InSpace (v :: Type -> Type) n a = (V a ~ v, N a ~ n, Additive v, Num n)
type SameSpace a b = (V a ~ V b, N a ~ N b)
type Monoid' = Monoid
basis :: (Additive t, Traversable t, Num a) => [t a]
newtype Point (f :: Type -> Type) a = P (f a)
_Point :: Iso' (Point f a) (f a)
origin :: (Additive f, Num a) => Point f a
relative :: (Additive f, Num a) => Point f a -> Iso' (Point f a) (f a)
newtype E (t :: Type -> Type) = E {
- el :: forall x. Lens' (t x) x
}
negated :: (Functor f, Num a) => f a -> f a
sumV :: (Foldable f, Additive v, Num a) => f (v a) -> v a
(*^) :: (Functor f, Num a) => a -> f a -> f a
(^*) :: (Functor f, Num a) => f a -> a -> f a
(^/) :: (Functor f, Fractional a) => f a -> a -> f a
basisFor :: (Traversable t, Num a) => t b -> [t a]
scaled :: (Traversable t, Num a) => t a -> t (t a)
unit :: (Additive t, Num a) => ASetter' (t a) a -> t a
outer :: (Functor f, Functor g, Num a) => f a -> g a -> f (g a)
class Additive f => Metric (f :: Type -> Type) where
- dot :: Num a => f a -> f a -> a
- quadrance :: Num a => f a -> a
- qd :: Num a => f a -> f a -> a
- distance :: Floating a => f a -> f a -> a
- norm :: Floating a => f a -> a
- signorm :: Floating a => f a -> f a
normalize :: (Floating a, Metric f, Epsilon a) => f a -> f a
class Additive (Diff p) => Affine (p :: Type -> Type) where
- type Diff (p :: Type -> Type) :: Type -> Type
- (.-.) :: Num a => p a -> p a -> Diff p a
- (.+^) :: Num a => p a -> Diff p a -> p a
- (.-^) :: Num a => p a -> Diff p a -> p a
qdA :: (Affine p, Foldable (Diff p), Num a) => p a -> p a -> a
distanceA :: (Floating a, Foldable (Diff p), Affine p) => p a -> p a -> a
(.#) :: Coercible b a => (b -> c) -> (a -> b) -> a -> c
(#.) :: Coercible c b => (b -> c) -> (a -> b) -> a -> c
unP :: Point f a -> f a
data family MVector s a :: Type
data family Vector a :: Type
animRect' :: (InSpace V2 n t, Monoid' m, TrailLike t, Enveloped t, Transformable t, Monoid t) => Rational -> QAnimation b V2 n m -> t
animRect :: (InSpace V2 n t, Monoid' m, TrailLike t, Enveloped t, Transformable t, Monoid t) => QAnimation b V2 n m -> t
animEnvelope' :: (OrderedField n, Metric v, Monoid' m) => Rational -> QAnimation b v n m -> QAnimation b v n m
animEnvelope :: (OrderedField n, Metric v, Monoid' m) => QAnimation b v n m -> QAnimation b v n m
type QAnimation b (v :: Type -> Type) n m = Active (QDiagram b v n m)
type Animation b (v :: Type -> Type) n = QAnimation b v n Any
mkHeight :: Num n => n -> SizeSpec V2 n
mkWidth :: Num n => n -> SizeSpec V2 n
dims2D :: n -> n -> SizeSpec V2 n
mkSizeSpec2D :: Num n => Maybe n -> Maybe n -> SizeSpec V2 n
extentY :: (InSpace v n a, R2 v, Enveloped a) => a -> Maybe (n, n)
extentX :: (InSpace v n a, R1 v, Enveloped a) => a -> Maybe (n, n)
height :: (InSpace V2 n a, Enveloped a) => a -> n
width :: (InSpace V2 n a, Enveloped a) => a -> n
sizeAdjustment :: (Additive v, Foldable v, OrderedField n) => SizeSpec v n -> BoundingBox v n -> (v n, Transformation v n)
sizedAs :: (InSpace v n a, SameSpace a b, HasLinearMap v, Transformable a, Enveloped a, Enveloped b) => b -> a -> a
sized :: (InSpace v n a, HasLinearMap v, Transformable a, Enveloped a) => SizeSpec v n -> a -> a
requiredScaling :: (Additive v, Foldable v, Fractional n, Ord n) => SizeSpec v n -> v n -> Transformation v n
requiredScale :: (Additive v, Foldable v, Fractional n, Ord n) => SizeSpec v n -> v n -> n
specToSize :: (Foldable v, Functor v, Num n, Ord n) => n -> SizeSpec v n -> v n
absolute :: (Additive v, Num n) => SizeSpec v n
dims :: v n -> SizeSpec v n
mkSizeSpec :: (Functor v, Num n) => v (Maybe n) -> SizeSpec v n
getSpec :: (Functor v, Num n, Ord n) => SizeSpec v n -> v (Maybe n)
data SizeSpec (v :: Type -> Type) n
bgFrame :: (TypeableFloat n, Renderable (Path V2 n) b) => n -> Colour Double -> QDiagram b V2 n Any -> QDiagram b V2 n Any
bg :: (TypeableFloat n, Renderable (Path V2 n) b) => Colour Double -> QDiagram b V2 n Any -> QDiagram b V2 n Any
boundingRect :: (InSpace V2 n a, SameSpace a t, Enveloped t, Transformable t, TrailLike t, Monoid t, Enveloped a) => a -> t
rectEnvelope :: (OrderedField n, Monoid' m) => Point V2 n -> V2 n -> QDiagram b V2 n m -> QDiagram b V2 n m
extrudeTop :: (OrderedField n, Monoid' m) => n -> QDiagram b V2 n m -> QDiagram b V2 n m
extrudeBottom :: (OrderedField n, Monoid' m) => n -> QDiagram b V2 n m -> QDiagram b V2 n m
extrudeRight :: (OrderedField n, Monoid' m) => n -> QDiagram b V2 n m -> QDiagram b V2 n m
extrudeLeft :: (OrderedField n, Monoid' m) => n -> QDiagram b V2 n m -> QDiagram b V2 n m
padY :: (Metric v, R2 v, Monoid' m, OrderedField n) => n -> QDiagram b v n m -> QDiagram b v n m
padX :: (Metric v, R2 v, OrderedField n, Monoid' m) => n -> QDiagram b v n m -> QDiagram b v n m
strutY :: (Metric v, R2 v, OrderedField n) => n -> QDiagram b v n m
strutX :: (Metric v, R1 v, OrderedField n) => n -> QDiagram b v n m
vsep :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a) => n -> [a] -> a
vcat' :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a) => CatOpts n -> [a] -> a
vcat :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a) => [a] -> a
hsep :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a) => n -> [a] -> a
hcat' :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a) => CatOpts n -> [a] -> a
hcat :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a) => [a] -> a
(|||) :: (InSpace V2 n a, Juxtaposable a, Semigroup a) => a -> a -> a
(===) :: (InSpace V2 n a, Juxtaposable a, Semigroup a) => a -> a -> a
boxGrid :: (Traversable v, Additive v, Num n, Enum n) => n -> BoundingBox v n -> [Point v n]
outside' :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> BoundingBox v n -> Bool
inside' :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> BoundingBox v n -> Bool
contains' :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> Point v n -> Bool
boxFit :: (InSpace v n a, HasBasis v, Enveloped a, Transformable a, Monoid a) => BoundingBox v n -> a -> a
boxTransform :: (Additive v, Fractional n) => BoundingBox v n -> BoundingBox v n -> Maybe (Transformation v n)
centerPoint :: (InSpace v n a, HasBasis v, Enveloped a) => a -> Point v n
mCenterPoint :: (InSpace v n a, HasBasis v, Enveloped a) => a -> Maybe (Point v n)
boxCenter :: (Additive v, Fractional n) => BoundingBox v n -> Maybe (Point v n)
boxExtents :: (Additive v, Num n) => BoundingBox v n -> v n
getAllCorners :: (Additive v, Traversable v) => BoundingBox v n -> [Point v n]
getCorners :: BoundingBox v n -> Maybe (Point v n, Point v n)
isEmptyBox :: BoundingBox v n -> Bool
boundingBox :: (InSpace v n a, HasBasis v, Enveloped a) => a -> BoundingBox v n
fromPoints :: (Additive v, Ord n) => [Point v n] -> BoundingBox v n
fromPoint :: Point v n -> BoundingBox v n
fromCorners :: (Additive v, Foldable v, Ord n) => Point v n -> Point v n -> BoundingBox v n
emptyBox :: BoundingBox v n
data BoundingBox (v :: Type -> Type) n
showLabels :: (TypeableFloat n, Renderable (Text n) b, Semigroup m) => QDiagram b V2 n m -> QDiagram b V2 n Any
showTrace :: (Enum n, TypeableFloat n, Renderable (Path V2 n) b) => QDiagram b V2 n Any -> QDiagram b V2 n Any
showTrace' :: (Enum n, TypeableFloat n, Renderable (Path V2 n) b) => TraceOpts n -> QDiagram b V2 n Any -> QDiagram b V2 n Any
showEnvelope :: (Enum n, TypeableFloat n, Renderable (Path V2 n) b) => QDiagram b V2 n Any -> QDiagram b V2 n Any
showEnvelope' :: (Enum n, TypeableFloat n, Renderable (Path V2 n) b) => EnvelopeOpts n -> QDiagram b V2 n Any -> QDiagram b V2 n Any
showOrigin' :: (TypeableFloat n, Renderable (Path V2 n) b, Monoid' m) => OriginOpts n -> QDiagram b V2 n m -> QDiagram b V2 n m
showOrigin :: (TypeableFloat n, Renderable (Path V2 n) b, Monoid' m) => QDiagram b V2 n m -> QDiagram b V2 n m
tScale :: Lens' (TraceOpts n) n
tPoints :: Lens' (TraceOpts n) Int
tMinSize :: Lens' (TraceOpts n) n
tColor :: Lens' (TraceOpts n) (Colour Double)
ePoints :: Lens' (EnvelopeOpts n) Int
eLineWidth :: Lens (EnvelopeOpts n1) (EnvelopeOpts n2) (Measure n1) (Measure n2)
eColor :: Lens' (EnvelopeOpts n) (Colour Double)
data TraceOpts n = TraceOpts {
- _tColor :: Colour Double
- _tScale :: n
- _tMinSize :: n
- _tPoints :: Int
}
oScale :: Lens' (OriginOpts n) n
oMinSize :: Lens' (OriginOpts n) n
oColor :: Lens' (OriginOpts n) (Colour Double)
data EnvelopeOpts n = EnvelopeOpts {
- _eColor :: Colour Double
- _eLineWidth :: Measure n
- _ePoints :: Int
}
data OriginOpts n = OriginOpts {
- _oColor :: Colour Double
- _oScale :: n
- _oMinSize :: n
}
cubicSpline :: (V t ~ v, N t ~ n, TrailLike t, Fractional (v n)) => Bool -> [Point v n] -> t
bspline :: (TrailLike t, V t ~ v, N t ~ n) => BSpline v n -> t
type BSpline (v :: Type -> Type) n = [Point v n]
facingZ :: (R3 v, Functor v, Fractional n) => Deformation v v n
perspectiveZ1 :: (R3 v, Functor v, Fractional n) => Deformation v v n
parallelZ0 :: (R3 v, Num n) => Deformation v v n
facingY :: (R2 v, Functor v, Fractional n) => Deformation v v n
facingX :: (R1 v, Functor v, Fractional n) => Deformation v v n
perspectiveY1 :: (R2 v, Functor v, Floating n) => Deformation v v n
parallelY0 :: (R2 v, Num n) => Deformation v v n
perspectiveX1 :: (R1 v, Functor v, Fractional n) => Deformation v v n
parallelX0 :: (R1 v, Num n) => Deformation v v n
asDeformation :: (Additive v, Num n) => Transformation v n -> Deformation v v n
newtype Deformation (v :: Type -> Type) (u :: Type -> Type) n = Deformation (Point v n -> Point u n)
class Deformable a b where
- deform' :: N a -> Deformation (V a) (V b) (N a) -> a -> b
- deform :: Deformation (V a) (V b) (N a) -> a -> b
connectOutside' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2) => ArrowOpts n -> n1 -> n2 -> QDiagram b V2 n Any -> QDiagram b V2 n Any
connectOutside :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2) => n1 -> n2 -> QDiagram b V2 n Any -> QDiagram b V2 n Any
connectPerim' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2) => ArrowOpts n -> n1 -> n2 -> Angle n -> Angle n -> QDiagram b V2 n Any -> QDiagram b V2 n Any
connectPerim :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2) => n1 -> n2 -> Angle n -> Angle n -> QDiagram b V2 n Any -> QDiagram b V2 n Any
connect' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2) => ArrowOpts n -> n1 -> n2 -> QDiagram b V2 n Any -> QDiagram b V2 n Any
connect :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2) => n1 -> n2 -> QDiagram b V2 n Any -> QDiagram b V2 n Any
arrowV' :: (TypeableFloat n, Renderable (Path V2 n) b) => ArrowOpts n -> V2 n -> QDiagram b V2 n Any
arrowV :: (TypeableFloat n, Renderable (Path V2 n) b) => V2 n -> QDiagram b V2 n Any
arrowAt' :: (TypeableFloat n, Renderable (Path V2 n) b) => ArrowOpts n -> Point V2 n -> V2 n -> QDiagram b V2 n Any
arrowAt :: (TypeableFloat n, Renderable (Path V2 n) b) => Point V2 n -> V2 n -> QDiagram b V2 n Any
arrowBetween' :: (TypeableFloat n, Renderable (Path V2 n) b) => ArrowOpts n -> Point V2 n -> Point V2 n -> QDiagram b V2 n Any
arrowBetween :: (TypeableFloat n, Renderable (Path V2 n) b) => Point V2 n -> Point V2 n -> QDiagram b V2 n Any
arrow' :: (TypeableFloat n, Renderable (Path V2 n) b) => ArrowOpts n -> n -> QDiagram b V2 n Any
arrow :: (TypeableFloat n, Renderable (Path V2 n) b) => n -> QDiagram b V2 n Any
shaftTexture :: TypeableFloat n => Lens' (ArrowOpts n) (Texture n)
tailTexture :: TypeableFloat n => Lens' (ArrowOpts n) (Texture n)
headTexture :: TypeableFloat n => Lens' (ArrowOpts n) (Texture n)
lengths :: Traversal' (ArrowOpts n) (Measure n)
gap :: Traversal' (ArrowOpts n) (Measure n)
gaps :: Traversal' (ArrowOpts n) (Measure n)
tailStyle :: Lens' (ArrowOpts n) (Style V2 n)
tailLength :: Lens' (ArrowOpts n) (Measure n)
tailGap :: Lens' (ArrowOpts n) (Measure n)
shaftStyle :: Lens' (ArrowOpts n) (Style V2 n)
headStyle :: Lens' (ArrowOpts n) (Style V2 n)
headLength :: Lens' (ArrowOpts n) (Measure n)
headGap :: Lens' (ArrowOpts n) (Measure n)
arrowTail :: Lens' (ArrowOpts n) (ArrowHT n)
arrowShaft :: Lens' (ArrowOpts n) (Trail V2 n)
arrowHead :: Lens' (ArrowOpts n) (ArrowHT n)
straightShaft :: OrderedField n => Trail V2 n
data ArrowOpts n = ArrowOpts {
- _arrowHead :: ArrowHT n
- _arrowTail :: ArrowHT n
- _arrowShaft :: Trail V2 n
- _headGap :: Measure n
- _tailGap :: Measure n
- _headStyle :: Style V2 n
- _headLength :: Measure n
- _tailStyle :: Style V2 n
- _tailLength :: Measure n
- _shaftStyle :: Style V2 n
}
block :: RealFloat n => ArrowHT n
quill :: (Floating n, Ord n) => ArrowHT n
halfDart' :: RealFloat n => ArrowHT n
dart' :: RealFloat n => ArrowHT n
thorn' :: RealFloat n => ArrowHT n
spike' :: RealFloat n => ArrowHT n
tri' :: RealFloat n => ArrowHT n
noTail :: ArrowHT n
lineTail :: RealFloat n => ArrowHT n
arrowtailQuill :: OrderedField n => Angle n -> ArrowHT n
arrowtailBlock :: RealFloat n => Angle n -> ArrowHT n
halfDart :: RealFloat n => ArrowHT n
dart :: RealFloat n => ArrowHT n
thorn :: RealFloat n => ArrowHT n
spike :: RealFloat n => ArrowHT n
tri :: RealFloat n => ArrowHT n
noHead :: ArrowHT n
lineHead :: RealFloat n => ArrowHT n
arrowheadThorn :: RealFloat n => Angle n -> ArrowHT n
arrowheadSpike :: RealFloat n => Angle n -> ArrowHT n
arrowheadHalfDart :: RealFloat n => Angle n -> ArrowHT n
arrowheadDart :: RealFloat n => Angle n -> ArrowHT n
arrowheadTriangle :: RealFloat n => Angle n -> ArrowHT n
type ArrowHT n = n -> n -> (Path V2 n, Path V2 n)
lighter :: HasStyle a => a -> a
bolder :: HasStyle a => a -> a
heavy :: HasStyle a => a -> a
ultraBold :: HasStyle a => a -> a
semiBold :: HasStyle a => a -> a
mediumWeight :: HasStyle a => a -> a
light :: HasStyle a => a -> a
ultraLight :: HasStyle a => a -> a
thinWeight :: HasStyle a => a -> a
bold :: HasStyle a => a -> a
oblique :: HasStyle a => a -> a
italic :: HasStyle a => a -> a
_fontSize :: (Typeable n, OrderedField n) => Lens' (Style v n) (Measure n)
_fontSizeR :: (Typeable n, OrderedField n) => Lens' (Style v n) (Measured n (Recommend n))
fontSizeL :: (N a ~ n, Typeable n, Num n, HasStyle a) => n -> a -> a
fontSizeO :: (N a ~ n, Typeable n, HasStyle a) => n -> a -> a
fontSizeN :: (N a ~ n, Typeable n, Num n, HasStyle a) => n -> a -> a
fontSizeG :: (N a ~ n, Typeable n, Num n, HasStyle a) => n -> a -> a
fontSize :: (N a ~ n, Typeable n, HasStyle a) => Measure n -> a -> a
_font :: Lens' (Style v n) (Maybe String)
font :: HasStyle a => String -> a -> a
baselineText :: (TypeableFloat n, Renderable (Text n) b) => String -> QDiagram b V2 n Any
alignedText :: (TypeableFloat n, Renderable (Text n) b) => n -> n -> String -> QDiagram b V2 n Any
topLeftText :: (TypeableFloat n, Renderable (Text n) b) => String -> QDiagram b V2 n Any
text :: (TypeableFloat n, Renderable (Text n) b) => String -> QDiagram b V2 n Any
fcA :: (InSpace V2 n a, Floating n, Typeable n, HasStyle a) => AlphaColour Double -> a -> a
fc :: (InSpace V2 n a, Floating n, Typeable n, HasStyle a) => Colour Double -> a -> a
recommendFillColor :: (InSpace V2 n a, Color c, Typeable n, Floating n, HasStyle a) => c -> a -> a
fillColor :: (InSpace V2 n a, Color c, Typeable n, Floating n, HasStyle a) => c -> a -> a
_fillTexture :: (Typeable n, Floating n) => Lens' (Style V2 n) (Texture n)
fillTexture :: (InSpace V2 n a, Typeable n, Floating n, HasStyle a) => Texture n -> a -> a
getFillTexture :: FillTexture n -> Texture n
_FillTexture :: Iso' (FillTexture n) (Recommend (Texture n))
lcA :: (InSpace V2 n a, Typeable n, Floating n, HasStyle a) => AlphaColour Double -> a -> a
lc :: (InSpace V2 n a, Typeable n, Floating n, HasStyle a) => Colour Double -> a -> a
lineColor :: (InSpace V2 n a, Color c, Typeable n, Floating n, HasStyle a) => c -> a -> a
_lineTexture :: (Floating n, Typeable n) => Lens' (Style V2 n) (Texture n)
lineTextureA :: (InSpace V2 n a, Typeable n, Floating n, HasStyle a) => LineTexture n -> a -> a
lineTexture :: (InSpace V2 n a, Typeable n, Floating n, HasStyle a) => Texture n -> a -> a
getLineTexture :: LineTexture n -> Texture n
_LineTexture :: Iso (LineTexture n) (LineTexture n') (Texture n) (Texture n')
mkRadialGradient :: Num n => [GradientStop n] -> Point V2 n -> n -> Point V2 n -> n -> SpreadMethod -> Texture n
mkLinearGradient :: Num n => [GradientStop n] -> Point V2 n -> Point V2 n -> SpreadMethod -> Texture n
mkStops :: [(Colour Double, d, Double)] -> [GradientStop d]
defaultRG :: Fractional n => Texture n
defaultLG :: Fractional n => Texture n
solid :: Color a => a -> Texture n
_AC :: Prism' (Texture n) (AlphaColour Double)
_RG :: Prism' (Texture n) (RGradient n)
_LG :: Prism' (Texture n) (LGradient n)
_SC :: Prism' (Texture n) SomeColor
rGradTrans :: Lens' (RGradient n) (Transformation V2 n)
rGradStops :: Lens' (RGradient n) [GradientStop n]
rGradSpreadMethod :: Lens' (RGradient n) SpreadMethod
rGradRadius1 :: Lens' (RGradient n) n
rGradRadius0 :: Lens' (RGradient n) n
rGradCenter1 :: Lens' (RGradient n) (Point V2 n)
rGradCenter0 :: Lens' (RGradient n) (Point V2 n)
data Texture n
- = SC SomeColor
- | LG (LGradient n)
- | RG (RGradient n)
lGradTrans :: Lens' (LGradient n) (Transformation V2 n)
lGradStops :: Lens' (LGradient n) [GradientStop n]
lGradStart :: Lens' (LGradient n) (Point V2 n)
lGradSpreadMethod :: Lens' (LGradient n) SpreadMethod
lGradEnd :: Lens' (LGradient n) (Point V2 n)
data RGradient n = RGradient {
- _rGradStops :: [GradientStop n]
- _rGradCenter0 :: Point V2 n
- _rGradRadius0 :: n
- _rGradCenter1 :: Point V2 n
- _rGradRadius1 :: n
- _rGradTrans :: Transformation V2 n
- _rGradSpreadMethod :: SpreadMethod
}
stopFraction :: Lens' (GradientStop n) n
stopColor :: Lens' (GradientStop n) SomeColor
data SpreadMethod
- = GradPad
- | GradReflect
- | GradRepeat
data LGradient n = LGradient {
- _lGradStops :: [GradientStop n]
- _lGradStart :: Point V2 n
- _lGradEnd :: Point V2 n
- _lGradTrans :: Transformation V2 n
- _lGradSpreadMethod :: SpreadMethod
}
data GradientStop d = GradientStop {
- _stopColor :: SomeColor
- _stopFraction :: d
}
raster :: Num n => (Int -> Int -> AlphaColour Double) -> Int -> Int -> DImage n Embedded
rasterDia :: (TypeableFloat n, Renderable (DImage n Embedded) b) => (Int -> Int -> AlphaColour Double) -> Int -> Int -> QDiagram b V2 n Any
uncheckedImageRef :: Num n => FilePath -> Int -> Int -> DImage n External
loadImageExt :: Num n => FilePath -> IO (Either String (DImage n External))
loadImageEmb :: Num n => FilePath -> IO (Either String (DImage n Embedded))
image :: (TypeableFloat n, Typeable a, Renderable (DImage n a) b) => DImage n a -> QDiagram b V2 n Any
data Embedded
data External
data Native t
data ImageData a where
- ImageRaster :: forall a. DynamicImage -> ImageData Embedded
- ImageRef :: forall a. FilePath -> ImageData External
- ImageNative :: forall a t. t -> ImageData (Native t)
data DImage a b = DImage (ImageData b) Int Int (Transformation V2 a)
intersectPointsT' :: OrderedField n => n -> Located (Trail V2 n) -> Located (Trail V2 n) -> [P2 n]
intersectPointsT :: OrderedField n => Located (Trail V2 n) -> Located (Trail V2 n) -> [P2 n]
intersectPointsP' :: OrderedField n => n -> Path V2 n -> Path V2 n -> [P2 n]
intersectPointsP :: OrderedField n => Path V2 n -> Path V2 n -> [P2 n]
intersectPoints' :: (InSpace V2 n t, SameSpace t s, ToPath t, ToPath s, OrderedField n) => n -> t -> s -> [P2 n]
intersectPoints :: (InSpace V2 n t, SameSpace t s, ToPath t, ToPath s, OrderedField n) => t -> s -> [P2 n]
clipped :: TypeableFloat n => Path V2 n -> QDiagram b V2 n Any -> QDiagram b V2 n Any
clipTo :: TypeableFloat n => Path V2 n -> QDiagram b V2 n Any -> QDiagram b V2 n Any
clipBy :: (HasStyle a, V a ~ V2, N a ~ n, TypeableFloat n) => Path V2 n -> a -> a
_clip :: (Typeable n, OrderedField n) => Lens' (Style V2 n) [Path V2 n]
_Clip :: Iso (Clip n) (Clip n') [Path V2 n] [Path V2 n']
_fillRule :: Lens' (Style V2 n) FillRule
fillRule :: HasStyle a => FillRule -> a -> a
strokeLocLoop :: (TypeableFloat n, Renderable (Path V2 n) b) => Located (Trail' Loop V2 n) -> QDiagram b V2 n Any
strokeLocLine :: (TypeableFloat n, Renderable (Path V2 n) b) => Located (Trail' Line V2 n) -> QDiagram b V2 n Any
strokeLocT :: (TypeableFloat n, Renderable (Path V2 n) b) => Located (Trail V2 n) -> QDiagram b V2 n Any
strokeLocTrail :: (TypeableFloat n, Renderable (Path V2 n) b) => Located (Trail V2 n) -> QDiagram b V2 n Any
strokeLoop :: (TypeableFloat n, Renderable (Path V2 n) b) => Trail' Loop V2 n -> QDiagram b V2 n Any
strokeLine :: (TypeableFloat n, Renderable (Path V2 n) b) => Trail' Line V2 n -> QDiagram b V2 n Any
strokeT' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName a) => StrokeOpts a -> Trail V2 n -> QDiagram b V2 n Any
strokeTrail' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName a) => StrokeOpts a -> Trail V2 n -> QDiagram b V2 n Any
strokeT :: (TypeableFloat n, Renderable (Path V2 n) b) => Trail V2 n -> QDiagram b V2 n Any
strokeTrail :: (TypeableFloat n, Renderable (Path V2 n) b) => Trail V2 n -> QDiagram b V2 n Any
strokePath' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName a) => StrokeOpts a -> Path V2 n -> QDiagram b V2 n Any
strokeP' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName a) => StrokeOpts a -> Path V2 n -> QDiagram b V2 n Any
strokePath :: (TypeableFloat n, Renderable (Path V2 n) b) => Path V2 n -> QDiagram b V2 n Any
strokeP :: (TypeableFloat n, Renderable (Path V2 n) b) => Path V2 n -> QDiagram b V2 n Any
stroke' :: (InSpace V2 n t, ToPath t, TypeableFloat n, Renderable (Path V2 n) b, IsName a) => StrokeOpts a -> t -> QDiagram b V2 n Any
stroke :: (InSpace V2 n t, ToPath t, TypeableFloat n, Renderable (Path V2 n) b) => t -> QDiagram b V2 n Any
vertexNames :: Lens (StrokeOpts a) (StrokeOpts a') [[a]] [[a']]
queryFillRule :: Lens' (StrokeOpts a) FillRule
data FillRule
- = Winding
- | EvenOdd
data StrokeOpts a = StrokeOpts {
- _vertexNames :: [[a]]
- _queryFillRule :: FillRule
}
roundedRect' :: (InSpace V2 n t, TrailLike t, RealFloat n) => n -> n -> RoundedRectOpts n -> t
roundedRect :: (InSpace V2 n t, TrailLike t, RealFloat n) => n -> n -> n -> t
radiusTR :: Lens' (RoundedRectOpts d) d
radiusTL :: Lens' (RoundedRectOpts d) d
radiusBR :: Lens' (RoundedRectOpts d) d
radiusBL :: Lens' (RoundedRectOpts d) d
dodecagon :: (InSpace V2 n t, TrailLike t) => n -> t
hendecagon :: (InSpace V2 n t, TrailLike t) => n -> t
decagon :: (InSpace V2 n t, TrailLike t) => n -> t
nonagon :: (InSpace V2 n t, TrailLike t) => n -> t
octagon :: (InSpace V2 n t, TrailLike t) => n -> t
septagon :: (InSpace V2 n t, TrailLike t) => n -> t
heptagon :: (InSpace V2 n t, TrailLike t) => n -> t
hexagon :: (InSpace V2 n t, TrailLike t) => n -> t
pentagon :: (InSpace V2 n t, TrailLike t) => n -> t
triangle :: (InSpace V2 n t, TrailLike t) => n -> t
eqTriangle :: (InSpace V2 n t, TrailLike t) => n -> t
regPoly :: (InSpace V2 n t, TrailLike t) => Int -> n -> t
rect :: (InSpace V2 n t, TrailLike t) => n -> n -> t
square :: (InSpace V2 n t, TrailLike t) => n -> t
unitSquare :: (InSpace V2 n t, TrailLike t) => t
vrule :: (InSpace V2 n t, TrailLike t) => n -> t
hrule :: (InSpace V2 n t, TrailLike t) => n -> t
data RoundedRectOpts d = RoundedRectOpts {
- _radiusTL :: d
- _radiusTR :: d
- _radiusBL :: d
- _radiusBR :: d
}
star :: OrderedField n => StarOpts -> [Point V2 n] -> Path V2 n
polygon :: (InSpace V2 n t, TrailLike t) => PolygonOpts n -> t
polyTrail :: OrderedField n => PolygonOpts n -> Located (Trail V2 n)
polyType :: Lens' (PolygonOpts n) (PolyType n)
polyOrient :: Lens' (PolygonOpts n) (PolyOrientation n)
polyCenter :: Lens' (PolygonOpts n) (Point V2 n)
data StarOpts
- = StarFun (Int -> Int)
- | StarSkip Int
data PolyType n
- = PolyPolar [Angle n] [n]
- | PolySides [Angle n] [n]
- | PolyRegular Int n
data PolyOrientation n
- = NoOrient
- | OrientH
- | OrientV
- | OrientTo (V2 n)
data PolygonOpts n = PolygonOpts {
- _polyType :: PolyType n
- _polyOrient :: PolyOrientation n
- _polyCenter :: Point V2 n
}
reversePath :: (Metric v, OrderedField n) => Path v n -> Path v n
scalePath :: (HasLinearMap v, Metric v, OrderedField n) => n -> Path v n -> Path v n
partitionPath :: (Located (Trail v n) -> Bool) -> Path v n -> (Path v n, Path v n)
explodePath :: (V t ~ v, N t ~ n, TrailLike t) => Path v n -> [[t]]
fixPath :: (Metric v, OrderedField n) => Path v n -> [[FixedSegment v n]]
pathLocSegments :: (Metric v, OrderedField n) => Path v n -> [[Located (Segment Closed v n)]]
pathCentroid :: (Metric v, OrderedField n) => Path v n -> Point v n
pathOffsets :: (Metric v, OrderedField n) => Path v n -> [v n]
pathVertices :: (Metric v, OrderedField n) => Path v n -> [[Point v n]]
pathVertices' :: (Metric v, OrderedField n) => n -> Path v n -> [[Point v n]]
pathFromLocTrail :: (Metric v, OrderedField n) => Located (Trail v n) -> Path v n
pathFromTrailAt :: (Metric v, OrderedField n) => Trail v n -> Point v n -> Path v n
pathFromTrail :: (Metric v, OrderedField n) => Trail v n -> Path v n
pathTrails :: Path v n -> [Located (Trail v n)]
newtype Path (v :: Type -> Type) n = Path [Located (Trail v n)]
class ToPath t where
- toPath :: t -> Path (V t) (N t)
boundaryFromMay :: (Metric v, OrderedField n, Semigroup m) => Subdiagram b v n m -> v n -> Maybe (Point v n)
boundaryFrom :: (OrderedField n, Metric v, Semigroup m) => Subdiagram b v n m -> v n -> Point v n
composeAligned :: (Monoid' m, Floating n, Ord n, Metric v) => (QDiagram b v n m -> QDiagram b v n m) -> ([QDiagram b v n m] -> QDiagram b v n m) -> [QDiagram b v n m] -> QDiagram b v n m
cat' :: (InSpace v n a, Metric v, Floating n, Juxtaposable a, Monoid' a, HasOrigin a) => v n -> CatOpts n -> [a] -> a
cat :: (InSpace v n a, Metric v, Floating n, Juxtaposable a, Monoid' a, HasOrigin a) => v n -> [a] -> a
sep :: Lens' (CatOpts n) n
catMethod :: Lens' (CatOpts n) CatMethod
atPoints :: (InSpace v n a, HasOrigin a, Monoid' a) => [Point v n] -> [a] -> a
position :: (InSpace v n a, HasOrigin a, Monoid' a) => [(Point v n, a)] -> a
appends :: (Juxtaposable a, Monoid' a) => a -> [(Vn a, a)] -> a
atDirection :: (InSpace v n a, Metric v, Floating n, Juxtaposable a, Semigroup a) => Direction v n -> a -> a -> a
beside :: (Juxtaposable a, Semigroup a) => Vn a -> a -> a -> a
beneath :: (Metric v, OrderedField n, Monoid' m) => QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m
intrudeEnvelope :: (Metric v, OrderedField n, Monoid' m) => v n -> QDiagram b v n m -> QDiagram b v n m
extrudeEnvelope :: (Metric v, OrderedField n, Monoid' m) => v n -> QDiagram b v n m -> QDiagram b v n m
strut :: (Metric v, OrderedField n) => v n -> QDiagram b v n m
frame :: (Metric v, OrderedField n, Monoid' m) => n -> QDiagram b v n m -> QDiagram b v n m
pad :: (Metric v, OrderedField n, Monoid' m) => n -> QDiagram b v n m -> QDiagram b v n m
phantom :: (InSpace v n a, Monoid' m, Enveloped a, Traced a) => a -> QDiagram b v n m
withTrace :: (InSpace v n a, Metric v, OrderedField n, Monoid' m, Traced a) => a -> QDiagram b v n m -> QDiagram b v n m
withEnvelope :: (InSpace v n a, Monoid' m, Enveloped a) => a -> QDiagram b v n m -> QDiagram b v n m
data CatMethod
- = Cat
- | Distrib
data CatOpts n
ellipseXY :: (TrailLike t, V t ~ V2, N t ~ n, Transformable t) => n -> n -> t
ellipse :: (TrailLike t, V t ~ V2, N t ~ n, Transformable t) => n -> t
circle :: (TrailLike t, V t ~ V2, N t ~ n, Transformable t) => n -> t
unitCircle :: (TrailLike t, V t ~ V2, N t ~ n) => t
annularWedge :: (TrailLike t, V t ~ V2, N t ~ n, RealFloat n) => n -> n -> Direction V2 n -> Angle n -> t
arcBetween :: (TrailLike t, V t ~ V2, N t ~ n, RealFloat n) => Point V2 n -> Point V2 n -> n -> t
wedge :: (InSpace V2 n t, OrderedField n, TrailLike t) => n -> Direction V2 n -> Angle n -> t
arcCW :: (InSpace V2 n t, RealFloat n, TrailLike t) => Direction V2 n -> Direction V2 n -> t
arcCCW :: (InSpace V2 n t, RealFloat n, TrailLike t) => Direction V2 n -> Direction V2 n -> t
arc' :: (InSpace V2 n t, OrderedField n, TrailLike t) => n -> Direction V2 n -> Angle n -> t
arc :: (InSpace V2 n t, OrderedField n, TrailLike t) => Direction V2 n -> Angle n -> t
explodeTrail :: (V t ~ v, N t ~ n, TrailLike t) => Located (Trail v n) -> [t]
(~~) :: (V t ~ v, N t ~ n, TrailLike t) => Point v n -> Point v n -> t
fromVertices :: TrailLike t => [Point (V t) (N t)] -> t
fromLocOffsets :: (V t ~ v, N t ~ n, V (v n) ~ v, N (v n) ~ n, TrailLike t) => Located [v n] -> t
fromOffsets :: TrailLike t => [Vn t] -> t
fromLocSegments :: TrailLike t => Located [Segment Closed (V t) (N t)] -> t
fromSegments :: TrailLike t => [Segment Closed (V t) (N t)] -> t
class (Metric (V t), OrderedField (N t)) => TrailLike t where
- trailLike :: Located (Trail (V t) (N t)) -> t
reverseLocLoop :: (Metric v, OrderedField n) => Located (Trail' Loop v n) -> Located (Trail' Loop v n)
reverseLoop :: (Metric v, OrderedField n) => Trail' Loop v n -> Trail' Loop v n
reverseLocLine :: (Metric v, OrderedField n) => Located (Trail' Line v n) -> Located (Trail' Line v n)
reverseLine :: (Metric v, OrderedField n) => Trail' Line v n -> Trail' Line v n
reverseLocTrail :: (Metric v, OrderedField n) => Located (Trail v n) -> Located (Trail v n)
reverseTrail :: (Metric v, OrderedField n) => Trail v n -> Trail v n
trailLocSegments :: (Metric v, OrderedField n) => Located (Trail v n) -> [Located (Segment Closed v n)]
unfixTrail :: (Metric v, Ord n, Floating n) => [FixedSegment v n] -> Located (Trail v n)
fixTrail :: (Metric v, OrderedField n) => Located (Trail v n) -> [FixedSegment v n]
loopVertices :: (Metric v, OrderedField n) => Located (Trail' Loop v n) -> [Point v n]
loopVertices' :: (Metric v, OrderedField n) => n -> Located (Trail' Loop v n) -> [Point v n]
lineVertices :: (Metric v, OrderedField n) => Located (Trail' Line v n) -> [Point v n]
lineVertices' :: (Metric v, OrderedField n) => n -> Located (Trail' Line v n) -> [Point v n]
trailVertices :: (Metric v, OrderedField n) => Located (Trail v n) -> [Point v n]
trailVertices' :: (Metric v, OrderedField n) => n -> Located (Trail v n) -> [Point v n]
lineOffset :: (Metric v, OrderedField n) => Trail' Line v n -> v n
loopOffsets :: (Metric v, OrderedField n) => Trail' Loop v n -> [v n]
lineOffsets :: Trail' Line v n -> [v n]
trailOffset :: (Metric v, OrderedField n) => Trail v n -> v n
trailOffsets :: (Metric v, OrderedField n) => Trail v n -> [v n]
trailSegments :: (Metric v, OrderedField n) => Trail v n -> [Segment Closed v n]
loopSegments :: Trail' Loop v n -> ([Segment Closed v n], Segment Open v n)
onLineSegments :: (Metric v, OrderedField n) => ([Segment Closed v n] -> [Segment Closed v n]) -> Trail' Line v n -> Trail' Line v n
lineSegments :: Trail' Line v n -> [Segment Closed v n]
isLoop :: Trail v n -> Bool
isLine :: Trail v n -> Bool
isTrailEmpty :: (Metric v, OrderedField n) => Trail v n -> Bool
isLineEmpty :: (Metric v, OrderedField n) => Trail' Line v n -> Bool
cutTrail :: (Metric v, OrderedField n) => Trail v n -> Trail v n
cutLoop :: (Metric v, OrderedField n) => Trail' Loop v n -> Trail' Line v n
closeTrail :: Trail v n -> Trail v n
closeLine :: Trail' Line v n -> Trail' Loop v n
glueTrail :: (Metric v, OrderedField n) => Trail v n -> Trail v n
glueLine :: (Metric v, OrderedField n) => Trail' Line v n -> Trail' Loop v n
trailFromVertices :: (Metric v, OrderedField n) => [Point v n] -> Trail v n
lineFromVertices :: (Metric v, OrderedField n) => [Point v n] -> Trail' Line v n
trailFromOffsets :: (Metric v, OrderedField n) => [v n] -> Trail v n
lineFromOffsets :: (Metric v, OrderedField n) => [v n] -> Trail' Line v n
trailFromSegments :: (Metric v, OrderedField n) => [Segment Closed v n] -> Trail v n
loopFromSegments :: (Metric v, OrderedField n) => [Segment Closed v n] -> Segment Open v n -> Trail' Loop v n
lineFromSegments :: (Metric v, OrderedField n) => [Segment Closed v n] -> Trail' Line v n
emptyTrail :: (Metric v, OrderedField n) => Trail v n
emptyLine :: (Metric v, OrderedField n) => Trail' Line v n
wrapLoop :: Trail' Loop v n -> Trail v n
wrapLine :: Trail' Line v n -> Trail v n
wrapTrail :: Trail' l v n -> Trail v n
onLine :: (Metric v, OrderedField n) => (Trail' Line v n -> Trail' Line v n) -> Trail v n -> Trail v n
withLine :: (Metric v, OrderedField n) => (Trail' Line v n -> r) -> Trail v n -> r
onTrail :: (Trail' Line v n -> Trail' l1 v n) -> (Trail' Loop v n -> Trail' l2 v n) -> Trail v n -> Trail v n
withTrail :: (Trail' Line v n -> r) -> (Trail' Loop v n -> r) -> Trail v n -> r
_LocLoop :: Prism' (Located (Trail v n)) (Located (Trail' Loop v n))
_LocLine :: Prism' (Located (Trail v n)) (Located (Trail' Line v n))
_Loop :: Prism' (Trail v n) (Trail' Loop v n)
_Line :: Prism' (Trail v n) (Trail' Line v n)
getSegment :: t -> GetSegment t
withTrail' :: (Trail' Line v n -> r) -> (Trail' Loop v n -> r) -> Trail' l v n -> r
offset :: (OrderedField n, Metric v, Measured (SegMeasure v n) t) => t -> v n
numSegs :: (Num c, Measured (SegMeasure v n) a) => a -> c
trailMeasure :: (SegMeasure v n :>: m, Measured (SegMeasure v n) t) => a -> (m -> a) -> t -> a
newtype SegTree (v :: Type -> Type) n = SegTree (FingerTree (SegMeasure v n) (Segment Closed v n))
data Line
data Loop
data Trail' l (v :: Type -> Type) n where
- Line :: forall l (v :: Type -> Type) n. SegTree v n -> Trail' Line v n
- Loop :: forall l (v :: Type -> Type) n. SegTree v n -> Segment Open v n -> Trail' Loop v n
newtype GetSegment t = GetSegment t
newtype GetSegmentCodomain (v :: Type -> Type) n = GetSegmentCodomain (Maybe (v n, Segment Closed v n, AnIso' n n))
data Trail (v :: Type -> Type) n where
- Trail :: forall (v :: Type -> Type) n l. Trail' l v n -> Trail v n
normalAtEnd :: (InSpace V2 n t, EndValues (Tangent t), Floating n) => t -> V2 n
normalAtStart :: (InSpace V2 n t, EndValues (Tangent t), Floating n) => t -> V2 n
normalAtParam :: (InSpace V2 n t, Parametric (Tangent t), Floating n) => t -> n -> V2 n
tangentAtEnd :: EndValues (Tangent t) => t -> Vn t
tangentAtStart :: EndValues (Tangent t) => t -> Vn t
tangentAtParam :: Parametric (Tangent t) => t -> N t -> Vn t
newtype Tangent t = Tangent t
oeOffset :: Lens' (OffsetEnvelope v n) (TotalOffset v n)
oeEnvelope :: Lens' (OffsetEnvelope v n) (Envelope v n)
type SegMeasure (v :: Type -> Type) n = SegCount ::: (ArcLength n ::: (OffsetEnvelope v n ::: ()))
getArcLengthBounded :: (Num n, Ord n) => n -> ArcLength n -> Interval n
getArcLengthFun :: ArcLength n -> n -> Interval n
getArcLengthCached :: ArcLength n -> Interval n
fixedSegIso :: (Num n, Additive v) => Iso' (FixedSegment v n) (Located (Segment Closed v n))
fromFixedSeg :: (Num n, Additive v) => FixedSegment v n -> Located (Segment Closed v n)
mkFixedSeg :: (Num n, Additive v) => Located (Segment Closed v n) -> FixedSegment v n
reverseSegment :: (Num n, Additive v) => Segment Closed v n -> Segment Closed v n
openCubic :: v n -> v n -> Segment Open v n
openLinear :: Segment Open v n
segOffset :: Segment Closed v n -> v n
bézier3 :: v n -> v n -> v n -> Segment Closed v n
bezier3 :: v n -> v n -> v n -> Segment Closed v n
straight :: v n -> Segment Closed v n
mapSegmentVectors :: (v n -> v' n') -> Segment c v n -> Segment c v' n'
data Open
data Closed
data Offset c (v :: Type -> Type) n where
- OffsetOpen :: forall c (v :: Type -> Type) n. Offset Open v n
- OffsetClosed :: forall c (v :: Type -> Type) n. v n -> Offset Closed v n
data Segment c (v :: Type -> Type) n
- = Linear !(Offset c v n)
- | Cubic !(v n) !(v n) !(Offset c v n)
data FixedSegment (v :: Type -> Type) n
- = FLinear (Point v n) (Point v n)
- | FCubic (Point v n) (Point v n) (Point v n) (Point v n)
newtype SegCount = SegCount (Sum Int)
newtype ArcLength n = ArcLength (Sum (Interval n), n -> Sum (Interval n))
newtype TotalOffset (v :: Type -> Type) n = TotalOffset (v n)
data OffsetEnvelope (v :: Type -> Type) n = OffsetEnvelope {
- _oeOffset :: !(TotalOffset v n)
- _oeEnvelope :: Envelope v n
}
_loc :: Lens' (Located a) (Point (V a) (N a))
located :: SameSpace a b => Lens (Located a) (Located b) a b
mapLoc :: SameSpace a b => (a -> b) -> Located a -> Located b
viewLoc :: Located a -> (Point (V a) (N a), a)
at :: a -> Point (V a) (N a) -> Located a
data Located a = Loc {
- loc :: Point (V a) (N a)
- unLoc :: a
}
snugCenterXYZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
centerXYZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a
snugCenterYZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
centerYZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a
snugCenterXZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
centerXZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a
snugCenterZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
centerZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a
snugZ :: (V a ~ v, N a ~ n, Alignable a, Traced a, HasOrigin a, R3 v, Fractional n) => n -> a -> a
alignZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => n -> a -> a
snugZMax :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
alignZMax :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a
snugZMin :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
alignZMin :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a
snugYMax :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
alignYMax :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a) => a -> a
snugYMin :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
alignYMin :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a) => a -> a
snugXMax :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
alignXMax :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a) => a -> a
snugXMin :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
alignXMin :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a) => a -> a
snugCenterXY :: (InSpace v n a, R2 v, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a
centerXY :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a) => a -> a
snugCenterY :: (InSpace v n a, R2 v, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a
centerY :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a) => a -> a
snugCenterX :: (InSpace v n a, R1 v, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a
centerX :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a) => a -> a
snugY :: (InSpace v n a, R2 v, Fractional n, Alignable a, Traced a, HasOrigin a) => n -> a -> a
alignY :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a) => n -> a -> a
snugX :: (InSpace v n a, R1 v, Fractional n, Alignable a, Traced a, HasOrigin a) => n -> a -> a
alignX :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a) => n -> a -> a
alignBR :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a
alignBL :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a
alignTR :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a
alignTL :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a
snugB :: (InSpace V2 n a, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a
alignB :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a
snugT :: (InSpace V2 n a, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a
alignT :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a
snugR :: (InSpace V2 n a, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a
alignR :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a
snugL :: (InSpace V2 n a, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a
alignL :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a
snugCenter :: (InSpace v n a, Traversable v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
snugCenterV :: (InSpace v n a, Fractional n, Alignable a, Traced a, HasOrigin a) => v n -> a -> a
center :: (InSpace v n a, Fractional n, Traversable v, Alignable a, HasOrigin a) => a -> a
centerV :: (InSpace v n a, Fractional n, Alignable a, HasOrigin a) => v n -> a -> a
snug :: (InSpace v n a, Fractional n, Alignable a, Traced a, HasOrigin a) => v n -> a -> a
snugBy :: (InSpace v n a, Fractional n, Alignable a, Traced a, HasOrigin a) => v n -> n -> a -> a
align :: (InSpace v n a, Fractional n, Alignable a, HasOrigin a) => v n -> a -> a
traceBoundary :: (V a ~ v, N a ~ n, Num n, Traced a) => v n -> a -> Point v n
envelopeBoundary :: (V a ~ v, N a ~ n, Enveloped a) => v n -> a -> Point v n
alignBy'Default :: (InSpace v n a, Fractional n, HasOrigin a) => (v n -> a -> Point v n) -> v n -> n -> a -> a
class Alignable a where
- alignBy' :: (InSpace v n a, Fractional n, HasOrigin a) => (v n -> a -> Point v n) -> v n -> n -> a -> a
- defaultBoundary :: (V a ~ v, N a ~ n) => v n -> a -> Point v n
- alignBy :: (InSpace v n a, Fractional n, HasOrigin a) => v n -> n -> a -> a
globalPackage :: IO FilePath
findSandbox :: [FilePath] -> IO (Maybe FilePath)
findHsFile :: FilePath -> IO (Maybe FilePath)
foldB :: (a -> a -> a) -> a -> [a] -> a
tau :: Floating a => a
iterateN :: Int -> (a -> a) -> a -> [a]
(##) :: AReview t b -> b -> t
(#) :: a -> (a -> b) -> b
applyAll :: [a -> a] -> a -> a
with :: Default d => d
camAspect :: (Floating n, CameraLens l) => Camera l n -> n
camLens :: Camera l n -> l n
camRight :: Fractional n => Camera l n -> Direction V3 n
camUp :: Camera l n -> Direction V3 n
camForward :: Camera l n -> Direction V3 n
mm50Narrow :: Floating n => PerspectiveLens n
mm50Wide :: Floating n => PerspectiveLens n
mm50 :: Floating n => PerspectiveLens n
facing_ZCamera :: (Floating n, Ord n, Typeable n, CameraLens l, Renderable (Camera l n) b) => l n -> QDiagram b V3 n Any
mm50Camera :: (Typeable n, Floating n, Ord n, Renderable (Camera PerspectiveLens n) b) => QDiagram b V3 n Any
orthoWidth :: Lens' (OrthoLens n) n
orthoHeight :: Lens' (OrthoLens n) n
verticalFieldOfView :: Lens' (PerspectiveLens n) (Angle n)
horizontalFieldOfView :: Lens' (PerspectiveLens n) (Angle n)
data OrthoLens n = OrthoLens {
- _orthoWidth :: n
- _orthoHeight :: n
}
data Camera (l :: Type -> Type) n
data PerspectiveLens n = PerspectiveLens {
- _horizontalFieldOfView :: Angle n
- _verticalFieldOfView :: Angle n
}
difference :: (CsgPrim a, CsgPrim b) => a n -> b n -> CSG n
intersection :: (CsgPrim a, CsgPrim b) => a n -> b n -> CSG n
union :: (CsgPrim a, CsgPrim b) => a n -> b n -> CSG n
cylinder :: Num n => Frustum n
cone :: Num n => Frustum n
frustum :: Num n => n -> n -> Frustum n
cube :: Num n => Box n
sphere :: Num n => Ellipsoid n
data Ellipsoid n = Ellipsoid (Transformation V3 n)
data Box n = Box (Transformation V3 n)
data Frustum n = Frustum n n (Transformation V3 n)
class Skinned t where
- skin :: (Renderable t b, N t ~ n, TypeableFloat n) => t -> QDiagram b V3 n Any
data CSG n
- = CsgEllipsoid (Ellipsoid n)
- | CsgBox (Box n)
- | CsgFrustum (Frustum n)
- | CsgUnion [CSG n]
- | CsgIntersection [CSG n]
- | CsgDifference (CSG n) (CSG n)
zDir :: (R3 v, Additive v, Num n) => Direction v n
unit_Z :: (R3 v, Additive v, Num n) => v n
unitZ :: (R3 v, Additive v, Num n) => v n
reflectAcross :: (InSpace v n t, Metric v, Fractional n, Transformable t) => Point v n -> v n -> t -> t
reflectionAcross :: (Metric v, Fractional n) => Point v n -> v n -> Transformation v n
reflectZ :: (InSpace v n t, R3 v, Transformable t) => t -> t
reflectionZ :: (Additive v, R3 v, Num n) => Transformation v n
translateZ :: (InSpace v n t, R3 v, Transformable t) => n -> t -> t
translationZ :: (Additive v, R3 v, Num n) => n -> Transformation v n
scaleZ :: (InSpace v n t, R3 v, Fractional n, Transformable t) => n -> t -> t
scalingZ :: (Additive v, R3 v, Fractional n) => n -> Transformation v n
pointAt' :: (Floating n, Ord n) => V3 n -> V3 n -> V3 n -> Transformation V3 n
pointAt :: (Floating n, Ord n) => Direction V3 n -> Direction V3 n -> Direction V3 n -> Transformation V3 n
rotateAbout :: (InSpace V3 n t, Floating n, Transformable t) => Point V3 n -> Direction V3 n -> Angle n -> t -> t
rotationAbout :: Floating n => Point V3 n -> Direction V3 n -> Angle n -> Transformation V3 n
aboutY :: Floating n => Angle n -> Transformation V3 n
aboutX :: Floating n => Angle n -> Transformation V3 n
aboutZ :: Floating n => Angle n -> Transformation V3 n
shearY :: (InSpace V2 n t, Transformable t) => n -> t -> t
shearingY :: Num n => n -> T2 n
shearX :: (InSpace V2 n t, Transformable t) => n -> t -> t
shearingX :: Num n => n -> T2 n
reflectAbout :: (InSpace V2 n t, OrderedField n, Transformable t) => P2 n -> Direction V2 n -> t -> t
reflectionAbout :: OrderedField n => P2 n -> Direction V2 n -> T2 n
reflectXY :: (InSpace v n t, R2 v, Transformable t) => t -> t
reflectionXY :: (Additive v, R2 v, Num n) => Transformation v n
reflectY :: (InSpace v n t, R2 v, Transformable t) => t -> t
reflectionY :: (Additive v, R2 v, Num n) => Transformation v n
reflectX :: (InSpace v n t, R1 v, Transformable t) => t -> t
reflectionX :: (Additive v, R1 v, Num n) => Transformation v n
scaleRotateTo :: (InSpace V2 n t, Transformable t, Floating n) => V2 n -> t -> t
scalingRotationTo :: Floating n => V2 n -> T2 n
translateY :: (InSpace v n t, R2 v, Transformable t) => n -> t -> t
translationY :: (Additive v, R2 v, Num n) => n -> Transformation v n
translateX :: (InSpace v n t, R1 v, Transformable t) => n -> t -> t
translationX :: (Additive v, R1 v, Num n) => n -> Transformation v n
scaleUToY :: (InSpace v n t, R2 v, Enveloped t, Transformable t) => n -> t -> t
scaleUToX :: (InSpace v n t, R1 v, Enveloped t, Transformable t) => n -> t -> t
scaleToY :: (InSpace v n t, R2 v, Enveloped t, Transformable t) => n -> t -> t
scaleToX :: (InSpace v n t, R2 v, Enveloped t, Transformable t) => n -> t -> t
scaleY :: (InSpace v n t, R2 v, Fractional n, Transformable t) => n -> t -> t
scalingY :: (Additive v, R2 v, Fractional n) => n -> Transformation v n
scaleX :: (InSpace v n t, R2 v, Fractional n, Transformable t) => n -> t -> t
scalingX :: (Additive v, R1 v, Fractional n) => n -> Transformation v n
rotateTo :: (InSpace V2 n t, OrderedField n, Transformable t) => Direction V2 n -> t -> t
rotationTo :: OrderedField n => Direction V2 n -> T2 n
rotateAround :: (InSpace V2 n t, Transformable t, Floating n) => P2 n -> Angle n -> t -> t
rotationAround :: Floating n => P2 n -> Angle n -> T2 n
rotated :: (InSpace V2 n a, Floating n, SameSpace a b, Transformable a, Transformable b) => Angle n -> Iso a b a b
rotateBy :: (InSpace V2 n t, Transformable t, Floating n) => n -> t -> t
signedAngleBetweenDirs :: RealFloat n => Direction V2 n -> Direction V2 n -> Angle n
signedAngleBetween :: RealFloat n => V2 n -> V2 n -> Angle n
leftTurn :: (Num n, Ord n) => V2 n -> V2 n -> Bool
angleV :: Floating n => Angle n -> V2 n
angleDir :: Floating n => Angle n -> Direction V2 n
yDir :: (R2 v, Additive v, Num n) => Direction v n
xDir :: (R1 v, Additive v, Num n) => Direction v n
unit_Y :: (R2 v, Additive v, Num n) => v n
unitY :: (R2 v, Additive v, Num n) => v n
unit_X :: (R1 v, Additive v, Num n) => v n
unitX :: (R1 v, Additive v, Num n) => v n
parallelLight :: (Typeable n, OrderedField n, Renderable (ParallelLight n) b) => Direction V3 n -> Colour Double -> QDiagram b V3 n Any
pointLight :: (Typeable n, Num n, Ord n, Renderable (PointLight n) b) => Colour Double -> QDiagram b V3 n Any
data PointLight n = PointLight (Point V3 n) (Colour Double)
data ParallelLight n = ParallelLight (V3 n) (Colour Double)
r3CylindricalIso :: RealFloat n => Iso' (V3 n) (n, Angle n, n)
r3SphericalIso :: RealFloat n => Iso' (V3 n) (n, Angle n, Angle n)
mkP3 :: n -> n -> n -> P3 n
p3Iso :: Iso' (P3 n) (n, n, n)
unp3 :: P3 n -> (n, n, n)
p3 :: (n, n, n) -> P3 n
unr3 :: V3 n -> (n, n, n)
mkR3 :: n -> n -> n -> V3 n
r3 :: (n, n, n) -> V3 n
r3Iso :: Iso' (V3 n) (n, n, n)
type P3 = Point V3
type T3 = Transformation V3
r2PolarIso :: RealFloat n => Iso' (V2 n) (n, Angle n)
mkP2 :: n -> n -> P2 n
unp2 :: P2 n -> (n, n)
p2 :: (n, n) -> P2 n
mkR2 :: n -> n -> V2 n
unr2 :: V2 n -> (n, n)
r2 :: (n, n) -> V2 n
type P2 = Point V2
type T2 = Transformation V2
class HasR (t :: Type -> Type) where
- _r :: RealFloat n => Lens' (t n) n
translated :: (InSpace v n a, SameSpace a b, Transformable a, Transformable b) => v n -> Iso a b a b
movedFrom :: (InSpace v n a, SameSpace a b, HasOrigin a, HasOrigin b) => Point v n -> Iso a b a b
movedTo :: (InSpace v n a, SameSpace a b, HasOrigin a, HasOrigin b) => Point v n -> Iso a b a b
transformed :: (InSpace v n a, SameSpace a b, Transformable a, Transformable b) => Transformation v n -> Iso a b a b
underT :: (InSpace v n a, SameSpace a b, Transformable a, Transformable b) => (a -> b) -> Transformation v n -> a -> b
conjugate :: (Additive v, Num n) => Transformation v n -> Transformation v n -> Transformation v n
highlightSize :: Traversal' (Style v n) Double
highlightIntensity :: Traversal' (Style v n) Double
_highlight :: Lens' (Style v n) (Maybe Specular)
highlight :: HasStyle d => Specular -> d -> d
_Highlight :: Iso' Highlight Specular
specularSize :: Lens' Specular Double
specularIntensity :: Lens' Specular Double
newtype Highlight = Highlight (Last Specular)
_ambient :: Lens' (Style v n) (Maybe Double)
ambient :: HasStyle d => Double -> d -> d
_Ambient :: Iso' Ambient Double
_diffuse :: Lens' (Style v n) (Maybe Double)
diffuse :: HasStyle d => Double -> d -> d
_Diffuse :: Iso' Diffuse Double
_sc :: Lens' (Style v n) (Maybe (Colour Double))
sc :: HasStyle d => Colour Double -> d -> d
_SurfaceColor :: Iso' SurfaceColor (Colour Double)
newtype SurfaceColor = SurfaceColor (Last (Colour Double))
newtype Diffuse = Diffuse (Last Double)
newtype Ambient = Ambient (Last Double)
data Specular = Specular {
- _specularIntensity :: Double
- _specularSize :: Double
}
clearValue :: QDiagram b v n m -> QDiagram b v n Any
resetValue :: (Eq m, Monoid m) => QDiagram b v n m -> QDiagram b v n Any
value :: Monoid m => m -> QDiagram b v n Any -> QDiagram b v n m
sample :: HasQuery t m => t -> Point (V t) (N t) -> m
inquire :: HasQuery t Any => t -> Point (V t) (N t) -> Bool
class HasQuery t m | t -> m where
- getQuery :: t -> Query (V t) (N t) m
dirBetween :: (Additive v, Num n) => Point v n -> Point v n -> Direction v n
angleBetweenDirs :: (Metric v, Floating n, Ord n) => Direction v n -> Direction v n -> Angle n
fromDir :: (Metric v, Floating n) => Direction v n -> v n
fromDirection :: (Metric v, Floating n) => Direction v n -> v n
direction :: v n -> Direction v n
_Dir :: Iso' (Direction v n) (v n)
data Direction (v :: Type -> Type) n
rotate :: (InSpace V2 n t, Transformable t, Floating n) => Angle n -> t -> t
rotation :: Floating n => Angle n -> Transformation V2 n
normalizeAngle :: (Floating n, Real n) => Angle n -> Angle n
angleBetween :: (Metric v, Floating n, Ord n) => v n -> v n -> Angle n
(@@) :: b -> AReview a b -> a
atan2A' :: OrderedField n => n -> n -> Angle n
atan2A :: RealFloat n => n -> n -> Angle n
atanA :: Floating n => n -> Angle n
acosA :: Floating n => n -> Angle n
asinA :: Floating n => n -> Angle n
tanA :: Floating n => Angle n -> n
cosA :: Floating n => Angle n -> n
sinA :: Floating n => Angle n -> n
angleRatio :: Floating n => Angle n -> Angle n -> n
quarterTurn :: Floating v => Angle v
halfTurn :: Floating v => Angle v
fullTurn :: Floating v => Angle v
deg :: Floating n => Iso' (Angle n) n
turn :: Floating n => Iso' (Angle n) n
rad :: Iso' (Angle n) n
data Angle n
class HasTheta (t :: Type -> Type) where
- _theta :: RealFloat n => Lens' (t n) (Angle n)
class HasTheta t => HasPhi (t :: Type -> Type) where
- _phi :: RealFloat n => Lens' (t n) (Angle n)
class Coordinates c where
- type FinalCoord c :: Type
- type PrevDim c :: Type
- type Decomposition c :: Type
- (^&) :: PrevDim c -> FinalCoord c -> c
- pr :: PrevDim c -> FinalCoord c -> c
- coords :: c -> Decomposition c
data a :& b = a :& b
centroid :: (Additive v, Fractional n) => [Point v n] -> Point v n
adjust :: (N t ~ n, Sectionable t, HasArcLength t, Fractional n) => t -> AdjustOpts n -> t
adjSide :: Lens' (AdjustOpts n) AdjustSide
adjMethod :: Lens' (AdjustOpts n) (AdjustMethod n)
adjEps :: Lens' (AdjustOpts n) n
data AdjustMethod n
- = ByParam n
- | ByAbsolute n
- | ToAbsolute n
data AdjustSide
- = Start
- | End
- | Both
data AdjustOpts n
stdTolerance :: Fractional a => a
domainBounds :: DomainBounds p => p -> (N p, N p)
type family Codomain p :: Type -> Type
class Parametric p where
- atParam :: p -> N p -> Codomain p (N p)
class DomainBounds p where
- domainLower :: p -> N p
- domainUpper :: p -> N p
class (Parametric p, DomainBounds p) => EndValues p where
- atStart :: p -> Codomain p (N p)
- atEnd :: p -> Codomain p (N p)
class DomainBounds p => Sectionable p where
- splitAtParam :: p -> N p -> (p, p)
- section :: p -> N p -> N p -> p
- reverseDomain :: p -> p
class Parametric p => HasArcLength p where
- arcLengthBounded :: N p -> p -> Interval (N p)
- arcLength :: N p -> p -> N p
- stdArcLength :: p -> N p
- arcLengthToParam :: N p -> p -> N p -> N p
- stdArcLengthToParam :: p -> N p -> N p
namePoint :: (IsName nm, Metric v, OrderedField n, Semigroup m) => (QDiagram b v n m -> Point v n) -> nm -> QDiagram b v n m -> QDiagram b v n m
named :: (IsName nm, Metric v, OrderedField n, Semigroup m) => nm -> QDiagram b v n m -> QDiagram b v n m
committed :: Iso (Recommend a) (Recommend b) a b
isCommitted :: Lens' (Recommend a) Bool
_recommend :: Lens (Recommend a) (Recommend b) a b
_Commit :: Prism' (Recommend a) a
_Recommend :: Prism' (Recommend a) a
_lineMiterLimit :: Lens' (Style v n) Double
lineMiterLimitA :: HasStyle a => LineMiterLimit -> a -> a
lineMiterLimit :: HasStyle a => Double -> a -> a
getLineMiterLimit :: LineMiterLimit -> Double
_LineMiterLimit :: Iso' LineMiterLimit Double
_lineJoin :: Lens' (Style v n) LineJoin
lineJoin :: HasStyle a => LineJoin -> a -> a
getLineJoin :: LineJoin -> LineJoin
_lineCap :: Lens' (Style v n) LineCap
lineCap :: HasStyle a => LineCap -> a -> a
getLineCap :: LineCap -> LineCap
_strokeOpacity :: Lens' (Style v n) Double
strokeOpacity :: HasStyle a => Double -> a -> a
getStrokeOpacity :: StrokeOpacity -> Double
_StrokeOpacity :: Iso' StrokeOpacity Double
_fillOpacity :: Lens' (Style v n) Double
fillOpacity :: HasStyle a => Double -> a -> a
getFillOpacity :: FillOpacity -> Double
_FillOpacity :: Iso' FillOpacity Double
_opacity :: Lens' (Style v n) Double
opacity :: HasStyle a => Double -> a -> a
getOpacity :: Opacity -> Double
_Opacity :: Iso' Opacity Double
colorToRGBA :: Color c => c -> (Double, Double, Double, Double)
colorToSRGBA :: Color c => c -> (Double, Double, Double, Double)
someToAlpha :: SomeColor -> AlphaColour Double
_SomeColor :: Iso' SomeColor (AlphaColour Double)
_dashingU :: Typeable n => Lens' (Style v n) (Maybe (Dashing n))
_dashing :: Typeable n => Lens' (Style v n) (Maybe (Measured n (Dashing n)))
dashingL :: (N a ~ n, HasStyle a, Typeable n, Num n) => [n] -> n -> a -> a
dashingO :: (N a ~ n, HasStyle a, Typeable n) => [n] -> n -> a -> a
dashingN :: (N a ~ n, HasStyle a, Typeable n, Num n) => [n] -> n -> a -> a
dashingG :: (N a ~ n, HasStyle a, Typeable n, Num n) => [n] -> n -> a -> a
dashing :: (N a ~ n, HasStyle a, Typeable n) => [Measure n] -> Measure n -> a -> a
getDashing :: Dashing n -> Dashing n
_lineWidthU :: Typeable n => Lens' (Style v n) (Maybe n)
_lw :: (Typeable n, OrderedField n) => Lens' (Style v n) (Measure n)
_lineWidth :: (Typeable n, OrderedField n) => Lens' (Style v n) (Measure n)
lwL :: (N a ~ n, HasStyle a, Typeable n, Num n) => n -> a -> a
lwO :: (N a ~ n, HasStyle a, Typeable n) => n -> a -> a
lwN :: (N a ~ n, HasStyle a, Typeable n, Num n) => n -> a -> a
lwG :: (N a ~ n, HasStyle a, Typeable n, Num n) => n -> a -> a
lw :: (N a ~ n, HasStyle a, Typeable n) => Measure n -> a -> a
lineWidthM :: (N a ~ n, HasStyle a, Typeable n) => LineWidthM n -> a -> a
lineWidth :: (N a ~ n, HasStyle a, Typeable n) => Measure n -> a -> a
getLineWidth :: LineWidth n -> n
_LineWidthM :: Iso' (LineWidthM n) (Measure n)
_LineWidth :: Iso' (LineWidth n) n
huge :: OrderedField n => Measure n
veryLarge :: OrderedField n => Measure n
large :: OrderedField n => Measure n
normal :: OrderedField n => Measure n
small :: OrderedField n => Measure n
verySmall :: OrderedField n => Measure n
tiny :: OrderedField n => Measure n
ultraThick :: OrderedField n => Measure n
veryThick :: OrderedField n => Measure n
thick :: OrderedField n => Measure n
medium :: OrderedField n => Measure n
thin :: OrderedField n => Measure n
veryThin :: OrderedField n => Measure n
ultraThin :: OrderedField n => Measure n
none :: OrderedField n => Measure n
data LineWidth n
data Dashing n = Dashing [n] n
class Color c where
- toAlphaColour :: c -> AlphaColour Double
- fromAlphaColour :: AlphaColour Double -> c
data SomeColor where
- SomeColor :: forall c. Color c => c -> SomeColor
data Opacity
data FillOpacity
data StrokeOpacity
data LineCap
- = LineCapButt
- | LineCapRound
- | LineCapSquare
data LineJoin
- = LineJoinMiter
- | LineJoinRound
- | LineJoinBevel
newtype LineMiterLimit = LineMiterLimit (Last Double)
project :: (Metric v, Fractional a) => v a -> v a -> v a
class R1 (t :: Type -> Type) where
- _x :: Lens' (t a) a
class R1 t => R2 (t :: Type -> Type) where
- _y :: Lens' (t a) a
- _xy :: Lens' (t a) (V2 a)
data V2 a = V2 !a !a
perp :: Num a => V2 a -> V2 a
class R2 t => R3 (t :: Type -> Type) where
- _z :: Lens' (t a) a
- _xyz :: Lens' (t a) (V3 a)
data V3 a = V3 !a !a !a
lensP :: Lens' (Point g a) (g a)
class Profunctor p => Choice (p :: Type -> Type -> Type) where
- left' :: p a b -> p (Either a c) (Either b c)
- right' :: p a b -> p (Either c a) (Either c b)
sequenceBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> t (f a) -> f (t a)
traverseBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> t a -> f (t b)
foldMapBy :: Foldable t => (r -> r -> r) -> r -> (a -> r) -> t a -> r
foldBy :: Foldable t => (a -> a -> a) -> a -> t a -> a
class (Foldable1 t, Traversable t) => Traversable1 (t :: Type -> Type) where
- traverse1 :: Apply f => (a -> f b) -> t a -> f (t b)
data Rightmost a
data Leftmost a
data Sequenced a (m :: Type -> Type)
data Traversed a (f :: Type -> Type)
newtype Indexed i a b = Indexed {
- runIndexed :: i -> a -> b
}
class Conjoined p => Indexable i (p :: Type -> Type -> Type)
class (Choice p, Corepresentable p, Comonad (Corep p), Traversable (Corep p), Strong p, Representable p, Monad (Rep p), MonadFix (Rep p), Distributive (Rep p), Costrong p, ArrowLoop p, ArrowApply p, ArrowChoice p, Closed p) => Conjoined (p :: Type -> Type -> Type) where
- distrib :: Functor f => p a b -> p (f a) (f b)
- conjoined :: ((p ~ ((->) :: Type -> Type -> Type)) -> q (a -> b) r) -> q (p a b) r -> q (p a b) r
indexing :: Indexable Int p => ((a -> Indexing f b) -> s -> Indexing f t) -> p a (f b) -> s -> f t
indexing64 :: Indexable Int64 p => ((a -> Indexing64 f b) -> s -> Indexing64 f t) -> p a (f b) -> s -> f t
withIndex :: (Indexable i p, Functor f) => p (i, s) (f (j, t)) -> Indexed i s (f t)
asIndex :: (Indexable i p, Contravariant f, Functor f) => p i (f i) -> Indexed i s (f s)
type Context' a = Context a a
data Context a b t = Context (b -> t) a
type Bazaar1' (p :: Type -> Type -> Type) a = Bazaar1 p a a
newtype Bazaar1 (p :: Type -> Type -> Type) a b t = Bazaar1 {
- runBazaar1 :: forall (f :: Type -> Type). Apply f => p a (f b) -> f t
}
type Bazaar' (p :: Type -> Type -> Type) a = Bazaar p a a
newtype Bazaar (p :: Type -> Type -> Type) a b t = Bazaar {
- runBazaar :: forall (f :: Type -> Type). Applicative f => p a (f b) -> f t
}
class Reversing t where
- reversing :: t -> t
data Level i a
data Magma i t b a
class (Profunctor p, Bifunctor p) => Reviewable (p :: Type -> Type -> Type)
retagged :: (Profunctor p, Bifunctor p) => p a b -> p s b
class (Applicative f, Distributive f, Traversable f) => Settable (f :: Type -> Type)
type Over' (p :: Type -> Type -> Type) (f :: Type -> Type) s a = Over p f s s a a
type Over (p :: k -> Type -> Type) (f :: k1 -> Type) s (t :: k1) (a :: k) (b :: k1) = p a (f b) -> s -> f t
type IndexedLensLike' i (f :: Type -> Type) s a = IndexedLensLike i f s s a a
type IndexedLensLike i (f :: k -> Type) s (t :: k) a (b :: k) = forall (p :: Type -> Type -> Type). Indexable i p => p a (f b) -> s -> f t
type LensLike' (f :: Type -> Type) s a = LensLike f s s a a
type LensLike (f :: k -> Type) s (t :: k) a (b :: k) = (a -> f b) -> s -> f t
type Optical' (p :: k1 -> k -> Type) (q :: k1 -> k -> Type) (f :: k1 -> k) (s :: k1) (a :: k1) = Optical p q f s s a a
type Optical (p :: k2 -> k -> Type) (q :: k1 -> k -> Type) (f :: k3 -> k) (s :: k1) (t :: k3) (a :: k2) (b :: k3) = p a (f b) -> q s (f t)
type Optic' (p :: k1 -> k -> Type) (f :: k1 -> k) (s :: k1) (a :: k1) = Optic p f s s a a
type Optic (p :: k1 -> k -> Type) (f :: k2 -> k) (s :: k1) (t :: k2) (a :: k1) (b :: k2) = p a (f b) -> p s (f t)
type Simple (f :: k -> k -> k1 -> k1 -> k2) (s :: k) (a :: k1) = f s s a a
type IndexPreservingFold1 s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Contravariant f, Apply f) => p a (f a) -> p s (f s)
type IndexedFold1 i s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Contravariant f, Apply f) => p a (f a) -> s -> f s
type Fold1 s a = forall (f :: Type -> Type). (Contravariant f, Apply f) => (a -> f a) -> s -> f s
type IndexPreservingFold s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Contravariant f, Applicative f) => p a (f a) -> p s (f s)
type IndexedFold i s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Contravariant f, Applicative f) => p a (f a) -> s -> f s
type Fold s a = forall (f :: Type -> Type). (Contravariant f, Applicative f) => (a -> f a) -> s -> f s
type IndexPreservingGetter s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Contravariant f, Functor f) => p a (f a) -> p s (f s)
type IndexedGetter i s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Contravariant f, Functor f) => p a (f a) -> s -> f s
type Getter s a = forall (f :: Type -> Type). (Contravariant f, Functor f) => (a -> f a) -> s -> f s
type As (a :: k2) = Equality' a a
type Equality' (s :: k2) (a :: k2) = Equality s s a a
type Equality (s :: k1) (t :: k2) (a :: k1) (b :: k2) = forall k3 (p :: k1 -> k3 -> Type) (f :: k2 -> k3). p a (f b) -> p s (f t)
type Prism' s a = Prism s s a a
type Prism s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Choice p, Applicative f) => p a (f b) -> p s (f t)
type AReview t b = Optic' (Tagged :: Type -> Type -> Type) Identity t b
type Review t b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Choice p, Bifunctor p, Settable f) => Optic' p f t b
type Iso' s a = Iso s s a a
type Iso s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Profunctor p, Functor f) => p a (f b) -> p s (f t)
type IndexPreservingSetter' s a = IndexPreservingSetter s s a a
type IndexPreservingSetter s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Settable f) => p a (f b) -> p s (f t)
type IndexedSetter' i s a = IndexedSetter i s s a a
type IndexedSetter i s t a b = forall (f :: Type -> Type) (p :: Type -> Type -> Type). (Indexable i p, Settable f) => p a (f b) -> s -> f t
type Setter' s a = Setter s s a a
type Setter s t a b = forall (f :: Type -> Type). Settable f => (a -> f b) -> s -> f t
type IndexPreservingTraversal1' s a = IndexPreservingTraversal1 s s a a
type IndexPreservingTraversal1 s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Apply f) => p a (f b) -> p s (f t)
type IndexPreservingTraversal' s a = IndexPreservingTraversal s s a a
type IndexPreservingTraversal s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Applicative f) => p a (f b) -> p s (f t)
type IndexedTraversal1' i s a = IndexedTraversal1 i s s a a
type IndexedTraversal1 i s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Apply f) => p a (f b) -> s -> f t
type IndexedTraversal' i s a = IndexedTraversal i s s a a
type IndexedTraversal i s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Applicative f) => p a (f b) -> s -> f t
type Traversal1' s a = Traversal1 s s a a
type Traversal1 s t a b = forall (f :: Type -> Type). Apply f => (a -> f b) -> s -> f t
type Traversal' s a = Traversal s s a a
type Traversal s t a b = forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t
type IndexPreservingLens' s a = IndexPreservingLens s s a a
type IndexPreservingLens s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Functor f) => p a (f b) -> p s (f t)
type IndexedLens' i s a = IndexedLens i s s a a
type IndexedLens i s t a b = forall (f :: Type -> Type) (p :: Type -> Type -> Type). (Indexable i p, Functor f) => p a (f b) -> s -> f t
type Lens' s a = Lens s s a a
type Lens s t a b = forall (f :: Type -> Type). Functor f => (a -> f b) -> s -> f t
type Setting' (p :: Type -> Type -> Type) s a = Setting p s s a a
type Setting (p :: Type -> Type -> Type) s t a b = p a (Identity b) -> s -> Identity t
type AnIndexedSetter' i s a = AnIndexedSetter i s s a a
type AnIndexedSetter i s t a b = Indexed i a (Identity b) -> s -> Identity t
type ASetter' s a = ASetter s s a a
type ASetter s t a b = (a -> Identity b) -> s -> Identity t
mapped :: Functor f => Setter (f a) (f b) a b
lifted :: Monad m => Setter (m a) (m b) a b
contramapped :: Contravariant f => Setter (f b) (f a) a b
setting :: ((a -> b) -> s -> t) -> IndexPreservingSetter s t a b
sets :: (Profunctor p, Profunctor q, Settable f) => (p a b -> q s t) -> Optical p q f s t a b
cloneSetter :: ASetter s t a b -> Setter s t a b
cloneIndexPreservingSetter :: ASetter s t a b -> IndexPreservingSetter s t a b
cloneIndexedSetter :: AnIndexedSetter i s t a b -> IndexedSetter i s t a b
over :: ASetter s t a b -> (a -> b) -> s -> t
set :: ASetter s t a b -> b -> s -> t
set' :: ASetter' s a -> a -> s -> s
(%~) :: ASetter s t a b -> (a -> b) -> s -> t
(.~) :: ASetter s t a b -> b -> s -> t
(?~) :: ASetter s t a (Maybe b) -> b -> s -> t
(<.~) :: ASetter s t a b -> b -> s -> (b, t)
(<?~) :: ASetter s t a (Maybe b) -> b -> s -> (b, t)
(+~) :: Num a => ASetter s t a a -> a -> s -> t
(*~) :: Num a => ASetter s t a a -> a -> s -> t
(-~) :: Num a => ASetter s t a a -> a -> s -> t
(//~) :: Fractional a => ASetter s t a a -> a -> s -> t
(^~) :: (Num a, Integral e) => ASetter s t a a -> e -> s -> t
(^^~) :: (Fractional a, Integral e) => ASetter s t a a -> e -> s -> t
(**~) :: Floating a => ASetter s t a a -> a -> s -> t
(||~) :: ASetter s t Bool Bool -> Bool -> s -> t
(&&~) :: ASetter s t Bool Bool -> Bool -> s -> t
assign :: MonadState s m => ASetter s s a b -> b -> m ()
(.=) :: MonadState s m => ASetter s s a b -> b -> m ()
(%=) :: MonadState s m => ASetter s s a b -> (a -> b) -> m ()
modifying :: MonadState s m => ASetter s s a b -> (a -> b) -> m ()
(?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m ()
(+=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()
(-=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()
(*=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()
(//=) :: (MonadState s m, Fractional a) => ASetter' s a -> a -> m ()
(^=) :: (MonadState s m, Num a, Integral e) => ASetter' s a -> e -> m ()
(^^=) :: (MonadState s m, Fractional a, Integral e) => ASetter' s a -> e -> m ()
(**=) :: (MonadState s m, Floating a) => ASetter' s a -> a -> m ()
(&&=) :: MonadState s m => ASetter' s Bool -> Bool -> m ()
(||=) :: MonadState s m => ASetter' s Bool -> Bool -> m ()
(<~) :: MonadState s m => ASetter s s a b -> m b -> m ()
(<.=) :: MonadState s m => ASetter s s a b -> b -> m b
(<?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m b
(<>~) :: Monoid a => ASetter s t a a -> a -> s -> t
(<>=) :: (MonadState s m, Monoid a) => ASetter' s a -> a -> m ()
scribe :: (MonadWriter t m, Monoid s) => ASetter s t a b -> b -> m ()
passing :: MonadWriter w m => Setter w w u v -> m (a, u -> v) -> m a
ipassing :: MonadWriter w m => IndexedSetter i w w u v -> m (a, i -> u -> v) -> m a
censoring :: MonadWriter w m => Setter w w u v -> (u -> v) -> m a -> m a
icensoring :: MonadWriter w m => IndexedSetter i w w u v -> (i -> u -> v) -> m a -> m a
locally :: MonadReader s m => ASetter s s a b -> (a -> b) -> m r -> m r
ilocally :: MonadReader s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m r -> m r
iover :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t
iset :: AnIndexedSetter i s t a b -> (i -> b) -> s -> t
isets :: ((i -> a -> b) -> s -> t) -> IndexedSetter i s t a b
(%@~) :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t
(.@~) :: AnIndexedSetter i s t a b -> (i -> b) -> s -> t
(%@=) :: MonadState s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m ()
imodifying :: MonadState s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m ()
(.@=) :: MonadState s m => AnIndexedSetter i s s a b -> (i -> b) -> m ()
assignA :: Arrow p => ASetter s t a b -> p s b -> p s t
mapOf :: ASetter s t a b -> (a -> b) -> s -> t
imapOf :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t
type AnIndexedLens' i s a = AnIndexedLens i s s a a
type AnIndexedLens i s t a b = Optical (Indexed i) ((->) :: Type -> Type -> Type) (Pretext (Indexed i) a b) s t a b
type ALens' s a = ALens s s a a
type ALens s t a b = LensLike (Pretext ((->) :: Type -> Type -> Type) a b) s t a b
lens :: (s -> a) -> (s -> b -> t) -> Lens s t a b
iplens :: (s -> a) -> (s -> b -> t) -> IndexPreservingLens s t a b
ilens :: (s -> (i, a)) -> (s -> b -> t) -> IndexedLens i s t a b
(&~) :: s -> State s a -> s
(%%~) :: LensLike f s t a b -> (a -> f b) -> s -> f t
(%%=) :: MonadState s m => Over p ((,) r) s s a b -> p a (r, b) -> m r
(??) :: Functor f => f (a -> b) -> a -> f b
choosing :: Functor f => LensLike f s t a b -> LensLike f s' t' a b -> LensLike f (Either s s') (Either t t') a b
chosen :: IndexPreservingLens (Either a a) (Either b b) a b
alongside :: LensLike (AlongsideLeft f b') s t a b -> LensLike (AlongsideRight f t) s' t' a' b' -> LensLike f (s, s') (t, t') (a, a') (b, b')
locus :: IndexedComonadStore p => Lens (p a c s) (p b c s) a b
cloneLens :: ALens s t a b -> Lens s t a b
cloneIndexPreservingLens :: ALens s t a b -> IndexPreservingLens s t a b
cloneIndexedLens :: AnIndexedLens i s t a b -> IndexedLens i s t a b
(<%~) :: LensLike ((,) b) s t a b -> (a -> b) -> s -> (b, t)
(<+~) :: Num a => LensLike ((,) a) s t a a -> a -> s -> (a, t)
(<-~) :: Num a => LensLike ((,) a) s t a a -> a -> s -> (a, t)
(<*~) :: Num a => LensLike ((,) a) s t a a -> a -> s -> (a, t)
(<//~) :: Fractional a => LensLike ((,) a) s t a a -> a -> s -> (a, t)
(<^~) :: (Num a, Integral e) => LensLike ((,) a) s t a a -> e -> s -> (a, t)
(<^^~) :: (Fractional a, Integral e) => LensLike ((,) a) s t a a -> e -> s -> (a, t)
(<**~) :: Floating a => LensLike ((,) a) s t a a -> a -> s -> (a, t)
(<||~) :: LensLike ((,) Bool) s t Bool Bool -> Bool -> s -> (Bool, t)
(<&&~) :: LensLike ((,) Bool) s t Bool Bool -> Bool -> s -> (Bool, t)
(<<%~) :: LensLike ((,) a) s t a b -> (a -> b) -> s -> (a, t)
(<<.~) :: LensLike ((,) a) s t a b -> b -> s -> (a, t)
(<<?~) :: LensLike ((,) a) s t a (Maybe b) -> b -> s -> (a, t)
(<<+~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s)
(<<-~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s)
(<<*~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s)
(<<//~) :: Fractional a => LensLike' ((,) a) s a -> a -> s -> (a, s)
(<<^~) :: (Num a, Integral e) => LensLike' ((,) a) s a -> e -> s -> (a, s)
(<<^^~) :: (Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> s -> (a, s)
(<<**~) :: Floating a => LensLike' ((,) a) s a -> a -> s -> (a, s)
(<<||~) :: LensLike' ((,) Bool) s Bool -> Bool -> s -> (Bool, s)
(<<&&~) :: LensLike' ((,) Bool) s Bool -> Bool -> s -> (Bool, s)
(<<<>~) :: Monoid r => LensLike' ((,) r) s r -> r -> s -> (r, s)
(<%=) :: MonadState s m => LensLike ((,) b) s s a b -> (a -> b) -> m b
(<+=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
(<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
(<*=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
(<//=) :: (MonadState s m, Fractional a) => LensLike' ((,) a) s a -> a -> m a
(<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a
(<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a
(<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m a
(<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
(<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
(<<%=) :: (Strong p, MonadState s m) => Over p ((,) a) s s a b -> p a b -> m a
(<<.=) :: MonadState s m => LensLike ((,) a) s s a b -> b -> m a
(<<?=) :: MonadState s m => LensLike ((,) a) s s a (Maybe b) -> b -> m a
(<<+=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
(<<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
(<<*=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
(<<//=) :: (MonadState s m, Fractional a) => LensLike' ((,) a) s a -> a -> m a
(<<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a
(<<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a
(<<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m a
(<<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
(<<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
(<<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r
(<<~) :: MonadState s m => ALens s s a b -> m b -> m b
(<<>~) :: Monoid m => LensLike ((,) m) s t m m -> m -> s -> (m, t)
(<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r
overA :: Arrow ar => LensLike (Context a b) s t a b -> ar a b -> ar s t
(<%@~) :: Over (Indexed i) ((,) b) s t a b -> (i -> a -> b) -> s -> (b, t)
(<<%@~) :: Over (Indexed i) ((,) a) s t a b -> (i -> a -> b) -> s -> (a, t)
(%%@~) :: Over (Indexed i) f s t a b -> (i -> a -> f b) -> s -> f t
(%%@=) :: MonadState s m => Over (Indexed i) ((,) r) s s a b -> (i -> a -> (r, b)) -> m r
(<%@=) :: MonadState s m => Over (Indexed i) ((,) b) s s a b -> (i -> a -> b) -> m b
(<<%@=) :: MonadState s m => Over (Indexed i) ((,) a) s s a b -> (i -> a -> b) -> m a
(^#) :: s -> ALens s t a b -> a
storing :: ALens s t a b -> b -> s -> t
(#~) :: ALens s t a b -> b -> s -> t
(#%~) :: ALens s t a b -> (a -> b) -> s -> t
(#%%~) :: Functor f => ALens s t a b -> (a -> f b) -> s -> f t
(#=) :: MonadState s m => ALens s s a b -> b -> m ()
(#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m ()
(<#%~) :: ALens s t a b -> (a -> b) -> s -> (b, t)
(<#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m b
(#%%=) :: MonadState s m => ALens s s a b -> (a -> (r, b)) -> m r
(<#~) :: ALens s t a b -> b -> s -> (b, t)
(<#=) :: MonadState s m => ALens s s a b -> b -> m b
devoid :: Over p f Void Void a b
united :: Lens' a ()
fusing :: Functor f => LensLike (Yoneda f) s t a b -> LensLike f s t a b
class Field19 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _19 :: Lens s t a b
class Field18 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _18 :: Lens s t a b
class Field17 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _17 :: Lens s t a b
class Field16 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _16 :: Lens s t a b
class Field15 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _15 :: Lens s t a b
class Field14 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _14 :: Lens s t a b
class Field13 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _13 :: Lens s t a b
class Field12 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _12 :: Lens s t a b
class Field11 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _11 :: Lens s t a b
class Field10 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _10 :: Lens s t a b
class Field9 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _9 :: Lens s t a b
class Field8 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _8 :: Lens s t a b
class Field7 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _7 :: Lens s t a b
class Field6 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _6 :: Lens s t a b
class Field5 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _5 :: Lens s t a b
class Field4 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _4 :: Lens s t a b
class Field3 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _3 :: Lens s t a b
class Field2 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _2 :: Lens s t a b
class Field1 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _1 :: Lens s t a b
_1' :: Field1 s t a b => Lens s t a b
_2' :: Field2 s t a b => Lens s t a b
_3' :: Field3 s t a b => Lens s t a b
_4' :: Field4 s t a b => Lens s t a b
_5' :: Field5 s t a b => Lens s t a b
_6' :: Field6 s t a b => Lens s t a b
_7' :: Field7 s t a b => Lens s t a b
_8' :: Field8 s t a b => Lens s t a b
_9' :: Field9 s t a b => Lens s t a b
_10' :: Field10 s t a b => Lens s t a b
_11' :: Field11 s t a b => Lens s t a b
_12' :: Field12 s t a b => Lens s t a b
_13' :: Field13 s t a b => Lens s t a b
_14' :: Field14 s t a b => Lens s t a b
_15' :: Field15 s t a b => Lens s t a b
_16' :: Field16 s t a b => Lens s t a b
_17' :: Field17 s t a b => Lens s t a b
_18' :: Field18 s t a b => Lens s t a b
_19' :: Field19 s t a b => Lens s t a b
type Accessing (p :: Type -> Type -> Type) m s a = p a (Const m a) -> s -> Const m s
type IndexedGetting i m s a = Indexed i a (Const m a) -> s -> Const m s
type Getting r s a = (a -> Const r a) -> s -> Const r s
to :: (Profunctor p, Contravariant f) => (s -> a) -> Optic' p f s a
ito :: (Indexable i p, Contravariant f) => (s -> (i, a)) -> Over' p f s a
like :: (Profunctor p, Contravariant f, Functor f) => a -> Optic' p f s a
ilike :: (Indexable i p, Contravariant f, Functor f) => i -> a -> Over' p f s a
view :: MonadReader s m => Getting a s a -> m a
views :: MonadReader s m => LensLike' (Const r :: Type -> Type) s a -> (a -> r) -> m r
(^.) :: s -> Getting a s a -> a
use :: MonadState s m => Getting a s a -> m a
uses :: MonadState s m => LensLike' (Const r :: Type -> Type) s a -> (a -> r) -> m r
listening :: MonadWriter w m => Getting u w u -> m a -> m (a, u)
ilistening :: MonadWriter w m => IndexedGetting i (i, u) w u -> m a -> m (a, (i, u))
listenings :: MonadWriter w m => Getting v w u -> (u -> v) -> m a -> m (a, v)
ilistenings :: MonadWriter w m => IndexedGetting i v w u -> (i -> u -> v) -> m a -> m (a, v)
iview :: MonadReader s m => IndexedGetting i (i, a) s a -> m (i, a)
iviews :: MonadReader s m => IndexedGetting i r s a -> (i -> a -> r) -> m r
iuse :: MonadState s m => IndexedGetting i (i, a) s a -> m (i, a)
iuses :: MonadState s m => IndexedGetting i r s a -> (i -> a -> r) -> m r
(^@.) :: s -> IndexedGetting i (i, a) s a -> (i, a)
getting :: (Profunctor p, Profunctor q, Functor f, Contravariant f) => Optical p q f s t a b -> Optical' p q f s a
unto :: (Profunctor p, Bifunctor p, Functor f) => (b -> t) -> Optic p f s t a b
un :: (Profunctor p, Bifunctor p, Functor f) => Getting a s a -> Optic' p f a s
re :: AReview t b -> Getter b t
review :: MonadReader b m => AReview t b -> m t
reviews :: MonadReader b m => AReview t b -> (t -> r) -> m r
reuse :: MonadState b m => AReview t b -> m t
reuses :: MonadState b m => AReview t b -> (t -> r) -> m r
type APrism' s a = APrism s s a a
type APrism s t a b = Market a b a (Identity b) -> Market a b s (Identity t)
withPrism :: APrism s t a b -> ((b -> t) -> (s -> Either t a) -> r) -> r
clonePrism :: APrism s t a b -> Prism s t a b
prism :: (b -> t) -> (s -> Either t a) -> Prism s t a b
prism' :: (b -> s) -> (s -> Maybe a) -> Prism s s a b
without :: APrism s t a b -> APrism u v c d -> Prism (Either s u) (Either t v) (Either a c) (Either b d)
aside :: APrism s t a b -> Prism (e, s) (e, t) (e, a) (e, b)
below :: Traversable f => APrism' s a -> Prism' (f s) (f a)
isn't :: APrism s t a b -> s -> Bool
matching :: APrism s t a b -> s -> Either t a
_Left :: Prism (Either a c) (Either b c) a b
_Right :: Prism (Either c a) (Either c b) a b
_Just :: Prism (Maybe a) (Maybe b) a b
_Nothing :: Prism' (Maybe a) ()
_Void :: Prism s s a Void
only :: Eq a => a -> Prism' a ()
nearly :: a -> (a -> Bool) -> Prism' a ()
_Show :: (Read a, Show a) => Prism' String a
folding :: Foldable f => (s -> f a) -> Fold s a
ifolding :: (Foldable f, Indexable i p, Contravariant g, Applicative g) => (s -> f (i, a)) -> Over p g s t a b
foldring :: (Contravariant f, Applicative f) => ((a -> f a -> f a) -> f a -> s -> f a) -> LensLike f s t a b
ifoldring :: (Indexable i p, Contravariant f, Applicative f) => ((i -> a -> f a -> f a) -> f a -> s -> f a) -> Over p f s t a b
folded :: Foldable f => IndexedFold Int (f a) a
folded64 :: Foldable f => IndexedFold Int64 (f a) a
repeated :: Apply f => LensLike' f a a
replicated :: Int -> Fold a a
cycled :: Apply f => LensLike f s t a b -> LensLike f s t a b
unfolded :: (b -> Maybe (a, b)) -> Fold b a
iterated :: Apply f => (a -> a) -> LensLike' f a a
filtered :: (Choice p, Applicative f) => (a -> Bool) -> Optic' p f a a
takingWhile :: (Conjoined p, Applicative f) => (a -> Bool) -> Over p (TakingWhile p f a a) s t a a -> Over p f s t a a
droppingWhile :: (Conjoined p, Profunctor q, Applicative f) => (a -> Bool) -> Optical p q (Compose (State Bool) f) s t a a -> Optical p q f s t a a
worded :: Applicative f => IndexedLensLike' Int f String String
lined :: Applicative f => IndexedLensLike' Int f String String
foldMapOf :: Getting r s a -> (a -> r) -> s -> r
foldOf :: Getting a s a -> s -> a
foldrOf :: Getting (Endo r) s a -> (a -> r -> r) -> r -> s -> r
foldlOf :: Getting (Dual (Endo r)) s a -> (r -> a -> r) -> r -> s -> r
toListOf :: Getting (Endo [a]) s a -> s -> [a]
toNonEmptyOf :: Getting (NonEmptyDList a) s a -> s -> NonEmpty a
(^..) :: s -> Getting (Endo [a]) s a -> [a]
andOf :: Getting All s Bool -> s -> Bool
orOf :: Getting Any s Bool -> s -> Bool
anyOf :: Getting Any s a -> (a -> Bool) -> s -> Bool
allOf :: Getting All s a -> (a -> Bool) -> s -> Bool
noneOf :: Getting Any s a -> (a -> Bool) -> s -> Bool
productOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a
sumOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a
traverseOf_ :: Functor f => Getting (Traversed r f) s a -> (a -> f r) -> s -> f ()
forOf_ :: Functor f => Getting (Traversed r f) s a -> s -> (a -> f r) -> f ()
sequenceAOf_ :: Functor f => Getting (Traversed a f) s (f a) -> s -> f ()
traverse1Of_ :: Functor f => Getting (TraversedF r f) s a -> (a -> f r) -> s -> f ()
for1Of_ :: Functor f => Getting (TraversedF r f) s a -> s -> (a -> f r) -> f ()
sequence1Of_ :: Functor f => Getting (TraversedF a f) s (f a) -> s -> f ()
mapMOf_ :: Monad m => Getting (Sequenced r m) s a -> (a -> m r) -> s -> m ()
forMOf_ :: Monad m => Getting (Sequenced r m) s a -> s -> (a -> m r) -> m ()
sequenceOf_ :: Monad m => Getting (Sequenced a m) s (m a) -> s -> m ()
asumOf :: Alternative f => Getting (Endo (f a)) s (f a) -> s -> f a
msumOf :: MonadPlus m => Getting (Endo (m a)) s (m a) -> s -> m a
elemOf :: Eq a => Getting Any s a -> a -> s -> Bool
notElemOf :: Eq a => Getting All s a -> a -> s -> Bool
concatMapOf :: Getting [r] s a -> (a -> [r]) -> s -> [r]
concatOf :: Getting [r] s [r] -> s -> [r]
lengthOf :: Getting (Endo (Endo Int)) s a -> s -> Int
(^?) :: s -> Getting (First a) s a -> Maybe a
(^?!) :: HasCallStack => s -> Getting (Endo a) s a -> a
firstOf :: Getting (Leftmost a) s a -> s -> Maybe a
first1Of :: Getting (First a) s a -> s -> a
lastOf :: Getting (Rightmost a) s a -> s -> Maybe a
last1Of :: Getting (Last a) s a -> s -> a
nullOf :: Getting All s a -> s -> Bool
notNullOf :: Getting Any s a -> s -> Bool
maximumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a
maximum1Of :: Ord a => Getting (Max a) s a -> s -> a
minimumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a
minimum1Of :: Ord a => Getting (Min a) s a -> s -> a
maximumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a
findOf :: Getting (Endo (Maybe a)) s a -> (a -> Bool) -> s -> Maybe a
findMOf :: Monad m => Getting (Endo (m (Maybe a))) s a -> (a -> m Bool) -> s -> m (Maybe a)
lookupOf :: Eq k => Getting (Endo (Maybe v)) s (k, v) -> k -> s -> Maybe v
foldr1Of :: HasCallStack => Getting (Endo (Maybe a)) s a -> (a -> a -> a) -> s -> a
foldl1Of :: HasCallStack => Getting (Dual (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a
foldrOf' :: Getting (Dual (Endo (Endo r))) s a -> (a -> r -> r) -> r -> s -> r
foldlOf' :: Getting (Endo (Endo r)) s a -> (r -> a -> r) -> r -> s -> r
foldr1Of' :: HasCallStack => Getting (Dual (Endo (Endo (Maybe a)))) s a -> (a -> a -> a) -> s -> a
foldl1Of' :: HasCallStack => Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a
foldrMOf :: Monad m => Getting (Dual (Endo (r -> m r))) s a -> (a -> r -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Getting (Endo (r -> m r)) s a -> (r -> a -> m r) -> r -> s -> m r
has :: Getting Any s a -> s -> Bool
hasn't :: Getting All s a -> s -> Bool
pre :: Getting (First a) s a -> IndexPreservingGetter s (Maybe a)
ipre :: IndexedGetting i (First (i, a)) s a -> IndexPreservingGetter s (Maybe (i, a))
preview :: MonadReader s m => Getting (First a) s a -> m (Maybe a)
ipreview :: MonadReader s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a))
previews :: MonadReader s m => Getting (First r) s a -> (a -> r) -> m (Maybe r)
ipreviews :: MonadReader s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r)
preuse :: MonadState s m => Getting (First a) s a -> m (Maybe a)
ipreuse :: MonadState s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a))
preuses :: MonadState s m => Getting (First r) s a -> (a -> r) -> m (Maybe r)
ipreuses :: MonadState s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r)
ifoldMapOf :: IndexedGetting i m s a -> (i -> a -> m) -> s -> m
ifoldrOf :: IndexedGetting i (Endo r) s a -> (i -> a -> r -> r) -> r -> s -> r
ifoldlOf :: IndexedGetting i (Dual (Endo r)) s a -> (i -> r -> a -> r) -> r -> s -> r
ianyOf :: IndexedGetting i Any s a -> (i -> a -> Bool) -> s -> Bool
iallOf :: IndexedGetting i All s a -> (i -> a -> Bool) -> s -> Bool
inoneOf :: IndexedGetting i Any s a -> (i -> a -> Bool) -> s -> Bool
itraverseOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> (i -> a -> f r) -> s -> f ()
iforOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> s -> (i -> a -> f r) -> f ()
imapMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> (i -> a -> m r) -> s -> m ()
iforMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> s -> (i -> a -> m r) -> m ()
iconcatMapOf :: IndexedGetting i [r] s a -> (i -> a -> [r]) -> s -> [r]
ifindOf :: IndexedGetting i (Endo (Maybe a)) s a -> (i -> a -> Bool) -> s -> Maybe a
ifindMOf :: Monad m => IndexedGetting i (Endo (m (Maybe a))) s a -> (i -> a -> m Bool) -> s -> m (Maybe a)
ifoldrOf' :: IndexedGetting i (Dual (Endo (r -> r))) s a -> (i -> a -> r -> r) -> r -> s -> r
ifoldlOf' :: IndexedGetting i (Endo (r -> r)) s a -> (i -> r -> a -> r) -> r -> s -> r
ifoldrMOf :: Monad m => IndexedGetting i (Dual (Endo (r -> m r))) s a -> (i -> a -> r -> m r) -> r -> s -> m r
ifoldlMOf :: Monad m => IndexedGetting i (Endo (r -> m r)) s a -> (i -> r -> a -> m r) -> r -> s -> m r
itoListOf :: IndexedGetting i (Endo [(i, a)]) s a -> s -> [(i, a)]
(^@..) :: s -> IndexedGetting i (Endo [(i, a)]) s a -> [(i, a)]
(^@?) :: s -> IndexedGetting i (Endo (Maybe (i, a))) s a -> Maybe (i, a)
(^@?!) :: HasCallStack => s -> IndexedGetting i (Endo (i, a)) s a -> (i, a)
elemIndexOf :: Eq a => IndexedGetting i (First i) s a -> a -> s -> Maybe i
elemIndicesOf :: Eq a => IndexedGetting i (Endo [i]) s a -> a -> s -> [i]
findIndexOf :: IndexedGetting i (First i) s a -> (a -> Bool) -> s -> Maybe i
findIndicesOf :: IndexedGetting i (Endo [i]) s a -> (a -> Bool) -> s -> [i]
ifiltered :: (Indexable i p, Applicative f) => (i -> a -> Bool) -> Optical' p (Indexed i) f a a
itakingWhile :: (Indexable i p, Profunctor q, Contravariant f, Applicative f) => (i -> a -> Bool) -> Optical' (Indexed i) q (Const (Endo (f s)) :: Type -> Type) s a -> Optical' p q f s a
idroppingWhile :: (Indexable i p, Profunctor q, Applicative f) => (i -> a -> Bool) -> Optical (Indexed i) q (Compose (State Bool) f) s t a a -> Optical p q f s t a a
foldByOf :: Fold s a -> (a -> a -> a) -> a -> s -> a
foldMapByOf :: Fold s a -> (r -> r -> r) -> r -> (a -> r) -> s -> r
class Ord k => TraverseMax k (m :: Type -> Type) | m -> k where
- traverseMax :: IndexedTraversal' k (m v) v
class Ord k => TraverseMin k (m :: Type -> Type) | m -> k where
- traverseMin :: IndexedTraversal' k (m v) v
type Traversing1' (p :: Type -> Type -> Type) (f :: Type -> Type) s a = Traversing1 p f s s a a
type Traversing' (p :: Type -> Type -> Type) (f :: Type -> Type) s a = Traversing p f s s a a
type Traversing1 (p :: Type -> Type -> Type) (f :: Type -> Type) s t a b = Over p (BazaarT1 p f a b) s t a b
type Traversing (p :: Type -> Type -> Type) (f :: Type -> Type) s t a b = Over p (BazaarT p f a b) s t a b
type AnIndexedTraversal1' i s a = AnIndexedTraversal1 i s s a a
type AnIndexedTraversal' i s a = AnIndexedTraversal i s s a a
type AnIndexedTraversal1 i s t a b = Over (Indexed i) (Bazaar1 (Indexed i) a b) s t a b
type AnIndexedTraversal i s t a b = Over (Indexed i) (Bazaar (Indexed i) a b) s t a b
type ATraversal1' s a = ATraversal1 s s a a
type ATraversal1 s t a b = LensLike (Bazaar1 ((->) :: Type -> Type -> Type) a b) s t a b
type ATraversal' s a = ATraversal s s a a
type ATraversal s t a b = LensLike (Bazaar ((->) :: Type -> Type -> Type) a b) s t a b
traverseOf :: LensLike f s t a b -> (a -> f b) -> s -> f t
forOf :: LensLike f s t a b -> s -> (a -> f b) -> f t
sequenceAOf :: LensLike f s t (f b) b -> s -> f t
mapMOf :: LensLike (WrappedMonad m) s t a b -> (a -> m b) -> s -> m t
forMOf :: LensLike (WrappedMonad m) s t a b -> s -> (a -> m b) -> m t
sequenceOf :: LensLike (WrappedMonad m) s t (m b) b -> s -> m t
transposeOf :: LensLike ZipList s t [a] a -> s -> [t]
mapAccumROf :: LensLike (Backwards (State acc)) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumLOf :: LensLike (State acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
scanr1Of :: LensLike (Backwards (State (Maybe a))) s t a a -> (a -> a -> a) -> s -> t
scanl1Of :: LensLike (State (Maybe a)) s t a a -> (a -> a -> a) -> s -> t
loci :: Traversal (Bazaar ((->) :: Type -> Type -> Type) a c s) (Bazaar ((->) :: Type -> Type -> Type) b c s) a b
iloci :: IndexedTraversal i (Bazaar (Indexed i) a c s) (Bazaar (Indexed i) b c s) a b
partsOf :: Functor f => Traversing ((->) :: Type -> Type -> Type) f s t a a -> LensLike f s t [a] [a]
ipartsOf :: (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a a -> Over p f s t [a] [a]
partsOf' :: ATraversal s t a a -> Lens s t [a] [a]
ipartsOf' :: (Indexable [i] p, Functor f) => Over (Indexed i) (Bazaar' (Indexed i) a) s t a a -> Over p f s t [a] [a]
unsafePartsOf :: Functor f => Traversing ((->) :: Type -> Type -> Type) f s t a b -> LensLike f s t [a] [b]
iunsafePartsOf :: (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a b -> Over p f s t [a] [b]
unsafePartsOf' :: ATraversal s t a b -> Lens s t [a] [b]
iunsafePartsOf' :: Over (Indexed i) (Bazaar (Indexed i) a b) s t a b -> IndexedLens [i] s t [a] [b]
unsafeSingular :: (HasCallStack, Conjoined p, Functor f) => Traversing p f s t a b -> Over p f s t a b
holesOf :: Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t]
holes1Of :: Conjoined p => Over p (Bazaar1 p a a) s t a a -> s -> NonEmpty (Pretext p a a t)
both :: Bitraversable r => Traversal (r a a) (r b b) a b
both1 :: Bitraversable1 r => Traversal1 (r a a) (r b b) a b
taking :: (Conjoined p, Applicative f) => Int -> Traversing p f s t a a -> Over p f s t a a
dropping :: (Conjoined p, Applicative f) => Int -> Over p (Indexing f) s t a a -> Over p f s t a a
cloneTraversal :: ATraversal s t a b -> Traversal s t a b
cloneIndexPreservingTraversal :: ATraversal s t a b -> IndexPreservingTraversal s t a b
cloneIndexedTraversal :: AnIndexedTraversal i s t a b -> IndexedTraversal i s t a b
cloneTraversal1 :: ATraversal1 s t a b -> Traversal1 s t a b
cloneIndexPreservingTraversal1 :: ATraversal1 s t a b -> IndexPreservingTraversal1 s t a b
cloneIndexedTraversal1 :: AnIndexedTraversal1 i s t a b -> IndexedTraversal1 i s t a b
itraverseOf :: (Indexed i a (f b) -> s -> f t) -> (i -> a -> f b) -> s -> f t
iforOf :: (Indexed i a (f b) -> s -> f t) -> s -> (i -> a -> f b) -> f t
imapMOf :: Over (Indexed i) (WrappedMonad m) s t a b -> (i -> a -> m b) -> s -> m t
iforMOf :: (Indexed i a (WrappedMonad m b) -> s -> WrappedMonad m t) -> s -> (i -> a -> m b) -> m t
imapAccumROf :: Over (Indexed i) (Backwards (State acc)) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
imapAccumLOf :: Over (Indexed i) (State acc) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
traversed :: Traversable f => IndexedTraversal Int (f a) (f b) a b
traversed1 :: Traversable1 f => IndexedTraversal1 Int (f a) (f b) a b
traversed64 :: Traversable f => IndexedTraversal Int64 (f a) (f b) a b
ignored :: Applicative f => pafb -> s -> f s
elementOf :: Applicative f => LensLike (Indexing f) s t a a -> Int -> IndexedLensLike Int f s t a a
element :: Traversable t => Int -> IndexedTraversal' Int (t a) a
elementsOf :: Applicative f => LensLike (Indexing f) s t a a -> (Int -> Bool) -> IndexedLensLike Int f s t a a
elements :: Traversable t => (Int -> Bool) -> IndexedTraversal' Int (t a) a
failover :: Alternative m => LensLike ((,) Any) s t a b -> (a -> b) -> s -> m t
ifailover :: Alternative m => Over (Indexed i) ((,) Any) s t a b -> (i -> a -> b) -> s -> m t
failing :: (Conjoined p, Applicative f) => Traversing p f s t a b -> Over p f s t a b -> Over p f s t a b
deepOf :: (Conjoined p, Applicative f) => LensLike f s t s t -> Traversing p f s t a b -> Over p f s t a b
confusing :: Applicative f => LensLike (Curried (Yoneda f) (Yoneda f)) s t a b -> LensLike f s t a b
traverseByOf :: Traversal s t a b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> s -> f t
sequenceByOf :: Traversal s t (f b) b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> s -> f t
ilevels :: Applicative f => Traversing (Indexed i) f s t a b -> IndexedLensLike Int f s t (Level i a) (Level j b)
type ReifiedPrism' s a = ReifiedPrism s s a a
newtype ReifiedPrism s t a b = Prism {
- runPrism :: Prism s t a b
}
type ReifiedIso' s a = ReifiedIso s s a a
newtype ReifiedIso s t a b = Iso {
- runIso :: Iso s t a b
}
type ReifiedIndexedSetter' i s a = ReifiedIndexedSetter i s s a a
newtype ReifiedIndexedSetter i s t a b = IndexedSetter {
- runIndexedSetter :: IndexedSetter i s t a b
}
type ReifiedSetter' s a = ReifiedSetter s s a a
newtype ReifiedSetter s t a b = Setter {
- runSetter :: Setter s t a b
}
newtype ReifiedIndexedFold i s a = IndexedFold {
- runIndexedFold :: IndexedFold i s a
}
newtype ReifiedFold s a = Fold {
- runFold :: Fold s a
}
newtype ReifiedIndexedGetter i s a = IndexedGetter {
- runIndexedGetter :: IndexedGetter i s a
}
newtype ReifiedGetter s a = Getter {
- runGetter :: Getter s a
}
type ReifiedTraversal' s a = ReifiedTraversal s s a a
newtype ReifiedTraversal s t a b = Traversal {
- runTraversal :: Traversal s t a b
}
type ReifiedIndexedTraversal' i s a = ReifiedIndexedTraversal i s s a a
newtype ReifiedIndexedTraversal i s t a b = IndexedTraversal {
- runIndexedTraversal :: IndexedTraversal i s t a b
}
type ReifiedIndexedLens' i s a = ReifiedIndexedLens i s s a a
newtype ReifiedIndexedLens i s t a b = IndexedLens {
- runIndexedLens :: IndexedLens i s t a b
}
type ReifiedLens' s a = ReifiedLens s s a a
newtype ReifiedLens s t a b = Lens {
- runLens :: Lens s t a b
}
class (FunctorWithIndex i t, FoldableWithIndex i t, Traversable t) => TraversableWithIndex i (t :: Type -> Type) | t -> i where
- itraverse :: Applicative f => (i -> a -> f b) -> t a -> f (t b)
- itraversed :: IndexedTraversal i (t a) (t b) a b
class Foldable f => FoldableWithIndex i (f :: Type -> Type) | f -> i where
- ifoldMap :: Monoid m => (i -> a -> m) -> f a -> m
- ifolded :: IndexedFold i (f a) a
- ifoldr :: (i -> a -> b -> b) -> b -> f a -> b
- ifoldl :: (i -> b -> a -> b) -> b -> f a -> b
- ifoldr' :: (i -> a -> b -> b) -> b -> f a -> b
- ifoldl' :: (i -> b -> a -> b) -> b -> f a -> b
class Functor f => FunctorWithIndex i (f :: Type -> Type) | f -> i where
- imap :: (i -> a -> b) -> f a -> f b
- imapped :: IndexedSetter i (f a) (f b) a b
(<.) :: Indexable i p => (Indexed i s t -> r) -> ((a -> b) -> s -> t) -> p a b -> r
selfIndex :: Indexable a p => p a fb -> a -> fb
reindexed :: Indexable j p => (i -> j) -> (Indexed i a b -> r) -> p a b -> r
icompose :: Indexable p c => (i -> j -> p) -> (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> c a b -> r
index :: (Indexable i p, Eq i, Applicative f) => i -> Optical' p (Indexed i) f a a
iany :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
iall :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
inone :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
itraverse_ :: (FoldableWithIndex i t, Applicative f) => (i -> a -> f b) -> t a -> f ()
ifor_ :: (FoldableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f ()
imapM_ :: (FoldableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m ()
iforM_ :: (FoldableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m ()
iconcatMap :: FoldableWithIndex i f => (i -> a -> [b]) -> f a -> [b]
ifind :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Maybe (i, a)
ifoldrM :: (FoldableWithIndex i f, Monad m) => (i -> a -> b -> m b) -> b -> f a -> m b
ifoldlM :: (FoldableWithIndex i f, Monad m) => (i -> b -> a -> m b) -> b -> f a -> m b
itoList :: FoldableWithIndex i f => f a -> [(i, a)]
ifor :: (TraversableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f (t b)
imapM :: (TraversableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m (t b)
iforM :: (TraversableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m (t b)
imapAccumR :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b)
imapAccumL :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b)
ifoldMapBy :: FoldableWithIndex i t => (r -> r -> r) -> r -> (i -> a -> r) -> t a -> r
ifoldMapByOf :: IndexedFold i t a -> (r -> r -> r) -> r -> (i -> a -> r) -> t -> r
itraverseBy :: TraversableWithIndex i t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> t a -> f (t b)
itraverseByOf :: IndexedTraversal i s t a b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> s -> f t
type AnEquality' (s :: k2) (a :: k2) = AnEquality s s a a
type AnEquality (s :: k1) (t :: k2) (a :: k1) (b :: k2) = Identical a (Proxy b) a (Proxy b) -> Identical a (Proxy b) s (Proxy t)
data Identical (a :: k) (b :: k1) (s :: k) (t :: k1) :: forall k k1. k -> k1 -> k -> k1 -> Type where
- Identical :: forall k k1 (a :: k) (b :: k1) (s :: k) (t :: k1). Identical a b a b
runEq :: AnEquality s t a b -> Identical s t a b
substEq :: AnEquality s t a b -> ((s ~ a) -> (t ~ b) -> r) -> r
mapEq :: AnEquality s t a b -> f s -> f a
fromEq :: AnEquality s t a b -> Equality b a t s
simply :: (Optic' p f s a -> r) -> Optic' p f s a -> r
simple :: Equality' a a
class Strict lazy strict | lazy -> strict, strict -> lazy where
- strict :: Iso' lazy strict
class Bifunctor p => Swapped (p :: Type -> Type -> Type) where
- swapped :: Iso (p a b) (p c d) (p b a) (p d c)
type AnIso' s a = AnIso s s a a
type AnIso s t a b = Exchange a b a (Identity b) -> Exchange a b s (Identity t)
pattern List :: forall l. IsList l => [Item l] -> l
pattern Reversed :: forall t. Reversing t => t -> t
pattern Swapped :: forall (p :: Type -> Type -> Type) c d. Swapped p => p d c -> p c d
pattern Lazy :: forall t s. Strict t s => t -> s
pattern Strict :: forall s t. Strict s t => t -> s
iso :: (s -> a) -> (b -> t) -> Iso s t a b
from :: AnIso s t a b -> Iso b a t s
withIso :: AnIso s t a b -> ((s -> a) -> (b -> t) -> r) -> r
cloneIso :: AnIso s t a b -> Iso s t a b
au :: Functor f => AnIso s t a b -> ((b -> t) -> f s) -> f a
auf :: Optic (Costar f) g s t a b -> (f a -> g b) -> f s -> g t
under :: AnIso s t a b -> (t -> s) -> b -> a
enum :: Enum a => Iso' Int a
mapping :: (Functor f, Functor g) => AnIso s t a b -> Iso (f s) (g t) (f a) (g b)
non :: Eq a => a -> Iso' (Maybe a) a
non' :: APrism' a () -> Iso' (Maybe a) a
anon :: a -> (a -> Bool) -> Iso' (Maybe a) a
curried :: Iso ((a, b) -> c) ((d, e) -> f) (a -> b -> c) (d -> e -> f)
uncurried :: Iso (a -> b -> c) (d -> e -> f) ((a, b) -> c) ((d, e) -> f)
flipped :: Iso (a -> b -> c) (a' -> b' -> c') (b -> a -> c) (b' -> a' -> c')
lazy :: Strict lazy strict => Iso' strict lazy
reversed :: Reversing a => Iso' a a
involuted :: (a -> a) -> Iso' a a
magma :: LensLike (Mafic a b) s t a b -> Iso s u (Magma Int t b a) (Magma j u c c)
imagma :: Over (Indexed i) (Molten i a b) s t a b -> Iso s t' (Magma i t b a) (Magma j t' c c)
contramapping :: Contravariant f => AnIso s t a b -> Iso (f a) (f b) (f s) (f t)
dimapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> AnIso s' t' a' b' -> Iso (p a s') (q b t') (p s a') (q t b')
lmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso (p a x) (q b y) (p s x) (q t y)
rmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso (p x s) (q y t) (p x a) (q y b)
bimapping :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> AnIso s' t' a' b' -> Iso (f s s') (g t t') (f a a') (g b b')
firsting :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso (f s x) (g t y) (f a x) (g b y)
seconding :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso (f x s) (g y t) (f x a) (g y b)
coerced :: (Coercible s a, Coercible t b) => Iso s t a b
class AsEmpty a where
- _Empty :: Prism' a ()
pattern Empty :: forall s. AsEmpty s => s
class Snoc s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _Snoc :: Prism s t (s, a) (t, b)
class Cons s t a b | s -> a, t -> b, s b -> t, t a -> s where
- _Cons :: Prism s t (a, s) (b, t)
pattern (:>) :: forall a b. Snoc a a b b => a -> b -> a
pattern (:<) :: forall b a. Cons b b a a => a -> b -> b
(<|) :: Cons s s a a => a -> s -> s
cons :: Cons s s a a => a -> s -> s
uncons :: Cons s s a a => s -> Maybe (a, s)
_head :: Cons s s a a => Traversal' s a
_tail :: Cons s s a a => Traversal' s s
_init :: Snoc s s a a => Traversal' s s
_last :: Snoc s s a a => Traversal' s a
(|>) :: Snoc s s a a => s -> a -> s
snoc :: Snoc s s a a => s -> a -> s
unsnoc :: Snoc s s a a => s -> Maybe (s, a)
class (Rewrapped s t, Rewrapped t s) => Rewrapping s t
class Wrapped s => Rewrapped s t
class Wrapped s where
- type Unwrapped s :: Type
- _Wrapped' :: Iso' s (Unwrapped s)
pattern Unwrapped :: forall t. Rewrapped t t => t -> Unwrapped t
pattern Wrapped :: forall s. Rewrapped s s => Unwrapped s -> s
_GWrapped' :: (Generic s, D1 d (C1 c (S1 s' (Rec0 a))) ~ Rep s, Unwrapped s ~ GUnwrapped (Rep s)) => Iso' s (Unwrapped s)
_Unwrapped' :: Wrapped s => Iso' (Unwrapped s) s
_Wrapped :: Rewrapping s t => Iso s t (Unwrapped s) (Unwrapped t)
_Unwrapped :: Rewrapping s t => Iso (Unwrapped t) (Unwrapped s) t s
op :: Wrapped s => (Unwrapped s -> s) -> s -> Unwrapped s
_Wrapping' :: Wrapped s => (Unwrapped s -> s) -> Iso' s (Unwrapped s)
_Unwrapping' :: Wrapped s => (Unwrapped s -> s) -> Iso' (Unwrapped s) s
_Wrapping :: Rewrapping s t => (Unwrapped s -> s) -> Iso s t (Unwrapped s) (Unwrapped t)
_Unwrapping :: Rewrapping s t => (Unwrapped s -> s) -> Iso (Unwrapped t) (Unwrapped s) t s
ala :: (Functor f, Rewrapping s t) => (Unwrapped s -> s) -> ((Unwrapped t -> t) -> f s) -> f (Unwrapped s)
alaf :: (Functor f, Functor g, Rewrapping s t) => (Unwrapped s -> s) -> (f t -> g s) -> f (Unwrapped t) -> g (Unwrapped s)
class (Magnified m ~ Magnified n, MonadReader b m, MonadReader a n) => Magnify (m :: Type -> Type) (n :: Type -> Type) b a | m -> b, n -> a, m a -> n, n b -> m where
- magnify :: LensLike' (Magnified m c) a b -> m c -> n c
class (MonadState s m, MonadState t n) => Zoom (m :: Type -> Type) (n :: Type -> Type) s t | m -> s, n -> t, m t -> n, n s -> m where
- zoom :: LensLike' (Zoomed m c) t s -> m c -> n c
type family Magnified (m :: Type -> Type) :: Type -> Type -> Type
type family Zoomed (m :: Type -> Type) :: Type -> Type -> Type
class GPlated1 (f :: k -> Type) (g :: k -> Type)
class GPlated a (g :: k -> Type)
class Plated a where
- plate :: Traversal' a a
deep :: (Conjoined p, Applicative f, Plated s) => Traversing p f s s a b -> Over p f s s a b
rewrite :: Plated a => (a -> Maybe a) -> a -> a
rewriteOf :: ASetter a b a b -> (b -> Maybe a) -> a -> b
rewriteOn :: Plated a => ASetter s t a a -> (a -> Maybe a) -> s -> t
rewriteOnOf :: ASetter s t a b -> ASetter a b a b -> (b -> Maybe a) -> s -> t
rewriteM :: (Monad m, Plated a) => (a -> m (Maybe a)) -> a -> m a
rewriteMOf :: Monad m => LensLike (WrappedMonad m) a b a b -> (b -> m (Maybe a)) -> a -> m b
rewriteMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m (Maybe a)) -> s -> m t
rewriteMOnOf :: Monad m => LensLike (WrappedMonad m) s t a b -> LensLike (WrappedMonad m) a b a b -> (b -> m (Maybe a)) -> s -> m t
universe :: Plated a => a -> [a]
universeOf :: Getting [a] a a -> a -> [a]
universeOn :: Plated a => Getting [a] s a -> s -> [a]
universeOnOf :: Getting [a] s a -> Getting [a] a a -> s -> [a]
cosmos :: Plated a => Fold a a
cosmosOf :: (Applicative f, Contravariant f) => LensLike' f a a -> LensLike' f a a
cosmosOn :: (Applicative f, Contravariant f, Plated a) => LensLike' f s a -> LensLike' f s a
cosmosOnOf :: (Applicative f, Contravariant f) => LensLike' f s a -> LensLike' f a a -> LensLike' f s a
transformOn :: Plated a => ASetter s t a a -> (a -> a) -> s -> t
transformOf :: ASetter a b a b -> (b -> b) -> a -> b
transformOnOf :: ASetter s t a b -> ASetter a b a b -> (b -> b) -> s -> t
transformM :: (Monad m, Plated a) => (a -> m a) -> a -> m a
transformMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m a) -> s -> m t
transformMOf :: Monad m => LensLike (WrappedMonad m) a b a b -> (b -> m b) -> a -> m b
transformMOnOf :: Monad m => LensLike (WrappedMonad m) s t a b -> LensLike (WrappedMonad m) a b a b -> (b -> m b) -> s -> m t
contexts :: Plated a => a -> [Context a a a]
contextsOf :: ATraversal' a a -> a -> [Context a a a]
contextsOn :: Plated a => ATraversal s t a a -> s -> [Context a a t]
contextsOnOf :: ATraversal s t a a -> ATraversal' a a -> s -> [Context a a t]
holes :: Plated a => a -> [Pretext ((->) :: Type -> Type -> Type) a a a]
holesOn :: Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t]
holesOnOf :: Conjoined p => LensLike (Bazaar p r r) s t a b -> Over p (Bazaar p r r) a b r r -> s -> [Pretext p r r t]
paraOf :: Getting (Endo [a]) a a -> (a -> [r] -> r) -> a -> r
para :: Plated a => (a -> [r] -> r) -> a -> r
composOpFold :: Plated a => b -> (b -> b -> b) -> (a -> b) -> a -> b
parts :: Plated a => Lens' a [a]
gplate :: (Generic a, GPlated a (Rep a)) => Traversal' a a
gplate1 :: (Generic1 f, GPlated1 f (Rep1 f)) => Traversal' (f a) (f a)
class Each s t a b | s -> a, t -> b, s b -> t, t a -> s where
- each :: Traversal s t a b
class Ixed m => At m
class Ixed m where
- ix :: Index m -> Traversal' m (IxValue m)
type family IxValue m :: Type
class Contains m
type family Index s :: Type
icontains :: Contains m => Index m -> IndexedLens' (Index m) m Bool
iix :: Ixed m => Index m -> IndexedTraversal' (Index m) m (IxValue m)
ixAt :: At m => Index m -> Traversal' m (IxValue m)
sans :: At m => Index m -> m -> m
iat :: At m => Index m -> IndexedLens' (Index m) m (Maybe (IxValue m))
makePrisms :: Name -> DecsQ
makeClassyPrisms :: Name -> DecsQ
type ClassyNamer = Name -> Maybe (Name, Name)
data DefName
- = TopName Name
- | MethodName Name Name
type FieldNamer = Name -> [Name] -> Name -> [DefName]
data LensRules
simpleLenses :: Lens' LensRules Bool
generateSignatures :: Lens' LensRules Bool
generateUpdateableOptics :: Lens' LensRules Bool
generateLazyPatterns :: Lens' LensRules Bool
createClass :: Lens' LensRules Bool
lensField :: Lens' LensRules FieldNamer
lensClass :: Lens' LensRules ClassyNamer
lensRules :: LensRules
underscoreNoPrefixNamer :: FieldNamer
lensRulesFor :: [(String, String)] -> LensRules
lookingupNamer :: [(String, String)] -> FieldNamer
mappingNamer :: (String -> [String]) -> FieldNamer
classyRules :: LensRules
classyRules_ :: LensRules
makeLenses :: Name -> DecsQ
makeClassy :: Name -> DecsQ
makeClassy_ :: Name -> DecsQ
makeLensesFor :: [(String, String)] -> Name -> DecsQ
makeClassyFor :: String -> String -> [(String, String)] -> Name -> DecsQ
makeLensesWith :: LensRules -> Name -> DecsQ
declareLenses :: DecsQ -> DecsQ
declareLensesFor :: [(String, String)] -> DecsQ -> DecsQ
declareClassy :: DecsQ -> DecsQ
declareClassyFor :: [(String, (String, String))] -> [(String, String)] -> DecsQ -> DecsQ
declarePrisms :: DecsQ -> DecsQ
declareWrapped :: DecsQ -> DecsQ
declareFields :: DecsQ -> DecsQ
declareLensesWith :: LensRules -> DecsQ -> DecsQ
makeWrapped :: Name -> DecsQ
underscoreFields :: LensRules
underscoreNamer :: FieldNamer
camelCaseFields :: LensRules
camelCaseNamer :: FieldNamer
classUnderscoreNoPrefixFields :: LensRules
classUnderscoreNoPrefixNamer :: FieldNamer
abbreviatedFields :: LensRules
abbreviatedNamer :: FieldNamer
makeFields :: Name -> DecsQ
makeFieldsNoPrefix :: Name -> DecsQ
defaultFieldRules :: LensRules
class Profunctor (p :: Type -> Type -> Type) where
- dimap :: (a -> b) -> (c -> d) -> p b c -> p a d
- lmap :: (a -> b) -> p b c -> p a c
- rmap :: (b -> c) -> p a b -> p a c
aspect :: (CameraLens l, Floating n) => l n -> n
module Diagrams.Backend.SVG
module Diagrams.Backend.SVG

Add Diagrams Inputs

addDiagramAsSVG Source #

Arguments

:: (PandocEffects effs, Member ToPandoc effs, Member UnusedId effs)
=> Maybe Text	id attribute for figure. Will use next unused "figure" id if Nothing
-> Maybe Text	caption for figure
-> Double	width in pixels (?)
-> Double	height in pixels (?)
-> QDiagram SVG V2 Double Any	diagram
-> Sem effs Text

Add diagram (via svg inserted as html).

re-exports

(<$) :: Functor f => a -> f b -> f a infixl 4 #

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

class Functor f => Applicative (f :: Type -> Type) where #

A functor with application, providing operations to

embed pure expressions (pure), and
sequence computations and combine their results (<*> and liftA2).

A minimal complete definition must include implementations of pure and of either <*> or liftA2. If it defines both, then they must behave the same as their default definitions:

(<*>) = liftA2 id

liftA2 f x y = f <$> x <*> y

Further, any definition must satisfy the following:

identity

pure id <*> v = v

composition

pure (.) <*> u <*> v <*> w = u <*> (v <*> w)

homomorphism

pure f <*> pure x = pure (f x)

interchange

u <*> pure y = pure ($ y) <*> u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

```
u *> v = (id <$ u) <*> v
```
```
u <* v = liftA2 const u v
```

As a consequence of these laws, the Functor instance for f will satisfy

```
fmap f x = pure f <*> x
```

It may be useful to note that supposing

forall x y. p (q x y) = f x . g y

it follows from the above that

liftA2 p (liftA2 q u v) = liftA2 f u . liftA2 g v

If f is also a Monad, it should satisfy

```
pure = return
```
```
(<*>) = ap
```
```
(*>) = (>>)
```

(which implies that pure and <*> satisfy the applicative functor laws).

Minimal complete definition

pure, ((<*>) | liftA2)

Methods

pure :: a -> f a #

Lift a value.

(<*>) :: f (a -> b) -> f a -> f b infixl 4 #

Sequential application.

A few functors support an implementation of <*> that is more efficient than the default one.

liftA2 :: (a -> b -> c) -> f a -> f b -> f c #

Lift a binary function to actions.

Some functors support an implementation of liftA2 that is more efficient than the default one. In particular, if fmap is an expensive operation, it is likely better to use liftA2 than to fmap over the structure and then use <*>.

(*>) :: f a -> f b -> f b infixl 4 #

Sequence actions, discarding the value of the first argument.

(<*) :: f a -> f b -> f a infixl 4 #

Sequence actions, discarding the value of the second argument.

Instances

Applicative []	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> [a] # (<>) :: [a -> b] -> [a] -> [b] # liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c] # (>) :: [a] -> [b] -> [b] # (<*) :: [a] -> [b] -> [a] #
Applicative Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> Maybe a # (<>) :: Maybe (a -> b) -> Maybe a -> Maybe b # liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c # (>) :: Maybe a -> Maybe b -> Maybe b # (<*) :: Maybe a -> Maybe b -> Maybe a #
Applicative IO	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> IO a # (<>) :: IO (a -> b) -> IO a -> IO b # liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c # (>) :: IO a -> IO b -> IO b # (<*) :: IO a -> IO b -> IO a #
Applicative Par1	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> Par1 a # (<>) :: Par1 (a -> b) -> Par1 a -> Par1 b # liftA2 :: (a -> b -> c) -> Par1 a -> Par1 b -> Par1 c # (>) :: Par1 a -> Par1 b -> Par1 b # (<*) :: Par1 a -> Par1 b -> Par1 a #
Applicative Q
Instance details Defined in Language.Haskell.TH.Syntax Methods pure :: a -> Q a # (<>) :: Q (a -> b) -> Q a -> Q b # liftA2 :: (a -> b -> c) -> Q a -> Q b -> Q c # (>) :: Q a -> Q b -> Q b # (<*) :: Q a -> Q b -> Q a #
Applicative Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods pure :: a -> Identity a # (<>) :: Identity (a -> b) -> Identity a -> Identity b # liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c # (>) :: Identity a -> Identity b -> Identity b # (<*) :: Identity a -> Identity b -> Identity a #
Applicative ZipList	f '<$>' 'ZipList' xs1 '<>' ... '<>' 'ZipList' xsN = 'ZipList' (zipWithN f xs1 ... xsN) where `zipWithN` refers to the `zipWith` function of the appropriate arity (`zipWith`, `zipWith3`, `zipWith4`, ...). For example: (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <> ZipList "567" <> ZipList [1..] = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..]) = ZipList {getZipList = ["a5","b6b6","c7c7c7"]} Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a -> ZipList a # (<>) :: ZipList (a -> b) -> ZipList a -> ZipList b # liftA2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c # (>) :: ZipList a -> ZipList b -> ZipList b # (<*) :: ZipList a -> ZipList b -> ZipList a #
Applicative Active
Instance details Defined in Data.Active Methods pure :: a -> Active a # (<>) :: Active (a -> b) -> Active a -> Active b # liftA2 :: (a -> b -> c) -> Active a -> Active b -> Active c # (>) :: Active a -> Active b -> Active b # (<*) :: Active a -> Active b -> Active a #
Applicative Duration
Instance details Defined in Data.Active Methods pure :: a -> Duration a # (<>) :: Duration (a -> b) -> Duration a -> Duration b # liftA2 :: (a -> b -> c) -> Duration a -> Duration b -> Duration c # (>) :: Duration a -> Duration b -> Duration b # (<*) :: Duration a -> Duration b -> Duration a #
Applicative IResult
Instance details Defined in Data.Aeson.Types.Internal Methods pure :: a -> IResult a # (<>) :: IResult (a -> b) -> IResult a -> IResult b # liftA2 :: (a -> b -> c) -> IResult a -> IResult b -> IResult c # (>) :: IResult a -> IResult b -> IResult b # (<*) :: IResult a -> IResult b -> IResult a #
Applicative Result
Instance details Defined in Data.Aeson.Types.Internal Methods pure :: a -> Result a # (<>) :: Result (a -> b) -> Result a -> Result b # liftA2 :: (a -> b -> c) -> Result a -> Result b -> Result c # (>) :: Result a -> Result b -> Result b # (<*) :: Result a -> Result b -> Result a #
Applicative Parser
Instance details Defined in Data.Aeson.Types.Internal Methods pure :: a -> Parser a # (<>) :: Parser (a -> b) -> Parser a -> Parser b # liftA2 :: (a -> b -> c) -> Parser a -> Parser b -> Parser c # (>) :: Parser a -> Parser b -> Parser b # (<*) :: Parser a -> Parser b -> Parser a #
Applicative Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods pure :: a -> Complex a # (<>) :: Complex (a -> b) -> Complex a -> Complex b # liftA2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c # (>) :: Complex a -> Complex b -> Complex b # (<*) :: Complex a -> Complex b -> Complex a #
Applicative Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Min a # (<>) :: Min (a -> b) -> Min a -> Min b # liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c # (>) :: Min a -> Min b -> Min b # (<*) :: Min a -> Min b -> Min a #
Applicative Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Max a # (<>) :: Max (a -> b) -> Max a -> Max b # liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c # (>) :: Max a -> Max b -> Max b # (<*) :: Max a -> Max b -> Max a #
Applicative First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> First a # (<>) :: First (a -> b) -> First a -> First b # liftA2 :: (a -> b -> c) -> First a -> First b -> First c # (>) :: First a -> First b -> First b # (<*) :: First a -> First b -> First a #
Applicative Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Last a # (<>) :: Last (a -> b) -> Last a -> Last b # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c # (>) :: Last a -> Last b -> Last b # (<*) :: Last a -> Last b -> Last a #
Applicative Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Option a # (<>) :: Option (a -> b) -> Option a -> Option b # liftA2 :: (a -> b -> c) -> Option a -> Option b -> Option c # (>) :: Option a -> Option b -> Option b # (<*) :: Option a -> Option b -> Option a #
Applicative STM	Since: base-4.8.0.0
Instance details Defined in GHC.Conc.Sync Methods pure :: a -> STM a # (<>) :: STM (a -> b) -> STM a -> STM b # liftA2 :: (a -> b -> c) -> STM a -> STM b -> STM c # (>) :: STM a -> STM b -> STM b # (<*) :: STM a -> STM b -> STM a #
Applicative First	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> First a # (<>) :: First (a -> b) -> First a -> First b # liftA2 :: (a -> b -> c) -> First a -> First b -> First c # (>) :: First a -> First b -> First b # (<*) :: First a -> First b -> First a #
Applicative Last	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> Last a # (<>) :: Last (a -> b) -> Last a -> Last b # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c # (>) :: Last a -> Last b -> Last b # (<*) :: Last a -> Last b -> Last a #
Applicative Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Dual a # (<>) :: Dual (a -> b) -> Dual a -> Dual b # liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c # (>) :: Dual a -> Dual b -> Dual b # (<*) :: Dual a -> Dual b -> Dual a #
Applicative Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Sum a # (<>) :: Sum (a -> b) -> Sum a -> Sum b # liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c # (>) :: Sum a -> Sum b -> Sum b # (<*) :: Sum a -> Sum b -> Sum a #
Applicative Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Product a # (<>) :: Product (a -> b) -> Product a -> Product b # liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c # (>) :: Product a -> Product b -> Product b # (<*) :: Product a -> Product b -> Product a #
Applicative Down	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods pure :: a -> Down a # (<>) :: Down (a -> b) -> Down a -> Down b # liftA2 :: (a -> b -> c) -> Down a -> Down b -> Down c # (>) :: Down a -> Down b -> Down b # (<*) :: Down a -> Down b -> Down a #
Applicative ReadP	Since: base-4.6.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods pure :: a -> ReadP a # (<>) :: ReadP (a -> b) -> ReadP a -> ReadP b # liftA2 :: (a -> b -> c) -> ReadP a -> ReadP b -> ReadP c # (>) :: ReadP a -> ReadP b -> ReadP b # (<*) :: ReadP a -> ReadP b -> ReadP a #
Applicative NonEmpty	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods pure :: a -> NonEmpty a # (<>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b # liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c # (>) :: NonEmpty a -> NonEmpty b -> NonEmpty b # (<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a #
Applicative MarkupM
Instance details Defined in Text.Blaze.Internal Methods pure :: a -> MarkupM a # (<>) :: MarkupM (a -> b) -> MarkupM a -> MarkupM b # liftA2 :: (a -> b -> c) -> MarkupM a -> MarkupM b -> MarkupM c # (>) :: MarkupM a -> MarkupM b -> MarkupM b # (<*) :: MarkupM a -> MarkupM b -> MarkupM a #
Applicative Vector
Instance details Defined in Data.Vector Methods pure :: a -> Vector a # (<>) :: Vector (a -> b) -> Vector a -> Vector b # liftA2 :: (a -> b -> c) -> Vector a -> Vector b -> Vector c # (>) :: Vector a -> Vector b -> Vector b # (<*) :: Vector a -> Vector b -> Vector a #
Applicative Headed
Instance details Defined in Colonnade.Encode Methods pure :: a -> Headed a # (<>) :: Headed (a -> b) -> Headed a -> Headed b # liftA2 :: (a -> b -> c) -> Headed a -> Headed b -> Headed c # (>) :: Headed a -> Headed b -> Headed b # (<*) :: Headed a -> Headed b -> Headed a #
Applicative Headless
Instance details Defined in Colonnade.Encode Methods pure :: a -> Headless a # (<>) :: Headless (a -> b) -> Headless a -> Headless b # liftA2 :: (a -> b -> c) -> Headless a -> Headless b -> Headless c # (>) :: Headless a -> Headless b -> Headless b # (<*) :: Headless a -> Headless b -> Headless a #
Applicative RGB
Instance details Defined in Data.Colour.RGB Methods pure :: a -> RGB a # (<>) :: RGB (a -> b) -> RGB a -> RGB b # liftA2 :: (a -> b -> c) -> RGB a -> RGB b -> RGB c # (>) :: RGB a -> RGB b -> RGB b # (<*) :: RGB a -> RGB b -> RGB a #
Applicative Tree
Instance details Defined in Data.Tree Methods pure :: a -> Tree a # (<>) :: Tree (a -> b) -> Tree a -> Tree b # liftA2 :: (a -> b -> c) -> Tree a -> Tree b -> Tree c # (>) :: Tree a -> Tree b -> Tree b # (<*) :: Tree a -> Tree b -> Tree a #
Applicative Seq	Since: containers-0.5.4
Instance details Defined in Data.Sequence.Internal Methods pure :: a -> Seq a # (<>) :: Seq (a -> b) -> Seq a -> Seq b # liftA2 :: (a -> b -> c) -> Seq a -> Seq b -> Seq c # (>) :: Seq a -> Seq b -> Seq b # (<*) :: Seq a -> Seq b -> Seq a #
Applicative CryptoFailable
Instance details Defined in Crypto.Error.Types Methods pure :: a -> CryptoFailable a # (<>) :: CryptoFailable (a -> b) -> CryptoFailable a -> CryptoFailable b # liftA2 :: (a -> b -> c) -> CryptoFailable a -> CryptoFailable b -> CryptoFailable c # (>) :: CryptoFailable a -> CryptoFailable b -> CryptoFailable b # (<*) :: CryptoFailable a -> CryptoFailable b -> CryptoFailable a #
Applicative Angle
Instance details Defined in Diagrams.Angle Methods pure :: a -> Angle a # (<>) :: Angle (a -> b) -> Angle a -> Angle b # liftA2 :: (a -> b -> c) -> Angle a -> Angle b -> Angle c # (>) :: Angle a -> Angle b -> Angle b # (<*) :: Angle a -> Angle b -> Angle a #
Applicative V2
Instance details Defined in Linear.V2 Methods pure :: a -> V2 a # (<>) :: V2 (a -> b) -> V2 a -> V2 b # liftA2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c # (>) :: V2 a -> V2 b -> V2 b # (<*) :: V2 a -> V2 b -> V2 a #
Applicative V3
Instance details Defined in Linear.V3 Methods pure :: a -> V3 a # (<>) :: V3 (a -> b) -> V3 a -> V3 b # liftA2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c # (>) :: V3 a -> V3 b -> V3 b # (<*) :: V3 a -> V3 b -> V3 a #
Applicative DList
Instance details Defined in Data.DList Methods pure :: a -> DList a # (<>) :: DList (a -> b) -> DList a -> DList b # liftA2 :: (a -> b -> c) -> DList a -> DList b -> DList c # (>) :: DList a -> DList b -> DList b # (<*) :: DList a -> DList b -> DList a #
Applicative Lua
Instance details Defined in Foreign.Lua.Core.Types Methods pure :: a -> Lua a # (<>) :: Lua (a -> b) -> Lua a -> Lua b # liftA2 :: (a -> b -> c) -> Lua a -> Lua b -> Lua c # (>) :: Lua a -> Lua b -> Lua b # (<*) :: Lua a -> Lua b -> Lua a #
Applicative Interval
Instance details Defined in Numeric.Interval.Kaucher Methods pure :: a -> Interval a # (<>) :: Interval (a -> b) -> Interval a -> Interval b # liftA2 :: (a -> b -> c) -> Interval a -> Interval b -> Interval c # (>) :: Interval a -> Interval b -> Interval b # (<*) :: Interval a -> Interval b -> Interval a #
Applicative Plucker
Instance details Defined in Linear.Plucker Methods pure :: a -> Plucker a # (<>) :: Plucker (a -> b) -> Plucker a -> Plucker b # liftA2 :: (a -> b -> c) -> Plucker a -> Plucker b -> Plucker c # (>) :: Plucker a -> Plucker b -> Plucker b # (<*) :: Plucker a -> Plucker b -> Plucker a #
Applicative Quaternion
Instance details Defined in Linear.Quaternion Methods pure :: a -> Quaternion a # (<>) :: Quaternion (a -> b) -> Quaternion a -> Quaternion b # liftA2 :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c # (>) :: Quaternion a -> Quaternion b -> Quaternion b # (<*) :: Quaternion a -> Quaternion b -> Quaternion a #
Applicative V0
Instance details Defined in Linear.V0 Methods pure :: a -> V0 a # (<>) :: V0 (a -> b) -> V0 a -> V0 b # liftA2 :: (a -> b -> c) -> V0 a -> V0 b -> V0 c # (>) :: V0 a -> V0 b -> V0 b # (<*) :: V0 a -> V0 b -> V0 a #
Applicative V4
Instance details Defined in Linear.V4 Methods pure :: a -> V4 a # (<>) :: V4 (a -> b) -> V4 a -> V4 b # liftA2 :: (a -> b -> c) -> V4 a -> V4 b -> V4 c # (>) :: V4 a -> V4 b -> V4 b # (<*) :: V4 a -> V4 b -> V4 a #
Applicative V1
Instance details Defined in Linear.V1 Methods pure :: a -> V1 a # (<>) :: V1 (a -> b) -> V1 a -> V1 b # liftA2 :: (a -> b -> c) -> V1 a -> V1 b -> V1 c # (>) :: V1 a -> V1 b -> V1 b # (<*) :: V1 a -> V1 b -> V1 a #
Applicative PandocIO
Instance details Defined in Text.Pandoc.Class Methods pure :: a -> PandocIO a # (<>) :: PandocIO (a -> b) -> PandocIO a -> PandocIO b # liftA2 :: (a -> b -> c) -> PandocIO a -> PandocIO b -> PandocIO c # (>) :: PandocIO a -> PandocIO b -> PandocIO b # (<*) :: PandocIO a -> PandocIO b -> PandocIO a #
Applicative PandocPure
Instance details Defined in Text.Pandoc.Class Methods pure :: a -> PandocPure a # (<>) :: PandocPure (a -> b) -> PandocPure a -> PandocPure b # liftA2 :: (a -> b -> c) -> PandocPure a -> PandocPure b -> PandocPure c # (>) :: PandocPure a -> PandocPure b -> PandocPure b # (<*) :: PandocPure a -> PandocPure b -> PandocPure a #
Applicative SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods pure :: a -> SmallArray a # (<>) :: SmallArray (a -> b) -> SmallArray a -> SmallArray b # liftA2 :: (a -> b -> c) -> SmallArray a -> SmallArray b -> SmallArray c # (>) :: SmallArray a -> SmallArray b -> SmallArray b # (<*) :: SmallArray a -> SmallArray b -> SmallArray a #
Applicative Array
Instance details Defined in Data.Primitive.Array Methods pure :: a -> Array a # (<>) :: Array (a -> b) -> Array a -> Array b # liftA2 :: (a -> b -> c) -> Array a -> Array b -> Array c # (>) :: Array a -> Array b -> Array b # (<*) :: Array a -> Array b -> Array a #
Applicative Stream
Instance details Defined in Codec.Compression.Zlib.Stream Methods pure :: a -> Stream a # (<>) :: Stream (a -> b) -> Stream a -> Stream b # liftA2 :: (a -> b -> c) -> Stream a -> Stream b -> Stream c # (>) :: Stream a -> Stream b -> Stream b # (<*) :: Stream a -> Stream b -> Stream a #
Applicative P	Since: base-4.5.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods pure :: a -> P a # (<>) :: P (a -> b) -> P a -> P b # liftA2 :: (a -> b -> c) -> P a -> P b -> P c # (>) :: P a -> P b -> P b # (<*) :: P a -> P b -> P a #
Applicative (Either e)	Since: base-3.0
Instance details Defined in Data.Either Methods pure :: a -> Either e a # (<>) :: Either e (a -> b) -> Either e a -> Either e b # liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c # (>) :: Either e a -> Either e b -> Either e b # (<*) :: Either e a -> Either e b -> Either e a #
Applicative (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> U1 a # (<>) :: U1 (a -> b) -> U1 a -> U1 b # liftA2 :: (a -> b -> c) -> U1 a -> U1 b -> U1 c # (>) :: U1 a -> U1 b -> U1 b # (<*) :: U1 a -> U1 b -> U1 a #
Monoid a => Applicative ((,) a)	For tuples, the `Monoid` constraint on `a` determines how the first values merge. For example, `String`s concatenate: ("hello ", (+15)) <> ("world!", 2002) ("hello world!",2017) Since: base-2.1*
Instance details Defined in GHC.Base Methods pure :: a0 -> (a, a0) # (<>) :: (a, a0 -> b) -> (a, a0) -> (a, b) # liftA2 :: (a0 -> b -> c) -> (a, a0) -> (a, b) -> (a, c) # (>) :: (a, a0) -> (a, b) -> (a, b) # (<*) :: (a, a0) -> (a, b) -> (a, a0) #
Monad m => Applicative (WrappedMonad m)	Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a -> WrappedMonad m a # (<>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c # (>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a #
Applicative (Prompt p)
Instance details Defined in Control.Monad.Prompt Methods pure :: a -> Prompt p a # (<>) :: Prompt p (a -> b) -> Prompt p a -> Prompt p b # liftA2 :: (a -> b -> c) -> Prompt p a -> Prompt p b -> Prompt p c # (>) :: Prompt p a -> Prompt p b -> Prompt p b # (<*) :: Prompt p a -> Prompt p b -> Prompt p a #
Applicative (RecPrompt p)
Instance details Defined in Control.Monad.Prompt Methods pure :: a -> RecPrompt p a # (<>) :: RecPrompt p (a -> b) -> RecPrompt p a -> RecPrompt p b # liftA2 :: (a -> b -> c) -> RecPrompt p a -> RecPrompt p b -> RecPrompt p c # (>) :: RecPrompt p a -> RecPrompt p b -> RecPrompt p b # (<*) :: RecPrompt p a -> RecPrompt p b -> RecPrompt p a #
Representable f => Applicative (Co f)
Instance details Defined in Data.Functor.Rep Methods pure :: a -> Co f a # (<>) :: Co f (a -> b) -> Co f a -> Co f b # liftA2 :: (a -> b -> c) -> Co f a -> Co f b -> Co f c # (>) :: Co f a -> Co f b -> Co f b # (<*) :: Co f a -> Co f b -> Co f a #
Applicative (Parser i)
Instance details Defined in Data.Attoparsec.Internal.Types Methods pure :: a -> Parser i a # (<>) :: Parser i (a -> b) -> Parser i a -> Parser i b # liftA2 :: (a -> b -> c) -> Parser i a -> Parser i b -> Parser i c # (>) :: Parser i a -> Parser i b -> Parser i b # (<*) :: Parser i a -> Parser i b -> Parser i a #
Arrow a => Applicative (ArrowMonad a)	Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods pure :: a0 -> ArrowMonad a a0 # (<>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b # liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c # (>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b # (<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 #
Applicative (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods pure :: a -> Proxy a # (<>) :: Proxy (a -> b) -> Proxy a -> Proxy b # liftA2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c # (>) :: Proxy a -> Proxy b -> Proxy b # (<*) :: Proxy a -> Proxy b -> Proxy a #
Applicative (Measured n)
Instance details Defined in Diagrams.Core.Measure Methods pure :: a -> Measured n a # (<>) :: Measured n (a -> b) -> Measured n a -> Measured n b # liftA2 :: (a -> b -> c) -> Measured n a -> Measured n b -> Measured n c # (>) :: Measured n a -> Measured n b -> Measured n b # (<*) :: Measured n a -> Measured n b -> Measured n a #
Applicative f => Applicative (Point f)
Instance details Defined in Linear.Affine Methods pure :: a -> Point f a # (<>) :: Point f (a -> b) -> Point f a -> Point f b # liftA2 :: (a -> b -> c) -> Point f a -> Point f b -> Point f c # (>) :: Point f a -> Point f b -> Point f b # (<*) :: Point f a -> Point f b -> Point f a #
(Functor m, Monad m) => Applicative (MaybeT m)
Instance details Defined in Control.Monad.Trans.Maybe Methods pure :: a -> MaybeT m a # (<>) :: MaybeT m (a -> b) -> MaybeT m a -> MaybeT m b # liftA2 :: (a -> b -> c) -> MaybeT m a -> MaybeT m b -> MaybeT m c # (>) :: MaybeT m a -> MaybeT m b -> MaybeT m b # (<*) :: MaybeT m a -> MaybeT m b -> MaybeT m a #
Applicative (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods pure :: a -> ReifiedFold s a # (<>) :: ReifiedFold s (a -> b) -> ReifiedFold s a -> ReifiedFold s b # liftA2 :: (a -> b -> c) -> ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s c # (>) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s b # (<*) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s a #
Applicative (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods pure :: a -> ReifiedGetter s a # (<>) :: ReifiedGetter s (a -> b) -> ReifiedGetter s a -> ReifiedGetter s b # liftA2 :: (a -> b -> c) -> ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s c # (>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b # (<*) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s a #
Alternative f => Applicative (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods pure :: a -> Cofree f a # (<>) :: Cofree f (a -> b) -> Cofree f a -> Cofree f b # liftA2 :: (a -> b -> c) -> Cofree f a -> Cofree f b -> Cofree f c # (>) :: Cofree f a -> Cofree f b -> Cofree f b # (<*) :: Cofree f a -> Cofree f b -> Cofree f a #
Functor f => Applicative (Free f)
Instance details Defined in Control.Monad.Free Methods pure :: a -> Free f a # (<>) :: Free f (a -> b) -> Free f a -> Free f b # liftA2 :: (a -> b -> c) -> Free f a -> Free f b -> Free f c # (>) :: Free f a -> Free f b -> Free f b # (<*) :: Free f a -> Free f b -> Free f a #
Applicative f => Applicative (Yoneda f)
Instance details Defined in Data.Functor.Yoneda Methods pure :: a -> Yoneda f a # (<>) :: Yoneda f (a -> b) -> Yoneda f a -> Yoneda f b # liftA2 :: (a -> b -> c) -> Yoneda f a -> Yoneda f b -> Yoneda f c # (>) :: Yoneda f a -> Yoneda f b -> Yoneda f b # (<*) :: Yoneda f a -> Yoneda f b -> Yoneda f a #
Applicative f => Applicative (Indexing f)
Instance details Defined in Control.Lens.Internal.Indexed Methods pure :: a -> Indexing f a # (<>) :: Indexing f (a -> b) -> Indexing f a -> Indexing f b # liftA2 :: (a -> b -> c) -> Indexing f a -> Indexing f b -> Indexing f c # (>) :: Indexing f a -> Indexing f b -> Indexing f b # (<*) :: Indexing f a -> Indexing f b -> Indexing f a #
Applicative f => Applicative (Indexing64 f)
Instance details Defined in Control.Lens.Internal.Indexed Methods pure :: a -> Indexing64 f a # (<>) :: Indexing64 f (a -> b) -> Indexing64 f a -> Indexing64 f b # liftA2 :: (a -> b -> c) -> Indexing64 f a -> Indexing64 f b -> Indexing64 f c # (>) :: Indexing64 f a -> Indexing64 f b -> Indexing64 f b # (<*) :: Indexing64 f a -> Indexing64 f b -> Indexing64 f a #
Applicative m => Applicative (HtmlT m)	Based on the monad instance.
Instance details Defined in Lucid.Base Methods pure :: a -> HtmlT m a # (<>) :: HtmlT m (a -> b) -> HtmlT m a -> HtmlT m b # liftA2 :: (a -> b -> c) -> HtmlT m a -> HtmlT m b -> HtmlT m c # (>) :: HtmlT m a -> HtmlT m b -> HtmlT m b # (<*) :: HtmlT m a -> HtmlT m b -> HtmlT m a #
Applicative m => Applicative (ListT m)
Instance details Defined in Control.Monad.Trans.List Methods pure :: a -> ListT m a # (<>) :: ListT m (a -> b) -> ListT m a -> ListT m b # liftA2 :: (a -> b -> c) -> ListT m a -> ListT m b -> ListT m c # (>) :: ListT m a -> ListT m b -> ListT m b # (<*) :: ListT m a -> ListT m b -> ListT m a #
Applicative (Sem f)
Instance details Defined in Polysemy.Internal Methods pure :: a -> Sem f a # (<>) :: Sem f (a -> b) -> Sem f a -> Sem f b # liftA2 :: (a -> b -> c) -> Sem f a -> Sem f b -> Sem f c # (>) :: Sem f a -> Sem f b -> Sem f b # (<*) :: Sem f a -> Sem f b -> Sem f a #
(Applicative (Rep p), Representable p) => Applicative (Prep p)
Instance details Defined in Data.Profunctor.Rep Methods pure :: a -> Prep p a # (<>) :: Prep p (a -> b) -> Prep p a -> Prep p b # liftA2 :: (a -> b -> c) -> Prep p a -> Prep p b -> Prep p c # (>) :: Prep p a -> Prep p b -> Prep p b # (<*) :: Prep p a -> Prep p b -> Prep p a #
Applicative (RVarT n)
Instance details Defined in Data.RVar Methods pure :: a -> RVarT n a # (<>) :: RVarT n (a -> b) -> RVarT n a -> RVarT n b # liftA2 :: (a -> b -> c) -> RVarT n a -> RVarT n b -> RVarT n c # (>) :: RVarT n a -> RVarT n b -> RVarT n b # (<*) :: RVarT n a -> RVarT n b -> RVarT n a #
Applicative f => Applicative (WrappedApplicative f)
Instance details Defined in Data.Functor.Bind.Class Methods pure :: a -> WrappedApplicative f a # (<>) :: WrappedApplicative f (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b # liftA2 :: (a -> b -> c) -> WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f c # (>) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f b # (<*) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f a #
Apply f => Applicative (MaybeApply f)
Instance details Defined in Data.Functor.Bind.Class Methods pure :: a -> MaybeApply f a # (<>) :: MaybeApply f (a -> b) -> MaybeApply f a -> MaybeApply f b # liftA2 :: (a -> b -> c) -> MaybeApply f a -> MaybeApply f b -> MaybeApply f c # (>) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f b # (<*) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f a #
Applicative f => Applicative (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> Rec1 f a # (<>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b # liftA2 :: (a -> b -> c) -> Rec1 f a -> Rec1 f b -> Rec1 f c # (>) :: Rec1 f a -> Rec1 f b -> Rec1 f b # (<*) :: Rec1 f a -> Rec1 f b -> Rec1 f a #
Applicative m => Applicative (IdentityT m)
Instance details Defined in Control.Monad.Trans.Identity Methods pure :: a -> IdentityT m a # (<>) :: IdentityT m (a -> b) -> IdentityT m a -> IdentityT m b # liftA2 :: (a -> b -> c) -> IdentityT m a -> IdentityT m b -> IdentityT m c # (>) :: IdentityT m a -> IdentityT m b -> IdentityT m b # (<*) :: IdentityT m a -> IdentityT m b -> IdentityT m a #
Monoid m => Applicative (Const m :: Type -> Type)	Since: base-2.0.1
Instance details Defined in Data.Functor.Const Methods pure :: a -> Const m a # (<>) :: Const m (a -> b) -> Const m a -> Const m b # liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c # (>) :: Const m a -> Const m b -> Const m b # (<*) :: Const m a -> Const m b -> Const m a #
Arrow a => Applicative (WrappedArrow a b)	Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 # (<>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c # (>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 #
Applicative (PromptT p m)
Instance details Defined in Control.Monad.Prompt Methods pure :: a -> PromptT p m a # (<>) :: PromptT p m (a -> b) -> PromptT p m a -> PromptT p m b # liftA2 :: (a -> b -> c) -> PromptT p m a -> PromptT p m b -> PromptT p m c # (>) :: PromptT p m a -> PromptT p m b -> PromptT p m b # (<*) :: PromptT p m a -> PromptT p m b -> PromptT p m a #
Applicative (RecPromptT p m)
Instance details Defined in Control.Monad.Prompt Methods pure :: a -> RecPromptT p m a # (<>) :: RecPromptT p m (a -> b) -> RecPromptT p m a -> RecPromptT p m b # liftA2 :: (a -> b -> c) -> RecPromptT p m a -> RecPromptT p m b -> RecPromptT p m c # (>) :: RecPromptT p m a -> RecPromptT p m b -> RecPromptT p m b # (<*) :: RecPromptT p m a -> RecPromptT p m b -> RecPromptT p m a #
Applicative f => Applicative (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> Ap f a # (<>) :: Ap f (a -> b) -> Ap f a -> Ap f b # liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c # (>) :: Ap f a -> Ap f b -> Ap f b # (<*) :: Ap f a -> Ap f b -> Ap f a #
Applicative f => Applicative (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Alt f a # (<>) :: Alt f (a -> b) -> Alt f a -> Alt f b # liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c # (>) :: Alt f a -> Alt f b -> Alt f b # (<*) :: Alt f a -> Alt f b -> Alt f a #
Biapplicative p => Applicative (Join p)
Instance details Defined in Data.Bifunctor.Join Methods pure :: a -> Join p a # (<>) :: Join p (a -> b) -> Join p a -> Join p b # liftA2 :: (a -> b -> c) -> Join p a -> Join p b -> Join p c # (>) :: Join p a -> Join p b -> Join p b # (<*) :: Join p a -> Join p b -> Join p a #
Biapplicative p => Applicative (Fix p)
Instance details Defined in Data.Bifunctor.Fix Methods pure :: a -> Fix p a # (<>) :: Fix p (a -> b) -> Fix p a -> Fix p b # liftA2 :: (a -> b -> c) -> Fix p a -> Fix p b -> Fix p c # (>) :: Fix p a -> Fix p b -> Fix p b # (<*) :: Fix p a -> Fix p b -> Fix p a #
Applicative w => Applicative (TracedT m w)
Instance details Defined in Control.Comonad.Trans.Traced Methods pure :: a -> TracedT m w a # (<>) :: TracedT m w (a -> b) -> TracedT m w a -> TracedT m w b # liftA2 :: (a -> b -> c) -> TracedT m w a -> TracedT m w b -> TracedT m w c # (>) :: TracedT m w a -> TracedT m w b -> TracedT m w b # (<*) :: TracedT m w a -> TracedT m w b -> TracedT m w a #
(Applicative f, Monad f) => Applicative (WhenMissing f x)	Equivalent to `ReaderT k (ReaderT x (MaybeT f))`. Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods pure :: a -> WhenMissing f x a # (<>) :: WhenMissing f x (a -> b) -> WhenMissing f x a -> WhenMissing f x b # liftA2 :: (a -> b -> c) -> WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x c # (>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b # (<*) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x a #
Applicative (Query v n)
Instance details Defined in Diagrams.Core.Query Methods pure :: a -> Query v n a # (<>) :: Query v n (a -> b) -> Query v n a -> Query v n b # liftA2 :: (a -> b -> c) -> Query v n a -> Query v n b -> Query v n c # (>) :: Query v n a -> Query v n b -> Query v n b # (<*) :: Query v n a -> Query v n b -> Query v n a #
Applicative (Indexed i a)
Instance details Defined in Control.Lens.Internal.Indexed Methods pure :: a0 -> Indexed i a a0 # (<>) :: Indexed i a (a0 -> b) -> Indexed i a a0 -> Indexed i a b # liftA2 :: (a0 -> b -> c) -> Indexed i a a0 -> Indexed i a b -> Indexed i a c # (>) :: Indexed i a a0 -> Indexed i a b -> Indexed i a b # (<*) :: Indexed i a a0 -> Indexed i a b -> Indexed i a a0 #
(Functor m, Monad m) => Applicative (ExceptT e m)
Instance details Defined in Control.Monad.Trans.Except Methods pure :: a -> ExceptT e m a # (<>) :: ExceptT e m (a -> b) -> ExceptT e m a -> ExceptT e m b # liftA2 :: (a -> b -> c) -> ExceptT e m a -> ExceptT e m b -> ExceptT e m c # (>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b # (<*) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m a #
(Functor f, Monad m) => Applicative (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods pure :: a -> FreeT f m a # (<>) :: FreeT f m (a -> b) -> FreeT f m a -> FreeT f m b # liftA2 :: (a -> b -> c) -> FreeT f m a -> FreeT f m b -> FreeT f m c # (>) :: FreeT f m a -> FreeT f m b -> FreeT f m b # (<*) :: FreeT f m a -> FreeT f m b -> FreeT f m a #
(Alternative f, Applicative w) => Applicative (CofreeT f w)
Instance details Defined in Control.Comonad.Trans.Cofree Methods pure :: a -> CofreeT f w a # (<>) :: CofreeT f w (a -> b) -> CofreeT f w a -> CofreeT f w b # liftA2 :: (a -> b -> c) -> CofreeT f w a -> CofreeT f w b -> CofreeT f w c # (>) :: CofreeT f w a -> CofreeT f w b -> CofreeT f w b # (<*) :: CofreeT f w a -> CofreeT f w b -> CofreeT f w a #
(Functor g, g ~ h) => Applicative (Curried g h)
Instance details Defined in Data.Functor.Day.Curried Methods pure :: a -> Curried g h a # (<>) :: Curried g h (a -> b) -> Curried g h a -> Curried g h b # liftA2 :: (a -> b -> c) -> Curried g h a -> Curried g h b -> Curried g h c # (>) :: Curried g h a -> Curried g h b -> Curried g h b # (<*) :: Curried g h a -> Curried g h b -> Curried g h a #
(Applicative f, Applicative g) => Applicative (Day f g)
Instance details Defined in Data.Functor.Day Methods pure :: a -> Day f g a # (<>) :: Day f g (a -> b) -> Day f g a -> Day f g b # liftA2 :: (a -> b -> c) -> Day f g a -> Day f g b -> Day f g c # (>) :: Day f g a -> Day f g b -> Day f g b # (<*) :: Day f g a -> Day f g b -> Day f g a #
(Functor m, Monad m) => Applicative (ErrorT e m)
Instance details Defined in Control.Monad.Trans.Error Methods pure :: a -> ErrorT e m a # (<>) :: ErrorT e m (a -> b) -> ErrorT e m a -> ErrorT e m b # liftA2 :: (a -> b -> c) -> ErrorT e m a -> ErrorT e m b -> ErrorT e m c # (>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b # (<*) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m a #
(Functor m, Monad m) => Applicative (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods pure :: a -> StateT s m a # (<>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c # (>) :: StateT s m a -> StateT s m b -> StateT s m b # (<*) :: StateT s m a -> StateT s m b -> StateT s m a #
Applicative f => Applicative (Backwards f)	Apply `f`-actions in the reverse order.
Instance details Defined in Control.Applicative.Backwards Methods pure :: a -> Backwards f a # (<>) :: Backwards f (a -> b) -> Backwards f a -> Backwards f b # liftA2 :: (a -> b -> c) -> Backwards f a -> Backwards f b -> Backwards f c # (>) :: Backwards f a -> Backwards f b -> Backwards f b # (<*) :: Backwards f a -> Backwards f b -> Backwards f a #
Applicative (Mafic a b)
Instance details Defined in Control.Lens.Internal.Magma Methods pure :: a0 -> Mafic a b a0 # (<>) :: Mafic a b (a0 -> b0) -> Mafic a b a0 -> Mafic a b b0 # liftA2 :: (a0 -> b0 -> c) -> Mafic a b a0 -> Mafic a b b0 -> Mafic a b c # (>) :: Mafic a b a0 -> Mafic a b b0 -> Mafic a b b0 # (<*) :: Mafic a b a0 -> Mafic a b b0 -> Mafic a b a0 #
Applicative (Flows i b)	This is an illegal `Applicative`.
Instance details Defined in Control.Lens.Internal.Level Methods pure :: a -> Flows i b a # (<>) :: Flows i b (a -> b0) -> Flows i b a -> Flows i b b0 # liftA2 :: (a -> b0 -> c) -> Flows i b a -> Flows i b b0 -> Flows i b c # (>) :: Flows i b a -> Flows i b b0 -> Flows i b b0 # (<*) :: Flows i b a -> Flows i b b0 -> Flows i b a #
Dim n => Applicative (V n)
Instance details Defined in Linear.V Methods pure :: a -> V n a # (<>) :: V n (a -> b) -> V n a -> V n b # liftA2 :: (a -> b -> c) -> V n a -> V n b -> V n c # (>) :: V n a -> V n b -> V n b # (<*) :: V n a -> V n b -> V n a #
Applicative m => Applicative (LoggingT message m)
Instance details Defined in Control.Monad.Log Methods pure :: a -> LoggingT message m a # (<>) :: LoggingT message m (a -> b) -> LoggingT message m a -> LoggingT message m b # liftA2 :: (a -> b -> c) -> LoggingT message m a -> LoggingT message m b -> LoggingT message m c # (>) :: LoggingT message m a -> LoggingT message m b -> LoggingT message m b # (<*) :: LoggingT message m a -> LoggingT message m b -> LoggingT message m a #
Monad m => Applicative (PureLoggingT log m)
Instance details Defined in Control.Monad.Log Methods pure :: a -> PureLoggingT log m a # (<>) :: PureLoggingT log m (a -> b) -> PureLoggingT log m a -> PureLoggingT log m b # liftA2 :: (a -> b -> c) -> PureLoggingT log m a -> PureLoggingT log m b -> PureLoggingT log m c # (>) :: PureLoggingT log m a -> PureLoggingT log m b -> PureLoggingT log m b # (<*) :: PureLoggingT log m a -> PureLoggingT log m b -> PureLoggingT log m a #
Applicative m => Applicative (DiscardLoggingT message m)
Instance details Defined in Control.Monad.Log Methods pure :: a -> DiscardLoggingT message m a # (<>) :: DiscardLoggingT message m (a -> b) -> DiscardLoggingT message m a -> DiscardLoggingT message m b # liftA2 :: (a -> b -> c) -> DiscardLoggingT message m a -> DiscardLoggingT message m b -> DiscardLoggingT message m c # (>) :: DiscardLoggingT message m a -> DiscardLoggingT message m b -> DiscardLoggingT message m b # (<*) :: DiscardLoggingT message m a -> DiscardLoggingT message m b -> DiscardLoggingT message m a #
(Monoid w, Applicative m) => Applicative (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods pure :: a -> WriterT w m a # (<>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b # liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c # (>) :: WriterT w m a -> WriterT w m b -> WriterT w m b # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a #
(Functor m, Monad m) => Applicative (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods pure :: a -> StateT s m a # (<>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c # (>) :: StateT s m a -> StateT s m b -> StateT s m b # (<*) :: StateT s m a -> StateT s m b -> StateT s m a #
(Monoid w, Applicative m) => Applicative (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods pure :: a -> WriterT w m a # (<>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b # liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c # (>) :: WriterT w m a -> WriterT w m b -> WriterT w m b # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a #
(Profunctor p, Arrow p) => Applicative (Tambara p a)
Instance details Defined in Data.Profunctor.Strong Methods pure :: a0 -> Tambara p a a0 # (<>) :: Tambara p a (a0 -> b) -> Tambara p a a0 -> Tambara p a b # liftA2 :: (a0 -> b -> c) -> Tambara p a a0 -> Tambara p a b -> Tambara p a c # (>) :: Tambara p a a0 -> Tambara p a b -> Tambara p a b # (<*) :: Tambara p a a0 -> Tambara p a b -> Tambara p a a0 #
Applicative f => Applicative (Star f a)
Instance details Defined in Data.Profunctor.Types Methods pure :: a0 -> Star f a a0 # (<>) :: Star f a (a0 -> b) -> Star f a a0 -> Star f a b # liftA2 :: (a0 -> b -> c) -> Star f a a0 -> Star f a b -> Star f a c # (>) :: Star f a a0 -> Star f a b -> Star f a b # (<*) :: Star f a a0 -> Star f a b -> Star f a a0 #
Applicative (Costar f a)
Instance details Defined in Data.Profunctor.Types Methods pure :: a0 -> Costar f a a0 # (<>) :: Costar f a (a0 -> b) -> Costar f a a0 -> Costar f a b # liftA2 :: (a0 -> b -> c) -> Costar f a a0 -> Costar f a b -> Costar f a c # (>) :: Costar f a a0 -> Costar f a b -> Costar f a b # (<*) :: Costar f a a0 -> Costar f a b -> Costar f a a0 #
Applicative (Tagged s)
Instance details Defined in Data.Tagged Methods pure :: a -> Tagged s a # (<>) :: Tagged s (a -> b) -> Tagged s a -> Tagged s b # liftA2 :: (a -> b -> c) -> Tagged s a -> Tagged s b -> Tagged s c # (>) :: Tagged s a -> Tagged s b -> Tagged s b # (<*) :: Tagged s a -> Tagged s b -> Tagged s a #
Applicative f => Applicative (Reverse f)	Derived instance.
Instance details Defined in Data.Functor.Reverse Methods pure :: a -> Reverse f a # (<>) :: Reverse f (a -> b) -> Reverse f a -> Reverse f b # liftA2 :: (a -> b -> c) -> Reverse f a -> Reverse f b -> Reverse f c # (>) :: Reverse f a -> Reverse f b -> Reverse f b # (<*) :: Reverse f a -> Reverse f b -> Reverse f a #
Applicative (Mag a b)
Instance details Defined in Data.Biapplicative Methods pure :: a0 -> Mag a b a0 # (<>) :: Mag a b (a0 -> b0) -> Mag a b a0 -> Mag a b b0 # liftA2 :: (a0 -> b0 -> c) -> Mag a b a0 -> Mag a b b0 -> Mag a b c # (>) :: Mag a b a0 -> Mag a b b0 -> Mag a b b0 # (<*) :: Mag a b a0 -> Mag a b b0 -> Mag a b a0 #
Monoid m => Applicative (Holes t m)
Instance details Defined in Control.Lens.Traversal Methods pure :: a -> Holes t m a # (<>) :: Holes t m (a -> b) -> Holes t m a -> Holes t m b # liftA2 :: (a -> b -> c) -> Holes t m a -> Holes t m b -> Holes t m c # (>) :: Holes t m a -> Holes t m b -> Holes t m b # (<*) :: Holes t m a -> Holes t m b -> Holes t m a #
Applicative ((->) a :: Type -> Type)	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a0 -> a -> a0 # (<>) :: (a -> (a0 -> b)) -> (a -> a0) -> a -> b # liftA2 :: (a0 -> b -> c) -> (a -> a0) -> (a -> b) -> a -> c # (>) :: (a -> a0) -> (a -> b) -> a -> b # (<*) :: (a -> a0) -> (a -> b) -> a -> a0 #
Monoid c => Applicative (K1 i c :: Type -> Type)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> K1 i c a # (<>) :: K1 i c (a -> b) -> K1 i c a -> K1 i c b # liftA2 :: (a -> b -> c0) -> K1 i c a -> K1 i c b -> K1 i c c0 # (>) :: K1 i c a -> K1 i c b -> K1 i c b # (<*) :: K1 i c a -> K1 i c b -> K1 i c a #
(Applicative f, Applicative g) => Applicative (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> (f :: g) a # (<>) :: (f :: g) (a -> b) -> (f :: g) a -> (f :: g) b # liftA2 :: (a -> b -> c) -> (f :: g) a -> (f :: g) b -> (f :: g) c # (>) :: (f :: g) a -> (f :: g) b -> (f :: g) b # (<) :: (f :: g) a -> (f :: g) b -> (f :: g) a #
(Applicative f, Applicative g) => Applicative (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods pure :: a -> Product f g a # (<>) :: Product f g (a -> b) -> Product f g a -> Product f g b # liftA2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c # (>) :: Product f g a -> Product f g b -> Product f g b # (<*) :: Product f g a -> Product f g b -> Product f g a #
(Monad f, Applicative f) => Applicative (WhenMatched f x y)	Equivalent to `ReaderT Key (ReaderT x (ReaderT y (MaybeT f)))` Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods pure :: a -> WhenMatched f x y a # (<>) :: WhenMatched f x y (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b # liftA2 :: (a -> b -> c) -> WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y c # (>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b # (<*) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y a #
(Applicative f, Monad f) => Applicative (WhenMissing f k x)	Equivalent to `ReaderT k (ReaderT x (MaybeT f))` . Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods pure :: a -> WhenMissing f k x a # (<>) :: WhenMissing f k x (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b # liftA2 :: (a -> b -> c) -> WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x c # (>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # (<*) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x a #
Applicative (Bazaar p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods pure :: a0 -> Bazaar p a b a0 # (<>) :: Bazaar p a b (a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 # liftA2 :: (a0 -> b0 -> c) -> Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b c # (>) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b b0 # (<*) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b a0 #
Applicative (Molten i a b)
Instance details Defined in Control.Lens.Internal.Magma Methods pure :: a0 -> Molten i a b a0 # (<>) :: Molten i a b (a0 -> b0) -> Molten i a b a0 -> Molten i a b b0 # liftA2 :: (a0 -> b0 -> c) -> Molten i a b a0 -> Molten i a b b0 -> Molten i a b c # (>) :: Molten i a b a0 -> Molten i a b b0 -> Molten i a b b0 # (<*) :: Molten i a b a0 -> Molten i a b b0 -> Molten i a b a0 #
Applicative m => Applicative (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods pure :: a -> ReaderT r m a # (<>) :: ReaderT r m (a -> b) -> ReaderT r m a -> ReaderT r m b # liftA2 :: (a -> b -> c) -> ReaderT r m a -> ReaderT r m b -> ReaderT r m c # (>) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m b # (<*) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m a #
Applicative (ContT r m)
Instance details Defined in Control.Monad.Trans.Cont Methods pure :: a -> ContT r m a # (<>) :: ContT r m (a -> b) -> ContT r m a -> ContT r m b # liftA2 :: (a -> b -> c) -> ContT r m a -> ContT r m b -> ContT r m c # (>) :: ContT r m a -> ContT r m b -> ContT r m b # (<*) :: ContT r m a -> ContT r m b -> ContT r m a #
Applicative (ParsecT s u m)
Instance details Defined in Text.Parsec.Prim Methods pure :: a -> ParsecT s u m a # (<>) :: ParsecT s u m (a -> b) -> ParsecT s u m a -> ParsecT s u m b # liftA2 :: (a -> b -> c) -> ParsecT s u m a -> ParsecT s u m b -> ParsecT s u m c # (>) :: ParsecT s u m a -> ParsecT s u m b -> ParsecT s u m b # (<*) :: ParsecT s u m a -> ParsecT s u m b -> ParsecT s u m a #
Applicative f => Applicative (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> M1 i c f a # (<>) :: M1 i c f (a -> b) -> M1 i c f a -> M1 i c f b # liftA2 :: (a -> b -> c0) -> M1 i c f a -> M1 i c f b -> M1 i c f c0 # (>) :: M1 i c f a -> M1 i c f b -> M1 i c f b # (<*) :: M1 i c f a -> M1 i c f b -> M1 i c f a #
(Applicative f, Applicative g) => Applicative (f :.: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> (f :.: g) a # (<>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b # liftA2 :: (a -> b -> c) -> (f :.: g) a -> (f :.: g) b -> (f :.: g) c # (>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b # (<*) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) a #
(Applicative f, Applicative g) => Applicative (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods pure :: a -> Compose f g a # (<>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b # liftA2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c # (>) :: Compose f g a -> Compose f g b -> Compose f g b # (<*) :: Compose f g a -> Compose f g b -> Compose f g a #
(Monad f, Applicative f) => Applicative (WhenMatched f k x y)	Equivalent to `ReaderT k (ReaderT x (ReaderT y (MaybeT f)))` Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods pure :: a -> WhenMatched f k x y a # (<>) :: WhenMatched f k x y (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b # liftA2 :: (a -> b -> c) -> WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y c # (>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # (<*) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y a #
(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Strict Methods pure :: a -> RWST r w s m a # (<>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c # (>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a #
Applicative (TakingWhile p f a b)
Instance details Defined in Control.Lens.Internal.Magma Methods pure :: a0 -> TakingWhile p f a b a0 # (<>) :: TakingWhile p f a b (a0 -> b0) -> TakingWhile p f a b a0 -> TakingWhile p f a b b0 # liftA2 :: (a0 -> b0 -> c) -> TakingWhile p f a b a0 -> TakingWhile p f a b b0 -> TakingWhile p f a b c # (>) :: TakingWhile p f a b a0 -> TakingWhile p f a b b0 -> TakingWhile p f a b b0 # (<*) :: TakingWhile p f a b a0 -> TakingWhile p f a b b0 -> TakingWhile p f a b a0 #
Applicative (BazaarT p g a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods pure :: a0 -> BazaarT p g a b a0 # (<>) :: BazaarT p g a b (a0 -> b0) -> BazaarT p g a b a0 -> BazaarT p g a b b0 # liftA2 :: (a0 -> b0 -> c) -> BazaarT p g a b a0 -> BazaarT p g a b b0 -> BazaarT p g a b c # (>) :: BazaarT p g a b a0 -> BazaarT p g a b b0 -> BazaarT p g a b b0 # (<*) :: BazaarT p g a b a0 -> BazaarT p g a b b0 -> BazaarT p g a b a0 #
(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Lazy Methods pure :: a -> RWST r w s m a # (<>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c # (>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a #
Reifies s (ReifiedApplicative f) => Applicative (ReflectedApplicative f s)
Instance details Defined in Data.Reflection Methods pure :: a -> ReflectedApplicative f s a # (<>) :: ReflectedApplicative f s (a -> b) -> ReflectedApplicative f s a -> ReflectedApplicative f s b # liftA2 :: (a -> b -> c) -> ReflectedApplicative f s a -> ReflectedApplicative f s b -> ReflectedApplicative f s c # (>) :: ReflectedApplicative f s a -> ReflectedApplicative f s b -> ReflectedApplicative f s b # (<*) :: ReflectedApplicative f s a -> ReflectedApplicative f s b -> ReflectedApplicative f s a #
Monad state => Applicative (Builder collection mutCollection step state err)
Instance details Defined in Basement.MutableBuilder Methods pure :: a -> Builder collection mutCollection step state err a # (<>) :: Builder collection mutCollection step state err (a -> b) -> Builder collection mutCollection step state err a -> Builder collection mutCollection step state err b # liftA2 :: (a -> b -> c) -> Builder collection mutCollection step state err a -> Builder collection mutCollection step state err b -> Builder collection mutCollection step state err c # (>) :: Builder collection mutCollection step state err a -> Builder collection mutCollection step state err b -> Builder collection mutCollection step state err b # (<*) :: Builder collection mutCollection step state err a -> Builder collection mutCollection step state err b -> Builder collection mutCollection step state err a #

class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where #

Functors representing data structures that can be traversed from left to right.

A definition of traverse must satisfy the following laws:

naturality: t . traverse f = traverse (t . f) for every applicative transformation t
identity: traverse Identity = Identity
composition: traverse (Compose . fmap g . f) = Compose . fmap (traverse g) . traverse f

A definition of sequenceA must satisfy the following laws:

naturality: t . sequenceA = sequenceA . fmap t for every applicative transformation t
identity: sequenceA . fmap Identity = Identity
composition: sequenceA . fmap Compose = Compose . fmap sequenceA . sequenceA

where an applicative transformation is a function

t :: (Applicative f, Applicative g) => f a -> g a

preserving the Applicative operations, i.e.

```
t (pure x) = pure x
```
```
t (x <*> y) = t x <*> t y
```

and the identity functor Identity and composition of functors Compose are defined as

  newtype Identity a = Identity a

  instance Functor Identity where
    fmap f (Identity x) = Identity (f x)

  instance Applicative Identity where
    pure x = Identity x
    Identity f <*> Identity x = Identity (f x)

  newtype Compose f g a = Compose (f (g a))

  instance (Functor f, Functor g) => Functor (Compose f g) where
    fmap f (Compose x) = Compose (fmap (fmap f) x)

  instance (Applicative f, Applicative g) => Applicative (Compose f g) where
    pure x = Compose (pure (pure x))
    Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)

(The naturality law is implied by parametricity.)

Instances are similar to Functor, e.g. given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Traversable Tree where
   traverse f Empty = pure Empty
   traverse f (Leaf x) = Leaf <$> f x
   traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r

This is suitable even for abstract types, as the laws for <*> imply a form of associativity.

The superclass instances should satisfy the following:

In the Functor instance, fmap should be equivalent to traversal with the identity applicative functor (fmapDefault).
In the Foldable instance, foldMap should be equivalent to traversal with a constant applicative functor (foldMapDefault).

Minimal complete definition

traverse | sequenceA

Methods

traverse :: Applicative f => (a -> f b) -> t a -> f (t b) #

Map each element of a structure to an action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see traverse_.

Instances

Traversable []	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> [a] -> f [b] # sequenceA :: Applicative f => [f a] -> f [a] # mapM :: Monad m => (a -> m b) -> [a] -> m [b] # sequence :: Monad m => [m a] -> m [a] #
Traversable Maybe	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) # sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) # mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) # sequence :: Monad m => Maybe (m a) -> m (Maybe a) #
Traversable Par1	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Par1 a -> f (Par1 b) # sequenceA :: Applicative f => Par1 (f a) -> f (Par1 a) # mapM :: Monad m => (a -> m b) -> Par1 a -> m (Par1 b) # sequence :: Monad m => Par1 (m a) -> m (Par1 a) #
Traversable Identity	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b) # sequenceA :: Applicative f => Identity (f a) -> f (Identity a) # mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b) # sequence :: Monad m => Identity (m a) -> m (Identity a) #
Traversable ZipList	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> ZipList a -> f (ZipList b) # sequenceA :: Applicative f => ZipList (f a) -> f (ZipList a) # mapM :: Monad m => (a -> m b) -> ZipList a -> m (ZipList b) # sequence :: Monad m => ZipList (m a) -> m (ZipList a) #
Traversable IResult
Instance details Defined in Data.Aeson.Types.Internal Methods traverse :: Applicative f => (a -> f b) -> IResult a -> f (IResult b) # sequenceA :: Applicative f => IResult (f a) -> f (IResult a) # mapM :: Monad m => (a -> m b) -> IResult a -> m (IResult b) # sequence :: Monad m => IResult (m a) -> m (IResult a) #
Traversable Result
Instance details Defined in Data.Aeson.Types.Internal Methods traverse :: Applicative f => (a -> f b) -> Result a -> f (Result b) # sequenceA :: Applicative f => Result (f a) -> f (Result a) # mapM :: Monad m => (a -> m b) -> Result a -> m (Result b) # sequence :: Monad m => Result (m a) -> m (Result a) #
Traversable Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b) # sequenceA :: Applicative f => Complex (f a) -> f (Complex a) # mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b) # sequence :: Monad m => Complex (m a) -> m (Complex a) #
Traversable Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Min a -> f (Min b) # sequenceA :: Applicative f => Min (f a) -> f (Min a) # mapM :: Monad m => (a -> m b) -> Min a -> m (Min b) # sequence :: Monad m => Min (m a) -> m (Min a) #
Traversable Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Max a -> f (Max b) # sequenceA :: Applicative f => Max (f a) -> f (Max a) # mapM :: Monad m => (a -> m b) -> Max a -> m (Max b) # sequence :: Monad m => Max (m a) -> m (Max a) #
Traversable First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Traversable Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Traversable Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Option a -> f (Option b) # sequenceA :: Applicative f => Option (f a) -> f (Option a) # mapM :: Monad m => (a -> m b) -> Option a -> m (Option b) # sequence :: Monad m => Option (m a) -> m (Option a) #
Traversable First	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Traversable Last	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Traversable Dual	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) # sequenceA :: Applicative f => Dual (f a) -> f (Dual a) # mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) # sequence :: Monad m => Dual (m a) -> m (Dual a) #
Traversable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) # sequenceA :: Applicative f => Sum (f a) -> f (Sum a) # mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) # sequence :: Monad m => Sum (m a) -> m (Sum a) #
Traversable Product	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) # sequenceA :: Applicative f => Product (f a) -> f (Product a) # mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) # sequence :: Monad m => Product (m a) -> m (Product a) #
Traversable Down	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Down a -> f (Down b) # sequenceA :: Applicative f => Down (f a) -> f (Down a) # mapM :: Monad m => (a -> m b) -> Down a -> m (Down b) # sequence :: Monad m => Down (m a) -> m (Down a) #
Traversable NonEmpty	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) # sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a) # mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b) # sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a) #
Traversable Vector
Instance details Defined in Data.Vector Methods traverse :: Applicative f => (a -> f b) -> Vector a -> f (Vector b) # sequenceA :: Applicative f => Vector (f a) -> f (Vector a) # mapM :: Monad m => (a -> m b) -> Vector a -> m (Vector b) # sequence :: Monad m => Vector (m a) -> m (Vector a) #
Traversable IntMap
Instance details Defined in Data.IntMap.Internal Methods traverse :: Applicative f => (a -> f b) -> IntMap a -> f (IntMap b) # sequenceA :: Applicative f => IntMap (f a) -> f (IntMap a) # mapM :: Monad m => (a -> m b) -> IntMap a -> m (IntMap b) # sequence :: Monad m => IntMap (m a) -> m (IntMap a) #
Traversable Tree
Instance details Defined in Data.Tree Methods traverse :: Applicative f => (a -> f b) -> Tree a -> f (Tree b) # sequenceA :: Applicative f => Tree (f a) -> f (Tree a) # mapM :: Monad m => (a -> m b) -> Tree a -> m (Tree b) # sequence :: Monad m => Tree (m a) -> m (Tree a) #
Traversable Seq
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Seq a -> f (Seq b) # sequenceA :: Applicative f => Seq (f a) -> f (Seq a) # mapM :: Monad m => (a -> m b) -> Seq a -> m (Seq b) # sequence :: Monad m => Seq (m a) -> m (Seq a) #
Traversable FingerTree
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> FingerTree a -> f (FingerTree b) # sequenceA :: Applicative f => FingerTree (f a) -> f (FingerTree a) # mapM :: Monad m => (a -> m b) -> FingerTree a -> m (FingerTree b) # sequence :: Monad m => FingerTree (m a) -> m (FingerTree a) #
Traversable Digit
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Digit a -> f (Digit b) # sequenceA :: Applicative f => Digit (f a) -> f (Digit a) # mapM :: Monad m => (a -> m b) -> Digit a -> m (Digit b) # sequence :: Monad m => Digit (m a) -> m (Digit a) #
Traversable Node
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Node a -> f (Node b) # sequenceA :: Applicative f => Node (f a) -> f (Node a) # mapM :: Monad m => (a -> m b) -> Node a -> m (Node b) # sequence :: Monad m => Node (m a) -> m (Node a) #
Traversable Elem
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Elem a -> f (Elem b) # sequenceA :: Applicative f => Elem (f a) -> f (Elem a) # mapM :: Monad m => (a -> m b) -> Elem a -> m (Elem b) # sequence :: Monad m => Elem (m a) -> m (Elem a) #
Traversable ViewL
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewL a -> f (ViewL b) # sequenceA :: Applicative f => ViewL (f a) -> f (ViewL a) # mapM :: Monad m => (a -> m b) -> ViewL a -> m (ViewL b) # sequence :: Monad m => ViewL (m a) -> m (ViewL a) #
Traversable ViewR
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewR a -> f (ViewR b) # sequenceA :: Applicative f => ViewR (f a) -> f (ViewR a) # mapM :: Monad m => (a -> m b) -> ViewR a -> m (ViewR b) # sequence :: Monad m => ViewR (m a) -> m (ViewR a) #
Traversable Recommend
Instance details Defined in Data.Monoid.Recommend Methods traverse :: Applicative f => (a -> f b) -> Recommend a -> f (Recommend b) # sequenceA :: Applicative f => Recommend (f a) -> f (Recommend a) # mapM :: Monad m => (a -> m b) -> Recommend a -> m (Recommend b) # sequence :: Monad m => Recommend (m a) -> m (Recommend a) #
Traversable V2
Instance details Defined in Linear.V2 Methods traverse :: Applicative f => (a -> f b) -> V2 a -> f (V2 b) # sequenceA :: Applicative f => V2 (f a) -> f (V2 a) # mapM :: Monad m => (a -> m b) -> V2 a -> m (V2 b) # sequence :: Monad m => V2 (m a) -> m (V2 a) #
Traversable V3
Instance details Defined in Linear.V3 Methods traverse :: Applicative f => (a -> f b) -> V3 a -> f (V3 b) # sequenceA :: Applicative f => V3 (f a) -> f (V3 a) # mapM :: Monad m => (a -> m b) -> V3 a -> m (V3 b) # sequence :: Monad m => V3 (m a) -> m (V3 a) #
Traversable HistoriedResponse
Instance details Defined in Network.HTTP.Client Methods traverse :: Applicative f => (a -> f b) -> HistoriedResponse a -> f (HistoriedResponse b) # sequenceA :: Applicative f => HistoriedResponse (f a) -> f (HistoriedResponse a) # mapM :: Monad m => (a -> m b) -> HistoriedResponse a -> m (HistoriedResponse b) # sequence :: Monad m => HistoriedResponse (m a) -> m (HistoriedResponse a) #
Traversable Response
Instance details Defined in Network.HTTP.Client.Types Methods traverse :: Applicative f => (a -> f b) -> Response a -> f (Response b) # sequenceA :: Applicative f => Response (f a) -> f (Response a) # mapM :: Monad m => (a -> m b) -> Response a -> m (Response b) # sequence :: Monad m => Response (m a) -> m (Response a) #
Traversable Interval
Instance details Defined in Numeric.Interval.Kaucher Methods traverse :: Applicative f => (a -> f b) -> Interval a -> f (Interval b) # sequenceA :: Applicative f => Interval (f a) -> f (Interval a) # mapM :: Monad m => (a -> m b) -> Interval a -> m (Interval b) # sequence :: Monad m => Interval (m a) -> m (Interval a) #
Traversable Plucker
Instance details Defined in Linear.Plucker Methods traverse :: Applicative f => (a -> f b) -> Plucker a -> f (Plucker b) # sequenceA :: Applicative f => Plucker (f a) -> f (Plucker a) # mapM :: Monad m => (a -> m b) -> Plucker a -> m (Plucker b) # sequence :: Monad m => Plucker (m a) -> m (Plucker a) #
Traversable Quaternion
Instance details Defined in Linear.Quaternion Methods traverse :: Applicative f => (a -> f b) -> Quaternion a -> f (Quaternion b) # sequenceA :: Applicative f => Quaternion (f a) -> f (Quaternion a) # mapM :: Monad m => (a -> m b) -> Quaternion a -> m (Quaternion b) # sequence :: Monad m => Quaternion (m a) -> m (Quaternion a) #
Traversable V0
Instance details Defined in Linear.V0 Methods traverse :: Applicative f => (a -> f b) -> V0 a -> f (V0 b) # sequenceA :: Applicative f => V0 (f a) -> f (V0 a) # mapM :: Monad m => (a -> m b) -> V0 a -> m (V0 b) # sequence :: Monad m => V0 (m a) -> m (V0 a) #
Traversable V4
Instance details Defined in Linear.V4 Methods traverse :: Applicative f => (a -> f b) -> V4 a -> f (V4 b) # sequenceA :: Applicative f => V4 (f a) -> f (V4 a) # mapM :: Monad m => (a -> m b) -> V4 a -> m (V4 b) # sequence :: Monad m => V4 (m a) -> m (V4 a) #
Traversable V1
Instance details Defined in Linear.V1 Methods traverse :: Applicative f => (a -> f b) -> V1 a -> f (V1 b) # sequenceA :: Applicative f => V1 (f a) -> f (V1 a) # mapM :: Monad m => (a -> m b) -> V1 a -> m (V1 b) # sequence :: Monad m => V1 (m a) -> m (V1 a) #
Traversable WithSeverity
Instance details Defined in Control.Monad.Log Methods traverse :: Applicative f => (a -> f b) -> WithSeverity a -> f (WithSeverity b) # sequenceA :: Applicative f => WithSeverity (f a) -> f (WithSeverity a) # mapM :: Monad m => (a -> m b) -> WithSeverity a -> m (WithSeverity b) # sequence :: Monad m => WithSeverity (m a) -> m (WithSeverity a) #
Traversable WithTimestamp
Instance details Defined in Control.Monad.Log Methods traverse :: Applicative f => (a -> f b) -> WithTimestamp a -> f (WithTimestamp b) # sequenceA :: Applicative f => WithTimestamp (f a) -> f (WithTimestamp a) # mapM :: Monad m => (a -> m b) -> WithTimestamp a -> m (WithTimestamp b) # sequence :: Monad m => WithTimestamp (m a) -> m (WithTimestamp a) #
Traversable WithCallStack
Instance details Defined in Control.Monad.Log Methods traverse :: Applicative f => (a -> f b) -> WithCallStack a -> f (WithCallStack b) # sequenceA :: Applicative f => WithCallStack (f a) -> f (WithCallStack a) # mapM :: Monad m => (a -> m b) -> WithCallStack a -> m (WithCallStack b) # sequence :: Monad m => WithCallStack (m a) -> m (WithCallStack a) #
Traversable Many
Instance details Defined in Text.Pandoc.Builder Methods traverse :: Applicative f => (a -> f b) -> Many a -> f (Many b) # sequenceA :: Applicative f => Many (f a) -> f (Many a) # mapM :: Monad m => (a -> m b) -> Many a -> m (Many b) # sequence :: Monad m => Many (m a) -> m (Many a) #
Traversable SimpleDocStream	Transform a document based on its annotations, possibly leveraging `Applicative` effects.
Instance details Defined in Data.Text.Prettyprint.Doc.Internal Methods traverse :: Applicative f => (a -> f b) -> SimpleDocStream a -> f (SimpleDocStream b) # sequenceA :: Applicative f => SimpleDocStream (f a) -> f (SimpleDocStream a) # mapM :: Monad m => (a -> m b) -> SimpleDocStream a -> m (SimpleDocStream b) # sequence :: Monad m => SimpleDocStream (m a) -> m (SimpleDocStream a) #
Traversable SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods traverse :: Applicative f => (a -> f b) -> SmallArray a -> f (SmallArray b) # sequenceA :: Applicative f => SmallArray (f a) -> f (SmallArray a) # mapM :: Monad m => (a -> m b) -> SmallArray a -> m (SmallArray b) # sequence :: Monad m => SmallArray (m a) -> m (SmallArray a) #
Traversable Array
Instance details Defined in Data.Primitive.Array Methods traverse :: Applicative f => (a -> f b) -> Array a -> f (Array b) # sequenceA :: Applicative f => Array (f a) -> f (Array a) # mapM :: Monad m => (a -> m b) -> Array a -> m (Array b) # sequence :: Monad m => Array (m a) -> m (Array a) #
Traversable NamedDoc Source #
Instance details Defined in Knit.Effect.Docs Methods traverse :: Applicative f => (a -> f b) -> NamedDoc a -> f (NamedDoc b) # sequenceA :: Applicative f => NamedDoc (f a) -> f (NamedDoc a) # mapM :: Monad m => (a -> m b) -> NamedDoc a -> m (NamedDoc b) # sequence :: Monad m => NamedDoc (m a) -> m (NamedDoc a) #
Traversable (Either a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) # sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) # sequence :: Monad m => Either a (m a0) -> m (Either a a0) #
Traversable (V1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> V1 a -> f (V1 b) # sequenceA :: Applicative f => V1 (f a) -> f (V1 a) # mapM :: Monad m => (a -> m b) -> V1 a -> m (V1 b) # sequence :: Monad m => V1 (m a) -> m (V1 a) #
Traversable (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> U1 a -> f (U1 b) # sequenceA :: Applicative f => U1 (f a) -> f (U1 a) # mapM :: Monad m => (a -> m b) -> U1 a -> m (U1 b) # sequence :: Monad m => U1 (m a) -> m (U1 a) #
Traversable ((,) a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> (a, a0) -> f (a, b) # sequenceA :: Applicative f => (a, f a0) -> f (a, a0) # mapM :: Monad m => (a0 -> m b) -> (a, a0) -> m (a, b) # sequence :: Monad m => (a, m a0) -> m (a, a0) #
Traversable (Map k)
Instance details Defined in Data.Map.Internal Methods traverse :: Applicative f => (a -> f b) -> Map k a -> f (Map k b) # sequenceA :: Applicative f => Map k (f a) -> f (Map k a) # mapM :: Monad m => (a -> m b) -> Map k a -> m (Map k b) # sequence :: Monad m => Map k (m a) -> m (Map k a) #
Traversable (HashMap k)
Instance details Defined in Data.HashMap.Base Methods traverse :: Applicative f => (a -> f b) -> HashMap k a -> f (HashMap k b) # sequenceA :: Applicative f => HashMap k (f a) -> f (HashMap k a) # mapM :: Monad m => (a -> m b) -> HashMap k a -> m (HashMap k b) # sequence :: Monad m => HashMap k (m a) -> m (HashMap k a) #
Ix i => Traversable (Array i)	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Array i a -> f (Array i b) # sequenceA :: Applicative f => Array i (f a) -> f (Array i a) # mapM :: Monad m => (a -> m b) -> Array i a -> m (Array i b) # sequence :: Monad m => Array i (m a) -> m (Array i a) #
Traversable (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a0 -> f b) -> Arg a a0 -> f (Arg a b) # sequenceA :: Applicative f => Arg a (f a0) -> f (Arg a a0) # mapM :: Monad m => (a0 -> m b) -> Arg a a0 -> m (Arg a b) # sequence :: Monad m => Arg a (m a0) -> m (Arg a a0) #
Traversable (Proxy :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Proxy a -> f (Proxy b) # sequenceA :: Applicative f => Proxy (f a) -> f (Proxy a) # mapM :: Monad m => (a -> m b) -> Proxy a -> m (Proxy b) # sequence :: Monad m => Proxy (m a) -> m (Proxy a) #
Traversable f => Traversable (Point f)
Instance details Defined in Linear.Affine Methods traverse :: Applicative f0 => (a -> f0 b) -> Point f a -> f0 (Point f b) # sequenceA :: Applicative f0 => Point f (f0 a) -> f0 (Point f a) # mapM :: Monad m => (a -> m b) -> Point f a -> m (Point f b) # sequence :: Monad m => Point f (m a) -> m (Point f a) #
Traversable f => Traversable (MaybeT f)
Instance details Defined in Control.Monad.Trans.Maybe Methods traverse :: Applicative f0 => (a -> f0 b) -> MaybeT f a -> f0 (MaybeT f b) # sequenceA :: Applicative f0 => MaybeT f (f0 a) -> f0 (MaybeT f a) # mapM :: Monad m => (a -> m b) -> MaybeT f a -> m (MaybeT f b) # sequence :: Monad m => MaybeT f (m a) -> m (MaybeT f a) #
Traversable (Level i)
Instance details Defined in Control.Lens.Internal.Level Methods traverse :: Applicative f => (a -> f b) -> Level i a -> f (Level i b) # sequenceA :: Applicative f => Level i (f a) -> f (Level i a) # mapM :: Monad m => (a -> m b) -> Level i a -> m (Level i b) # sequence :: Monad m => Level i (m a) -> m (Level i a) #
Traversable f => Traversable (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods traverse :: Applicative f0 => (a -> f0 b) -> Cofree f a -> f0 (Cofree f b) # sequenceA :: Applicative f0 => Cofree f (f0 a) -> f0 (Cofree f a) # mapM :: Monad m => (a -> m b) -> Cofree f a -> m (Cofree f b) # sequence :: Monad m => Cofree f (m a) -> m (Cofree f a) #
Traversable f => Traversable (Free f)
Instance details Defined in Control.Monad.Free Methods traverse :: Applicative f0 => (a -> f0 b) -> Free f a -> f0 (Free f b) # sequenceA :: Applicative f0 => Free f (f0 a) -> f0 (Free f a) # mapM :: Monad m => (a -> m b) -> Free f a -> m (Free f b) # sequence :: Monad m => Free f (m a) -> m (Free f a) #
Traversable f => Traversable (Yoneda f)
Instance details Defined in Data.Functor.Yoneda Methods traverse :: Applicative f0 => (a -> f0 b) -> Yoneda f a -> f0 (Yoneda f b) # sequenceA :: Applicative f0 => Yoneda f (f0 a) -> f0 (Yoneda f a) # mapM :: Monad m => (a -> m b) -> Yoneda f a -> m (Yoneda f b) # sequence :: Monad m => Yoneda f (m a) -> m (Yoneda f a) #
Traversable f => Traversable (ListT f)
Instance details Defined in Control.Monad.Trans.List Methods traverse :: Applicative f0 => (a -> f0 b) -> ListT f a -> f0 (ListT f b) # sequenceA :: Applicative f0 => ListT f (f0 a) -> f0 (ListT f a) # mapM :: Monad m => (a -> m b) -> ListT f a -> m (ListT f b) # sequence :: Monad m => ListT f (m a) -> m (ListT f a) #
Traversable f => Traversable (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) # sequenceA :: Applicative f0 => Rec1 f (f0 a) -> f0 (Rec1 f a) # mapM :: Monad m => (a -> m b) -> Rec1 f a -> m (Rec1 f b) # sequence :: Monad m => Rec1 f (m a) -> m (Rec1 f a) #
Traversable (URec Char :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Char a -> f (URec Char b) # sequenceA :: Applicative f => URec Char (f a) -> f (URec Char a) # mapM :: Monad m => (a -> m b) -> URec Char a -> m (URec Char b) # sequence :: Monad m => URec Char (m a) -> m (URec Char a) #
Traversable (URec Double :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Double a -> f (URec Double b) # sequenceA :: Applicative f => URec Double (f a) -> f (URec Double a) # mapM :: Monad m => (a -> m b) -> URec Double a -> m (URec Double b) # sequence :: Monad m => URec Double (m a) -> m (URec Double a) #
Traversable (URec Float :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Float a -> f (URec Float b) # sequenceA :: Applicative f => URec Float (f a) -> f (URec Float a) # mapM :: Monad m => (a -> m b) -> URec Float a -> m (URec Float b) # sequence :: Monad m => URec Float (m a) -> m (URec Float a) #
Traversable (URec Int :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Int a -> f (URec Int b) # sequenceA :: Applicative f => URec Int (f a) -> f (URec Int a) # mapM :: Monad m => (a -> m b) -> URec Int a -> m (URec Int b) # sequence :: Monad m => URec Int (m a) -> m (URec Int a) #
Traversable (URec Word :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Word a -> f (URec Word b) # sequenceA :: Applicative f => URec Word (f a) -> f (URec Word a) # mapM :: Monad m => (a -> m b) -> URec Word a -> m (URec Word b) # sequence :: Monad m => URec Word (m a) -> m (URec Word a) #
Traversable (URec (Ptr ()) :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec (Ptr ()) a -> f (URec (Ptr ()) b) # sequenceA :: Applicative f => URec (Ptr ()) (f a) -> f (URec (Ptr ()) a) # mapM :: Monad m => (a -> m b) -> URec (Ptr ()) a -> m (URec (Ptr ()) b) # sequence :: Monad m => URec (Ptr ()) (m a) -> m (URec (Ptr ()) a) #
Traversable f => Traversable (IdentityT f)
Instance details Defined in Control.Monad.Trans.Identity Methods traverse :: Applicative f0 => (a -> f0 b) -> IdentityT f a -> f0 (IdentityT f b) # sequenceA :: Applicative f0 => IdentityT f (f0 a) -> f0 (IdentityT f a) # mapM :: Monad m => (a -> m b) -> IdentityT f a -> m (IdentityT f b) # sequence :: Monad m => IdentityT f (m a) -> m (IdentityT f a) #
Traversable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b) # sequenceA :: Applicative f => Const m (f a) -> f (Const m a) # mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b) # sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a) #
Traversable f => Traversable (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Ap f a -> f0 (Ap f b) # sequenceA :: Applicative f0 => Ap f (f0 a) -> f0 (Ap f a) # mapM :: Monad m => (a -> m b) -> Ap f a -> m (Ap f b) # sequence :: Monad m => Ap f (m a) -> m (Ap f a) #
Traversable f => Traversable (Alt f)	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) # sequenceA :: Applicative f0 => Alt f (f0 a) -> f0 (Alt f a) # mapM :: Monad m => (a -> m b) -> Alt f a -> m (Alt f b) # sequence :: Monad m => Alt f (m a) -> m (Alt f a) #
Bitraversable p => Traversable (Join p)
Instance details Defined in Data.Bifunctor.Join Methods traverse :: Applicative f => (a -> f b) -> Join p a -> f (Join p b) # sequenceA :: Applicative f => Join p (f a) -> f (Join p a) # mapM :: Monad m => (a -> m b) -> Join p a -> m (Join p b) # sequence :: Monad m => Join p (m a) -> m (Join p a) #
Bitraversable p => Traversable (Fix p)
Instance details Defined in Data.Bifunctor.Fix Methods traverse :: Applicative f => (a -> f b) -> Fix p a -> f (Fix p b) # sequenceA :: Applicative f => Fix p (f a) -> f (Fix p a) # mapM :: Monad m => (a -> m b) -> Fix p a -> m (Fix p b) # sequence :: Monad m => Fix p (m a) -> m (Fix p a) #
Traversable f => Traversable (ExceptT e f)
Instance details Defined in Control.Monad.Trans.Except Methods traverse :: Applicative f0 => (a -> f0 b) -> ExceptT e f a -> f0 (ExceptT e f b) # sequenceA :: Applicative f0 => ExceptT e f (f0 a) -> f0 (ExceptT e f a) # mapM :: Monad m => (a -> m b) -> ExceptT e f a -> m (ExceptT e f b) # sequence :: Monad m => ExceptT e f (m a) -> m (ExceptT e f a) #
Traversable f => Traversable (FreeF f a)
Instance details Defined in Control.Monad.Trans.Free Methods traverse :: Applicative f0 => (a0 -> f0 b) -> FreeF f a a0 -> f0 (FreeF f a b) # sequenceA :: Applicative f0 => FreeF f a (f0 a0) -> f0 (FreeF f a a0) # mapM :: Monad m => (a0 -> m b) -> FreeF f a a0 -> m (FreeF f a b) # sequence :: Monad m => FreeF f a (m a0) -> m (FreeF f a a0) #
(Monad m, Traversable m, Traversable f) => Traversable (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods traverse :: Applicative f0 => (a -> f0 b) -> FreeT f m a -> f0 (FreeT f m b) # sequenceA :: Applicative f0 => FreeT f m (f0 a) -> f0 (FreeT f m a) # mapM :: Monad m0 => (a -> m0 b) -> FreeT f m a -> m0 (FreeT f m b) # sequence :: Monad m0 => FreeT f m (m0 a) -> m0 (FreeT f m a) #
Traversable f => Traversable (CofreeF f a)
Instance details Defined in Control.Comonad.Trans.Cofree Methods traverse :: Applicative f0 => (a0 -> f0 b) -> CofreeF f a a0 -> f0 (CofreeF f a b) # sequenceA :: Applicative f0 => CofreeF f a (f0 a0) -> f0 (CofreeF f a a0) # mapM :: Monad m => (a0 -> m b) -> CofreeF f a a0 -> m (CofreeF f a b) # sequence :: Monad m => CofreeF f a (m a0) -> m (CofreeF f a a0) #
(Traversable f, Traversable w) => Traversable (CofreeT f w)
Instance details Defined in Control.Comonad.Trans.Cofree Methods traverse :: Applicative f0 => (a -> f0 b) -> CofreeT f w a -> f0 (CofreeT f w b) # sequenceA :: Applicative f0 => CofreeT f w (f0 a) -> f0 (CofreeT f w a) # mapM :: Monad m => (a -> m b) -> CofreeT f w a -> m (CofreeT f w b) # sequence :: Monad m => CofreeT f w (m a) -> m (CofreeT f w a) #
Traversable f => Traversable (ErrorT e f)
Instance details Defined in Control.Monad.Trans.Error Methods traverse :: Applicative f0 => (a -> f0 b) -> ErrorT e f a -> f0 (ErrorT e f b) # sequenceA :: Applicative f0 => ErrorT e f (f0 a) -> f0 (ErrorT e f a) # mapM :: Monad m => (a -> m b) -> ErrorT e f a -> m (ErrorT e f b) # sequence :: Monad m => ErrorT e f (m a) -> m (ErrorT e f a) #
Traversable f => Traversable (Backwards f)	Derived instance.
Instance details Defined in Control.Applicative.Backwards Methods traverse :: Applicative f0 => (a -> f0 b) -> Backwards f a -> f0 (Backwards f b) # sequenceA :: Applicative f0 => Backwards f (f0 a) -> f0 (Backwards f a) # mapM :: Monad m => (a -> m b) -> Backwards f a -> m (Backwards f b) # sequence :: Monad m => Backwards f (m a) -> m (Backwards f a) #
Traversable f => Traversable (AlongsideLeft f b)
Instance details Defined in Control.Lens.Internal.Getter Methods traverse :: Applicative f0 => (a -> f0 b0) -> AlongsideLeft f b a -> f0 (AlongsideLeft f b b0) # sequenceA :: Applicative f0 => AlongsideLeft f b (f0 a) -> f0 (AlongsideLeft f b a) # mapM :: Monad m => (a -> m b0) -> AlongsideLeft f b a -> m (AlongsideLeft f b b0) # sequence :: Monad m => AlongsideLeft f b (m a) -> m (AlongsideLeft f b a) #
Traversable f => Traversable (AlongsideRight f a)
Instance details Defined in Control.Lens.Internal.Getter Methods traverse :: Applicative f0 => (a0 -> f0 b) -> AlongsideRight f a a0 -> f0 (AlongsideRight f a b) # sequenceA :: Applicative f0 => AlongsideRight f a (f0 a0) -> f0 (AlongsideRight f a a0) # mapM :: Monad m => (a0 -> m b) -> AlongsideRight f a a0 -> m (AlongsideRight f a b) # sequence :: Monad m => AlongsideRight f a (m a0) -> m (AlongsideRight f a a0) #
Traversable (V n)
Instance details Defined in Linear.V Methods traverse :: Applicative f => (a -> f b) -> V n a -> f (V n b) # sequenceA :: Applicative f => V n (f a) -> f (V n a) # mapM :: Monad m => (a -> m b) -> V n a -> m (V n b) # sequence :: Monad m => V n (m a) -> m (V n a) #
Traversable f => Traversable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b) # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a) # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) # sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) #
Traversable f => Traversable (WriterT w f)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 (WriterT w f b) # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 (WriterT w f a) # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) # sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) #
Traversable (Forget r a)
Instance details Defined in Data.Profunctor.Types Methods traverse :: Applicative f => (a0 -> f b) -> Forget r a a0 -> f (Forget r a b) # sequenceA :: Applicative f => Forget r a (f a0) -> f (Forget r a a0) # mapM :: Monad m => (a0 -> m b) -> Forget r a a0 -> m (Forget r a b) # sequence :: Monad m => Forget r a (m a0) -> m (Forget r a a0) #
Traversable (Tagged s)
Instance details Defined in Data.Tagged Methods traverse :: Applicative f => (a -> f b) -> Tagged s a -> f (Tagged s b) # sequenceA :: Applicative f => Tagged s (f a) -> f (Tagged s a) # mapM :: Monad m => (a -> m b) -> Tagged s a -> m (Tagged s b) # sequence :: Monad m => Tagged s (m a) -> m (Tagged s a) #
Traversable f => Traversable (Reverse f)	Traverse from right to left.
Instance details Defined in Data.Functor.Reverse Methods traverse :: Applicative f0 => (a -> f0 b) -> Reverse f a -> f0 (Reverse f b) # sequenceA :: Applicative f0 => Reverse f (f0 a) -> f0 (Reverse f a) # mapM :: Monad m => (a -> m b) -> Reverse f a -> m (Reverse f b) # sequence :: Monad m => Reverse f (m a) -> m (Reverse f a) #
Traversable (K1 i c :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> K1 i c a -> f (K1 i c b) # sequenceA :: Applicative f => K1 i c (f a) -> f (K1 i c a) # mapM :: Monad m => (a -> m b) -> K1 i c a -> m (K1 i c b) # sequence :: Monad m => K1 i c (m a) -> m (K1 i c a) #
(Traversable f, Traversable g) => Traversable (f :+: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) # sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a) # mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b) # sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a) #
(Traversable f, Traversable g) => Traversable (f :*: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) # sequenceA :: Applicative f0 => (f :: g) (f0 a) -> f0 ((f :: g) a) # mapM :: Monad m => (a -> m b) -> (f :: g) a -> m ((f :: g) b) # sequence :: Monad m => (f :: g) (m a) -> m ((f :: g) a) #
(Traversable f, Traversable g) => Traversable (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods traverse :: Applicative f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b) # sequenceA :: Applicative f0 => Product f g (f0 a) -> f0 (Product f g a) # mapM :: Monad m => (a -> m b) -> Product f g a -> m (Product f g b) # sequence :: Monad m => Product f g (m a) -> m (Product f g a) #
Traversable (Magma i t b)
Instance details Defined in Control.Lens.Internal.Magma Methods traverse :: Applicative f => (a -> f b0) -> Magma i t b a -> f (Magma i t b b0) # sequenceA :: Applicative f => Magma i t b (f a) -> f (Magma i t b a) # mapM :: Monad m => (a -> m b0) -> Magma i t b a -> m (Magma i t b b0) # sequence :: Monad m => Magma i t b (m a) -> m (Magma i t b a) #
Traversable f => Traversable (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> M1 i c f a -> f0 (M1 i c f b) # sequenceA :: Applicative f0 => M1 i c f (f0 a) -> f0 (M1 i c f a) # mapM :: Monad m => (a -> m b) -> M1 i c f a -> m (M1 i c f b) # sequence :: Monad m => M1 i c f (m a) -> m (M1 i c f a) #
(Traversable f, Traversable g) => Traversable (f :.: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) # sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((f :.: g) a) # mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b) # sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a) #
(Traversable f, Traversable g) => Traversable (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods traverse :: Applicative f0 => (a -> f0 b) -> Compose f g a -> f0 (Compose f g b) # sequenceA :: Applicative f0 => Compose f g (f0 a) -> f0 (Compose f g a) # mapM :: Monad m => (a -> m b) -> Compose f g a -> m (Compose f g b) # sequence :: Monad m => Compose f g (m a) -> m (Compose f g a) #
Bitraversable p => Traversable (WrappedBifunctor p a)
Instance details Defined in Data.Bifunctor.Wrapped Methods traverse :: Applicative f => (a0 -> f b) -> WrappedBifunctor p a a0 -> f (WrappedBifunctor p a b) # sequenceA :: Applicative f => WrappedBifunctor p a (f a0) -> f (WrappedBifunctor p a a0) # mapM :: Monad m => (a0 -> m b) -> WrappedBifunctor p a a0 -> m (WrappedBifunctor p a b) # sequence :: Monad m => WrappedBifunctor p a (m a0) -> m (WrappedBifunctor p a a0) #
Traversable g => Traversable (Joker g a)
Instance details Defined in Data.Bifunctor.Joker Methods traverse :: Applicative f => (a0 -> f b) -> Joker g a a0 -> f (Joker g a b) # sequenceA :: Applicative f => Joker g a (f a0) -> f (Joker g a a0) # mapM :: Monad m => (a0 -> m b) -> Joker g a a0 -> m (Joker g a b) # sequence :: Monad m => Joker g a (m a0) -> m (Joker g a a0) #
Bitraversable p => Traversable (Flip p a)
Instance details Defined in Data.Bifunctor.Flip Methods traverse :: Applicative f => (a0 -> f b) -> Flip p a a0 -> f (Flip p a b) # sequenceA :: Applicative f => Flip p a (f a0) -> f (Flip p a a0) # mapM :: Monad m => (a0 -> m b) -> Flip p a a0 -> m (Flip p a b) # sequence :: Monad m => Flip p a (m a0) -> m (Flip p a a0) #
Traversable (Clown f a :: Type -> Type)
Instance details Defined in Data.Bifunctor.Clown Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Clown f a a0 -> f0 (Clown f a b) # sequenceA :: Applicative f0 => Clown f a (f0 a0) -> f0 (Clown f a a0) # mapM :: Monad m => (a0 -> m b) -> Clown f a a0 -> m (Clown f a b) # sequence :: Monad m => Clown f a (m a0) -> m (Clown f a a0) #
(Traversable f, Bitraversable p) => Traversable (Tannen f p a)
Instance details Defined in Data.Bifunctor.Tannen Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Tannen f p a a0 -> f0 (Tannen f p a b) # sequenceA :: Applicative f0 => Tannen f p a (f0 a0) -> f0 (Tannen f p a a0) # mapM :: Monad m => (a0 -> m b) -> Tannen f p a a0 -> m (Tannen f p a b) # sequence :: Monad m => Tannen f p a (m a0) -> m (Tannen f p a a0) #
(Bitraversable p, Traversable g) => Traversable (Biff p f g a)
Instance details Defined in Data.Bifunctor.Biff Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Biff p f g a a0 -> f0 (Biff p f g a b) # sequenceA :: Applicative f0 => Biff p f g a (f0 a0) -> f0 (Biff p f g a a0) # mapM :: Monad m => (a0 -> m b) -> Biff p f g a a0 -> m (Biff p f g a b) # sequence :: Monad m => Biff p f g a (m a0) -> m (Biff p f g a a0) #

class Semigroup a where #

The class of semigroups (types with an associative binary operation).

Instances should satisfy the associativity law:

```
x <> (y <> z) = (x <> y) <> z
```

Since: base-4.9.0.0

Minimal complete definition

(<>)

Methods

(<>) :: a -> a -> a infixr 6 #

An associative operation.

sconcat :: NonEmpty a -> a #

Reduce a non-empty list with <>

The default definition should be sufficient, but this can be overridden for efficiency.

stimes :: Integral b => b -> a -> a #

Repeat a value n times.

Given that this works on a Semigroup it is allowed to fail if you request 0 or fewer repetitions, and the default definition will do so.

By making this a member of the class, idempotent semigroups and monoids can upgrade this to execute in O(1) by picking stimes = stimesIdempotent or stimes = stimesIdempotentMonoid respectively.

Instances

Semigroup Ordering	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Ordering -> Ordering -> Ordering # sconcat :: NonEmpty Ordering -> Ordering # stimes :: Integral b => b -> Ordering -> Ordering #
Semigroup ()	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: () -> () -> () # sconcat :: NonEmpty () -> () # stimes :: Integral b => b -> () -> () #
Semigroup ByteString
Instance details Defined in Data.ByteString.Internal Methods (<>) :: ByteString -> ByteString -> ByteString # sconcat :: NonEmpty ByteString -> ByteString # stimes :: Integral b => b -> ByteString -> ByteString #
Semigroup ByteString
Instance details Defined in Data.ByteString.Lazy.Internal Methods (<>) :: ByteString -> ByteString -> ByteString # sconcat :: NonEmpty ByteString -> ByteString # stimes :: Integral b => b -> ByteString -> ByteString #
Semigroup Builder
Instance details Defined in Data.Text.Internal.Builder Methods (<>) :: Builder -> Builder -> Builder # sconcat :: NonEmpty Builder -> Builder # stimes :: Integral b => b -> Builder -> Builder #
Semigroup More
Instance details Defined in Data.Attoparsec.Internal.Types Methods (<>) :: More -> More -> More # sconcat :: NonEmpty More -> More # stimes :: Integral b => b -> More -> More #
Semigroup Void	Since: base-4.9.0.0
Instance details Defined in Data.Void Methods (<>) :: Void -> Void -> Void # sconcat :: NonEmpty Void -> Void # stimes :: Integral b => b -> Void -> Void #
Semigroup All	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: All -> All -> All # sconcat :: NonEmpty All -> All # stimes :: Integral b => b -> All -> All #
Semigroup Any	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Any -> Any -> Any # sconcat :: NonEmpty Any -> Any # stimes :: Integral b => b -> Any -> Any #
Semigroup String
Instance details Defined in Basement.UTF8.Base Methods (<>) :: String -> String -> String # sconcat :: NonEmpty String -> String # stimes :: Integral b => b -> String -> String #
Semigroup Attribute
Instance details Defined in Text.Blaze.Internal Methods (<>) :: Attribute -> Attribute -> Attribute # sconcat :: NonEmpty Attribute -> Attribute # stimes :: Integral b => b -> Attribute -> Attribute #
Semigroup Cell
Instance details Defined in Text.Blaze.Colonnade Methods (<>) :: Cell -> Cell -> Cell # sconcat :: NonEmpty Cell -> Cell # stimes :: Integral b => b -> Cell -> Cell #
Semigroup AttributeValue
Instance details Defined in Text.Blaze.Internal Methods (<>) :: AttributeValue -> AttributeValue -> AttributeValue # sconcat :: NonEmpty AttributeValue -> AttributeValue # stimes :: Integral b => b -> AttributeValue -> AttributeValue #
Semigroup ChoiceString
Instance details Defined in Text.Blaze.Internal Methods (<>) :: ChoiceString -> ChoiceString -> ChoiceString # sconcat :: NonEmpty ChoiceString -> ChoiceString # stimes :: Integral b => b -> ChoiceString -> ChoiceString #
Semigroup IntSet	Since: containers-0.5.7
Instance details Defined in Data.IntSet.Internal Methods (<>) :: IntSet -> IntSet -> IntSet # sconcat :: NonEmpty IntSet -> IntSet # stimes :: Integral b => b -> IntSet -> IntSet #
Semigroup Name
Instance details Defined in Diagrams.Core.Names Methods (<>) :: Name -> Name -> Name # sconcat :: NonEmpty Name -> Name # stimes :: Integral b => b -> Name -> Name #
Semigroup Font
Instance details Defined in Diagrams.TwoD.Text Methods (<>) :: Font -> Font -> Font # sconcat :: NonEmpty Font -> Font # stimes :: Integral b => b -> Font -> Font #
Semigroup FontSlant
Instance details Defined in Diagrams.TwoD.Text Methods (<>) :: FontSlant -> FontSlant -> FontSlant # sconcat :: NonEmpty FontSlant -> FontSlant # stimes :: Integral b => b -> FontSlant -> FontSlant #
Semigroup FontWeight	Last semigroup structure
Instance details Defined in Diagrams.TwoD.Text Methods (<>) :: FontWeight -> FontWeight -> FontWeight # sconcat :: NonEmpty FontWeight -> FontWeight # stimes :: Integral b => b -> FontWeight -> FontWeight #
Semigroup Crossings
Instance details Defined in Diagrams.TwoD.Path Methods (<>) :: Crossings -> Crossings -> Crossings # sconcat :: NonEmpty Crossings -> Crossings # stimes :: Integral b => b -> Crossings -> Crossings #
Semigroup FillRule
Instance details Defined in Diagrams.TwoD.Path Methods (<>) :: FillRule -> FillRule -> FillRule # sconcat :: NonEmpty FillRule -> FillRule # stimes :: Integral b => b -> FillRule -> FillRule #
Semigroup SegCount
Instance details Defined in Diagrams.Segment Methods (<>) :: SegCount -> SegCount -> SegCount # sconcat :: NonEmpty SegCount -> SegCount # stimes :: Integral b => b -> SegCount -> SegCount #
Semigroup Highlight
Instance details Defined in Diagrams.ThreeD.Attributes Methods (<>) :: Highlight -> Highlight -> Highlight # sconcat :: NonEmpty Highlight -> Highlight # stimes :: Integral b => b -> Highlight -> Highlight #
Semigroup SurfaceColor
Instance details Defined in Diagrams.ThreeD.Attributes Methods (<>) :: SurfaceColor -> SurfaceColor -> SurfaceColor # sconcat :: NonEmpty SurfaceColor -> SurfaceColor # stimes :: Integral b => b -> SurfaceColor -> SurfaceColor #
Semigroup Diffuse
Instance details Defined in Diagrams.ThreeD.Attributes Methods (<>) :: Diffuse -> Diffuse -> Diffuse # sconcat :: NonEmpty Diffuse -> Diffuse # stimes :: Integral b => b -> Diffuse -> Diffuse #
Semigroup Ambient
Instance details Defined in Diagrams.ThreeD.Attributes Methods (<>) :: Ambient -> Ambient -> Ambient # sconcat :: NonEmpty Ambient -> Ambient # stimes :: Integral b => b -> Ambient -> Ambient #
Semigroup Opacity
Instance details Defined in Diagrams.Attributes Methods (<>) :: Opacity -> Opacity -> Opacity # sconcat :: NonEmpty Opacity -> Opacity # stimes :: Integral b => b -> Opacity -> Opacity #
Semigroup FillOpacity
Instance details Defined in Diagrams.Attributes Methods (<>) :: FillOpacity -> FillOpacity -> FillOpacity # sconcat :: NonEmpty FillOpacity -> FillOpacity # stimes :: Integral b => b -> FillOpacity -> FillOpacity #
Semigroup StrokeOpacity
Instance details Defined in Diagrams.Attributes Methods (<>) :: StrokeOpacity -> StrokeOpacity -> StrokeOpacity # sconcat :: NonEmpty StrokeOpacity -> StrokeOpacity # stimes :: Integral b => b -> StrokeOpacity -> StrokeOpacity #
Semigroup LineCap	Last semigroup structure.
Instance details Defined in Diagrams.Attributes Methods (<>) :: LineCap -> LineCap -> LineCap # sconcat :: NonEmpty LineCap -> LineCap # stimes :: Integral b => b -> LineCap -> LineCap #
Semigroup LineJoin	Last semigroup structure.
Instance details Defined in Diagrams.Attributes Methods (<>) :: LineJoin -> LineJoin -> LineJoin # sconcat :: NonEmpty LineJoin -> LineJoin # stimes :: Integral b => b -> LineJoin -> LineJoin #
Semigroup LineMiterLimit
Instance details Defined in Diagrams.Attributes Methods (<>) :: LineMiterLimit -> LineMiterLimit -> LineMiterLimit # sconcat :: NonEmpty LineMiterLimit -> LineMiterLimit # stimes :: Integral b => b -> LineMiterLimit -> LineMiterLimit #
Semigroup Element
Instance details Defined in Graphics.Svg.Core Methods (<>) :: Element -> Element -> Element # sconcat :: NonEmpty Element -> Element # stimes :: Integral b => b -> Element -> Element #
Semigroup CookieJar
Instance details Defined in Network.HTTP.Client.Types Methods (<>) :: CookieJar -> CookieJar -> CookieJar # sconcat :: NonEmpty CookieJar -> CookieJar # stimes :: Integral b => b -> CookieJar -> CookieJar #
Semigroup RequestBody
Instance details Defined in Network.HTTP.Client.Types Methods (<>) :: RequestBody -> RequestBody -> RequestBody # sconcat :: NonEmpty RequestBody -> RequestBody # stimes :: Integral b => b -> RequestBody -> RequestBody #
Semigroup Source
Instance details Defined in Data.Ipynb Methods (<>) :: Source -> Source -> Source # sconcat :: NonEmpty Source -> Source # stimes :: Integral b => b -> Source -> Source #
Semigroup MimeBundle
Instance details Defined in Data.Ipynb Methods (<>) :: MimeBundle -> MimeBundle -> MimeBundle # sconcat :: NonEmpty MimeBundle -> MimeBundle # stimes :: Integral b => b -> MimeBundle -> MimeBundle #
Semigroup Pandoc
Instance details Defined in Text.Pandoc.Definition Methods (<>) :: Pandoc -> Pandoc -> Pandoc # sconcat :: NonEmpty Pandoc -> Pandoc # stimes :: Integral b => b -> Pandoc -> Pandoc #
Semigroup Inlines
Instance details Defined in Text.Pandoc.Builder Methods (<>) :: Inlines -> Inlines -> Inlines # sconcat :: NonEmpty Inlines -> Inlines # stimes :: Integral b => b -> Inlines -> Inlines #
Semigroup Meta
Instance details Defined in Text.Pandoc.Definition Methods (<>) :: Meta -> Meta -> Meta # sconcat :: NonEmpty Meta -> Meta # stimes :: Integral b => b -> Meta -> Meta #
Semigroup FileTree
Instance details Defined in Text.Pandoc.Class Methods (<>) :: FileTree -> FileTree -> FileTree # sconcat :: NonEmpty FileTree -> FileTree # stimes :: Integral b => b -> FileTree -> FileTree #
Semigroup Translations
Instance details Defined in Text.Pandoc.Translations Methods (<>) :: Translations -> Translations -> Translations # sconcat :: NonEmpty Translations -> Translations # stimes :: Integral b => b -> Translations -> Translations #
Semigroup MediaBag
Instance details Defined in Text.Pandoc.MediaBag Methods (<>) :: MediaBag -> MediaBag -> MediaBag # sconcat :: NonEmpty MediaBag -> MediaBag # stimes :: Integral b => b -> MediaBag -> MediaBag #
Semigroup Extensions
Instance details Defined in Text.Pandoc.Extensions Methods (<>) :: Extensions -> Extensions -> Extensions # sconcat :: NonEmpty Extensions -> Extensions # stimes :: Integral b => b -> Extensions -> Extensions #
Semigroup Doc
Instance details Defined in Text.PrettyPrint.HughesPJ Methods (<>) :: Doc -> Doc -> Doc # sconcat :: NonEmpty Doc -> Doc # stimes :: Integral b => b -> Doc -> Doc #
Semigroup ByteArray
Instance details Defined in Data.Primitive.ByteArray Methods (<>) :: ByteArray -> ByteArray -> ByteArray # sconcat :: NonEmpty ByteArray -> ByteArray # stimes :: Integral b => b -> ByteArray -> ByteArray #
Semigroup PandocWithRequirements Source #
Instance details Defined in Knit.Effect.Pandoc Methods (<>) :: PandocWithRequirements -> PandocWithRequirements -> PandocWithRequirements # sconcat :: NonEmpty PandocWithRequirements -> PandocWithRequirements # stimes :: Integral b => b -> PandocWithRequirements -> PandocWithRequirements #
Semigroup [a]	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: [a] -> [a] -> [a] # sconcat :: NonEmpty [a] -> [a] # stimes :: Integral b => b -> [a] -> [a] #
Semigroup a => Semigroup (Maybe a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Maybe a -> Maybe a -> Maybe a # sconcat :: NonEmpty (Maybe a) -> Maybe a # stimes :: Integral b => b -> Maybe a -> Maybe a #
Semigroup a => Semigroup (IO a)	Since: base-4.10.0.0
Instance details Defined in GHC.Base Methods (<>) :: IO a -> IO a -> IO a # sconcat :: NonEmpty (IO a) -> IO a # stimes :: Integral b => b -> IO a -> IO a #
Semigroup p => Semigroup (Par1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: Par1 p -> Par1 p -> Par1 p # sconcat :: NonEmpty (Par1 p) -> Par1 p # stimes :: Integral b => b -> Par1 p -> Par1 p #
Ord a => Semigroup (Set a)	Since: containers-0.5.7
Instance details Defined in Data.Set.Internal Methods (<>) :: Set a -> Set a -> Set a # sconcat :: NonEmpty (Set a) -> Set a # stimes :: Integral b => b -> Set a -> Set a #
Semigroup a => Semigroup (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (<>) :: Identity a -> Identity a -> Identity a # sconcat :: NonEmpty (Identity a) -> Identity a # stimes :: Integral b => b -> Identity a -> Identity a #
Storable a => Semigroup (Vector a)
Instance details Defined in Data.Vector.Storable Methods (<>) :: Vector a -> Vector a -> Vector a # sconcat :: NonEmpty (Vector a) -> Vector a # stimes :: Integral b => b -> Vector a -> Vector a #
Ord n => Semigroup (Era n)
Instance details Defined in Data.Active Methods (<>) :: Era n -> Era n -> Era n # sconcat :: NonEmpty (Era n) -> Era n # stimes :: Integral b => b -> Era n -> Era n #
Semigroup a => Semigroup (Dynamic a)	`Dynamic a` is a `Semigroup` whenever `a` is: the eras are combined according to their semigroup structure, and the values of type `a` are combined pointwise. Note that `Dynamic a` cannot be an instance of `Monoid` since `Era` is not.
Instance details Defined in Data.Active Methods (<>) :: Dynamic a -> Dynamic a -> Dynamic a # sconcat :: NonEmpty (Dynamic a) -> Dynamic a # stimes :: Integral b => b -> Dynamic a -> Dynamic a #
Semigroup a => Semigroup (Active a)	Active values over a type with a `Semigroup` instance are also an instance of `Semigroup`. Two active values are combined pointwise; the resulting value is constant iff both inputs are.
Instance details Defined in Data.Active Methods (<>) :: Active a -> Active a -> Active a # sconcat :: NonEmpty (Active a) -> Active a # stimes :: Integral b => b -> Active a -> Active a #
Num n => Semigroup (Duration n)
Instance details Defined in Data.Active Methods (<>) :: Duration n -> Duration n -> Duration n # sconcat :: NonEmpty (Duration n) -> Duration n # stimes :: Integral b => b -> Duration n -> Duration n #
Semigroup (IResult a)
Instance details Defined in Data.Aeson.Types.Internal Methods (<>) :: IResult a -> IResult a -> IResult a # sconcat :: NonEmpty (IResult a) -> IResult a # stimes :: Integral b => b -> IResult a -> IResult a #
Semigroup (Result a)
Instance details Defined in Data.Aeson.Types.Internal Methods (<>) :: Result a -> Result a -> Result a # sconcat :: NonEmpty (Result a) -> Result a # stimes :: Integral b => b -> Result a -> Result a #
Semigroup (Parser a)
Instance details Defined in Data.Aeson.Types.Internal Methods (<>) :: Parser a -> Parser a -> Parser a # sconcat :: NonEmpty (Parser a) -> Parser a # stimes :: Integral b => b -> Parser a -> Parser a #
Semigroup (Predicate a)
Instance details Defined in Data.Functor.Contravariant Methods (<>) :: Predicate a -> Predicate a -> Predicate a # sconcat :: NonEmpty (Predicate a) -> Predicate a # stimes :: Integral b => b -> Predicate a -> Predicate a #
Semigroup (Comparison a)
Instance details Defined in Data.Functor.Contravariant Methods (<>) :: Comparison a -> Comparison a -> Comparison a # sconcat :: NonEmpty (Comparison a) -> Comparison a # stimes :: Integral b => b -> Comparison a -> Comparison a #
Semigroup (Equivalence a)
Instance details Defined in Data.Functor.Contravariant Methods (<>) :: Equivalence a -> Equivalence a -> Equivalence a # sconcat :: NonEmpty (Equivalence a) -> Equivalence a # stimes :: Integral b => b -> Equivalence a -> Equivalence a #
Ord a => Semigroup (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Min a -> Min a -> Min a # sconcat :: NonEmpty (Min a) -> Min a # stimes :: Integral b => b -> Min a -> Min a #
Ord a => Semigroup (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Max a -> Max a -> Max a # sconcat :: NonEmpty (Max a) -> Max a # stimes :: Integral b => b -> Max a -> Max a #
Semigroup (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: First a -> First a -> First a # sconcat :: NonEmpty (First a) -> First a # stimes :: Integral b => b -> First a -> First a #
Semigroup (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Last a -> Last a -> Last a # sconcat :: NonEmpty (Last a) -> Last a # stimes :: Integral b => b -> Last a -> Last a #
Monoid m => Semigroup (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m #
Semigroup a => Semigroup (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Option a -> Option a -> Option a # sconcat :: NonEmpty (Option a) -> Option a # stimes :: Integral b => b -> Option a -> Option a #
Semigroup (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: First a -> First a -> First a # sconcat :: NonEmpty (First a) -> First a # stimes :: Integral b => b -> First a -> First a #
Semigroup (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Last a -> Last a -> Last a # sconcat :: NonEmpty (Last a) -> Last a # stimes :: Integral b => b -> Last a -> Last a #
Semigroup a => Semigroup (Dual a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Dual a -> Dual a -> Dual a # sconcat :: NonEmpty (Dual a) -> Dual a # stimes :: Integral b => b -> Dual a -> Dual a #
Semigroup (Endo a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Endo a -> Endo a -> Endo a # sconcat :: NonEmpty (Endo a) -> Endo a # stimes :: Integral b => b -> Endo a -> Endo a #
Num a => Semigroup (Sum a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Sum a -> Sum a -> Sum a # sconcat :: NonEmpty (Sum a) -> Sum a # stimes :: Integral b => b -> Sum a -> Sum a #
Num a => Semigroup (Product a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Product a -> Product a -> Product a # sconcat :: NonEmpty (Product a) -> Product a # stimes :: Integral b => b -> Product a -> Product a #
Semigroup a => Semigroup (Down a)	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods (<>) :: Down a -> Down a -> Down a # sconcat :: NonEmpty (Down a) -> Down a # stimes :: Integral b => b -> Down a -> Down a #
Semigroup (NonEmpty a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a # sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a # stimes :: Integral b => b -> NonEmpty a -> NonEmpty a #
PrimType ty => Semigroup (UArray ty)
Instance details Defined in Basement.UArray.Base Methods (<>) :: UArray ty -> UArray ty -> UArray ty # sconcat :: NonEmpty (UArray ty) -> UArray ty # stimes :: Integral b => b -> UArray ty -> UArray ty #
PrimType ty => Semigroup (Block ty)
Instance details Defined in Basement.Block.Base Methods (<>) :: Block ty -> Block ty -> Block ty # sconcat :: NonEmpty (Block ty) -> Block ty # stimes :: Integral b => b -> Block ty -> Block ty #
Semigroup (CountOf ty)
Instance details Defined in Basement.Types.OffsetSize Methods (<>) :: CountOf ty -> CountOf ty -> CountOf ty # sconcat :: NonEmpty (CountOf ty) -> CountOf ty # stimes :: Integral b => b -> CountOf ty -> CountOf ty #
Monoid a => Semigroup (MarkupM a)
Instance details Defined in Text.Blaze.Internal Methods (<>) :: MarkupM a -> MarkupM a -> MarkupM a # sconcat :: NonEmpty (MarkupM a) -> MarkupM a # stimes :: Integral b => b -> MarkupM a -> MarkupM a #
Semigroup s => Semigroup (CI s)
Instance details Defined in Data.CaseInsensitive.Internal Methods (<>) :: CI s -> CI s -> CI s # sconcat :: NonEmpty (CI s) -> CI s # stimes :: Integral b => b -> CI s -> CI s #
Semigroup (Vector a)
Instance details Defined in Data.Vector Methods (<>) :: Vector a -> Vector a -> Vector a # sconcat :: NonEmpty (Vector a) -> Vector a # stimes :: Integral b => b -> Vector a -> Vector a #
Num a => Semigroup (TransferFunction a)
Instance details Defined in Data.Colour.RGBSpace Methods (<>) :: TransferFunction a -> TransferFunction a -> TransferFunction a # sconcat :: NonEmpty (TransferFunction a) -> TransferFunction a # stimes :: Integral b => b -> TransferFunction a -> TransferFunction a #
Num a => Semigroup (Colour a)
Instance details Defined in Data.Colour.Internal Methods (<>) :: Colour a -> Colour a -> Colour a # sconcat :: NonEmpty (Colour a) -> Colour a # stimes :: Integral b => b -> Colour a -> Colour a #
Num a => Semigroup (AlphaColour a)	`AlphaColour` forms a monoid with `over` and `transparent`.
Instance details Defined in Data.Colour.Internal Methods (<>) :: AlphaColour a -> AlphaColour a -> AlphaColour a # sconcat :: NonEmpty (AlphaColour a) -> AlphaColour a # stimes :: Integral b => b -> AlphaColour a -> AlphaColour a #
Semigroup (IntMap a)	Since: containers-0.5.7
Instance details Defined in Data.IntMap.Internal Methods (<>) :: IntMap a -> IntMap a -> IntMap a # sconcat :: NonEmpty (IntMap a) -> IntMap a # stimes :: Integral b => b -> IntMap a -> IntMap a #
Semigroup (Seq a)	Since: containers-0.5.7
Instance details Defined in Data.Sequence.Internal Methods (<>) :: Seq a -> Seq a -> Seq a # sconcat :: NonEmpty (Seq a) -> Seq a # stimes :: Integral b => b -> Seq a -> Seq a #
Ord a => Semigroup (SortedList a)	`SortedList` forms a semigroup with `merge` as composition.
Instance details Defined in Diagrams.Core.Trace Methods (<>) :: SortedList a -> SortedList a -> SortedList a # sconcat :: NonEmpty (SortedList a) -> SortedList a # stimes :: Integral b => b -> SortedList a -> SortedList a #
Semigroup t => Semigroup (TransInv t)
Instance details Defined in Diagrams.Core.Transform Methods (<>) :: TransInv t -> TransInv t -> TransInv t # sconcat :: NonEmpty (TransInv t) -> TransInv t # stimes :: Integral b => b -> TransInv t -> TransInv t #
Semigroup a => Semigroup (Recommend a)	`Commit` overrides `Recommend`. Two values wrapped in the same constructor (both `Recommend` or both `Commit`) are combined according to the underlying `Semigroup` instance.
Instance details Defined in Data.Monoid.Recommend Methods (<>) :: Recommend a -> Recommend a -> Recommend a # sconcat :: NonEmpty (Recommend a) -> Recommend a # stimes :: Integral b => b -> Recommend a -> Recommend a #
Semigroup (FontSize n)
Instance details Defined in Diagrams.TwoD.Text Methods (<>) :: FontSize n -> FontSize n -> FontSize n # sconcat :: NonEmpty (FontSize n) -> FontSize n # stimes :: Integral b => b -> FontSize n -> FontSize n #
Semigroup (LineTexture n)
Instance details Defined in Diagrams.TwoD.Attributes Methods (<>) :: LineTexture n -> LineTexture n -> LineTexture n # sconcat :: NonEmpty (LineTexture n) -> LineTexture n # stimes :: Integral b => b -> LineTexture n -> LineTexture n #
Semigroup (FillTexture n)
Instance details Defined in Diagrams.TwoD.Attributes Methods (<>) :: FillTexture n -> FillTexture n -> FillTexture n # sconcat :: NonEmpty (FillTexture n) -> FillTexture n # stimes :: Integral b => b -> FillTexture n -> FillTexture n #
Semigroup (Clip n)
Instance details Defined in Diagrams.TwoD.Path Methods (<>) :: Clip n -> Clip n -> Clip n # sconcat :: NonEmpty (Clip n) -> Clip n # stimes :: Integral b => b -> Clip n -> Clip n #
(Num n, Ord n) => Semigroup (ArcLength n)
Instance details Defined in Diagrams.Segment Methods (<>) :: ArcLength n -> ArcLength n -> ArcLength n # sconcat :: NonEmpty (ArcLength n) -> ArcLength n # stimes :: Integral b => b -> ArcLength n -> ArcLength n #
Num n => Semigroup (Angle n)
Instance details Defined in Diagrams.Angle Methods (<>) :: Angle n -> Angle n -> Angle n # sconcat :: NonEmpty (Angle n) -> Angle n # stimes :: Integral b => b -> Angle n -> Angle n #
Semigroup (LineWidth n)
Instance details Defined in Diagrams.Attributes Methods (<>) :: LineWidth n -> LineWidth n -> LineWidth n # sconcat :: NonEmpty (LineWidth n) -> LineWidth n # stimes :: Integral b => b -> LineWidth n -> LineWidth n #
Semigroup (Dashing n)
Instance details Defined in Diagrams.Attributes Methods (<>) :: Dashing n -> Dashing n -> Dashing n # sconcat :: NonEmpty (Dashing n) -> Dashing n # stimes :: Integral b => b -> Dashing n -> Dashing n #
Semigroup (Rightmost a)
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Rightmost a -> Rightmost a -> Rightmost a # sconcat :: NonEmpty (Rightmost a) -> Rightmost a # stimes :: Integral b => b -> Rightmost a -> Rightmost a #
Semigroup (Leftmost a)
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Leftmost a -> Leftmost a -> Leftmost a # sconcat :: NonEmpty (Leftmost a) -> Leftmost a # stimes :: Integral b => b -> Leftmost a -> Leftmost a #
Semigroup (DList a)
Instance details Defined in Data.DList Methods (<>) :: DList a -> DList a -> DList a # sconcat :: NonEmpty (DList a) -> DList a # stimes :: Integral b => b -> DList a -> DList a #
Semigroup (Notebook a)
Instance details Defined in Data.Ipynb Methods (<>) :: Notebook a -> Notebook a -> Notebook a # sconcat :: NonEmpty (Notebook a) -> Notebook a # stimes :: Integral b => b -> Notebook a -> Notebook a #
Prim a => Semigroup (Vector a)
Instance details Defined in Data.Vector.Primitive Methods (<>) :: Vector a -> Vector a -> Vector a # sconcat :: NonEmpty (Vector a) -> Vector a # stimes :: Integral b => b -> Vector a -> Vector a #
(Hashable a, Eq a) => Semigroup (HashSet a)
Instance details Defined in Data.HashSet.Base Methods (<>) :: HashSet a -> HashSet a -> HashSet a # sconcat :: NonEmpty (HashSet a) -> HashSet a # stimes :: Integral b => b -> HashSet a -> HashSet a #
Ord a => Semigroup (Min a)
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Min a -> Min a -> Min a # sconcat :: NonEmpty (Min a) -> Min a # stimes :: Integral b => b -> Min a -> Min a #
Ord a => Semigroup (Max a)
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Max a -> Max a -> Max a # sconcat :: NonEmpty (Max a) -> Max a # stimes :: Integral b => b -> Max a -> Max a #
Semigroup (NonEmptyDList a)
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: NonEmptyDList a -> NonEmptyDList a -> NonEmptyDList a # sconcat :: NonEmpty (NonEmptyDList a) -> NonEmptyDList a # stimes :: Integral b => b -> NonEmptyDList a -> NonEmptyDList a #
Semigroup (Doc ann)	x `<>` y = `hcat` [x, y] `>>>` `"hello" <> "world" :: Doc ann`helloworld
Instance details Defined in Data.Text.Prettyprint.Doc.Internal Methods (<>) :: Doc ann -> Doc ann -> Doc ann # sconcat :: NonEmpty (Doc ann) -> Doc ann # stimes :: Integral b => b -> Doc ann -> Doc ann #
Semigroup (Many Block)
Instance details Defined in Text.Pandoc.Builder Methods (<>) :: Many Block -> Many Block -> Many Block # sconcat :: NonEmpty (Many Block) -> Many Block # stimes :: Integral b => b -> Many Block -> Many Block #
Semigroup (Doc a)
Instance details Defined in Text.PrettyPrint.Annotated.HughesPJ Methods (<>) :: Doc a -> Doc a -> Doc a # sconcat :: NonEmpty (Doc a) -> Doc a # stimes :: Integral b => b -> Doc a -> Doc a #
PrimUnlifted a => Semigroup (UnliftedArray a)	Since: primitive-0.6.4.0
Instance details Defined in Data.Primitive.UnliftedArray Methods (<>) :: UnliftedArray a -> UnliftedArray a -> UnliftedArray a # sconcat :: NonEmpty (UnliftedArray a) -> UnliftedArray a # stimes :: Integral b => b -> UnliftedArray a -> UnliftedArray a #
Semigroup (PrimArray a)	Since: primitive-0.6.4.0
Instance details Defined in Data.Primitive.PrimArray Methods (<>) :: PrimArray a -> PrimArray a -> PrimArray a # sconcat :: NonEmpty (PrimArray a) -> PrimArray a # stimes :: Integral b => b -> PrimArray a -> PrimArray a #
Semigroup (SmallArray a)	Since: primitive-0.6.3.0
Instance details Defined in Data.Primitive.SmallArray Methods (<>) :: SmallArray a -> SmallArray a -> SmallArray a # sconcat :: NonEmpty (SmallArray a) -> SmallArray a # stimes :: Integral b => b -> SmallArray a -> SmallArray a #
Semigroup (Array a)	Since: primitive-0.6.3.0
Instance details Defined in Data.Primitive.Array Methods (<>) :: Array a -> Array a -> Array a # sconcat :: NonEmpty (Array a) -> Array a # stimes :: Integral b => b -> Array a -> Array a #
Semigroup (MergeSet a)
Instance details Defined in Data.Set.Internal Methods (<>) :: MergeSet a -> MergeSet a -> MergeSet a # sconcat :: NonEmpty (MergeSet a) -> MergeSet a # stimes :: Integral b => b -> MergeSet a -> MergeSet a #
Applicative m => Semigroup (Ap m)
Instance details Defined in Control.Monad.Log Methods (<>) :: Ap m -> Ap m -> Ap m # sconcat :: NonEmpty (Ap m) -> Ap m # stimes :: Integral b => b -> Ap m -> Ap m #
Semigroup b => Semigroup (a -> b)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a -> b) -> (a -> b) -> a -> b # sconcat :: NonEmpty (a -> b) -> a -> b # stimes :: Integral b0 => b0 -> (a -> b) -> a -> b #
Semigroup (Either a b)	Since: base-4.9.0.0
Instance details Defined in Data.Either Methods (<>) :: Either a b -> Either a b -> Either a b # sconcat :: NonEmpty (Either a b) -> Either a b # stimes :: Integral b0 => b0 -> Either a b -> Either a b #
Semigroup (V1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: V1 p -> V1 p -> V1 p # sconcat :: NonEmpty (V1 p) -> V1 p # stimes :: Integral b => b -> V1 p -> V1 p #
Semigroup (U1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: U1 p -> U1 p -> U1 p # sconcat :: NonEmpty (U1 p) -> U1 p # stimes :: Integral b => b -> U1 p -> U1 p #
(Semigroup a, Semigroup b) => Semigroup (a, b)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b) -> (a, b) -> (a, b) # sconcat :: NonEmpty (a, b) -> (a, b) # stimes :: Integral b0 => b0 -> (a, b) -> (a, b) #
Ord k => Semigroup (Map k v)
Instance details Defined in Data.Map.Internal Methods (<>) :: Map k v -> Map k v -> Map k v # sconcat :: NonEmpty (Map k v) -> Map k v # stimes :: Integral b => b -> Map k v -> Map k v #
Semigroup a => Semigroup (Op a b)
Instance details Defined in Data.Functor.Contravariant Methods (<>) :: Op a b -> Op a b -> Op a b # sconcat :: NonEmpty (Op a b) -> Op a b # stimes :: Integral b0 => b0 -> Op a b -> Op a b #
(Eq k, Hashable k) => Semigroup (HashMap k v)
Instance details Defined in Data.HashMap.Base Methods (<>) :: HashMap k v -> HashMap k v -> HashMap k v # sconcat :: NonEmpty (HashMap k v) -> HashMap k v # stimes :: Integral b => b -> HashMap k v -> HashMap k v #
Semigroup (Parser i a)
Instance details Defined in Data.Attoparsec.Internal.Types Methods (<>) :: Parser i a -> Parser i a -> Parser i a # sconcat :: NonEmpty (Parser i a) -> Parser i a # stimes :: Integral b => b -> Parser i a -> Parser i a #
Semigroup (Proxy s)	Since: base-4.9.0.0
Instance details Defined in Data.Proxy Methods (<>) :: Proxy s -> Proxy s -> Proxy s # sconcat :: NonEmpty (Proxy s) -> Proxy s # stimes :: Integral b => b -> Proxy s -> Proxy s #
Ord n => Semigroup (Envelope v n)	Envelopes form a semigroup with pointwise maximum as composition. Hence, if `e1` is the envelope for diagram `d1`, and `e2` is the envelope for `d2`, then e1 `mappend` e2 is the envelope for d1 `atop` d2.
Instance details Defined in Diagrams.Core.Envelope Methods (<>) :: Envelope v n -> Envelope v n -> Envelope v n # sconcat :: NonEmpty (Envelope v n) -> Envelope v n # stimes :: Integral b => b -> Envelope v n -> Envelope v n #
Ord n => Semigroup (Trace v n)	Traces form a semigroup with pointwise minimum as composition. Hence, if `t1` is the trace for diagram `d1`, and `e2` is the trace for `d2`, then e1 `mappend` e2 is the trace for d1 `atop` d2.
Instance details Defined in Diagrams.Core.Trace Methods (<>) :: Trace v n -> Trace v n -> Trace v n # sconcat :: NonEmpty (Trace v n) -> Trace v n # stimes :: Integral b => b -> Trace v n -> Trace v n #
Typeable n => Semigroup (Attribute v n)	Attributes form a semigroup, where the semigroup operation simply returns the right-hand attribute when the types do not match, and otherwise uses the semigroup operation specific to the (matching) types.
Instance details Defined in Diagrams.Core.Style Methods (<>) :: Attribute v n -> Attribute v n -> Attribute v n # sconcat :: NonEmpty (Attribute v n) -> Attribute v n # stimes :: Integral b => b -> Attribute v n -> Attribute v n #
Typeable n => Semigroup (Style v n)	Combine a style by combining the attributes; if the two styles have attributes of the same type they are combined according to their semigroup structure.
Instance details Defined in Diagrams.Core.Style Methods (<>) :: Style v n -> Style v n -> Style v n # sconcat :: NonEmpty (Style v n) -> Style v n # stimes :: Integral b => b -> Style v n -> Style v n #
Semigroup (a :-: a)
Instance details Defined in Diagrams.Core.Transform Methods (<>) :: (a :-: a) -> (a :-: a) -> a :-: a # sconcat :: NonEmpty (a :-: a) -> a :-: a # stimes :: Integral b => b -> (a :-: a) -> a :-: a #
(Additive v, Num n) => Semigroup (Transformation v n)	Transformations are closed under composition; `t1 <> t2` is the transformation which performs first `t2`, then `t1`.
Instance details Defined in Diagrams.Core.Transform Methods (<>) :: Transformation v n -> Transformation v n -> Transformation v n # sconcat :: NonEmpty (Transformation v n) -> Transformation v n # stimes :: Integral b => b -> Transformation v n -> Transformation v n #
Semigroup a => Semigroup (Measured n a)
Instance details Defined in Diagrams.Core.Measure Methods (<>) :: Measured n a -> Measured n a -> Measured n a # sconcat :: NonEmpty (Measured n a) -> Measured n a # stimes :: Integral b => b -> Measured n a -> Measured n a #
(Additive v, Ord n) => Semigroup (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox Methods (<>) :: BoundingBox v n -> BoundingBox v n -> BoundingBox v n # sconcat :: NonEmpty (BoundingBox v n) -> BoundingBox v n # stimes :: Integral b => b -> BoundingBox v n -> BoundingBox v n #
Semigroup (Path v n)
Instance details Defined in Diagrams.Path Methods (<>) :: Path v n -> Path v n -> Path v n # sconcat :: NonEmpty (Path v n) -> Path v n # stimes :: Integral b => b -> Path v n -> Path v n #
(Ord n, Floating n, Metric v) => Semigroup (SegTree v n)
Instance details Defined in Diagrams.Trail Methods (<>) :: SegTree v n -> SegTree v n -> SegTree v n # sconcat :: NonEmpty (SegTree v n) -> SegTree v n # stimes :: Integral b => b -> SegTree v n -> SegTree v n #
(OrderedField n, Metric v) => Semigroup (Trail v n)	Two `Trail`s are combined by first ensuring they are both lines (using `cutTrail` on loops) and then concatenating them. The result, in general, is a line. However, there is a special case for the empty line, which acts as the identity (so combining the empty line with a loop results in a loop).
Instance details Defined in Diagrams.Trail Methods (<>) :: Trail v n -> Trail v n -> Trail v n # sconcat :: NonEmpty (Trail v n) -> Trail v n # stimes :: Integral b => b -> Trail v n -> Trail v n #
(Num n, Additive v) => Semigroup (TotalOffset v n)
Instance details Defined in Diagrams.Segment Methods (<>) :: TotalOffset v n -> TotalOffset v n -> TotalOffset v n # sconcat :: NonEmpty (TotalOffset v n) -> TotalOffset v n # stimes :: Integral b => b -> TotalOffset v n -> TotalOffset v n #
(Metric v, OrderedField n) => Semigroup (OffsetEnvelope v n)
Instance details Defined in Diagrams.Segment Methods (<>) :: OffsetEnvelope v n -> OffsetEnvelope v n -> OffsetEnvelope v n # sconcat :: NonEmpty (OffsetEnvelope v n) -> OffsetEnvelope v n # stimes :: Integral b => b -> OffsetEnvelope v n -> OffsetEnvelope v n #
Monad m => Semigroup (Sequenced a m)
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Sequenced a m -> Sequenced a m -> Sequenced a m # sconcat :: NonEmpty (Sequenced a m) -> Sequenced a m # stimes :: Integral b => b -> Sequenced a m -> Sequenced a m #
Applicative f => Semigroup (Traversed a f)
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Traversed a f -> Traversed a f -> Traversed a f # sconcat :: NonEmpty (Traversed a f) -> Traversed a f # stimes :: Integral b => b -> Traversed a f -> Traversed a f #
Semigroup (ReifiedFold s a)
Instance details Defined in Control.Lens.Reified Methods (<>) :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a # sconcat :: NonEmpty (ReifiedFold s a) -> ReifiedFold s a # stimes :: Integral b => b -> ReifiedFold s a -> ReifiedFold s a #
Measured v a => Semigroup (FingerTree v a)
Instance details Defined in Data.FingerTree Methods (<>) :: FingerTree v a -> FingerTree v a -> FingerTree v a # sconcat :: NonEmpty (FingerTree v a) -> FingerTree v a # stimes :: Integral b => b -> FingerTree v a -> FingerTree v a #
Semigroup (Deepening i a)
Instance details Defined in Control.Lens.Internal.Level Methods (<>) :: Deepening i a -> Deepening i a -> Deepening i a # sconcat :: NonEmpty (Deepening i a) -> Deepening i a # stimes :: Integral b => b -> Deepening i a -> Deepening i a #
Semigroup (f a) => Semigroup (Indexing f a)
Instance details Defined in Control.Lens.Internal.Indexed Methods (<>) :: Indexing f a -> Indexing f a -> Indexing f a # sconcat :: NonEmpty (Indexing f a) -> Indexing f a # stimes :: Integral b => b -> Indexing f a -> Indexing f a #
(Contravariant f, Applicative f) => Semigroup (Folding f a)
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Folding f a -> Folding f a -> Folding f a # sconcat :: NonEmpty (Folding f a) -> Folding f a # stimes :: Integral b => b -> Folding f a -> Folding f a #
Apply f => Semigroup (TraversedF a f)
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: TraversedF a f -> TraversedF a f -> TraversedF a f # sconcat :: NonEmpty (TraversedF a f) -> TraversedF a f # stimes :: Integral b => b -> TraversedF a f -> TraversedF a f #
(a ~ (), Applicative m) => Semigroup (HtmlT m a)	Since: lucid-2.9.7
Instance details Defined in Lucid.Base Methods (<>) :: HtmlT m a -> HtmlT m a -> HtmlT m a # sconcat :: NonEmpty (HtmlT m a) -> HtmlT m a # stimes :: Integral b => b -> HtmlT m a -> HtmlT m a #
(Additive v, Ord n) => Semigroup (NonEmptyBoundingBox v n)
Instance details Defined in Diagrams.BoundingBox Methods (<>) :: NonEmptyBoundingBox v n -> NonEmptyBoundingBox v n -> NonEmptyBoundingBox v n # sconcat :: NonEmpty (NonEmptyBoundingBox v n) -> NonEmptyBoundingBox v n # stimes :: Integral b => b -> NonEmptyBoundingBox v n -> NonEmptyBoundingBox v n #
Semigroup (f p) => Semigroup (Rec1 f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: Rec1 f p -> Rec1 f p -> Rec1 f p # sconcat :: NonEmpty (Rec1 f p) -> Rec1 f p # stimes :: Integral b => b -> Rec1 f p -> Rec1 f p #
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) # sconcat :: NonEmpty (a, b, c) -> (a, b, c) # stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c) #
Semigroup a => Semigroup (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (<>) :: Const a b -> Const a b -> Const a b # sconcat :: NonEmpty (Const a b) -> Const a b # stimes :: Integral b0 => b0 -> Const a b -> Const a b #
(Applicative f, Semigroup a) => Semigroup (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Ap f a -> Ap f a -> Ap f a # sconcat :: NonEmpty (Ap f a) -> Ap f a # stimes :: Integral b => b -> Ap f a -> Ap f a #
Alternative f => Semigroup (Alt f a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Alt f a -> Alt f a -> Alt f a # sconcat :: NonEmpty (Alt f a) -> Alt f a # stimes :: Integral b => b -> Alt f a -> Alt f a #
Semigroup (Colonnade h a c)
Instance details Defined in Colonnade.Encode Methods (<>) :: Colonnade h a c -> Colonnade h a c -> Colonnade h a c # sconcat :: NonEmpty (Colonnade h a c) -> Colonnade h a c # stimes :: Integral b => b -> Colonnade h a c -> Colonnade h a c #
Semigroup (Render NullBackend v n)
Instance details Defined in Diagrams.Core.Types Methods (<>) :: Render NullBackend v n -> Render NullBackend v n -> Render NullBackend v n # sconcat :: NonEmpty (Render NullBackend v n) -> Render NullBackend v n # stimes :: Integral b => b -> Render NullBackend v n -> Render NullBackend v n #
Semigroup (Render SVG V2 n)
Instance details Defined in Diagrams.Backend.SVG Methods (<>) :: Render SVG V2 n -> Render SVG V2 n -> Render SVG V2 n # sconcat :: NonEmpty (Render SVG V2 n) -> Render SVG V2 n # stimes :: Integral b => b -> Render SVG V2 n -> Render SVG V2 n #
Semigroup m => Semigroup (Query v n m)
Instance details Defined in Diagrams.Core.Query Methods (<>) :: Query v n m -> Query v n m -> Query v n m # sconcat :: NonEmpty (Query v n m) -> Query v n m # stimes :: Integral b => b -> Query v n m -> Query v n m #
Semigroup (Deformation v v n)
Instance details Defined in Diagrams.Deform Methods (<>) :: Deformation v v n -> Deformation v v n -> Deformation v v n # sconcat :: NonEmpty (Deformation v v n) -> Deformation v v n # stimes :: Integral b => b -> Deformation v v n -> Deformation v v n #
(OrderedField n, Metric v) => Semigroup (Trail' Line v n)
Instance details Defined in Diagrams.Trail Methods (<>) :: Trail' Line v n -> Trail' Line v n -> Trail' Line v n # sconcat :: NonEmpty (Trail' Line v n) -> Trail' Line v n # stimes :: Integral b => b -> Trail' Line v n -> Trail' Line v n #
Semigroup (ReifiedIndexedFold i s a)
Instance details Defined in Control.Lens.Reified Methods (<>) :: ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a # sconcat :: NonEmpty (ReifiedIndexedFold i s a) -> ReifiedIndexedFold i s a # stimes :: Integral b => b -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a #
ArrowPlus p => Semigroup (Tambara p a b)
Instance details Defined in Data.Profunctor.Strong Methods (<>) :: Tambara p a b -> Tambara p a b -> Tambara p a b # sconcat :: NonEmpty (Tambara p a b) -> Tambara p a b # stimes :: Integral b0 => b0 -> Tambara p a b -> Tambara p a b #
Reifies s (ReifiedMonoid a) => Semigroup (ReflectedMonoid a s)
Instance details Defined in Data.Reflection Methods (<>) :: ReflectedMonoid a s -> ReflectedMonoid a s -> ReflectedMonoid a s # sconcat :: NonEmpty (ReflectedMonoid a s) -> ReflectedMonoid a s # stimes :: Integral b => b -> ReflectedMonoid a s -> ReflectedMonoid a s #
Semigroup a => Semigroup (Tagged s a)
Instance details Defined in Data.Tagged Methods (<>) :: Tagged s a -> Tagged s a -> Tagged s a # sconcat :: NonEmpty (Tagged s a) -> Tagged s a # stimes :: Integral b => b -> Tagged s a -> Tagged s a #
Semigroup c => Semigroup (K1 i c p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: K1 i c p -> K1 i c p -> K1 i c p # sconcat :: NonEmpty (K1 i c p) -> K1 i c p # stimes :: Integral b => b -> K1 i c p -> K1 i c p #
(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: (f :: g) p -> (f :: g) p -> (f :: g) p # sconcat :: NonEmpty ((f :: g) p) -> (f :: g) p # stimes :: Integral b => b -> (f :: g) p -> (f :*: g) p #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) # stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d) #
Semigroup (Cornice h p a c)
Instance details Defined in Colonnade.Encode Methods (<>) :: Cornice h p a c -> Cornice h p a c -> Cornice h p a c # sconcat :: NonEmpty (Cornice h p a c) -> Cornice h p a c # stimes :: Integral b => b -> Cornice h p a c -> Cornice h p a c #
(Metric v, OrderedField n, Semigroup m) => Semigroup (QDiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods (<>) :: QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m # sconcat :: NonEmpty (QDiagram b v n m) -> QDiagram b v n m # stimes :: Integral b0 => b0 -> QDiagram b v n m -> QDiagram b v n m #
Semigroup (SubMap b v n m)
Instance details Defined in Diagrams.Core.Types Methods (<>) :: SubMap b v n m -> SubMap b v n m -> SubMap b v n m # sconcat :: NonEmpty (SubMap b v n m) -> SubMap b v n m # stimes :: Integral b0 => b0 -> SubMap b v n m -> SubMap b v n m #
(Action d u, Semigroup u) => Semigroup (DUALTreeNE d u a l)
Instance details Defined in Data.Tree.DUAL.Internal Methods (<>) :: DUALTreeNE d u a l -> DUALTreeNE d u a l -> DUALTreeNE d u a l # sconcat :: NonEmpty (DUALTreeNE d u a l) -> DUALTreeNE d u a l # stimes :: Integral b => b -> DUALTreeNE d u a l -> DUALTreeNE d u a l #
(Semigroup u, Action d u) => Semigroup (DUALTreeU d u a l)
Instance details Defined in Data.Tree.DUAL.Internal Methods (<>) :: DUALTreeU d u a l -> DUALTreeU d u a l -> DUALTreeU d u a l # sconcat :: NonEmpty (DUALTreeU d u a l) -> DUALTreeU d u a l # stimes :: Integral b => b -> DUALTreeU d u a l -> DUALTreeU d u a l #
(Semigroup u, Action d u) => Semigroup (DUALTree d u a l)
Instance details Defined in Data.Tree.DUAL.Internal Methods (<>) :: DUALTree d u a l -> DUALTree d u a l -> DUALTree d u a l # sconcat :: NonEmpty (DUALTree d u a l) -> DUALTree d u a l # stimes :: Integral b => b -> DUALTree d u a l -> DUALTree d u a l #
Semigroup a => Semigroup (ParsecT s u m a)	The `Semigroup` instance for `ParsecT` is used to append the result of several parsers, for example: (many $ char `a`) <> (many $ char `b`) The above will parse a string like `"aabbb"` and return a successful parse result `"aabbb"`. Compare against the below which will produce a result of `"bbb"` for the same input: (many $ char `a`) >> (many $ char `b`) (many $ char `a`) > (many $ char `b`) Since: parsec-3.1.12*
Instance details Defined in Text.Parsec.Prim Methods (<>) :: ParsecT s u m a -> ParsecT s u m a -> ParsecT s u m a # sconcat :: NonEmpty (ParsecT s u m a) -> ParsecT s u m a # stimes :: Integral b => b -> ParsecT s u m a -> ParsecT s u m a #
Semigroup (f p) => Semigroup (M1 i c f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: M1 i c f p -> M1 i c f p -> M1 i c f p # sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p # stimes :: Integral b => b -> M1 i c f p -> M1 i c f p #
Semigroup (f (g p)) => Semigroup ((f :.: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p # sconcat :: NonEmpty ((f :.: g) p) -> (f :.: g) p # stimes :: Integral b => b -> (f :.: g) p -> (f :.: g) p #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) # stimes :: Integral b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e) #
Contravariant g => Semigroup (BazaarT p g a b t)
Instance details Defined in Control.Lens.Internal.Bazaar Methods (<>) :: BazaarT p g a b t -> BazaarT p g a b t -> BazaarT p g a b t # sconcat :: NonEmpty (BazaarT p g a b t) -> BazaarT p g a b t # stimes :: Integral b0 => b0 -> BazaarT p g a b t -> BazaarT p g a b t #
Contravariant g => Semigroup (BazaarT1 p g a b t)
Instance details Defined in Control.Lens.Internal.Bazaar Methods (<>) :: BazaarT1 p g a b t -> BazaarT1 p g a b t -> BazaarT1 p g a b t # sconcat :: NonEmpty (BazaarT1 p g a b t) -> BazaarT1 p g a b t # stimes :: Integral b0 => b0 -> BazaarT1 p g a b t -> BazaarT1 p g a b t #

liftA :: Applicative f => (a -> b) -> f a -> f b #

Lift a function to actions. This function may be used as a value for fmap in a Functor instance.

liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d #

Lift a ternary function to actions.

(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 #

An infix synonym for fmap.

The name of this operator is an allusion to $. Note the similarities between their types:

 ($)  ::              (a -> b) ->   a ->   b
(<$>) :: Functor f => (a -> b) -> f a -> f b

Whereas $ is function application, <$> is function application lifted over a Functor.

Examples

Expand

Convert from a Maybe Int to a Maybe String using show:

>>> show <$> Nothing
Nothing
>>> show <$> Just 3
Just "3"

Convert from an Either Int Int to an Either Int String using show:

>>> show <$> Left 17
Left 17
>>> show <$> Right 17
Right "17"

Double each element of a list:

>>> (*2) <$> [1,2,3]
[2,4,6]

Apply even to the second element of a pair:

>>> even <$> (2,2)
(2,True)

newtype Const a (b :: k) :: forall k. Type -> k -> Type #

The Const functor.

Constructors

Const
Fields getConst :: a

Instances

Generic1 (Const a :: k -> Type)
Instance details Defined in Data.Functor.Const Associated Types type Rep1 (Const a) :: k -> Type # Methods from1 :: Const a a0 -> Rep1 (Const a) a0 # to1 :: Rep1 (Const a) a0 -> Const a a0 #
ToJSON2 (Const :: Type -> Type -> Type)
Instance details Defined in Data.Aeson.Types.ToJSON Methods liftToJSON2 :: (a -> Value) -> ([a] -> Value) -> (b -> Value) -> ([b] -> Value) -> Const a b -> Value # liftToJSONList2 :: (a -> Value) -> ([a] -> Value) -> (b -> Value) -> ([b] -> Value) -> [Const a b] -> Value # liftToEncoding2 :: (a -> Encoding) -> ([a] -> Encoding) -> (b -> Encoding) -> ([b] -> Encoding) -> Const a b -> Encoding # liftToEncodingList2 :: (a -> Encoding) -> ([a] -> Encoding) -> (b -> Encoding) -> ([b] -> Encoding) -> [Const a b] -> Encoding #
Bitraversable (Const :: Type -> Type -> Type)	Since: base-4.10.0.0
Instance details Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Const a b -> f (Const c d) #
Bifoldable (Const :: Type -> Type -> Type)	Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => Const m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Const a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Const a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Const a b -> c #
Bifunctor (Const :: Type -> Type -> Type)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d # first :: (a -> b) -> Const a c -> Const b c # second :: (b -> c) -> Const a b -> Const a c #
Biapplicative (Const :: Type -> Type -> Type)
Instance details Defined in Data.Biapplicative Methods bipure :: a -> b -> Const a b # (<<>>) :: Const (a -> b) (c -> d) -> Const a c -> Const b d # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Const a d -> Const b e -> Const c f # (>>) :: Const a b -> Const c d -> Const c d # (<<*) :: Const a b -> Const c d -> Const a b #
Bitraversable1 (Const :: Type -> Type -> Type)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Const a c -> f (Const b d) # bisequence1 :: Apply f => Const (f a) (f b) -> f (Const a b) #
Biapply (Const :: Type -> Type -> Type)
Instance details Defined in Data.Functor.Bind.Class Methods (<<.>>) :: Const (a -> b) (c -> d) -> Const a c -> Const b d # (.>>) :: Const a b -> Const c d -> Const c d # (<<.) :: Const a b -> Const c d -> Const a b #
Functor (Const m :: Type -> Type)	Since: base-2.1
Instance details Defined in Data.Functor.Const Methods fmap :: (a -> b) -> Const m a -> Const m b # (<$) :: a -> Const m b -> Const m a #
Monoid m => Applicative (Const m :: Type -> Type)	Since: base-2.0.1
Instance details Defined in Data.Functor.Const Methods pure :: a -> Const m a # (<>) :: Const m (a -> b) -> Const m a -> Const m b # liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c # (>) :: Const m a -> Const m b -> Const m b # (<*) :: Const m a -> Const m b -> Const m a #
Foldable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldr :: (a -> b -> b) -> b -> Const m a -> b # foldr' :: (a -> b -> b) -> b -> Const m a -> b # foldl :: (b -> a -> b) -> b -> Const m a -> b # foldl' :: (b -> a -> b) -> b -> Const m a -> b # foldr1 :: (a -> a -> a) -> Const m a -> a # foldl1 :: (a -> a -> a) -> Const m a -> a # toList :: Const m a -> [a] # null :: Const m a -> Bool # length :: Const m a -> Int # elem :: Eq a => a -> Const m a -> Bool # maximum :: Ord a => Const m a -> a # minimum :: Ord a => Const m a -> a # sum :: Num a => Const m a -> a # product :: Num a => Const m a -> a #
Traversable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b) # sequenceA :: Applicative f => Const m (f a) -> f (Const m a) # mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b) # sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a) #
Semigroup m => Apply (Const m :: Type -> Type)
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Const m (a -> b) -> Const m a -> Const m b # (.>) :: Const m a -> Const m b -> Const m b # (<.) :: Const m a -> Const m b -> Const m a # liftF2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c #
Contravariant (Const a :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a0 -> b) -> Const a b -> Const a a0 # (>$) :: b -> Const a b -> Const a a0 #
ToJSON a => ToJSON1 (Const a :: Type -> Type)
Instance details Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a0 -> Value) -> ([a0] -> Value) -> Const a a0 -> Value # liftToJSONList :: (a0 -> Value) -> ([a0] -> Value) -> [Const a a0] -> Value # liftToEncoding :: (a0 -> Encoding) -> ([a0] -> Encoding) -> Const a a0 -> Encoding # liftToEncodingList :: (a0 -> Encoding) -> ([a0] -> Encoding) -> [Const a a0] -> Encoding #
Bounded a => Bounded (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods minBound :: Const a b # maxBound :: Const a b #
Enum a => Enum (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods succ :: Const a b -> Const a b # pred :: Const a b -> Const a b # toEnum :: Int -> Const a b # fromEnum :: Const a b -> Int # enumFrom :: Const a b -> [Const a b] # enumFromThen :: Const a b -> Const a b -> [Const a b] # enumFromTo :: Const a b -> Const a b -> [Const a b] # enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b] #
Eq a => Eq (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (==) :: Const a b -> Const a b -> Bool # (/=) :: Const a b -> Const a b -> Bool #
Floating a => Floating (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods pi :: Const a b # exp :: Const a b -> Const a b # log :: Const a b -> Const a b # sqrt :: Const a b -> Const a b # (**) :: Const a b -> Const a b -> Const a b # logBase :: Const a b -> Const a b -> Const a b # sin :: Const a b -> Const a b # cos :: Const a b -> Const a b # tan :: Const a b -> Const a b # asin :: Const a b -> Const a b # acos :: Const a b -> Const a b # atan :: Const a b -> Const a b # sinh :: Const a b -> Const a b # cosh :: Const a b -> Const a b # tanh :: Const a b -> Const a b # asinh :: Const a b -> Const a b # acosh :: Const a b -> Const a b # atanh :: Const a b -> Const a b # log1p :: Const a b -> Const a b # expm1 :: Const a b -> Const a b # log1pexp :: Const a b -> Const a b # log1mexp :: Const a b -> Const a b #
Fractional a => Fractional (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (/) :: Const a b -> Const a b -> Const a b # recip :: Const a b -> Const a b # fromRational :: Rational -> Const a b #
Integral a => Integral (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods quot :: Const a b -> Const a b -> Const a b # rem :: Const a b -> Const a b -> Const a b # div :: Const a b -> Const a b -> Const a b # mod :: Const a b -> Const a b -> Const a b # quotRem :: Const a b -> Const a b -> (Const a b, Const a b) # divMod :: Const a b -> Const a b -> (Const a b, Const a b) # toInteger :: Const a b -> Integer #
Num a => Num (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (+) :: Const a b -> Const a b -> Const a b # (-) :: Const a b -> Const a b -> Const a b # (*) :: Const a b -> Const a b -> Const a b # negate :: Const a b -> Const a b # abs :: Const a b -> Const a b # signum :: Const a b -> Const a b # fromInteger :: Integer -> Const a b #
Ord a => Ord (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods compare :: Const a b -> Const a b -> Ordering # (<) :: Const a b -> Const a b -> Bool # (<=) :: Const a b -> Const a b -> Bool # (>) :: Const a b -> Const a b -> Bool # (>=) :: Const a b -> Const a b -> Bool # max :: Const a b -> Const a b -> Const a b # min :: Const a b -> Const a b -> Const a b #
Read a => Read (Const a b)	This instance would be equivalent to the derived instances of the `Const` newtype if the `runConst` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Const Methods readsPrec :: Int -> ReadS (Const a b) # readList :: ReadS [Const a b] # readPrec :: ReadPrec (Const a b) # readListPrec :: ReadPrec [Const a b] #
Real a => Real (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods toRational :: Const a b -> Rational #
RealFloat a => RealFloat (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods floatRadix :: Const a b -> Integer # floatDigits :: Const a b -> Int # floatRange :: Const a b -> (Int, Int) # decodeFloat :: Const a b -> (Integer, Int) # encodeFloat :: Integer -> Int -> Const a b # exponent :: Const a b -> Int # significand :: Const a b -> Const a b # scaleFloat :: Int -> Const a b -> Const a b # isNaN :: Const a b -> Bool # isInfinite :: Const a b -> Bool # isDenormalized :: Const a b -> Bool # isNegativeZero :: Const a b -> Bool # isIEEE :: Const a b -> Bool # atan2 :: Const a b -> Const a b -> Const a b #
RealFrac a => RealFrac (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods properFraction :: Integral b0 => Const a b -> (b0, Const a b) # truncate :: Integral b0 => Const a b -> b0 # round :: Integral b0 => Const a b -> b0 # ceiling :: Integral b0 => Const a b -> b0 # floor :: Integral b0 => Const a b -> b0 #
Show a => Show (Const a b)	This instance would be equivalent to the derived instances of the `Const` newtype if the `runConst` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Const Methods showsPrec :: Int -> Const a b -> ShowS # show :: Const a b -> String # showList :: [Const a b] -> ShowS #
Ix a => Ix (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods range :: (Const a b, Const a b) -> [Const a b] # index :: (Const a b, Const a b) -> Const a b -> Int # unsafeIndex :: (Const a b, Const a b) -> Const a b -> Int inRange :: (Const a b, Const a b) -> Const a b -> Bool # rangeSize :: (Const a b, Const a b) -> Int # unsafeRangeSize :: (Const a b, Const a b) -> Int
IsString a => IsString (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.String Methods fromString :: String -> Const a b #
Generic (Const a b)
Instance details Defined in Data.Functor.Const Associated Types type Rep (Const a b) :: Type -> Type # Methods from :: Const a b -> Rep (Const a b) x # to :: Rep (Const a b) x -> Const a b #
Semigroup a => Semigroup (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (<>) :: Const a b -> Const a b -> Const a b # sconcat :: NonEmpty (Const a b) -> Const a b # stimes :: Integral b0 => b0 -> Const a b -> Const a b #
Monoid a => Monoid (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods mempty :: Const a b # mappend :: Const a b -> Const a b -> Const a b # mconcat :: [Const a b] -> Const a b #
ToJSON a => ToJSON (Const a b)
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSON :: Const a b -> Value # toEncoding :: Const a b -> Encoding # toJSONList :: [Const a b] -> Value # toEncodingList :: [Const a b] -> Encoding #
Storable a => Storable (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods sizeOf :: Const a b -> Int # alignment :: Const a b -> Int # peekElemOff :: Ptr (Const a b) -> Int -> IO (Const a b) # pokeElemOff :: Ptr (Const a b) -> Int -> Const a b -> IO () # peekByteOff :: Ptr b0 -> Int -> IO (Const a b) # pokeByteOff :: Ptr b0 -> Int -> Const a b -> IO () # peek :: Ptr (Const a b) -> IO (Const a b) # poke :: Ptr (Const a b) -> Const a b -> IO () #
Bits a => Bits (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (.&.) :: Const a b -> Const a b -> Const a b # (.\|.) :: Const a b -> Const a b -> Const a b # xor :: Const a b -> Const a b -> Const a b # complement :: Const a b -> Const a b # shift :: Const a b -> Int -> Const a b # rotate :: Const a b -> Int -> Const a b # zeroBits :: Const a b # bit :: Int -> Const a b # setBit :: Const a b -> Int -> Const a b # clearBit :: Const a b -> Int -> Const a b # complementBit :: Const a b -> Int -> Const a b # testBit :: Const a b -> Int -> Bool # bitSizeMaybe :: Const a b -> Maybe Int # bitSize :: Const a b -> Int # isSigned :: Const a b -> Bool # shiftL :: Const a b -> Int -> Const a b # unsafeShiftL :: Const a b -> Int -> Const a b # shiftR :: Const a b -> Int -> Const a b # unsafeShiftR :: Const a b -> Int -> Const a b # rotateL :: Const a b -> Int -> Const a b # rotateR :: Const a b -> Int -> Const a b # popCount :: Const a b -> Int #
FiniteBits a => FiniteBits (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods finiteBitSize :: Const a b -> Int # countLeadingZeros :: Const a b -> Int # countTrailingZeros :: Const a b -> Int #
Wrapped (Const a x)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Const a x) :: Type # Methods _Wrapped' :: Iso' (Const a x) (Unwrapped (Const a x)) #
Newtype (Const a x)
Instance details Defined in Control.Newtype.Generics Associated Types type O (Const a x) :: Type # Methods pack :: O (Const a x) -> Const a x # unpack :: Const a x -> O (Const a x) #
Pretty a => Pretty (Const a b)
Instance details Defined in Data.Text.Prettyprint.Doc.Internal Methods pretty :: Const a b -> Doc ann # prettyList :: [Const a b] -> Doc ann #
t ~ Const a' x' => Rewrapped (Const a x) t
Instance details Defined in Control.Lens.Wrapped
type Rep1 (Const a :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const type Rep1 (Const a :: k -> Type) = D1 (MetaData "Const" "Data.Functor.Const" "base" True) (C1 (MetaCons "Const" PrefixI True) (S1 (MetaSel (Just "getConst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const type Rep (Const a b) = D1 (MetaData "Const" "Data.Functor.Const" "base" True) (C1 (MetaCons "Const" PrefixI True) (S1 (MetaSel (Just "getConst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Unwrapped (Const a x)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Const a x) = a
type O (Const a x)
Instance details Defined in Control.Newtype.Generics type O (Const a x) = a

newtype Identity a #

Identity functor and monad. (a non-strict monad)

Since: base-4.8.0.0

Constructors

Identity
Fields runIdentity :: a

Instances

Monad Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods (>>=) :: Identity a -> (a -> Identity b) -> Identity b # (>>) :: Identity a -> Identity b -> Identity b # return :: a -> Identity a # fail :: String -> Identity a #
Functor Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fmap :: (a -> b) -> Identity a -> Identity b # (<$) :: a -> Identity b -> Identity a #
MonadFix Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods mfix :: (a -> Identity a) -> Identity a #
Applicative Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods pure :: a -> Identity a # (<>) :: Identity (a -> b) -> Identity a -> Identity b # liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c # (>) :: Identity a -> Identity b -> Identity b # (<*) :: Identity a -> Identity b -> Identity a #
Foldable Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m # foldMap :: Monoid m => (a -> m) -> Identity a -> m # foldr :: (a -> b -> b) -> b -> Identity a -> b # foldr' :: (a -> b -> b) -> b -> Identity a -> b # foldl :: (b -> a -> b) -> b -> Identity a -> b # foldl' :: (b -> a -> b) -> b -> Identity a -> b # foldr1 :: (a -> a -> a) -> Identity a -> a # foldl1 :: (a -> a -> a) -> Identity a -> a # toList :: Identity a -> [a] # null :: Identity a -> Bool # length :: Identity a -> Int # elem :: Eq a => a -> Identity a -> Bool # maximum :: Ord a => Identity a -> a # minimum :: Ord a => Identity a -> a # sum :: Num a => Identity a -> a # product :: Num a => Identity a -> a #
Traversable Identity	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b) # sequenceA :: Applicative f => Identity (f a) -> f (Identity a) # mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b) # sequence :: Monad m => Identity (m a) -> m (Identity a) #
Apply Identity
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Identity (a -> b) -> Identity a -> Identity b # (.>) :: Identity a -> Identity b -> Identity b # (<.) :: Identity a -> Identity b -> Identity a # liftF2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c #
Representable Identity
Instance details Defined in Data.Functor.Rep Associated Types type Rep Identity :: Type # Methods tabulate :: (Rep Identity -> a) -> Identity a # index :: Identity a -> Rep Identity -> a #
ToJSON1 Identity
Instance details Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a -> Value) -> ([a] -> Value) -> Identity a -> Value # liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [Identity a] -> Value # liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> Identity a -> Encoding # liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [Identity a] -> Encoding #
Additive Identity
Instance details Defined in Linear.Vector Methods zero :: Num a => Identity a # (^+^) :: Num a => Identity a -> Identity a -> Identity a # (^-^) :: Num a => Identity a -> Identity a -> Identity a # lerp :: Num a => a -> Identity a -> Identity a -> Identity a # liftU2 :: (a -> a -> a) -> Identity a -> Identity a -> Identity a # liftI2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c #
Metric Identity
Instance details Defined in Linear.Metric Methods dot :: Num a => Identity a -> Identity a -> a # quadrance :: Num a => Identity a -> a # qd :: Num a => Identity a -> Identity a -> a # distance :: Floating a => Identity a -> Identity a -> a # norm :: Floating a => Identity a -> a # signorm :: Floating a => Identity a -> Identity a #
Affine Identity
Instance details Defined in Linear.Affine Associated Types type Diff Identity :: Type -> Type # Methods (.-.) :: Num a => Identity a -> Identity a -> Diff Identity a # (.+^) :: Num a => Identity a -> Diff Identity a -> Identity a # (.-^) :: Num a => Identity a -> Diff Identity a -> Identity a #
R1 Identity
Instance details Defined in Linear.V1 Methods _x :: Lens' (Identity a) a #
Traversable1 Identity
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Identity a -> f (Identity b) # sequence1 :: Apply f => Identity (f b) -> f (Identity b) #
Settable Identity	So you can pass our `Setter` into combinators from other lens libraries.
Instance details Defined in Control.Lens.Internal.Setter Methods untainted :: Identity a -> a # untaintedDot :: Profunctor p => p a (Identity b) -> p a b # taintedDot :: Profunctor p => p a b -> p a (Identity b) #
Bind Identity
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Identity a -> (a -> Identity b) -> Identity b # join :: Identity (Identity a) -> Identity a #
TraversableWithIndex () Identity
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (() -> a -> f b) -> Identity a -> f (Identity b) # itraversed :: IndexedTraversal () (Identity a) (Identity b) a b #
FoldableWithIndex () Identity
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (() -> a -> m) -> Identity a -> m # ifolded :: IndexedFold () (Identity a) a # ifoldr :: (() -> a -> b -> b) -> b -> Identity a -> b # ifoldl :: (() -> b -> a -> b) -> b -> Identity a -> b # ifoldr' :: (() -> a -> b -> b) -> b -> Identity a -> b # ifoldl' :: (() -> b -> a -> b) -> b -> Identity a -> b #
FunctorWithIndex () Identity
Instance details Defined in Control.Lens.Indexed Methods imap :: (() -> a -> b) -> Identity a -> Identity b # imapped :: IndexedSetter () (Identity a) (Identity b) a b #
MonadBaseControl Identity Identity
Instance details Defined in Control.Monad.Trans.Control Associated Types type StM Identity a :: Type # Methods liftBaseWith :: (RunInBase Identity Identity -> Identity a) -> Identity a # restoreM :: StM Identity a -> Identity a #
Sieve ReifiedGetter Identity
Instance details Defined in Control.Lens.Reified Methods sieve :: ReifiedGetter a b -> a -> Identity b #
Cosieve ReifiedGetter Identity
Instance details Defined in Control.Lens.Reified Methods cosieve :: ReifiedGetter a b -> Identity a -> b #
Monad m => Lift Identity m	This instance is incoherent with the others. However, by the law `lift (return x) == return x`, the results must always be the same.
Instance details Defined in Data.Random.Lift Methods lift :: Identity a -> m a #
MonadTrans t => Lift Identity (t Identity)	This instance is again incoherent with the others, but provides a more-specific instance to resolve the overlap between the `Lift m (t m)` and `Lift Identity m` instances.
Instance details Defined in Data.Random.Lift Methods lift :: Identity a -> t Identity a #
Bounded a => Bounded (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods minBound :: Identity a # maxBound :: Identity a #
Enum a => Enum (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods succ :: Identity a -> Identity a # pred :: Identity a -> Identity a # toEnum :: Int -> Identity a # fromEnum :: Identity a -> Int # enumFrom :: Identity a -> [Identity a] # enumFromThen :: Identity a -> Identity a -> [Identity a] # enumFromTo :: Identity a -> Identity a -> [Identity a] # enumFromThenTo :: Identity a -> Identity a -> Identity a -> [Identity a] #
Eq a => Eq (Identity a)	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods (==) :: Identity a -> Identity a -> Bool # (/=) :: Identity a -> Identity a -> Bool #
Floating a => Floating (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods pi :: Identity a # exp :: Identity a -> Identity a # log :: Identity a -> Identity a # sqrt :: Identity a -> Identity a # (**) :: Identity a -> Identity a -> Identity a # logBase :: Identity a -> Identity a -> Identity a # sin :: Identity a -> Identity a # cos :: Identity a -> Identity a # tan :: Identity a -> Identity a # asin :: Identity a -> Identity a # acos :: Identity a -> Identity a # atan :: Identity a -> Identity a # sinh :: Identity a -> Identity a # cosh :: Identity a -> Identity a # tanh :: Identity a -> Identity a # asinh :: Identity a -> Identity a # acosh :: Identity a -> Identity a # atanh :: Identity a -> Identity a # log1p :: Identity a -> Identity a # expm1 :: Identity a -> Identity a # log1pexp :: Identity a -> Identity a # log1mexp :: Identity a -> Identity a #
Fractional a => Fractional (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (/) :: Identity a -> Identity a -> Identity a # recip :: Identity a -> Identity a # fromRational :: Rational -> Identity a #
Integral a => Integral (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods quot :: Identity a -> Identity a -> Identity a # rem :: Identity a -> Identity a -> Identity a # div :: Identity a -> Identity a -> Identity a # mod :: Identity a -> Identity a -> Identity a # quotRem :: Identity a -> Identity a -> (Identity a, Identity a) # divMod :: Identity a -> Identity a -> (Identity a, Identity a) # toInteger :: Identity a -> Integer #
Num a => Num (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (+) :: Identity a -> Identity a -> Identity a # (-) :: Identity a -> Identity a -> Identity a # (*) :: Identity a -> Identity a -> Identity a # negate :: Identity a -> Identity a # abs :: Identity a -> Identity a # signum :: Identity a -> Identity a # fromInteger :: Integer -> Identity a #
Ord a => Ord (Identity a)	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods compare :: Identity a -> Identity a -> Ordering # (<) :: Identity a -> Identity a -> Bool # (<=) :: Identity a -> Identity a -> Bool # (>) :: Identity a -> Identity a -> Bool # (>=) :: Identity a -> Identity a -> Bool # max :: Identity a -> Identity a -> Identity a # min :: Identity a -> Identity a -> Identity a #
Read a => Read (Identity a)	This instance would be equivalent to the derived instances of the `Identity` newtype if the `runIdentity` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods readsPrec :: Int -> ReadS (Identity a) # readList :: ReadS [Identity a] # readPrec :: ReadPrec (Identity a) # readListPrec :: ReadPrec [Identity a] #
Real a => Real (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods toRational :: Identity a -> Rational #
RealFloat a => RealFloat (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods floatRadix :: Identity a -> Integer # floatDigits :: Identity a -> Int # floatRange :: Identity a -> (Int, Int) # decodeFloat :: Identity a -> (Integer, Int) # encodeFloat :: Integer -> Int -> Identity a # exponent :: Identity a -> Int # significand :: Identity a -> Identity a # scaleFloat :: Int -> Identity a -> Identity a # isNaN :: Identity a -> Bool # isInfinite :: Identity a -> Bool # isDenormalized :: Identity a -> Bool # isNegativeZero :: Identity a -> Bool # isIEEE :: Identity a -> Bool # atan2 :: Identity a -> Identity a -> Identity a #
RealFrac a => RealFrac (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods properFraction :: Integral b => Identity a -> (b, Identity a) # truncate :: Integral b => Identity a -> b # round :: Integral b => Identity a -> b # ceiling :: Integral b => Identity a -> b # floor :: Integral b => Identity a -> b #
Show a => Show (Identity a)	This instance would be equivalent to the derived instances of the `Identity` newtype if the `runIdentity` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods showsPrec :: Int -> Identity a -> ShowS # show :: Identity a -> String # showList :: [Identity a] -> ShowS #
Ix a => Ix (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods range :: (Identity a, Identity a) -> [Identity a] # index :: (Identity a, Identity a) -> Identity a -> Int # unsafeIndex :: (Identity a, Identity a) -> Identity a -> Int inRange :: (Identity a, Identity a) -> Identity a -> Bool # rangeSize :: (Identity a, Identity a) -> Int # unsafeRangeSize :: (Identity a, Identity a) -> Int
IsString a => IsString (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.String Methods fromString :: String -> Identity a #
Generic (Identity a)
Instance details Defined in Data.Functor.Identity Associated Types type Rep (Identity a) :: Type -> Type # Methods from :: Identity a -> Rep (Identity a) x # to :: Rep (Identity a) x -> Identity a #
Semigroup a => Semigroup (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (<>) :: Identity a -> Identity a -> Identity a # sconcat :: NonEmpty (Identity a) -> Identity a # stimes :: Integral b => b -> Identity a -> Identity a #
Monoid a => Monoid (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods mempty :: Identity a # mappend :: Identity a -> Identity a -> Identity a # mconcat :: [Identity a] -> Identity a #
ToJSON a => ToJSON (Identity a)
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSON :: Identity a -> Value # toEncoding :: Identity a -> Encoding # toJSONList :: [Identity a] -> Value # toEncodingList :: [Identity a] -> Encoding #
ToJSONKey a => ToJSONKey (Identity a)
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSONKey :: ToJSONKeyFunction (Identity a) # toJSONKeyList :: ToJSONKeyFunction [Identity a] #
Storable a => Storable (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods sizeOf :: Identity a -> Int # alignment :: Identity a -> Int # peekElemOff :: Ptr (Identity a) -> Int -> IO (Identity a) # pokeElemOff :: Ptr (Identity a) -> Int -> Identity a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Identity a) # pokeByteOff :: Ptr b -> Int -> Identity a -> IO () # peek :: Ptr (Identity a) -> IO (Identity a) # poke :: Ptr (Identity a) -> Identity a -> IO () #
Bits a => Bits (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods (.&.) :: Identity a -> Identity a -> Identity a # (.\|.) :: Identity a -> Identity a -> Identity a # xor :: Identity a -> Identity a -> Identity a # complement :: Identity a -> Identity a # shift :: Identity a -> Int -> Identity a # rotate :: Identity a -> Int -> Identity a # zeroBits :: Identity a # bit :: Int -> Identity a # setBit :: Identity a -> Int -> Identity a # clearBit :: Identity a -> Int -> Identity a # complementBit :: Identity a -> Int -> Identity a # testBit :: Identity a -> Int -> Bool # bitSizeMaybe :: Identity a -> Maybe Int # bitSize :: Identity a -> Int # isSigned :: Identity a -> Bool # shiftL :: Identity a -> Int -> Identity a # unsafeShiftL :: Identity a -> Int -> Identity a # shiftR :: Identity a -> Int -> Identity a # unsafeShiftR :: Identity a -> Int -> Identity a # rotateL :: Identity a -> Int -> Identity a # rotateR :: Identity a -> Int -> Identity a # popCount :: Identity a -> Int #
FiniteBits a => FiniteBits (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods finiteBitSize :: Identity a -> Int # countLeadingZeros :: Identity a -> Int # countTrailingZeros :: Identity a -> Int #
Wrapped (Identity a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Identity a) :: Type # Methods _Wrapped' :: Iso' (Identity a) (Unwrapped (Identity a)) #
Ixed (Identity a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Identity a) -> Traversal' (Identity a) (IxValue (Identity a)) #
Newtype (Identity a)	Since: newtype-generics-0.5.1
Instance details Defined in Control.Newtype.Generics Associated Types type O (Identity a) :: Type # Methods pack :: O (Identity a) -> Identity a # unpack :: Identity a -> O (Identity a) #
Pretty a => Pretty (Identity a)	`>>>` `pretty (Identity 1)`1
Instance details Defined in Data.Text.Prettyprint.Doc.Internal Methods pretty :: Identity a -> Doc ann # prettyList :: [Identity a] -> Doc ann #
Generic1 Identity
Instance details Defined in Data.Functor.Identity Associated Types type Rep1 Identity :: k -> Type # Methods from1 :: Identity a -> Rep1 Identity a # to1 :: Rep1 Identity a -> Identity a #
t ~ Identity b => Rewrapped (Identity a) t
Instance details Defined in Control.Lens.Wrapped
Lift (RVarT Identity) (RVarT m)
Instance details Defined in Data.Random.Lift Methods lift :: RVarT Identity a -> RVarT m a #
Field1 (Identity a) (Identity b) a b
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (Identity a) (Identity b) a b #
Each (Identity a) (Identity b) a b	`each` :: `Traversal` (`Identity` a) (`Identity` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Identity a) (Identity b) a b #
type Rep Identity
Instance details Defined in Data.Functor.Rep type Rep Identity = ()
type Diff Identity
Instance details Defined in Linear.Affine type Diff Identity = Identity
type StM Identity a
Instance details Defined in Control.Monad.Trans.Control type StM Identity a = a
type Rep (Identity a)	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity type Rep (Identity a) = D1 (MetaData "Identity" "Data.Functor.Identity" "base" True) (C1 (MetaCons "Identity" PrefixI True) (S1 (MetaSel (Just "runIdentity") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Unwrapped (Identity a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Identity a) = a
type IxValue (Identity a)
Instance details Defined in Control.Lens.At type IxValue (Identity a) = a
type Index (Identity a)
Instance details Defined in Control.Lens.At type Index (Identity a) = ()
type O (Identity a)
Instance details Defined in Control.Newtype.Generics type O (Identity a) = a
type Rep1 Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity type Rep1 Identity = D1 (MetaData "Identity" "Data.Functor.Identity" "base" True) (C1 (MetaCons "Identity" PrefixI True) (S1 (MetaSel (Just "runIdentity") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

simulate :: Rational -> Active a -> [a] #

simulate r act simulates the Active value act, returning a list of "snapshots" taken at regular intervals from the start time to the end time. The interval used is determined by the rate r, which denotes the "frame rate", that is, the number of snapshots per unit time.

If the Active value is constant (and thus has no start or end times), a list of length 1 is returned, containing the constant value.

discrete :: [a] -> Active a #

Create an Active which takes on each value in the given list in turn during the time [0,1], with each value getting an equal amount of time. In other words, discrete creates a "slide show" that starts at time 0 and ends at time 1. The first element is used prior to time 0, and the last element is used after time 1.

It is an error to call discrete on the empty list.

movie :: [Active a] -> Active a #

Splice together a list of active values using |>>. The list must be nonempty.

(|>>) :: Active a -> Active a -> Active a #

"Splice" two Active values together: shift the second to start immediately after the first (using after), and produce the value which acts like the first up to the common end/start point, then like the second after that. If both are constant, return the first.

(->>) :: Semigroup a => Active a -> Active a -> Active a infixr 5 #

Sequence/overlay two Active values: shift the second to start immediately after the first (using after), then compose them (using <>).

after :: Active a -> Active a -> Active a #

a1 `after` a2 produces an active that behaves like a1 but is shifted to start at the end time of a2. If either a1 or a2 are constant, a1 is returned unchanged.

atTime :: Time Rational -> Active a -> Active a #

atTime t a is an active value with the same behavior as a, shifted so that it starts at time t. If a is constant it is returned unchanged.

setEra :: Era Rational -> Active a -> Active a #

Set the era of an Active value. Note that this will change a constant Active into a dynamic one which happens to have the same value at all times.

trimAfter :: Monoid a => Active a -> Active a #

"Trim" an active value so that it is empty after the end of its era. For example, trimAfter ui can be visualized as

See the documentation of trim for more details.

trimBefore :: Monoid a => Active a -> Active a #

"Trim" an active value so that it is empty before the start of its era. For example, trimBefore ui can be visualized as

See the documentation of trim for more details.

trim :: Monoid a => Active a -> Active a #

"Trim" an active value so that it is empty outside its era. trim has no effect on constant values.

For example, trim ui can be visualized as

Actually, trim ui is not well-typed, since it is not guaranteed that ui's values will be monoidal (and usually they won't be)! But the above image still provides a good intuitive idea of what trim is doing. To make this precise we could consider something like trim (First . Just $ ui).

See also trimBefore and trimActive, which trim only before or after the era, respectively.

clampAfter :: Active a -> Active a #

"Clamp" an active value so that it is constant after the end of its era. For example, clampBefore ui can be visualized as

See the documentation of clamp for more information.

clampBefore :: Active a -> Active a #

"Clamp" an active value so that it is constant before the start of its era. For example, clampBefore ui can be visualized as

See the documentation of clamp for more information.

clamp :: Active a -> Active a #

"Clamp" an active value so that it is constant before and after its era. Before the era, clamp a takes on the value of a at the start of the era. Likewise, after the era, clamp a takes on the value of a at the end of the era. clamp has no effect on constant values.

For example, clamp ui can be visualized as

See also clampBefore and clampAfter, which clamp only before or after the era, respectively.

snapshot :: Time Rational -> Active a -> Active a #

Take a "snapshot" of an active value at a particular time, resulting in a constant value.

backwards :: Active a -> Active a #

Reverse an active value so the start of its era gets mapped to the end and vice versa. For example, backwards ui can be visualized as

shift :: Duration Rational -> Active a -> Active a #

shift d act shifts the start time of act by duration d. Has no effect on constant values.

during :: Active a -> Active a -> Active a #

a1 `during` a2 stretches and shifts a1 so that it has the same era as a2. Has no effect if either of a1 or a2 are constant.

stretchTo :: Duration Rational -> Active a -> Active a #

stretchTo d stretches an Active so it has duration d. Has no effect if (1) d is non-positive, or (2) the Active value is constant, or (3) the Active value has zero duration. [AJG: conditions (1) and (3) no longer true: to consider changing]

stretch :: Rational -> Active a -> Active a #

stretch s act "stretches" the active act so that it takes s times as long (retaining the same start time).

interval :: Fractional a => Time Rational -> Time Rational -> Active a #

interval a b is an active value starting at time a, ending at time b, and taking the value t at time t.

ui :: Fractional a => Active a #

ui represents the unit interval, which takes on the value t at time t, and has as its era [0,1]. It is equivalent to interval 0 1, and can be visualized as follows:

On the x-axis is time, and the value that ui takes on is on the y-axis. The shaded portion represents the era. Note that the value of ui (as with any active) is still defined outside its era, and this can make a difference when it is combined with other active values with different eras. Applying a function with fmap affects all values, both inside and outside the era. To manipulate values outside the era specifically, see clamp and trim.

To alter the values that ui takes on without altering its era, use its Functor and Applicative instances. For example, (*2) <$> ui varies from 0 to 2 over the era [0,1]. To alter the era, you can use stretch or shift.

isDynamic :: Active a -> Bool #

Test whether an Active value is Dynamic.

isConstant :: Active a -> Bool #

Test whether an Active value is constant.

activeEra :: Active a -> Maybe (Era Rational) #

Get the Era of an Active value (or Nothing if it is a constant/pure value).

activeEnd :: Active a -> a #

Get the value of an Active a at the end of its era.

activeStart :: Active a -> a #

Get the value of an Active a at the beginning of its era.

runActive :: Active a -> Time Rational -> a #

Interpret an Active value as a function from time.

modActive :: (a -> b) -> (Dynamic a -> Dynamic b) -> Active a -> Active b #

Modify an Active value using a case analysis to see whether it is constant or dynamic.

onActive :: (a -> b) -> (Dynamic a -> b) -> Active a -> b #

Fold for Actives. Process an 'Active a', given a function to apply if it is a pure (constant) value, and a function to apply if it is a Dynamic.

mkActive :: Time Rational -> Time Rational -> (Time Rational -> a) -> Active a #

Create a dynamic Active from a start time, an end time, and a time-varying value.

fromDynamic :: Dynamic a -> Active a #

Create an Active value from a Dynamic.

shiftDynamic :: Duration Rational -> Dynamic a -> Dynamic a #

Shift a Dynamic value by a certain duration.

onDynamic :: (Time Rational -> Time Rational -> (Time Rational -> a) -> b) -> Dynamic a -> b #

Fold for Dynamic.

mkDynamic :: Time Rational -> Time Rational -> (Time Rational -> a) -> Dynamic a #

Create a Dynamic from a start time, an end time, and a time-varying value.

duration :: Num n => Era n -> Duration n #

Compute the Duration of an Era.

end :: Era n -> Time n #

Get the end Time of an Era.

start :: Era n -> Time n #

Get the start Time of an Era.

mkEra :: Time n -> Time n -> Era n #

Create an Era by specifying start and end Times.

fromDuration :: Duration n -> n #

A convenient unwrapper function to turn a duration into a numeric value.

toDuration :: n -> Duration n #

A convenient wrapper function to convert a numeric value into a duration.

data Era n #

An Era is a concrete span of time, that is, a pair of times representing the start and end of the era. Eras form a semigroup: the combination of two Eras is the smallest Era which contains both. They do not form a Monoid, since there is no Era which acts as the identity with respect to this combining operation.

Era is abstract. To construct Era values, use mkEra; to deconstruct, use start and end.

Instances

Show n => Show (Era n)
Instance details Defined in Data.Active Methods showsPrec :: Int -> Era n -> ShowS # show :: Era n -> String # showList :: [Era n] -> ShowS #
Ord n => Semigroup (Era n)
Instance details Defined in Data.Active Methods (<>) :: Era n -> Era n -> Era n # sconcat :: NonEmpty (Era n) -> Era n # stimes :: Integral b => b -> Era n -> Era n #

data Dynamic a #

A Dynamic a can be thought of as an a value that changes over the course of a particular Era. It's envisioned that Dynamic will be mostly an internal implementation detail and that Active will be most commonly used. But you never know what uses people might find for things.

Constructors

Dynamic
Fields era :: Era Rational runDynamic :: Time Rational -> a

Instances

Functor Dynamic
Instance details Defined in Data.Active Methods fmap :: (a -> b) -> Dynamic a -> Dynamic b # (<$) :: a -> Dynamic b -> Dynamic a #
Apply Dynamic	`Dynamic` is an instance of `Apply` (i.e. `Applicative` without `pure`): a time-varying function is applied to a time-varying value pointwise; the era of the result is the combination of the function and value eras. Note, however, that `Dynamic` is not an instance of `Applicative` since there is no way to implement `pure`: the era would have to be empty, but there is no such thing as an empty era (that is, `Era` is not an instance of `Monoid`).
Instance details Defined in Data.Active Methods (<.>) :: Dynamic (a -> b) -> Dynamic a -> Dynamic b # (.>) :: Dynamic a -> Dynamic b -> Dynamic b # (<.) :: Dynamic a -> Dynamic b -> Dynamic a # liftF2 :: (a -> b -> c) -> Dynamic a -> Dynamic b -> Dynamic c #
Semigroup a => Semigroup (Dynamic a)	`Dynamic a` is a `Semigroup` whenever `a` is: the eras are combined according to their semigroup structure, and the values of type `a` are combined pointwise. Note that `Dynamic a` cannot be an instance of `Monoid` since `Era` is not.
Instance details Defined in Data.Active Methods (<>) :: Dynamic a -> Dynamic a -> Dynamic a # sconcat :: NonEmpty (Dynamic a) -> Dynamic a # stimes :: Integral b => b -> Dynamic a -> Dynamic a #

data Active a #

There are two types of Active values:

An Active can simply be a Dynamic, that is, a time-varying value with start and end times.
An Active value can also be a constant: a single value, constant across time, with no start and end times.

The addition of constant values enable Monoid and Applicative instances for Active.

Instances

Functor Active
Instance details Defined in Data.Active Methods fmap :: (a -> b) -> Active a -> Active b # (<$) :: a -> Active b -> Active a #
Applicative Active
Instance details Defined in Data.Active Methods pure :: a -> Active a # (<>) :: Active (a -> b) -> Active a -> Active b # liftA2 :: (a -> b -> c) -> Active a -> Active b -> Active c # (>) :: Active a -> Active b -> Active b # (<*) :: Active a -> Active b -> Active a #
Apply Active
Instance details Defined in Data.Active Methods (<.>) :: Active (a -> b) -> Active a -> Active b # (.>) :: Active a -> Active b -> Active b # (<.) :: Active a -> Active b -> Active a # liftF2 :: (a -> b -> c) -> Active a -> Active b -> Active c #
Semigroup a => Semigroup (Active a)	Active values over a type with a `Semigroup` instance are also an instance of `Semigroup`. Two active values are combined pointwise; the resulting value is constant iff both inputs are.
Instance details Defined in Data.Active Methods (<>) :: Active a -> Active a -> Active a # sconcat :: NonEmpty (Active a) -> Active a # stimes :: Integral b => b -> Active a -> Active a #
(Monoid a, Semigroup a) => Monoid (Active a)
Instance details Defined in Data.Active Methods mempty :: Active a # mappend :: Active a -> Active a -> Active a # mconcat :: [Active a] -> Active a #
Wrapped (Active a)
Instance details Defined in Data.Active Associated Types type Unwrapped (Active a) :: Type # Methods _Wrapped' :: Iso' (Active a) (Unwrapped (Active a)) #
Active a1 ~ t => Rewrapped (Active a2) t
Instance details Defined in Data.Active
type V (Active a)
Instance details Defined in Diagrams.Animation.Active type V (Active a) = V a
type N (Active a)
Instance details Defined in Diagrams.Animation.Active type N (Active a) = N a
type Unwrapped (Active a)
Instance details Defined in Data.Active type Unwrapped (Active a) = MaybeApply Dynamic a

fromTime :: Time n -> n #

A convenient unwrapper function to turn a time into a numeric value.

toTime :: n -> Time n #

A convenient wrapper function to convert a numeric value into a time.

data Duration n #

An abstract type representing elapsed time between two points in time. Note that durations can be negative. Literal numeric values may be used as Durations thanks to the Num and Fractional instances.

Instances

Functor Duration
Instance details Defined in Data.Active Methods fmap :: (a -> b) -> Duration a -> Duration b # (<$) :: a -> Duration b -> Duration a #
Applicative Duration
Instance details Defined in Data.Active Methods pure :: a -> Duration a # (<>) :: Duration (a -> b) -> Duration a -> Duration b # liftA2 :: (a -> b -> c) -> Duration a -> Duration b -> Duration c # (>) :: Duration a -> Duration b -> Duration b # (<*) :: Duration a -> Duration b -> Duration a #
Additive Duration
Instance details Defined in Data.Active Methods zero :: Num a => Duration a # (^+^) :: Num a => Duration a -> Duration a -> Duration a # (^-^) :: Num a => Duration a -> Duration a -> Duration a # lerp :: Num a => a -> Duration a -> Duration a -> Duration a # liftU2 :: (a -> a -> a) -> Duration a -> Duration a -> Duration a # liftI2 :: (a -> b -> c) -> Duration a -> Duration b -> Duration c #
Enum n => Enum (Duration n)
Instance details Defined in Data.Active Methods succ :: Duration n -> Duration n # pred :: Duration n -> Duration n # toEnum :: Int -> Duration n # fromEnum :: Duration n -> Int # enumFrom :: Duration n -> [Duration n] # enumFromThen :: Duration n -> Duration n -> [Duration n] # enumFromTo :: Duration n -> Duration n -> [Duration n] # enumFromThenTo :: Duration n -> Duration n -> Duration n -> [Duration n] #
Eq n => Eq (Duration n)
Instance details Defined in Data.Active Methods (==) :: Duration n -> Duration n -> Bool # (/=) :: Duration n -> Duration n -> Bool #
Fractional n => Fractional (Duration n)
Instance details Defined in Data.Active Methods (/) :: Duration n -> Duration n -> Duration n # recip :: Duration n -> Duration n # fromRational :: Rational -> Duration n #
Num n => Num (Duration n)
Instance details Defined in Data.Active Methods (+) :: Duration n -> Duration n -> Duration n # (-) :: Duration n -> Duration n -> Duration n # (*) :: Duration n -> Duration n -> Duration n # negate :: Duration n -> Duration n # abs :: Duration n -> Duration n # signum :: Duration n -> Duration n # fromInteger :: Integer -> Duration n #
Ord n => Ord (Duration n)
Instance details Defined in Data.Active Methods compare :: Duration n -> Duration n -> Ordering # (<) :: Duration n -> Duration n -> Bool # (<=) :: Duration n -> Duration n -> Bool # (>) :: Duration n -> Duration n -> Bool # (>=) :: Duration n -> Duration n -> Bool # max :: Duration n -> Duration n -> Duration n # min :: Duration n -> Duration n -> Duration n #
Read n => Read (Duration n)
Instance details Defined in Data.Active Methods readsPrec :: Int -> ReadS (Duration n) # readList :: ReadS [Duration n] # readPrec :: ReadPrec (Duration n) # readListPrec :: ReadPrec [Duration n] #
Real n => Real (Duration n)
Instance details Defined in Data.Active Methods toRational :: Duration n -> Rational #
RealFrac n => RealFrac (Duration n)
Instance details Defined in Data.Active Methods properFraction :: Integral b => Duration n -> (b, Duration n) # truncate :: Integral b => Duration n -> b # round :: Integral b => Duration n -> b # ceiling :: Integral b => Duration n -> b # floor :: Integral b => Duration n -> b #
Show n => Show (Duration n)
Instance details Defined in Data.Active Methods showsPrec :: Int -> Duration n -> ShowS # show :: Duration n -> String # showList :: [Duration n] -> ShowS #
Num n => Semigroup (Duration n)
Instance details Defined in Data.Active Methods (<>) :: Duration n -> Duration n -> Duration n # sconcat :: NonEmpty (Duration n) -> Duration n # stimes :: Integral b => b -> Duration n -> Duration n #
Num n => Monoid (Duration n)
Instance details Defined in Data.Active Methods mempty :: Duration n # mappend :: Duration n -> Duration n -> Duration n # mconcat :: [Duration n] -> Duration n #
Wrapped (Duration n)
Instance details Defined in Data.Active Associated Types type Unwrapped (Duration n) :: Type # Methods _Wrapped' :: Iso' (Duration n) (Unwrapped (Duration n)) #
Duration n1 ~ t => Rewrapped (Duration n2) t
Instance details Defined in Data.Active
type Unwrapped (Duration n)
Instance details Defined in Data.Active type Unwrapped (Duration n) = n

data Time n #

An abstract type for representing points in time. Note that literal numeric values may be used as Times, thanks to the the Num and Fractional instances.

Instances

Functor Time
Instance details Defined in Data.Active Methods fmap :: (a -> b) -> Time a -> Time b # (<$) :: a -> Time b -> Time a #
Affine Time
Instance details Defined in Data.Active Associated Types type Diff Time :: Type -> Type # Methods (.-.) :: Num a => Time a -> Time a -> Diff Time a # (.+^) :: Num a => Time a -> Diff Time a -> Time a # (.-^) :: Num a => Time a -> Diff Time a -> Time a #
Enum n => Enum (Time n)
Instance details Defined in Data.Active Methods succ :: Time n -> Time n # pred :: Time n -> Time n # toEnum :: Int -> Time n # fromEnum :: Time n -> Int # enumFrom :: Time n -> [Time n] # enumFromThen :: Time n -> Time n -> [Time n] # enumFromTo :: Time n -> Time n -> [Time n] # enumFromThenTo :: Time n -> Time n -> Time n -> [Time n] #
Eq n => Eq (Time n)
Instance details Defined in Data.Active Methods (==) :: Time n -> Time n -> Bool # (/=) :: Time n -> Time n -> Bool #
Fractional n => Fractional (Time n)
Instance details Defined in Data.Active Methods (/) :: Time n -> Time n -> Time n # recip :: Time n -> Time n # fromRational :: Rational -> Time n #
Num n => Num (Time n)
Instance details Defined in Data.Active Methods (+) :: Time n -> Time n -> Time n # (-) :: Time n -> Time n -> Time n # (*) :: Time n -> Time n -> Time n # negate :: Time n -> Time n # abs :: Time n -> Time n # signum :: Time n -> Time n # fromInteger :: Integer -> Time n #
Ord n => Ord (Time n)
Instance details Defined in Data.Active Methods compare :: Time n -> Time n -> Ordering # (<) :: Time n -> Time n -> Bool # (<=) :: Time n -> Time n -> Bool # (>) :: Time n -> Time n -> Bool # (>=) :: Time n -> Time n -> Bool # max :: Time n -> Time n -> Time n # min :: Time n -> Time n -> Time n #
Read n => Read (Time n)
Instance details Defined in Data.Active Methods readsPrec :: Int -> ReadS (Time n) # readList :: ReadS [Time n] # readPrec :: ReadPrec (Time n) # readListPrec :: ReadPrec [Time n] #
Real n => Real (Time n)
Instance details Defined in Data.Active Methods toRational :: Time n -> Rational #
RealFrac n => RealFrac (Time n)
Instance details Defined in Data.Active Methods properFraction :: Integral b => Time n -> (b, Time n) # truncate :: Integral b => Time n -> b # round :: Integral b => Time n -> b # ceiling :: Integral b => Time n -> b # floor :: Integral b => Time n -> b #
Show n => Show (Time n)
Instance details Defined in Data.Active Methods showsPrec :: Int -> Time n -> ShowS # show :: Time n -> String # showList :: [Time n] -> ShowS #
Wrapped (Time n)
Instance details Defined in Data.Active Associated Types type Unwrapped (Time n) :: Type # Methods _Wrapped' :: Iso' (Time n) (Unwrapped (Time n)) #
Time n1 ~ t => Rewrapped (Time n2) t
Instance details Defined in Data.Active
type Diff Time
Instance details Defined in Data.Active type Diff Time = Duration
type Unwrapped (Time n)
Instance details Defined in Data.Active type Unwrapped (Time n) = n

class Contravariant (f :: Type -> Type) where #

The class of contravariant functors.

Whereas in Haskell, one can think of a Functor as containing or producing values, a contravariant functor is a functor that can be thought of as consuming values.

As an example, consider the type of predicate functions a -> Bool. One such predicate might be negative x = x < 0, which classifies integers as to whether they are negative. However, given this predicate, we can re-use it in other situations, providing we have a way to map values to integers. For instance, we can use the negative predicate on a person's bank balance to work out if they are currently overdrawn:

newtype Predicate a = Predicate { getPredicate :: a -> Bool }

instance Contravariant Predicate where
  contramap f (Predicate p) = Predicate (p . f)
                                         |   `- First, map the input...
                                         `----- then apply the predicate.

overdrawn :: Predicate Person
overdrawn = contramap personBankBalance negative

Any instance should be subject to the following laws:

contramap id = id
contramap f . contramap g = contramap (g . f)

Note, that the second law follows from the free theorem of the type of contramap and the first law, so you need only check that the former condition holds.

Minimal complete definition

contramap

Methods

contramap :: (a -> b) -> f b -> f a #

(>$) :: b -> f b -> f a infixl 4 #

Replace all locations in the output with the same value. The default definition is contramap . const, but this may be overridden with a more efficient version.

Instances

Contravariant ToJSONKeyFunction
Instance details Defined in Data.Aeson.Types.ToJSON Methods contramap :: (a -> b) -> ToJSONKeyFunction b -> ToJSONKeyFunction a # (>$) :: b -> ToJSONKeyFunction b -> ToJSONKeyFunction a #
Contravariant Predicate	A `Predicate` is a `Contravariant` `Functor`, because `contramap` can apply its function argument to the input of the predicate.
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Predicate b -> Predicate a # (>$) :: b -> Predicate b -> Predicate a #
Contravariant Comparison	A `Comparison` is a `Contravariant` `Functor`, because `contramap` can apply its function argument to each input of the comparison function.
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Comparison b -> Comparison a # (>$) :: b -> Comparison b -> Comparison a #
Contravariant Equivalence	Equivalence relations are `Contravariant`, because you can apply the contramapped function to each input to the equivalence relation.
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Equivalence b -> Equivalence a # (>$) :: b -> Equivalence b -> Equivalence a #
Contravariant Headless
Instance details Defined in Colonnade.Encode Methods contramap :: (a -> b) -> Headless b -> Headless a # (>$) :: b -> Headless b -> Headless a #
Contravariant (V1 :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> V1 b -> V1 a # (>$) :: b -> V1 b -> V1 a #
Contravariant (U1 :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> U1 b -> U1 a # (>$) :: b -> U1 b -> U1 a #
Contravariant (Op a)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a0 -> b) -> Op a b -> Op a a0 # (>$) :: b -> Op a b -> Op a a0 #
Contravariant (Proxy :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Proxy b -> Proxy a # (>$) :: b -> Proxy b -> Proxy a #
Contravariant m => Contravariant (MaybeT m)
Instance details Defined in Control.Monad.Trans.Maybe Methods contramap :: (a -> b) -> MaybeT m b -> MaybeT m a # (>$) :: b -> MaybeT m b -> MaybeT m a #
Contravariant f => Contravariant (Indexing f)
Instance details Defined in Control.Lens.Internal.Indexed Methods contramap :: (a -> b) -> Indexing f b -> Indexing f a # (>$) :: b -> Indexing f b -> Indexing f a #
Contravariant f => Contravariant (Indexing64 f)
Instance details Defined in Control.Lens.Internal.Indexed Methods contramap :: (a -> b) -> Indexing64 f b -> Indexing64 f a # (>$) :: b -> Indexing64 f b -> Indexing64 f a #
Contravariant m => Contravariant (ListT m)
Instance details Defined in Control.Monad.Trans.List Methods contramap :: (a -> b) -> ListT m b -> ListT m a # (>$) :: b -> ListT m b -> ListT m a #
Contravariant f => Contravariant (Rec1 f)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Rec1 f b -> Rec1 f a # (>$) :: b -> Rec1 f b -> Rec1 f a #
Contravariant f => Contravariant (IdentityT f)
Instance details Defined in Control.Monad.Trans.Identity Methods contramap :: (a -> b) -> IdentityT f b -> IdentityT f a # (>$) :: b -> IdentityT f b -> IdentityT f a #
Contravariant (Const a :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a0 -> b) -> Const a b -> Const a a0 # (>$) :: b -> Const a b -> Const a a0 #
Contravariant f => Contravariant (Alt f)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Alt f b -> Alt f a # (>$) :: b -> Alt f b -> Alt f a #
Contravariant m => Contravariant (ExceptT e m)
Instance details Defined in Control.Monad.Trans.Except Methods contramap :: (a -> b) -> ExceptT e m b -> ExceptT e m a # (>$) :: b -> ExceptT e m b -> ExceptT e m a #
Contravariant m => Contravariant (ErrorT e m)
Instance details Defined in Control.Monad.Trans.Error Methods contramap :: (a -> b) -> ErrorT e m b -> ErrorT e m a # (>$) :: b -> ErrorT e m b -> ErrorT e m a #
Contravariant m => Contravariant (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Strict Methods contramap :: (a -> b) -> StateT s m b -> StateT s m a # (>$) :: b -> StateT s m b -> StateT s m a #
Contravariant f => Contravariant (Backwards f)	Derived instance.
Instance details Defined in Control.Applicative.Backwards Methods contramap :: (a -> b) -> Backwards f b -> Backwards f a # (>$) :: b -> Backwards f b -> Backwards f a #
Contravariant f => Contravariant (AlongsideLeft f b)
Instance details Defined in Control.Lens.Internal.Getter Methods contramap :: (a -> b0) -> AlongsideLeft f b b0 -> AlongsideLeft f b a # (>$) :: b0 -> AlongsideLeft f b b0 -> AlongsideLeft f b a #
Contravariant f => Contravariant (AlongsideRight f a)
Instance details Defined in Control.Lens.Internal.Getter Methods contramap :: (a0 -> b) -> AlongsideRight f a b -> AlongsideRight f a a0 # (>$) :: b -> AlongsideRight f a b -> AlongsideRight f a a0 #
Contravariant m => Contravariant (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods contramap :: (a -> b) -> WriterT w m b -> WriterT w m a # (>$) :: b -> WriterT w m b -> WriterT w m a #
Contravariant m => Contravariant (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods contramap :: (a -> b) -> StateT s m b -> StateT s m a # (>$) :: b -> StateT s m b -> StateT s m a #
Contravariant m => Contravariant (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods contramap :: (a -> b) -> WriterT w m b -> WriterT w m a # (>$) :: b -> WriterT w m b -> WriterT w m a #
Contravariant f => Contravariant (Reverse f)	Derived instance.
Instance details Defined in Data.Functor.Reverse Methods contramap :: (a -> b) -> Reverse f b -> Reverse f a # (>$) :: b -> Reverse f b -> Reverse f a #
Contravariant (K1 i c :: Type -> Type)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> K1 i c b -> K1 i c a # (>$) :: b -> K1 i c b -> K1 i c a #
(Contravariant f, Contravariant g) => Contravariant (f :+: g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> (f :+: g) b -> (f :+: g) a # (>$) :: b -> (f :+: g) b -> (f :+: g) a #
(Contravariant f, Contravariant g) => Contravariant (f :*: g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> (f :: g) b -> (f :: g) a # (>$) :: b -> (f :: g) b -> (f :: g) a #
(Contravariant f, Contravariant g) => Contravariant (Product f g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Product f g b -> Product f g a # (>$) :: b -> Product f g b -> Product f g a #
(Contravariant f, Contravariant g) => Contravariant (Sum f g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Sum f g b -> Sum f g a # (>$) :: b -> Sum f g b -> Sum f g a #
Contravariant m => Contravariant (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods contramap :: (a -> b) -> ReaderT r m b -> ReaderT r m a # (>$) :: b -> ReaderT r m b -> ReaderT r m a #
Contravariant f => Contravariant (M1 i c f)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> M1 i c f b -> M1 i c f a # (>$) :: b -> M1 i c f b -> M1 i c f a #
(Functor f, Contravariant g) => Contravariant (f :.: g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> (f :.: g) b -> (f :.: g) a # (>$) :: b -> (f :.: g) b -> (f :.: g) a #
(Functor f, Contravariant g) => Contravariant (Compose f g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Compose f g b -> Compose f g a # (>$) :: b -> Compose f g b -> Compose f g a #
Contravariant m => Contravariant (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Strict Methods contramap :: (a -> b) -> RWST r w s m b -> RWST r w s m a # (>$) :: b -> RWST r w s m b -> RWST r w s m a #
Contravariant f => Contravariant (TakingWhile p f a b)
Instance details Defined in Control.Lens.Internal.Magma Methods contramap :: (a0 -> b0) -> TakingWhile p f a b b0 -> TakingWhile p f a b a0 # (>$) :: b0 -> TakingWhile p f a b b0 -> TakingWhile p f a b a0 #
(Profunctor p, Contravariant g) => Contravariant (BazaarT p g a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods contramap :: (a0 -> b0) -> BazaarT p g a b b0 -> BazaarT p g a b a0 # (>$) :: b0 -> BazaarT p g a b b0 -> BazaarT p g a b a0 #
(Profunctor p, Contravariant g) => Contravariant (BazaarT1 p g a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods contramap :: (a0 -> b0) -> BazaarT1 p g a b b0 -> BazaarT1 p g a b a0 # (>$) :: b0 -> BazaarT1 p g a b b0 -> BazaarT1 p g a b a0 #
(Profunctor p, Contravariant g) => Contravariant (PretextT p g a b)
Instance details Defined in Control.Lens.Internal.Context Methods contramap :: (a0 -> b0) -> PretextT p g a b b0 -> PretextT p g a b a0 # (>$) :: b0 -> PretextT p g a b b0 -> PretextT p g a b a0 #
Contravariant m => Contravariant (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Lazy Methods contramap :: (a -> b) -> RWST r w s m b -> RWST r w s m a # (>$) :: b -> RWST r w s m b -> RWST r w s m a #

option :: b -> (a -> b) -> Option a -> b #

Fold an Option case-wise, just like maybe.

mtimesDefault :: (Integral b, Monoid a) => b -> a -> a #

Repeat a value n times.

mtimesDefault n a = a <> a <> ... <> a  -- using <> (n-1) times

Implemented using stimes and mempty.

This is a suitable definition for an mtimes member of Monoid.

diff :: Semigroup m => m -> Endo m #

This lets you use a difference list of a Semigroup as a Monoid.

cycle1 :: Semigroup m => m -> m #

A generalization of cycle to an arbitrary Semigroup. May fail to terminate for some values in some semigroups.

newtype Min a #

Constructors

Min
Fields getMin :: a

Instances

Monad Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Min a -> (a -> Min b) -> Min b # (>>) :: Min a -> Min b -> Min b # return :: a -> Min a # fail :: String -> Min a #
Functor Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Min a -> Min b # (<$) :: a -> Min b -> Min a #
MonadFix Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mfix :: (a -> Min a) -> Min a #
Applicative Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Min a # (<>) :: Min (a -> b) -> Min a -> Min b # liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c # (>) :: Min a -> Min b -> Min b # (<*) :: Min a -> Min b -> Min a #
Foldable Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Min m -> m # foldMap :: Monoid m => (a -> m) -> Min a -> m # foldr :: (a -> b -> b) -> b -> Min a -> b # foldr' :: (a -> b -> b) -> b -> Min a -> b # foldl :: (b -> a -> b) -> b -> Min a -> b # foldl' :: (b -> a -> b) -> b -> Min a -> b # foldr1 :: (a -> a -> a) -> Min a -> a # foldl1 :: (a -> a -> a) -> Min a -> a # toList :: Min a -> [a] # null :: Min a -> Bool # length :: Min a -> Int # elem :: Eq a => a -> Min a -> Bool # maximum :: Ord a => Min a -> a # minimum :: Ord a => Min a -> a # sum :: Num a => Min a -> a # product :: Num a => Min a -> a #
Traversable Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Min a -> f (Min b) # sequenceA :: Applicative f => Min (f a) -> f (Min a) # mapM :: Monad m => (a -> m b) -> Min a -> m (Min b) # sequence :: Monad m => Min (m a) -> m (Min a) #
Apply Min
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Min (a -> b) -> Min a -> Min b # (.>) :: Min a -> Min b -> Min b # (<.) :: Min a -> Min b -> Min a # liftF2 :: (a -> b -> c) -> Min a -> Min b -> Min c #
ToJSON1 Min
Instance details Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a -> Value) -> ([a] -> Value) -> Min a -> Value # liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [Min a] -> Value # liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> Min a -> Encoding # liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [Min a] -> Encoding #
Traversable1 Min
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Min a -> f (Min b) # sequence1 :: Apply f => Min (f b) -> f (Min b) #
Bind Min
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Min a -> (a -> Min b) -> Min b # join :: Min (Min a) -> Min a #
Bounded a => Bounded (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: Min a # maxBound :: Min a #
Enum a => Enum (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: Min a -> Min a # pred :: Min a -> Min a # toEnum :: Int -> Min a # fromEnum :: Min a -> Int # enumFrom :: Min a -> [Min a] # enumFromThen :: Min a -> Min a -> [Min a] # enumFromTo :: Min a -> Min a -> [Min a] # enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] #
Eq a => Eq (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Min a -> Min a -> Bool # (/=) :: Min a -> Min a -> Bool #
Data a => Data (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Min a -> c (Min a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Min a) # toConstr :: Min a -> Constr # dataTypeOf :: Min a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Min a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Min a)) # gmapT :: (forall b. Data b => b -> b) -> Min a -> Min a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r # gmapQ :: (forall d. Data d => d -> u) -> Min a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Min a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) #
Num a => Num (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (+) :: Min a -> Min a -> Min a # (-) :: Min a -> Min a -> Min a # (*) :: Min a -> Min a -> Min a # negate :: Min a -> Min a # abs :: Min a -> Min a # signum :: Min a -> Min a # fromInteger :: Integer -> Min a #
Ord a => Ord (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Min a -> Min a -> Ordering # (<) :: Min a -> Min a -> Bool # (<=) :: Min a -> Min a -> Bool # (>) :: Min a -> Min a -> Bool # (>=) :: Min a -> Min a -> Bool # max :: Min a -> Min a -> Min a # min :: Min a -> Min a -> Min a #
Read a => Read (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Min a) # readList :: ReadS [Min a] # readPrec :: ReadPrec (Min a) # readListPrec :: ReadPrec [Min a] #
Show a => Show (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Min a -> ShowS # show :: Min a -> String # showList :: [Min a] -> ShowS #
Generic (Min a)
Instance details Defined in Data.Semigroup Associated Types type Rep (Min a) :: Type -> Type # Methods from :: Min a -> Rep (Min a) x # to :: Rep (Min a) x -> Min a #
Ord a => Semigroup (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Min a -> Min a -> Min a # sconcat :: NonEmpty (Min a) -> Min a # stimes :: Integral b => b -> Min a -> Min a #
(Ord a, Bounded a) => Monoid (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Min a # mappend :: Min a -> Min a -> Min a # mconcat :: [Min a] -> Min a #
ToJSON a => ToJSON (Min a)
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSON :: Min a -> Value # toEncoding :: Min a -> Encoding # toJSONList :: [Min a] -> Value # toEncodingList :: [Min a] -> Encoding #
Wrapped (Min a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Min a) :: Type # Methods _Wrapped' :: Iso' (Min a) (Unwrapped (Min a)) #
Newtype (Min a)	Since: newtype-generics-0.5.1
Instance details Defined in Control.Newtype.Generics Associated Types type O (Min a) :: Type # Methods pack :: O (Min a) -> Min a # unpack :: Min a -> O (Min a) #
Generic1 Min
Instance details Defined in Data.Semigroup Associated Types type Rep1 Min :: k -> Type # Methods from1 :: Min a -> Rep1 Min a # to1 :: Rep1 Min a -> Min a #
t ~ Min b => Rewrapped (Min a) t
Instance details Defined in Control.Lens.Wrapped
type Rep (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (Min a) = D1 (MetaData "Min" "Data.Semigroup" "base" True) (C1 (MetaCons "Min" PrefixI True) (S1 (MetaSel (Just "getMin") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Unwrapped (Min a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Min a) = a
type O (Min a)
Instance details Defined in Control.Newtype.Generics type O (Min a) = a
type Rep1 Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 Min = D1 (MetaData "Min" "Data.Semigroup" "base" True) (C1 (MetaCons "Min" PrefixI True) (S1 (MetaSel (Just "getMin") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Max a #

Constructors

Max
Fields getMax :: a

Instances

Monad Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Max a -> (a -> Max b) -> Max b # (>>) :: Max a -> Max b -> Max b # return :: a -> Max a # fail :: String -> Max a #
Functor Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Max a -> Max b # (<$) :: a -> Max b -> Max a #
MonadFix Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mfix :: (a -> Max a) -> Max a #
Applicative Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Max a # (<>) :: Max (a -> b) -> Max a -> Max b # liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c # (>) :: Max a -> Max b -> Max b # (<*) :: Max a -> Max b -> Max a #
Foldable Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Max m -> m # foldMap :: Monoid m => (a -> m) -> Max a -> m # foldr :: (a -> b -> b) -> b -> Max a -> b # foldr' :: (a -> b -> b) -> b -> Max a -> b # foldl :: (b -> a -> b) -> b -> Max a -> b # foldl' :: (b -> a -> b) -> b -> Max a -> b # foldr1 :: (a -> a -> a) -> Max a -> a # foldl1 :: (a -> a -> a) -> Max a -> a # toList :: Max a -> [a] # null :: Max a -> Bool # length :: Max a -> Int # elem :: Eq a => a -> Max a -> Bool # maximum :: Ord a => Max a -> a # minimum :: Ord a => Max a -> a # sum :: Num a => Max a -> a # product :: Num a => Max a -> a #
Traversable Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Max a -> f (Max b) # sequenceA :: Applicative f => Max (f a) -> f (Max a) # mapM :: Monad m => (a -> m b) -> Max a -> m (Max b) # sequence :: Monad m => Max (m a) -> m (Max a) #
Apply Max
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Max (a -> b) -> Max a -> Max b # (.>) :: Max a -> Max b -> Max b # (<.) :: Max a -> Max b -> Max a # liftF2 :: (a -> b -> c) -> Max a -> Max b -> Max c #
ToJSON1 Max
Instance details Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a -> Value) -> ([a] -> Value) -> Max a -> Value # liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [Max a] -> Value # liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> Max a -> Encoding # liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [Max a] -> Encoding #
Traversable1 Max
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Max a -> f (Max b) # sequence1 :: Apply f => Max (f b) -> f (Max b) #
Bind Max
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Max a -> (a -> Max b) -> Max b # join :: Max (Max a) -> Max a #
Bounded a => Bounded (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: Max a # maxBound :: Max a #
Enum a => Enum (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: Max a -> Max a # pred :: Max a -> Max a # toEnum :: Int -> Max a # fromEnum :: Max a -> Int # enumFrom :: Max a -> [Max a] # enumFromThen :: Max a -> Max a -> [Max a] # enumFromTo :: Max a -> Max a -> [Max a] # enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] #
Eq a => Eq (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Max a -> Max a -> Bool # (/=) :: Max a -> Max a -> Bool #
Data a => Data (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Max a -> c (Max a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Max a) # toConstr :: Max a -> Constr # dataTypeOf :: Max a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Max a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Max a)) # gmapT :: (forall b. Data b => b -> b) -> Max a -> Max a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r # gmapQ :: (forall d. Data d => d -> u) -> Max a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Max a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) #
Num a => Num (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (+) :: Max a -> Max a -> Max a # (-) :: Max a -> Max a -> Max a # (*) :: Max a -> Max a -> Max a # negate :: Max a -> Max a # abs :: Max a -> Max a # signum :: Max a -> Max a # fromInteger :: Integer -> Max a #
Ord a => Ord (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Max a -> Max a -> Ordering # (<) :: Max a -> Max a -> Bool # (<=) :: Max a -> Max a -> Bool # (>) :: Max a -> Max a -> Bool # (>=) :: Max a -> Max a -> Bool # max :: Max a -> Max a -> Max a # min :: Max a -> Max a -> Max a #
Read a => Read (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Max a) # readList :: ReadS [Max a] # readPrec :: ReadPrec (Max a) # readListPrec :: ReadPrec [Max a] #
Show a => Show (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Max a -> ShowS # show :: Max a -> String # showList :: [Max a] -> ShowS #
Generic (Max a)
Instance details Defined in Data.Semigroup Associated Types type Rep (Max a) :: Type -> Type # Methods from :: Max a -> Rep (Max a) x # to :: Rep (Max a) x -> Max a #
Ord a => Semigroup (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Max a -> Max a -> Max a # sconcat :: NonEmpty (Max a) -> Max a # stimes :: Integral b => b -> Max a -> Max a #
(Ord a, Bounded a) => Monoid (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Max a # mappend :: Max a -> Max a -> Max a # mconcat :: [Max a] -> Max a #
ToJSON a => ToJSON (Max a)
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSON :: Max a -> Value # toEncoding :: Max a -> Encoding # toJSONList :: [Max a] -> Value # toEncodingList :: [Max a] -> Encoding #
Wrapped (Max a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Max a) :: Type # Methods _Wrapped' :: Iso' (Max a) (Unwrapped (Max a)) #
Newtype (Max a)	Since: newtype-generics-0.5.1
Instance details Defined in Control.Newtype.Generics Associated Types type O (Max a) :: Type # Methods pack :: O (Max a) -> Max a # unpack :: Max a -> O (Max a) #
Generic1 Max
Instance details Defined in Data.Semigroup Associated Types type Rep1 Max :: k -> Type # Methods from1 :: Max a -> Rep1 Max a # to1 :: Rep1 Max a -> Max a #
t ~ Max b => Rewrapped (Max a) t
Instance details Defined in Control.Lens.Wrapped
type Rep (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (Max a) = D1 (MetaData "Max" "Data.Semigroup" "base" True) (C1 (MetaCons "Max" PrefixI True) (S1 (MetaSel (Just "getMax") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Unwrapped (Max a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Max a) = a
type O (Max a)
Instance details Defined in Control.Newtype.Generics type O (Max a) = a
type Rep1 Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 Max = D1 (MetaData "Max" "Data.Semigroup" "base" True) (C1 (MetaCons "Max" PrefixI True) (S1 (MetaSel (Just "getMax") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

data Arg a b #

Arg isn't itself a Semigroup in its own right, but it can be placed inside Min and Max to compute an arg min or arg max.

Constructors

Arg a b

Instances

Bitraversable Arg	Since: base-4.10.0.0
Instance details Defined in Data.Semigroup Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) #
Bifoldable Arg	Since: base-4.10.0.0
Instance details Defined in Data.Semigroup Methods bifold :: Monoid m => Arg m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Arg a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Arg a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Arg a b -> c #
Bifunctor Arg	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d # first :: (a -> b) -> Arg a c -> Arg b c # second :: (b -> c) -> Arg a b -> Arg a c #
Biapplicative Arg
Instance details Defined in Data.Biapplicative Methods bipure :: a -> b -> Arg a b # (<<>>) :: Arg (a -> b) (c -> d) -> Arg a c -> Arg b d # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Arg a d -> Arg b e -> Arg c f # (>>) :: Arg a b -> Arg c d -> Arg c d # (<<*) :: Arg a b -> Arg c d -> Arg a b #
Bitraversable1 Arg
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Arg a c -> f (Arg b d) # bisequence1 :: Apply f => Arg (f a) (f b) -> f (Arg a b) #
Biapply Arg
Instance details Defined in Data.Functor.Bind.Class Methods (<<.>>) :: Arg (a -> b) (c -> d) -> Arg a c -> Arg b d # (.>>) :: Arg a b -> Arg c d -> Arg c d # (<<.) :: Arg a b -> Arg c d -> Arg a b #
Functor (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a0 -> b) -> Arg a a0 -> Arg a b # (<$) :: a0 -> Arg a b -> Arg a a0 #
Foldable (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Arg a m -> m # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # toList :: Arg a a0 -> [a0] # null :: Arg a a0 -> Bool # length :: Arg a a0 -> Int # elem :: Eq a0 => a0 -> Arg a a0 -> Bool # maximum :: Ord a0 => Arg a a0 -> a0 # minimum :: Ord a0 => Arg a a0 -> a0 # sum :: Num a0 => Arg a a0 -> a0 # product :: Num a0 => Arg a a0 -> a0 #
Traversable (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a0 -> f b) -> Arg a a0 -> f (Arg a b) # sequenceA :: Applicative f => Arg a (f a0) -> f (Arg a a0) # mapM :: Monad m => (a0 -> m b) -> Arg a a0 -> m (Arg a b) # sequence :: Monad m => Arg a (m a0) -> m (Arg a a0) #
Generic1 (Arg a :: Type -> Type)
Instance details Defined in Data.Semigroup Associated Types type Rep1 (Arg a) :: k -> Type # Methods from1 :: Arg a a0 -> Rep1 (Arg a) a0 # to1 :: Rep1 (Arg a) a0 -> Arg a a0 #
Eq a => Eq (Arg a b)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Arg a b -> Arg a b -> Bool # (/=) :: Arg a b -> Arg a b -> Bool #
(Data a, Data b) => Data (Arg a b)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Arg a b -> c (Arg a b) # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Arg a b) # toConstr :: Arg a b -> Constr # dataTypeOf :: Arg a b -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Arg a b)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Arg a b)) # gmapT :: (forall b0. Data b0 => b0 -> b0) -> Arg a b -> Arg a b # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r # gmapQ :: (forall d. Data d => d -> u) -> Arg a b -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Arg a b -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) #
Ord a => Ord (Arg a b)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Arg a b -> Arg a b -> Ordering # (<) :: Arg a b -> Arg a b -> Bool # (<=) :: Arg a b -> Arg a b -> Bool # (>) :: Arg a b -> Arg a b -> Bool # (>=) :: Arg a b -> Arg a b -> Bool # max :: Arg a b -> Arg a b -> Arg a b # min :: Arg a b -> Arg a b -> Arg a b #
(Read a, Read b) => Read (Arg a b)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Arg a b) # readList :: ReadS [Arg a b] # readPrec :: ReadPrec (Arg a b) # readListPrec :: ReadPrec [Arg a b] #
(Show a, Show b) => Show (Arg a b)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Arg a b -> ShowS # show :: Arg a b -> String # showList :: [Arg a b] -> ShowS #
Generic (Arg a b)
Instance details Defined in Data.Semigroup Associated Types type Rep (Arg a b) :: Type -> Type # Methods from :: Arg a b -> Rep (Arg a b) x # to :: Rep (Arg a b) x -> Arg a b #
type Rep1 (Arg a :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 (Arg a :: Type -> Type) = D1 (MetaData "Arg" "Data.Semigroup" "base" False) (C1 (MetaCons "Arg" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))
type Rep (Arg a b)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (Arg a b) = D1 (MetaData "Arg" "Data.Semigroup" "base" False) (C1 (MetaCons "Arg" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 b)))

type ArgMin a b = Min (Arg a b) #

type ArgMax a b = Max (Arg a b) #

newtype First a #

Use Option (First a) to get the behavior of First from Data.Monoid.

Constructors

First
Fields getFirst :: a

Instances

Monad First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: First a -> (a -> First b) -> First b # (>>) :: First a -> First b -> First b # return :: a -> First a # fail :: String -> First a #
Functor First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> First a -> First b # (<$) :: a -> First b -> First a #
MonadFix First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mfix :: (a -> First a) -> First a #
Applicative First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> First a # (<>) :: First (a -> b) -> First a -> First b # liftA2 :: (a -> b -> c) -> First a -> First b -> First c # (>) :: First a -> First b -> First b # (<*) :: First a -> First b -> First a #
Foldable First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # toList :: First a -> [a] # null :: First a -> Bool # length :: First a -> Int # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # sum :: Num a => First a -> a # product :: Num a => First a -> a #
Traversable First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Apply First
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: First (a -> b) -> First a -> First b # (.>) :: First a -> First b -> First b # (<.) :: First a -> First b -> First a # liftF2 :: (a -> b -> c) -> First a -> First b -> First c #
ToJSON1 First
Instance details Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a -> Value) -> ([a] -> Value) -> First a -> Value # liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [First a] -> Value # liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> First a -> Encoding # liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [First a] -> Encoding #
Traversable1 First
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> First a -> f (First b) # sequence1 :: Apply f => First (f b) -> f (First b) #
Bind First
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: First a -> (a -> First b) -> First b # join :: First (First a) -> First a #
Bounded a => Bounded (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: First a # maxBound :: First a #
Enum a => Enum (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: First a -> First a # pred :: First a -> First a # toEnum :: Int -> First a # fromEnum :: First a -> Int # enumFrom :: First a -> [First a] # enumFromThen :: First a -> First a -> [First a] # enumFromTo :: First a -> First a -> [First a] # enumFromThenTo :: First a -> First a -> First a -> [First a] #
Eq a => Eq (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: First a -> First a -> Bool # (/=) :: First a -> First a -> Bool #
Data a => Data (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> First a -> c (First a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a) # toConstr :: First a -> Constr # dataTypeOf :: First a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (First a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a)) # gmapT :: (forall b. Data b => b -> b) -> First a -> First a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r # gmapQ :: (forall d. Data d => d -> u) -> First a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) #
Ord a => Ord (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: First a -> First a -> Ordering # (<) :: First a -> First a -> Bool # (<=) :: First a -> First a -> Bool # (>) :: First a -> First a -> Bool # (>=) :: First a -> First a -> Bool # max :: First a -> First a -> First a # min :: First a -> First a -> First a #
Read a => Read (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (First a) # readList :: ReadS [First a] # readPrec :: ReadPrec (First a) # readListPrec :: ReadPrec [First a] #
Show a => Show (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> First a -> ShowS # show :: First a -> String # showList :: [First a] -> ShowS #
Generic (First a)
Instance details Defined in Data.Semigroup Associated Types type Rep (First a) :: Type -> Type # Methods from :: First a -> Rep (First a) x # to :: Rep (First a) x -> First a #
Semigroup (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: First a -> First a -> First a # sconcat :: NonEmpty (First a) -> First a # stimes :: Integral b => b -> First a -> First a #
ToJSON a => ToJSON (First a)
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSON :: First a -> Value # toEncoding :: First a -> Encoding # toJSONList :: [First a] -> Value # toEncodingList :: [First a] -> Encoding #
Wrapped (First a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (First a) :: Type # Methods _Wrapped' :: Iso' (First a) (Unwrapped (First a)) #
Newtype (First a)	Since: newtype-generics-0.5.1
Instance details Defined in Control.Newtype.Generics Associated Types type O (First a) :: Type # Methods pack :: O (First a) -> First a # unpack :: First a -> O (First a) #
Generic1 First
Instance details Defined in Data.Semigroup Associated Types type Rep1 First :: k -> Type # Methods from1 :: First a -> Rep1 First a # to1 :: Rep1 First a -> First a #
t ~ First b => Rewrapped (First a) t
Instance details Defined in Control.Lens.Wrapped
type Rep (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (First a) = D1 (MetaData "First" "Data.Semigroup" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Unwrapped (First a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (First a) = a
type O (First a)
Instance details Defined in Control.Newtype.Generics type O (First a) = a
type Rep1 First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 First = D1 (MetaData "First" "Data.Semigroup" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Last a #

Use Option (Last a) to get the behavior of Last from Data.Monoid

Constructors

Last
Fields getLast :: a

Instances

Monad Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Last a -> (a -> Last b) -> Last b # (>>) :: Last a -> Last b -> Last b # return :: a -> Last a # fail :: String -> Last a #
Functor Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Last a -> Last b # (<$) :: a -> Last b -> Last a #
MonadFix Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mfix :: (a -> Last a) -> Last a #
Applicative Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Last a # (<>) :: Last (a -> b) -> Last a -> Last b # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c # (>) :: Last a -> Last b -> Last b # (<*) :: Last a -> Last b -> Last a #
Foldable Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # toList :: Last a -> [a] # null :: Last a -> Bool # length :: Last a -> Int # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # minimum :: Ord a => Last a -> a # sum :: Num a => Last a -> a # product :: Num a => Last a -> a #
Traversable Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Apply Last
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Last (a -> b) -> Last a -> Last b # (.>) :: Last a -> Last b -> Last b # (<.) :: Last a -> Last b -> Last a # liftF2 :: (a -> b -> c) -> Last a -> Last b -> Last c #
ToJSON1 Last
Instance details Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a -> Value) -> ([a] -> Value) -> Last a -> Value # liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [Last a] -> Value # liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> Last a -> Encoding # liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [Last a] -> Encoding #
Traversable1 Last
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Last a -> f (Last b) # sequence1 :: Apply f => Last (f b) -> f (Last b) #
Bind Last
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Last a -> (a -> Last b) -> Last b # join :: Last (Last a) -> Last a #
Bounded a => Bounded (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: Last a # maxBound :: Last a #
Enum a => Enum (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: Last a -> Last a # pred :: Last a -> Last a # toEnum :: Int -> Last a # fromEnum :: Last a -> Int # enumFrom :: Last a -> [Last a] # enumFromThen :: Last a -> Last a -> [Last a] # enumFromTo :: Last a -> Last a -> [Last a] # enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] #
Eq a => Eq (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Last a -> Last a -> Bool # (/=) :: Last a -> Last a -> Bool #
Data a => Data (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Last a -> c (Last a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a) # toConstr :: Last a -> Constr # dataTypeOf :: Last a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Last a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a)) # gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r # gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) #
Ord a => Ord (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Last a -> Last a -> Ordering # (<) :: Last a -> Last a -> Bool # (<=) :: Last a -> Last a -> Bool # (>) :: Last a -> Last a -> Bool # (>=) :: Last a -> Last a -> Bool # max :: Last a -> Last a -> Last a # min :: Last a -> Last a -> Last a #
Read a => Read (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Last a) # readList :: ReadS [Last a] # readPrec :: ReadPrec (Last a) # readListPrec :: ReadPrec [Last a] #
Show a => Show (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Last a -> ShowS # show :: Last a -> String # showList :: [Last a] -> ShowS #
Generic (Last a)
Instance details Defined in Data.Semigroup Associated Types type Rep (Last a) :: Type -> Type # Methods from :: Last a -> Rep (Last a) x # to :: Rep (Last a) x -> Last a #
Semigroup (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Last a -> Last a -> Last a # sconcat :: NonEmpty (Last a) -> Last a # stimes :: Integral b => b -> Last a -> Last a #
ToJSON a => ToJSON (Last a)
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSON :: Last a -> Value # toEncoding :: Last a -> Encoding # toJSONList :: [Last a] -> Value # toEncodingList :: [Last a] -> Encoding #
Wrapped (Last a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Last a) :: Type # Methods _Wrapped' :: Iso' (Last a) (Unwrapped (Last a)) #
Newtype (Last a)	Since: newtype-generics-0.5.1
Instance details Defined in Control.Newtype.Generics Associated Types type O (Last a) :: Type # Methods pack :: O (Last a) -> Last a # unpack :: Last a -> O (Last a) #
Generic1 Last
Instance details Defined in Data.Semigroup Associated Types type Rep1 Last :: k -> Type # Methods from1 :: Last a -> Rep1 Last a # to1 :: Rep1 Last a -> Last a #
t ~ Last b => Rewrapped (Last a) t
Instance details Defined in Control.Lens.Wrapped
type Rep (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (Last a) = D1 (MetaData "Last" "Data.Semigroup" "base" True) (C1 (MetaCons "Last" PrefixI True) (S1 (MetaSel (Just "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Unwrapped (Last a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Last a) = a
type O (Last a)
Instance details Defined in Control.Newtype.Generics type O (Last a) = a
type Rep1 Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 Last = D1 (MetaData "Last" "Data.Semigroup" "base" True) (C1 (MetaCons "Last" PrefixI True) (S1 (MetaSel (Just "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype WrappedMonoid m #

Provide a Semigroup for an arbitrary Monoid.

NOTE: This is not needed anymore since Semigroup became a superclass of Monoid in base-4.11 and this newtype be deprecated at some point in the future.

Constructors

WrapMonoid
Fields unwrapMonoid :: m

Instances

ToJSON1 WrappedMonoid
Instance details Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a -> Value) -> ([a] -> Value) -> WrappedMonoid a -> Value # liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [WrappedMonoid a] -> Value # liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> WrappedMonoid a -> Encoding # liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [WrappedMonoid a] -> Encoding #
Bounded m => Bounded (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: WrappedMonoid m # maxBound :: WrappedMonoid m #
Enum a => Enum (WrappedMonoid a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods succ :: WrappedMonoid a -> WrappedMonoid a # pred :: WrappedMonoid a -> WrappedMonoid a # toEnum :: Int -> WrappedMonoid a # fromEnum :: WrappedMonoid a -> Int # enumFrom :: WrappedMonoid a -> [WrappedMonoid a] # enumFromThen :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] # enumFromTo :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] # enumFromThenTo :: WrappedMonoid a -> WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] #
Eq m => Eq (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool #
Data m => Data (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> WrappedMonoid m -> c (WrappedMonoid m) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (WrappedMonoid m) # toConstr :: WrappedMonoid m -> Constr # dataTypeOf :: WrappedMonoid m -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (WrappedMonoid m)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (WrappedMonoid m)) # gmapT :: (forall b. Data b => b -> b) -> WrappedMonoid m -> WrappedMonoid m # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r # gmapQ :: (forall d. Data d => d -> u) -> WrappedMonoid m -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> WrappedMonoid m -> u # gmapM :: Monad m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) # gmapMp :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) # gmapMo :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) #
Ord m => Ord (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: WrappedMonoid m -> WrappedMonoid m -> Ordering # (<) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (<=) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (>) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (>=) :: WrappedMonoid m -> WrappedMonoid m -> Bool # max :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # min :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m #
Read m => Read (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (WrappedMonoid m) # readList :: ReadS [WrappedMonoid m] # readPrec :: ReadPrec (WrappedMonoid m) # readListPrec :: ReadPrec [WrappedMonoid m] #
Show m => Show (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> WrappedMonoid m -> ShowS # show :: WrappedMonoid m -> String # showList :: [WrappedMonoid m] -> ShowS #
Generic (WrappedMonoid m)
Instance details Defined in Data.Semigroup Associated Types type Rep (WrappedMonoid m) :: Type -> Type # Methods from :: WrappedMonoid m -> Rep (WrappedMonoid m) x # to :: Rep (WrappedMonoid m) x -> WrappedMonoid m #
Monoid m => Semigroup (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m #
Monoid m => Monoid (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m #
ToJSON a => ToJSON (WrappedMonoid a)
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSON :: WrappedMonoid a -> Value # toEncoding :: WrappedMonoid a -> Encoding # toJSONList :: [WrappedMonoid a] -> Value # toEncodingList :: [WrappedMonoid a] -> Encoding #
Wrapped (WrappedMonoid a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedMonoid a) :: Type # Methods _Wrapped' :: Iso' (WrappedMonoid a) (Unwrapped (WrappedMonoid a)) #
Newtype (WrappedMonoid m)	Since: newtype-generics-0.5.1
Instance details Defined in Control.Newtype.Generics Associated Types type O (WrappedMonoid m) :: Type # Methods pack :: O (WrappedMonoid m) -> WrappedMonoid m # unpack :: WrappedMonoid m -> O (WrappedMonoid m) #
Generic1 WrappedMonoid
Instance details Defined in Data.Semigroup Associated Types type Rep1 WrappedMonoid :: k -> Type # Methods from1 :: WrappedMonoid a -> Rep1 WrappedMonoid a # to1 :: Rep1 WrappedMonoid a -> WrappedMonoid a #
t ~ WrappedMonoid b => Rewrapped (WrappedMonoid a) t
Instance details Defined in Control.Lens.Wrapped
type Rep (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (WrappedMonoid m) = D1 (MetaData "WrappedMonoid" "Data.Semigroup" "base" True) (C1 (MetaCons "WrapMonoid" PrefixI True) (S1 (MetaSel (Just "unwrapMonoid") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 m)))
type Unwrapped (WrappedMonoid a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (WrappedMonoid a) = a
type O (WrappedMonoid m)
Instance details Defined in Control.Newtype.Generics type O (WrappedMonoid m) = m
type Rep1 WrappedMonoid	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 WrappedMonoid = D1 (MetaData "WrappedMonoid" "Data.Semigroup" "base" True) (C1 (MetaCons "WrapMonoid" PrefixI True) (S1 (MetaSel (Just "unwrapMonoid") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Option a #

Option is effectively Maybe with a better instance of Monoid, built off of an underlying Semigroup instead of an underlying Monoid.

Ideally, this type would not exist at all and we would just fix the Monoid instance of Maybe.

In GHC 8.4 and higher, the Monoid instance for Maybe has been corrected to lift a Semigroup instance instead of a Monoid instance. Consequently, this type is no longer useful. It will be marked deprecated in GHC 8.8 and removed in GHC 8.10.

Constructors

Option
Fields getOption :: Maybe a

Instances

Monad Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (>>=) :: Option a -> (a -> Option b) -> Option b # (>>) :: Option a -> Option b -> Option b # return :: a -> Option a # fail :: String -> Option a #
Functor Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fmap :: (a -> b) -> Option a -> Option b # (<$) :: a -> Option b -> Option a #
MonadFix Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mfix :: (a -> Option a) -> Option a #
Applicative Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods pure :: a -> Option a # (<>) :: Option (a -> b) -> Option a -> Option b # liftA2 :: (a -> b -> c) -> Option a -> Option b -> Option c # (>) :: Option a -> Option b -> Option b # (<*) :: Option a -> Option b -> Option a #
Foldable Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods fold :: Monoid m => Option m -> m # foldMap :: Monoid m => (a -> m) -> Option a -> m # foldr :: (a -> b -> b) -> b -> Option a -> b # foldr' :: (a -> b -> b) -> b -> Option a -> b # foldl :: (b -> a -> b) -> b -> Option a -> b # foldl' :: (b -> a -> b) -> b -> Option a -> b # foldr1 :: (a -> a -> a) -> Option a -> a # foldl1 :: (a -> a -> a) -> Option a -> a # toList :: Option a -> [a] # null :: Option a -> Bool # length :: Option a -> Int # elem :: Eq a => a -> Option a -> Bool # maximum :: Ord a => Option a -> a # minimum :: Ord a => Option a -> a # sum :: Num a => Option a -> a # product :: Num a => Option a -> a #
Traversable Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Option a -> f (Option b) # sequenceA :: Applicative f => Option (f a) -> f (Option a) # mapM :: Monad m => (a -> m b) -> Option a -> m (Option b) # sequence :: Monad m => Option (m a) -> m (Option a) #
MonadPlus Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mzero :: Option a # mplus :: Option a -> Option a -> Option a #
Alternative Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods empty :: Option a # (<\|>) :: Option a -> Option a -> Option a # some :: Option a -> Option [a] # many :: Option a -> Option [a] #
Apply Option
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Option (a -> b) -> Option a -> Option b # (.>) :: Option a -> Option b -> Option b # (<.) :: Option a -> Option b -> Option a # liftF2 :: (a -> b -> c) -> Option a -> Option b -> Option c #
ToJSON1 Option
Instance details Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a -> Value) -> ([a] -> Value) -> Option a -> Value # liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [Option a] -> Value # liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> Option a -> Encoding # liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [Option a] -> Encoding #
Bind Option
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Option a -> (a -> Option b) -> Option b # join :: Option (Option a) -> Option a #
(Selector s, GToJSON enc arity (K1 i (Maybe a) :: Type -> Type), KeyValuePair enc pairs, Monoid pairs) => RecordToPairs enc pairs arity (S1 s (K1 i (Option a) :: Type -> Type))
Instance details Defined in Data.Aeson.Types.ToJSON Methods recordToPairs :: Options -> ToArgs enc arity a0 -> S1 s (K1 i (Option a)) a0 -> pairs
Eq a => Eq (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: Option a -> Option a -> Bool # (/=) :: Option a -> Option a -> Bool #
Data a => Data (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Option a -> c (Option a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Option a) # toConstr :: Option a -> Constr # dataTypeOf :: Option a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Option a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Option a)) # gmapT :: (forall b. Data b => b -> b) -> Option a -> Option a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Option a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Option a -> r # gmapQ :: (forall d. Data d => d -> u) -> Option a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Option a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) #
Ord a => Ord (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: Option a -> Option a -> Ordering # (<) :: Option a -> Option a -> Bool # (<=) :: Option a -> Option a -> Bool # (>) :: Option a -> Option a -> Bool # (>=) :: Option a -> Option a -> Bool # max :: Option a -> Option a -> Option a # min :: Option a -> Option a -> Option a #
Read a => Read (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (Option a) # readList :: ReadS [Option a] # readPrec :: ReadPrec (Option a) # readListPrec :: ReadPrec [Option a] #
Show a => Show (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> Option a -> ShowS # show :: Option a -> String # showList :: [Option a] -> ShowS #
Generic (Option a)
Instance details Defined in Data.Semigroup Associated Types type Rep (Option a) :: Type -> Type # Methods from :: Option a -> Rep (Option a) x # to :: Rep (Option a) x -> Option a #
Semigroup a => Semigroup (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: Option a -> Option a -> Option a # sconcat :: NonEmpty (Option a) -> Option a # stimes :: Integral b => b -> Option a -> Option a #
Semigroup a => Monoid (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Option a # mappend :: Option a -> Option a -> Option a # mconcat :: [Option a] -> Option a #
ToJSON a => ToJSON (Option a)
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSON :: Option a -> Value # toEncoding :: Option a -> Encoding # toJSONList :: [Option a] -> Value # toEncodingList :: [Option a] -> Encoding #
Wrapped (Option a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Option a) :: Type # Methods _Wrapped' :: Iso' (Option a) (Unwrapped (Option a)) #
Newtype (Option a)	Since: newtype-generics-0.5.1
Instance details Defined in Control.Newtype.Generics Associated Types type O (Option a) :: Type # Methods pack :: O (Option a) -> Option a # unpack :: Option a -> O (Option a) #
Generic1 Option
Instance details Defined in Data.Semigroup Associated Types type Rep1 Option :: k -> Type # Methods from1 :: Option a -> Rep1 Option a # to1 :: Rep1 Option a -> Option a #
t ~ Option b => Rewrapped (Option a) t
Instance details Defined in Control.Lens.Wrapped
(Action a a', Action (SM a) l) => Action (SM a) (Option a', l)
Instance details Defined in Data.Monoid.MList Methods act :: SM a -> (Option a', l) -> (Option a', l) #
MList l => MList (a ::: l)
Instance details Defined in Data.Monoid.MList Methods empty :: a ::: l #
MList t => (a ::: t) :>: a
Instance details Defined in Data.Monoid.MList Methods inj :: a -> a ::: t # get :: (a ::: t) -> Option a # alt :: (Option a -> Option a) -> (a ::: t) -> a ::: t #
t :>: a => (b ::: t) :>: a
Instance details Defined in Data.Monoid.MList Methods inj :: a -> b ::: t # get :: (b ::: t) -> Option a # alt :: (Option a -> Option a) -> (b ::: t) -> b ::: t #
(Metric v, OrderedField n) => Measured (SegMeasure v n) (SegMeasure v n)
Instance details Defined in Diagrams.Segment Methods measure :: SegMeasure v n -> SegMeasure v n #
(Floating n, Ord n, Metric v) => Measured (SegMeasure v n) (SegTree v n)
Instance details Defined in Diagrams.Trail Methods measure :: SegTree v n -> SegMeasure v n #
(OrderedField n, Metric v) => Measured (SegMeasure v n) (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods measure :: Segment Closed v n -> SegMeasure v n #
type Rep (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (Option a) = D1 (MetaData "Option" "Data.Semigroup" "base" True) (C1 (MetaCons "Option" PrefixI True) (S1 (MetaSel (Just "getOption") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe a))))
type V (Option a)
Instance details Defined in Diagrams.Core.V type V (Option a) = V a
type N (Option a)
Instance details Defined in Diagrams.Core.V type N (Option a) = N a
type Unwrapped (Option a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Option a) = Maybe a
type O (Option a)
Instance details Defined in Control.Newtype.Generics type O (Option a) = Maybe a
type Rep1 Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 Option = D1 (MetaData "Option" "Data.Semigroup" "base" True) (C1 (MetaCons "Option" PrefixI True) (S1 (MetaSel (Just "getOption") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 Maybe)))

class Bifunctor (p :: Type -> Type -> Type) where #

A bifunctor is a type constructor that takes two type arguments and is a functor in both arguments. That is, unlike with Functor, a type constructor such as Either does not need to be partially applied for a Bifunctor instance, and the methods in this class permit mapping functions over the Left value or the Right value, or both at the same time.

Formally, the class Bifunctor represents a bifunctor from Hask -> Hask.

Intuitively it is a bifunctor where both the first and second arguments are covariant.

You can define a Bifunctor by either defining bimap or by defining both first and second.

If you supply bimap, you should ensure that:

bimap id id ≡ id

If you supply first and second, ensure:

first id ≡ id
second id ≡ id

If you supply both, you should also ensure:

bimap f g ≡ first f . second g

These ensure by parametricity:

bimap  (f . g) (h . i) ≡ bimap f h . bimap g i
first  (f . g) ≡ first  f . first  g
second (f . g) ≡ second f . second g

Since: base-4.8.0.0

Minimal complete definition

bimap | first, second

Methods

bimap :: (a -> b) -> (c -> d) -> p a c -> p b d #

Map over both arguments at the same time.

bimap f g ≡ first f . second g

Examples

Expand

>>> bimap toUpper (+1) ('j', 3)
('J',4)

>>> bimap toUpper (+1) (Left 'j')
Left 'J'

>>> bimap toUpper (+1) (Right 3)
Right 4

Instances

Bifunctor Either	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> Either a c -> Either b d # first :: (a -> b) -> Either a c -> Either b c # second :: (b -> c) -> Either a b -> Either a c #
Bifunctor (,)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d) # first :: (a -> b) -> (a, c) -> (b, c) # second :: (b -> c) -> (a, b) -> (a, c) #
Bifunctor Arg	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d # first :: (a -> b) -> Arg a c -> Arg b c # second :: (b -> c) -> Arg a b -> Arg a c #
Bifunctor ((,,) x1)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, a, c) -> (x1, b, d) # first :: (a -> b) -> (x1, a, c) -> (x1, b, c) # second :: (b -> c) -> (x1, a, b) -> (x1, a, c) #
Bifunctor (Const :: Type -> Type -> Type)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d # first :: (a -> b) -> Const a c -> Const b c # second :: (b -> c) -> Const a b -> Const a c #
Functor f => Bifunctor (FreeF f)
Instance details Defined in Control.Monad.Trans.Free Methods bimap :: (a -> b) -> (c -> d) -> FreeF f a c -> FreeF f b d # first :: (a -> b) -> FreeF f a c -> FreeF f b c # second :: (b -> c) -> FreeF f a b -> FreeF f a c #
Functor f => Bifunctor (CofreeF f)
Instance details Defined in Control.Comonad.Trans.Cofree Methods bimap :: (a -> b) -> (c -> d) -> CofreeF f a c -> CofreeF f b d # first :: (a -> b) -> CofreeF f a c -> CofreeF f b c # second :: (b -> c) -> CofreeF f a b -> CofreeF f a c #
Functor f => Bifunctor (AlongsideLeft f)
Instance details Defined in Control.Lens.Internal.Getter Methods bimap :: (a -> b) -> (c -> d) -> AlongsideLeft f a c -> AlongsideLeft f b d # first :: (a -> b) -> AlongsideLeft f a c -> AlongsideLeft f b c # second :: (b -> c) -> AlongsideLeft f a b -> AlongsideLeft f a c #
Functor f => Bifunctor (AlongsideRight f)
Instance details Defined in Control.Lens.Internal.Getter Methods bimap :: (a -> b) -> (c -> d) -> AlongsideRight f a c -> AlongsideRight f b d # first :: (a -> b) -> AlongsideRight f a c -> AlongsideRight f b c # second :: (b -> c) -> AlongsideRight f a b -> AlongsideRight f a c #
Bifunctor (Tagged :: Type -> Type -> Type)
Instance details Defined in Data.Tagged Methods bimap :: (a -> b) -> (c -> d) -> Tagged a c -> Tagged b d # first :: (a -> b) -> Tagged a c -> Tagged b c # second :: (b -> c) -> Tagged a b -> Tagged a c #
Bifunctor (K1 i :: Type -> Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> K1 i a c -> K1 i b d # first :: (a -> b) -> K1 i a c -> K1 i b c # second :: (b -> c) -> K1 i a b -> K1 i a c #
Bifunctor ((,,,) x1 x2)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, a, c) -> (x1, x2, b, d) # first :: (a -> b) -> (x1, x2, a, c) -> (x1, x2, b, c) # second :: (b -> c) -> (x1, x2, a, b) -> (x1, x2, a, c) #
Bifunctor ((,,,,) x1 x2 x3)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, d) # first :: (a -> b) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, c) # second :: (b -> c) -> (x1, x2, x3, a, b) -> (x1, x2, x3, a, c) #
Bifunctor p => Bifunctor (WrappedBifunctor p)
Instance details Defined in Data.Bifunctor.Wrapped Methods bimap :: (a -> b) -> (c -> d) -> WrappedBifunctor p a c -> WrappedBifunctor p b d # first :: (a -> b) -> WrappedBifunctor p a c -> WrappedBifunctor p b c # second :: (b -> c) -> WrappedBifunctor p a b -> WrappedBifunctor p a c #
Functor g => Bifunctor (Joker g :: Type -> Type -> Type)
Instance details Defined in Data.Bifunctor.Joker Methods bimap :: (a -> b) -> (c -> d) -> Joker g a c -> Joker g b d # first :: (a -> b) -> Joker g a c -> Joker g b c # second :: (b -> c) -> Joker g a b -> Joker g a c #
Bifunctor p => Bifunctor (Flip p)
Instance details Defined in Data.Bifunctor.Flip Methods bimap :: (a -> b) -> (c -> d) -> Flip p a c -> Flip p b d # first :: (a -> b) -> Flip p a c -> Flip p b c # second :: (b -> c) -> Flip p a b -> Flip p a c #
Functor f => Bifunctor (Clown f :: Type -> Type -> Type)
Instance details Defined in Data.Bifunctor.Clown Methods bimap :: (a -> b) -> (c -> d) -> Clown f a c -> Clown f b d # first :: (a -> b) -> Clown f a c -> Clown f b c # second :: (b -> c) -> Clown f a b -> Clown f a c #
Bifunctor ((,,,,,) x1 x2 x3 x4)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, d) # first :: (a -> b) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, c) # second :: (b -> c) -> (x1, x2, x3, x4, a, b) -> (x1, x2, x3, x4, a, c) #
(Bifunctor p, Bifunctor q) => Bifunctor (Sum p q)
Instance details Defined in Data.Bifunctor.Sum Methods bimap :: (a -> b) -> (c -> d) -> Sum p q a c -> Sum p q b d # first :: (a -> b) -> Sum p q a c -> Sum p q b c # second :: (b -> c) -> Sum p q a b -> Sum p q a c #
(Bifunctor f, Bifunctor g) => Bifunctor (Product f g)
Instance details Defined in Data.Bifunctor.Product Methods bimap :: (a -> b) -> (c -> d) -> Product f g a c -> Product f g b d # first :: (a -> b) -> Product f g a c -> Product f g b c # second :: (b -> c) -> Product f g a b -> Product f g a c #
Bifunctor ((,,,,,,) x1 x2 x3 x4 x5)	Since: base-4.8.0.0
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, d) # first :: (a -> b) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, c) # second :: (b -> c) -> (x1, x2, x3, x4, x5, a, b) -> (x1, x2, x3, x4, x5, a, c) #
(Functor f, Bifunctor p) => Bifunctor (Tannen f p)
Instance details Defined in Data.Bifunctor.Tannen Methods bimap :: (a -> b) -> (c -> d) -> Tannen f p a c -> Tannen f p b d # first :: (a -> b) -> Tannen f p a c -> Tannen f p b c # second :: (b -> c) -> Tannen f p a b -> Tannen f p a c #
(Bifunctor p, Functor f, Functor g) => Bifunctor (Biff p f g)
Instance details Defined in Data.Bifunctor.Biff Methods bimap :: (a -> b) -> (c -> d) -> Biff p f g a c -> Biff p f g b d # first :: (a -> b) -> Biff p f g a c -> Biff p f g b c # second :: (b -> c) -> Biff p f g a b -> Biff p f g a c #

stimesMonoid :: (Integral b, Monoid a) => b -> a -> a #

This is a valid definition of stimes for a Monoid.

Unlike the default definition of stimes, it is defined for 0 and so it should be preferred where possible.

stimesIdempotent :: Integral b => b -> a -> a #

This is a valid definition of stimes for an idempotent Semigroup.

When x <> x = x, this definition should be preferred, because it works in O(1) rather than O(log n).

newtype Dual a #

The dual of a Monoid, obtained by swapping the arguments of mappend.

>>> getDual (mappend (Dual "Hello") (Dual "World"))
"WorldHello"

Constructors

Dual
Fields getDual :: a

Instances

Monad Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Dual a -> (a -> Dual b) -> Dual b # (>>) :: Dual a -> Dual b -> Dual b # return :: a -> Dual a # fail :: String -> Dual a #
Functor Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Dual a -> Dual b # (<$) :: a -> Dual b -> Dual a #
Applicative Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Dual a # (<>) :: Dual (a -> b) -> Dual a -> Dual b # liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c # (>) :: Dual a -> Dual b -> Dual b # (<*) :: Dual a -> Dual b -> Dual a #
Foldable Dual	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> m # foldr :: (a -> b -> b) -> b -> Dual a -> b # foldr' :: (a -> b -> b) -> b -> Dual a -> b # foldl :: (b -> a -> b) -> b -> Dual a -> b # foldl' :: (b -> a -> b) -> b -> Dual a -> b # foldr1 :: (a -> a -> a) -> Dual a -> a # foldl1 :: (a -> a -> a) -> Dual a -> a # toList :: Dual a -> [a] # null :: Dual a -> Bool # length :: Dual a -> Int # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # minimum :: Ord a => Dual a -> a # sum :: Num a => Dual a -> a # product :: Num a => Dual a -> a #
Traversable Dual	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) # sequenceA :: Applicative f => Dual (f a) -> f (Dual a) # mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) # sequence :: Monad m => Dual (m a) -> m (Dual a) #
Apply Dual
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Dual (a -> b) -> Dual a -> Dual b # (.>) :: Dual a -> Dual b -> Dual b # (<.) :: Dual a -> Dual b -> Dual a # liftF2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c #
Representable Dual
Instance details Defined in Data.Functor.Rep Associated Types type Rep Dual :: Type # Methods tabulate :: (Rep Dual -> a) -> Dual a # index :: Dual a -> Rep Dual -> a #
ToJSON1 Dual
Instance details Defined in Data.Aeson.Types.ToJSON Methods liftToJSON :: (a -> Value) -> ([a] -> Value) -> Dual a -> Value # liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [Dual a] -> Value # liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> Dual a -> Encoding # liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [Dual a] -> Encoding #
Traversable1 Dual
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Dual a -> f (Dual b) # sequence1 :: Apply f => Dual (f b) -> f (Dual b) #
Bind Dual
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Dual a -> (a -> Dual b) -> Dual b # join :: Dual (Dual a) -> Dual a #
Bounded a => Bounded (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Dual a # maxBound :: Dual a #
Eq a => Eq (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Dual a -> Dual a -> Bool # (/=) :: Dual a -> Dual a -> Bool #
Ord a => Ord (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Dual a -> Dual a -> Ordering # (<) :: Dual a -> Dual a -> Bool # (<=) :: Dual a -> Dual a -> Bool # (>) :: Dual a -> Dual a -> Bool # (>=) :: Dual a -> Dual a -> Bool # max :: Dual a -> Dual a -> Dual a # min :: Dual a -> Dual a -> Dual a #
Read a => Read (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Dual a) # readList :: ReadS [Dual a] # readPrec :: ReadPrec (Dual a) # readListPrec :: ReadPrec [Dual a] #
Show a => Show (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Dual a -> ShowS # show :: Dual a -> String # showList :: [Dual a] -> ShowS #
Generic (Dual a)
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Dual a) :: Type -> Type # Methods from :: Dual a -> Rep (Dual a) x # to :: Rep (Dual a) x -> Dual a #
Semigroup a => Semigroup (Dual a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Dual a -> Dual a -> Dual a # sconcat :: NonEmpty (Dual a) -> Dual a # stimes :: Integral b => b -> Dual a -> Dual a #
Monoid a => Monoid (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a # mappend :: Dual a -> Dual a -> Dual a # mconcat :: [Dual a] -> Dual a #
ToJSON a => ToJSON (Dual a)
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSON :: Dual a -> Value # toEncoding :: Dual a -> Encoding # toJSONList :: [Dual a] -> Value # toEncodingList :: [Dual a] -> Encoding #
Default a => Default (Dual a)
Instance details Defined in Data.Default.Class Methods def :: Dual a #
AsEmpty a => AsEmpty (Dual a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Dual a) () #
Wrapped (Dual a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Dual a) :: Type # Methods _Wrapped' :: Iso' (Dual a) (Unwrapped (Dual a)) #
Newtype (Dual a)	Since: newtype-generics-0.5.1
Instance details Defined in Control.Newtype.Generics Associated Types type O (Dual a) :: Type # Methods pack :: O (Dual a) -> Dual a # unpack :: Dual a -> O (Dual a) #
Generic1 Dual
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Dual :: k -> Type # Methods from1 :: Dual a -> Rep1 Dual a # to1 :: Rep1 Dual a -> Dual a #
t ~ Dual b => Rewrapped (Dual a) t
Instance details Defined in Control.Lens.Wrapped
type Rep Dual
Instance details Defined in Data.Functor.Rep type Rep Dual = ()
type Rep (Dual a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep (Dual a) = D1 (MetaData "Dual" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Dual" PrefixI True) (S1 (MetaSel (Just "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Unwrapped (Dual a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Dual a) = a
type O (Dual a)
Instance details Defined in Control.Newtype.Generics type O (Dual a) = a
type Rep1 Dual	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep1 Dual = D1 (MetaData "Dual" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Dual" PrefixI True) (S1 (MetaSel (Just "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Endo a #

The monoid of endomorphisms under composition.

>>> let computation = Endo ("Hello, " ++) <> Endo (++ "!")
>>> appEndo computation "Haskell"
"Hello, Haskell!"

Constructors

Endo
Fields appEndo :: a -> a

Instances

Generic (Endo a)
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Endo a) :: Type -> Type # Methods from :: Endo a -> Rep (Endo a) x # to :: Rep (Endo a) x -> Endo a #
Semigroup (Endo a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Endo a -> Endo a -> Endo a # sconcat :: NonEmpty (Endo a) -> Endo a # stimes :: Integral b => b -> Endo a -> Endo a #
Monoid (Endo a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a # mappend :: Endo a -> Endo a -> Endo a # mconcat :: [Endo a] -> Endo a #
Default (Endo a)
Instance details Defined in Data.Default.Class Methods def :: Endo a #
Wrapped (Endo a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Endo a) :: Type # Methods _Wrapped' :: Iso' (Endo a) (Unwrapped (Endo a)) #
Newtype (Endo a)
Instance details Defined in Control.Newtype.Generics Associated Types type O (Endo a) :: Type # Methods pack :: O (Endo a) -> Endo a # unpack :: Endo a -> O (Endo a) #
t ~ Endo b => Rewrapped (Endo a) t
Instance details Defined in Control.Lens.Wrapped
type Rep (Endo a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep (Endo a) = D1 (MetaData "Endo" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Endo" PrefixI True) (S1 (MetaSel (Just "appEndo") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (a -> a))))
type Unwrapped (Endo a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Endo a) = a -> a
type O (Endo a)
Instance details Defined in Control.Newtype.Generics type O (Endo a) = a -> a

newtype All #

Boolean monoid under conjunction (&&).

>>> getAll (All True <> mempty <> All False)
False

>>> getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8]))
False

Constructors

All
Fields getAll :: Bool

Instances

Bounded All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: All # maxBound :: All #
Eq All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: All -> All -> Bool # (/=) :: All -> All -> Bool #
Ord All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: All -> All -> Ordering # (<) :: All -> All -> Bool # (<=) :: All -> All -> Bool # (>) :: All -> All -> Bool # (>=) :: All -> All -> Bool # max :: All -> All -> All # min :: All -> All -> All #
Read All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS All # readList :: ReadS [All] # readPrec :: ReadPrec All # readListPrec :: ReadPrec [All] #
Show All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> All -> ShowS # show :: All -> String # showList :: [All] -> ShowS #
Generic All
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep All :: Type -> Type # Methods from :: All -> Rep All x # to :: Rep All x -> All #
Semigroup All	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: All -> All -> All # sconcat :: NonEmpty All -> All # stimes :: Integral b => b -> All -> All #
Monoid All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All # mappend :: All -> All -> All # mconcat :: [All] -> All #
Default All
Instance details Defined in Data.Default.Class Methods def :: All #
AsEmpty All
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' All () #
Wrapped All
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped All :: Type # Methods _Wrapped' :: Iso' All (Unwrapped All) #
Newtype All
Instance details Defined in Control.Newtype.Generics Associated Types type O All :: Type # Methods pack :: O All -> All # unpack :: All -> O All #
t ~ All => Rewrapped All t
Instance details Defined in Control.Lens.Wrapped
RealFloat n => HasQuery (Clip n) All	A point inside a clip if the point is in `All` invididual clipping paths.
Instance details Defined in Diagrams.TwoD.Path Methods getQuery :: Clip n -> Query (V (Clip n)) (N (Clip n)) All #
type Rep All	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep All = D1 (MetaData "All" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "All" PrefixI True) (S1 (MetaSel (Just "getAll") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Bool)))
type Unwrapped All
Instance details Defined in Control.Lens.Wrapped type Unwrapped All = Bool
type O All
Instance details Defined in Control.Newtype.Generics type O All = Bool

newtype Any #

Boolean monoid under disjunction (||).

>>> getAny (Any True <> mempty <> Any False)
True

>>> getAny (mconcat (map (\x -> Any (even x)) [2,4,6,7,8]))
True

Constructors

Any
Fields getAny :: Bool

Instances

Bounded Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Any # maxBound :: Any #
Eq Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Any -> Any -> Bool # (/=) :: Any -> Any -> Bool #
Ord Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Any -> Any -> Ordering # (<) :: Any -> Any -> Bool # (<=) :: Any -> Any -> Bool # (>) :: Any -> Any -> Bool # (>=) :: Any -> Any -> Bool # max :: Any -> Any -> Any # min :: Any -> Any -> Any #
Read Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS Any # readList :: ReadS [Any] # readPrec :: ReadPrec Any # readListPrec :: ReadPrec [Any] #
Show Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Any -> ShowS # show :: Any -> String # showList :: [Any] -> ShowS #
Generic Any
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep Any :: Type -> Type # Methods from :: Any -> Rep Any x # to :: Rep Any x -> Any #
Semigroup Any	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Any -> Any -> Any # sconcat :: NonEmpty Any -> Any # stimes :: Integral b => b -> Any -> Any #
Monoid Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any # mappend :: Any -> Any -> Any # mconcat :: [Any] -> Any #
Default Any
Instance details Defined in Data.Default.Class Methods def :: Any #
AsEmpty Any
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Any () #
Wrapped Any
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped Any :: Type # Methods _Wrapped' :: Iso' Any (Unwrapped Any) #
Newtype Any
Instance details Defined in Control.Newtype.Generics Associated Types type O Any :: Type # Methods pack :: O Any -> Any # unpack :: Any -> O Any #
t ~ Any => Rewrapped Any t
Instance details Defined in Control.Lens.Wrapped
(Num n, Ord n) => HasQuery (Ellipsoid n) Any
Instance details Defined in Diagrams.ThreeD.Shapes Methods getQuery :: Ellipsoid n -> Query (V (Ellipsoid n)) (N (Ellipsoid n)) Any #
(Num n, Ord n) => HasQuery (Box n) Any
Instance details Defined in Diagrams.ThreeD.Shapes Methods getQuery :: Box n -> Query (V (Box n)) (N (Box n)) Any #
OrderedField n => HasQuery (Frustum n) Any
Instance details Defined in Diagrams.ThreeD.Shapes Methods getQuery :: Frustum n -> Query (V (Frustum n)) (N (Frustum n)) Any #
(Floating n, Ord n) => HasQuery (CSG n) Any
Instance details Defined in Diagrams.ThreeD.Shapes Methods getQuery :: CSG n -> Query (V (CSG n)) (N (CSG n)) Any #
(Additive v, Foldable v, Ord n) => HasQuery (BoundingBox v n) Any
Instance details Defined in Diagrams.BoundingBox Methods getQuery :: BoundingBox v n -> Query (V (BoundingBox v n)) (N (BoundingBox v n)) Any #
RealFloat n => HasQuery (DImage n a) Any
Instance details Defined in Diagrams.TwoD.Image Methods getQuery :: DImage n a -> Query (V (DImage n a)) (N (DImage n a)) Any #
type Rep Any	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep Any = D1 (MetaData "Any" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Any" PrefixI True) (S1 (MetaSel (Just "getAny") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Bool)))
type Unwrapped Any
Instance details Defined in Control.Lens.Wrapped type Unwrapped Any = Bool
type O Any
Instance details Defined in Control.Newtype.Generics type O Any = Bool

newtype Sum a #

Monoid under addition.

>>> getSum (Sum 1 <> Sum 2 <> mempty)
3

Constructors

Sum
Fields getSum :: a

Instances

Monad Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b # (>>) :: Sum a -> Sum b -> Sum b # return :: a -> Sum a # fail :: String -> Sum a #
Functor Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Sum a -> Sum b # (<$) :: a -> Sum b -> Sum a #
Applicative Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Sum a # (<>) :: Sum (a -> b) -> Sum a -> Sum b # liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c # (>) :: Sum a -> Sum b -> Sum b # (<*) :: Sum a -> Sum b -> Sum a #
Foldable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # toList :: Sum a -> [a] # null :: Sum a -> Bool # length :: Sum a -> Int # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # minimum :: Ord a => Sum a -> a # sum :: Num a => Sum a -> a # product :: Num a => Sum a -> a #
Traversable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) # sequenceA :: Applicative f => Sum (f a) -> f (Sum a) # mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) # sequence :: Monad m => Sum (m a) -> m (Sum a) #
Apply Sum
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Sum (a -> b) -> Sum a -> Sum b # (.>) :: Sum a -> Sum b -> Sum b # (<.) :: Sum a -> Sum b -> Sum a # liftF2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c #
Representable Sum
Instance details Defined in Data.Functor.Rep Associated Types type Rep Sum :: Type # Methods tabulate :: (Rep Sum -> a) -> Sum a # index :: Sum a -> Rep Sum -> a #
Traversable1 Sum
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Sum a -> f (Sum b) # sequence1 :: Apply f => Sum (f b) -> f (Sum b) #
Bind Sum
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Sum a -> (a -> Sum b) -> Sum b # join :: Sum (Sum a) -> Sum a #
Bounded a => Bounded (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Sum a # maxBound :: Sum a #
Eq a => Eq (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Sum a -> Sum a -> Bool # (/=) :: Sum a -> Sum a -> Bool #
Num a => Num (Sum a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Sum a -> Sum a -> Sum a # (-) :: Sum a -> Sum a -> Sum a # (*) :: Sum a -> Sum a -> Sum a # negate :: Sum a -> Sum a # abs :: Sum a -> Sum a # signum :: Sum a -> Sum a # fromInteger :: Integer -> Sum a #
Ord a => Ord (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Sum a -> Sum a -> Ordering # (<) :: Sum a -> Sum a -> Bool # (<=) :: Sum a -> Sum a -> Bool # (>) :: Sum a -> Sum a -> Bool # (>=) :: Sum a -> Sum a -> Bool # max :: Sum a -> Sum a -> Sum a # min :: Sum a -> Sum a -> Sum a #
Read a => Read (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Sum a) # readList :: ReadS [Sum a] # readPrec :: ReadPrec (Sum a) # readListPrec :: ReadPrec [Sum a] #
Show a => Show (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Sum a -> ShowS # show :: Sum a -> String # showList :: [Sum a] -> ShowS #
Generic (Sum a)
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Sum a) :: Type -> Type # Methods from :: Sum a -> Rep (Sum a) x # to :: Rep (Sum a) x -> Sum a #
Num a => Semigroup (Sum a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Sum a -> Sum a -> Sum a # sconcat :: NonEmpty (Sum a) -> Sum a # stimes :: Integral b => b -> Sum a -> Sum a #
Num a => Monoid (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a # mappend :: Sum a -> Sum a -> Sum a # mconcat :: [Sum a] -> Sum a #
Num a => Default (Sum a)
Instance details Defined in Data.Default.Class Methods def :: Sum a #
(Eq a, Num a) => AsEmpty (Sum a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Sum a) () #
Wrapped (Sum a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Sum a) :: Type # Methods _Wrapped' :: Iso' (Sum a) (Unwrapped (Sum a)) #
Newtype (Sum a)
Instance details Defined in Control.Newtype.Generics Associated Types type O (Sum a) :: Type # Methods pack :: O (Sum a) -> Sum a # unpack :: Sum a -> O (Sum a) #
Generic1 Sum
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Sum :: k -> Type # Methods from1 :: Sum a -> Rep1 Sum a # to1 :: Rep1 Sum a -> Sum a #
t ~ Sum b => Rewrapped (Sum a) t
Instance details Defined in Control.Lens.Wrapped
type Rep Sum
Instance details Defined in Data.Functor.Rep type Rep Sum = ()
type Rep (Sum a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep (Sum a) = D1 (MetaData "Sum" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Sum" PrefixI True) (S1 (MetaSel (Just "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Unwrapped (Sum a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Sum a) = a
type O (Sum a)
Instance details Defined in Control.Newtype.Generics type O (Sum a) = a
type Rep1 Sum	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep1 Sum = D1 (MetaData "Sum" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Sum" PrefixI True) (S1 (MetaSel (Just "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Product a #

Monoid under multiplication.

>>> getProduct (Product 3 <> Product 4 <> mempty)
12

Constructors

Product
Fields getProduct :: a

Instances

Monad Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Product a -> (a -> Product b) -> Product b # (>>) :: Product a -> Product b -> Product b # return :: a -> Product a # fail :: String -> Product a #
Functor Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Product a -> Product b # (<$) :: a -> Product b -> Product a #
Applicative Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Product a # (<>) :: Product (a -> b) -> Product a -> Product b # liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c # (>) :: Product a -> Product b -> Product b # (<*) :: Product a -> Product b -> Product a #
Foldable Product	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # toList :: Product a -> [a] # null :: Product a -> Bool # length :: Product a -> Int # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # sum :: Num a => Product a -> a # product :: Num a => Product a -> a #
Traversable Product	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) # sequenceA :: Applicative f => Product (f a) -> f (Product a) # mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) # sequence :: Monad m => Product (m a) -> m (Product a) #
Apply Product
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: Product (a -> b) -> Product a -> Product b # (.>) :: Product a -> Product b -> Product b # (<.) :: Product a -> Product b -> Product a # liftF2 :: (a -> b -> c) -> Product a -> Product b -> Product c #
Representable Product
Instance details Defined in Data.Functor.Rep Associated Types type Rep Product :: Type # Methods tabulate :: (Rep Product -> a) -> Product a # index :: Product a -> Rep Product -> a #
Traversable1 Product
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Product a -> f (Product b) # sequence1 :: Apply f => Product (f b) -> f (Product b) #
Bind Product
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Product a -> (a -> Product b) -> Product b # join :: Product (Product a) -> Product a #
Bounded a => Bounded (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Product a # maxBound :: Product a #
Eq a => Eq (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Product a -> Product a -> Bool # (/=) :: Product a -> Product a -> Bool #
Num a => Num (Product a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Product a -> Product a -> Product a # (-) :: Product a -> Product a -> Product a # (*) :: Product a -> Product a -> Product a # negate :: Product a -> Product a # abs :: Product a -> Product a # signum :: Product a -> Product a # fromInteger :: Integer -> Product a #
Ord a => Ord (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Product a -> Product a -> Ordering # (<) :: Product a -> Product a -> Bool # (<=) :: Product a -> Product a -> Bool # (>) :: Product a -> Product a -> Bool # (>=) :: Product a -> Product a -> Bool # max :: Product a -> Product a -> Product a # min :: Product a -> Product a -> Product a #
Read a => Read (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Product a) # readList :: ReadS [Product a] # readPrec :: ReadPrec (Product a) # readListPrec :: ReadPrec [Product a] #
Show a => Show (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Product a -> ShowS # show :: Product a -> String # showList :: [Product a] -> ShowS #
Generic (Product a)
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Product a) :: Type -> Type # Methods from :: Product a -> Rep (Product a) x # to :: Rep (Product a) x -> Product a #
Num a => Semigroup (Product a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Product a -> Product a -> Product a # sconcat :: NonEmpty (Product a) -> Product a # stimes :: Integral b => b -> Product a -> Product a #
Num a => Monoid (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a # mappend :: Product a -> Product a -> Product a # mconcat :: [Product a] -> Product a #
Num a => Default (Product a)
Instance details Defined in Data.Default.Class Methods def :: Product a #
(Eq a, Num a) => AsEmpty (Product a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Product a) () #
Wrapped (Product a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Product a) :: Type # Methods _Wrapped' :: Iso' (Product a) (Unwrapped (Product a)) #
Newtype (Product a)
Instance details Defined in Control.Newtype.Generics Associated Types type O (Product a) :: Type # Methods pack :: O (Product a) -> Product a # unpack :: Product a -> O (Product a) #
Generic1 Product
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Product :: k -> Type # Methods from1 :: Product a -> Rep1 Product a # to1 :: Rep1 Product a -> Product a #
t ~ Product b => Rewrapped (Product a) t
Instance details Defined in Control.Lens.Wrapped
type Rep Product
Instance details Defined in Data.Functor.Rep type Rep Product = ()
type Rep (Product a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep (Product a) = D1 (MetaData "Product" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Product" PrefixI True) (S1 (MetaSel (Just "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Unwrapped (Product a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Product a) = a
type O (Product a)
Instance details Defined in Control.Newtype.Generics type O (Product a) = a
type Rep1 Product	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep1 Product = D1 (MetaData "Product" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Product" PrefixI True) (S1 (MetaSel (Just "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

(&) :: a -> (a -> b) -> b infixl 1 #

& is a reverse application operator. This provides notational convenience. Its precedence is one higher than that of the forward application operator $, which allows & to be nested in $.

>>> 5 & (+1) & show
"6"

Since: base-4.8.0.0

(<&>) :: Functor f => f a -> (a -> b) -> f b infixl 1 #

Flipped version of <$>.

(<&>) = flip fmap

Examples

Expand

Apply (+1) to a list, a Just and a Right:

>>> Just 2 <&> (+1)
Just 3

>>> [1,2,3] <&> (+1)
[2,3,4]

>>> Right 3 <&> (+1)
Right 4

Since: base-4.11.0.0

stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a #

This is a valid definition of stimes for an idempotent Monoid.

When mappend x x = x, this definition should be preferred, because it works in O(1) rather than O(log n)

yellowgreen :: (Ord a, Floating a) => Colour a #

yellow :: (Ord a, Floating a) => Colour a #

whitesmoke :: (Ord a, Floating a) => Colour a #

white :: (Ord a, Floating a) => Colour a #

wheat :: (Ord a, Floating a) => Colour a #

violet :: (Ord a, Floating a) => Colour a #

turquoise :: (Ord a, Floating a) => Colour a #

tomato :: (Ord a, Floating a) => Colour a #

thistle :: (Ord a, Floating a) => Colour a #

teal :: (Ord a, Floating a) => Colour a #

steelblue :: (Ord a, Floating a) => Colour a #

springgreen :: (Ord a, Floating a) => Colour a #

snow :: (Ord a, Floating a) => Colour a #

slategrey :: (Ord a, Floating a) => Colour a #

slategray :: (Ord a, Floating a) => Colour a #

slateblue :: (Ord a, Floating a) => Colour a #

skyblue :: (Ord a, Floating a) => Colour a #

silver :: (Ord a, Floating a) => Colour a #

sienna :: (Ord a, Floating a) => Colour a #

seashell :: (Ord a, Floating a) => Colour a #

seagreen :: (Ord a, Floating a) => Colour a #

sandybrown :: (Ord a, Floating a) => Colour a #

salmon :: (Ord a, Floating a) => Colour a #

saddlebrown :: (Ord a, Floating a) => Colour a #

royalblue :: (Ord a, Floating a) => Colour a #

rosybrown :: (Ord a, Floating a) => Colour a #

red :: (Ord a, Floating a) => Colour a #

purple :: (Ord a, Floating a) => Colour a #

powderblue :: (Ord a, Floating a) => Colour a #

plum :: (Ord a, Floating a) => Colour a #

pink :: (Ord a, Floating a) => Colour a #

peru :: (Ord a, Floating a) => Colour a #

peachpuff :: (Ord a, Floating a) => Colour a #

papayawhip :: (Ord a, Floating a) => Colour a #

palevioletred :: (Ord a, Floating a) => Colour a #

paleturquoise :: (Ord a, Floating a) => Colour a #

palegreen :: (Ord a, Floating a) => Colour a #

palegoldenrod :: (Ord a, Floating a) => Colour a #

orchid :: (Ord a, Floating a) => Colour a #

orangered :: (Ord a, Floating a) => Colour a #

orange :: (Ord a, Floating a) => Colour a #

olivedrab :: (Ord a, Floating a) => Colour a #

olive :: (Ord a, Floating a) => Colour a #

oldlace :: (Ord a, Floating a) => Colour a #

navy :: (Ord a, Floating a) => Colour a #

navajowhite :: (Ord a, Floating a) => Colour a #

moccasin :: (Ord a, Floating a) => Colour a #

mistyrose :: (Ord a, Floating a) => Colour a #

mintcream :: (Ord a, Floating a) => Colour a #

midnightblue :: (Ord a, Floating a) => Colour a #

mediumvioletred :: (Ord a, Floating a) => Colour a #

mediumturquoise :: (Ord a, Floating a) => Colour a #

mediumspringgreen :: (Ord a, Floating a) => Colour a #

mediumslateblue :: (Ord a, Floating a) => Colour a #

mediumseagreen :: (Ord a, Floating a) => Colour a #

mediumpurple :: (Ord a, Floating a) => Colour a #

mediumorchid :: (Ord a, Floating a) => Colour a #

mediumblue :: (Ord a, Floating a) => Colour a #

mediumaquamarine :: (Ord a, Floating a) => Colour a #

maroon :: (Ord a, Floating a) => Colour a #

magenta :: (Ord a, Floating a) => Colour a #

linen :: (Ord a, Floating a) => Colour a #

limegreen :: (Ord a, Floating a) => Colour a #

lime :: (Ord a, Floating a) => Colour a #

lightyellow :: (Ord a, Floating a) => Colour a #

lightsteelblue :: (Ord a, Floating a) => Colour a #

lightslategrey :: (Ord a, Floating a) => Colour a #

lightslategray :: (Ord a, Floating a) => Colour a #

lightskyblue :: (Ord a, Floating a) => Colour a #

lightseagreen :: (Ord a, Floating a) => Colour a #

lightsalmon :: (Ord a, Floating a) => Colour a #

lightpink :: (Ord a, Floating a) => Colour a #

lightgrey :: (Ord a, Floating a) => Colour a #

lightgreen :: (Ord a, Floating a) => Colour a #

lightgray :: (Ord a, Floating a) => Colour a #

lightgoldenrodyellow :: (Ord a, Floating a) => Colour a #

lightcyan :: (Ord a, Floating a) => Colour a #

lightcoral :: (Ord a, Floating a) => Colour a #

lightblue :: (Ord a, Floating a) => Colour a #

lemonchiffon :: (Ord a, Floating a) => Colour a #

lawngreen :: (Ord a, Floating a) => Colour a #

lavenderblush :: (Ord a, Floating a) => Colour a #

lavender :: (Ord a, Floating a) => Colour a #

khaki :: (Ord a, Floating a) => Colour a #

ivory :: (Ord a, Floating a) => Colour a #

indigo :: (Ord a, Floating a) => Colour a #

indianred :: (Ord a, Floating a) => Colour a #

hotpink :: (Ord a, Floating a) => Colour a #

honeydew :: (Ord a, Floating a) => Colour a #

greenyellow :: (Ord a, Floating a) => Colour a #

green :: (Ord a, Floating a) => Colour a #

grey :: (Ord a, Floating a) => Colour a #

gray :: (Ord a, Floating a) => Colour a #

goldenrod :: (Ord a, Floating a) => Colour a #

gold :: (Ord a, Floating a) => Colour a #

ghostwhite :: (Ord a, Floating a) => Colour a #

gainsboro :: (Ord a, Floating a) => Colour a #

fuchsia :: (Ord a, Floating a) => Colour a #

forestgreen :: (Ord a, Floating a) => Colour a #

floralwhite :: (Ord a, Floating a) => Colour a #

firebrick :: (Ord a, Floating a) => Colour a #

dodgerblue :: (Ord a, Floating a) => Colour a #

dimgrey :: (Ord a, Floating a) => Colour a #

dimgray :: (Ord a, Floating a) => Colour a #

deepskyblue :: (Ord a, Floating a) => Colour a #

deeppink :: (Ord a, Floating a) => Colour a #

darkviolet :: (Ord a, Floating a) => Colour a #

darkturquoise :: (Ord a, Floating a) => Colour a #

darkslategrey :: (Ord a, Floating a) => Colour a #

darkslategray :: (Ord a, Floating a) => Colour a #

darkslateblue :: (Ord a, Floating a) => Colour a #

darkseagreen :: (Ord a, Floating a) => Colour a #

darksalmon :: (Ord a, Floating a) => Colour a #

darkred :: (Ord a, Floating a) => Colour a #

darkorchid :: (Ord a, Floating a) => Colour a #

darkorange :: (Ord a, Floating a) => Colour a #

darkolivegreen :: (Ord a, Floating a) => Colour a #

darkmagenta :: (Ord a, Floating a) => Colour a #

darkkhaki :: (Ord a, Floating a) => Colour a #

darkgrey :: (Ord a, Floating a) => Colour a #

darkgreen :: (Ord a, Floating a) => Colour a #

darkgray :: (Ord a, Floating a) => Colour a #

darkgoldenrod :: (Ord a, Floating a) => Colour a #

darkcyan :: (Ord a, Floating a) => Colour a #

darkblue :: (Ord a, Floating a) => Colour a #

cyan :: (Ord a, Floating a) => Colour a #

crimson :: (Ord a, Floating a) => Colour a #

cornsilk :: (Ord a, Floating a) => Colour a #

cornflowerblue :: (Ord a, Floating a) => Colour a #

coral :: (Ord a, Floating a) => Colour a #

chocolate :: (Ord a, Floating a) => Colour a #

chartreuse :: (Ord a, Floating a) => Colour a #

cadetblue :: (Ord a, Floating a) => Colour a #

burlywood :: (Ord a, Floating a) => Colour a #

brown :: (Ord a, Floating a) => Colour a #

blueviolet :: (Ord a, Floating a) => Colour a #

blue :: (Ord a, Floating a) => Colour a #

blanchedalmond :: (Ord a, Floating a) => Colour a #

bisque :: (Ord a, Floating a) => Colour a #

beige :: (Ord a, Floating a) => Colour a #

azure :: (Ord a, Floating a) => Colour a #

aquamarine :: (Ord a, Floating a) => Colour a #

aqua :: (Ord a, Floating a) => Colour a #

antiquewhite :: (Ord a, Floating a) => Colour a #

aliceblue :: (Ord a, Floating a) => Colour a #

readColourName :: (MonadFail m, Monad m, Ord a, Floating a) => String -> m (Colour a) #

sRGBSpace :: (Ord a, Floating a) => RGBSpace a #

The sRGB colour space

sRGB24read :: (Ord b, Floating b) => String -> Colour b #

Read a colour in hexadecimal form, e.g. "#00aaff" or "00aaff"

sRGB24reads :: (Ord b, Floating b) => ReadS (Colour b) #

Read a colour in hexadecimal form, e.g. "#00aaff" or "00aaff"

sRGB24show :: (RealFrac b, Floating b) => Colour b -> String #

Show a colour in hexadecimal form, e.g. "#00aaff"

sRGB24shows :: (RealFrac b, Floating b) => Colour b -> ShowS #

Show a colour in hexadecimal form, e.g. "#00aaff"

toSRGB24 :: (RealFrac b, Floating b) => Colour b -> RGB Word8 #

Return the approximate 24-bit sRGB colour components as three 8-bit components. Out of range values are clamped.

toSRGBBounded :: (RealFrac b, Floating b, Integral a, Bounded a) => Colour b -> RGB a #

Return the approximate sRGB colour components in the range [0..maxBound]. Out of range values are clamped.

toSRGB :: (Ord b, Floating b) => Colour b -> RGB b #

Return the sRGB colour components in the range [0..1].

sRGB24 :: (Ord b, Floating b) => Word8 -> Word8 -> Word8 -> Colour b #

Construct a colour from a 24-bit (three 8-bit words) sRGB specification.

sRGBBounded :: (Ord b, Floating b, Integral a, Bounded a) => a -> a -> a -> Colour b #

Construct a colour from an sRGB specification. Input components are expected to be in the range [0..maxBound].

sRGB :: (Ord b, Floating b) => b -> b -> b -> Colour b #

Construct a colour from an sRGB specification. Input components are expected to be in the range [0..1].

data RGB a #

An RGB triple for an unspecified colour space.

Constructors

RGB
Fields channelRed :: !a channelGreen :: !a channelBlue :: !a

Instances

Functor RGB
Instance details Defined in Data.Colour.RGB Methods fmap :: (a -> b) -> RGB a -> RGB b # (<$) :: a -> RGB b -> RGB a #
Applicative RGB
Instance details Defined in Data.Colour.RGB Methods pure :: a -> RGB a # (<>) :: RGB (a -> b) -> RGB a -> RGB b # liftA2 :: (a -> b -> c) -> RGB a -> RGB b -> RGB c # (>) :: RGB a -> RGB b -> RGB b # (<*) :: RGB a -> RGB b -> RGB a #
Eq a => Eq (RGB a)
Instance details Defined in Data.Colour.RGB Methods (==) :: RGB a -> RGB a -> Bool # (/=) :: RGB a -> RGB a -> Bool #
Read a => Read (RGB a)
Instance details Defined in Data.Colour.RGB Methods readsPrec :: Int -> ReadS (RGB a) # readList :: ReadS [RGB a] # readPrec :: ReadPrec (RGB a) # readListPrec :: ReadPrec [RGB a] #
Show a => Show (RGB a)
Instance details Defined in Data.Colour.RGB Methods showsPrec :: Int -> RGB a -> ShowS # show :: RGB a -> String # showList :: [RGB a] -> ShowS #

alphaChannel :: AlphaColour a -> a #

Returns the opacity of an AlphaColour.

blend :: (Num a, AffineSpace f) => a -> f a -> f a -> f a #

Compute the weighted average of two points. e.g.

blend 0.4 a b = 0.4*a + 0.6*b

The weight can be negative, or greater than 1.0; however, be aware that non-convex combinations may lead to out of gamut colours.

withOpacity :: Num a => Colour a -> a -> AlphaColour a #

Creates an AlphaColour from a Colour with a given opacity.

c `withOpacity` o == dissolve o (opaque c)

dissolve :: Num a => a -> AlphaColour a -> AlphaColour a #

Returns an AlphaColour more transparent by a factor of o.

opaque :: Num a => Colour a -> AlphaColour a #

Creates an opaque AlphaColour from a Colour.

alphaColourConvert :: (Fractional b, Real a) => AlphaColour a -> AlphaColour b #

Change the type used to represent the colour coordinates.

transparent :: Num a => AlphaColour a #

This AlphaColour is entirely transparent and has no associated colour channel.

black :: Num a => Colour a #

colourConvert :: (Fractional b, Real a) => Colour a -> Colour b #

Change the type used to represent the colour coordinates.

data Colour a #

This type represents the human preception of colour. The a parameter is a numeric type used internally for the representation.

The Monoid instance allows one to add colours, but beware that adding colours can take you out of gamut. Consider using blend whenever possible.

Instances

AffineSpace Colour
Instance details Defined in Data.Colour.Internal Methods affineCombo :: Num a => [(a, Colour a)] -> Colour a -> Colour a #
ColourOps Colour
Instance details Defined in Data.Colour.Internal Methods over :: Num a => AlphaColour a -> Colour a -> Colour a # darken :: Num a => a -> Colour a -> Colour a #
Eq a => Eq (Colour a)
Instance details Defined in Data.Colour.Internal Methods (==) :: Colour a -> Colour a -> Bool # (/=) :: Colour a -> Colour a -> Bool #
Num a => Semigroup (Colour a)
Instance details Defined in Data.Colour.Internal Methods (<>) :: Colour a -> Colour a -> Colour a # sconcat :: NonEmpty (Colour a) -> Colour a # stimes :: Integral b => b -> Colour a -> Colour a #
Num a => Monoid (Colour a)
Instance details Defined in Data.Colour.Internal Methods mempty :: Colour a # mappend :: Colour a -> Colour a -> Colour a # mconcat :: [Colour a] -> Colour a #
a ~ Double => Color (Colour a)
Instance details Defined in Diagrams.Attributes Methods toAlphaColour :: Colour a -> AlphaColour Double # fromAlphaColour :: AlphaColour Double -> Colour a #
(Ord a, Floating a) => FromColor (Colour a)
Instance details Defined in Skylighting.Types Methods fromColor :: Color -> Colour a #
(RealFrac a, Floating a) => ToColor (Colour a)
Instance details Defined in Skylighting.Types Methods toColor :: Colour a -> Maybe Color #

data AlphaColour a #

This type represents a Colour that may be semi-transparent.

The Monoid instance allows you to composite colours.

x `mappend` y == x `over` y

To get the (pre-multiplied) colour channel of an AlphaColour c, simply composite c over black.

c `over` black

Instances

AffineSpace AlphaColour
Instance details Defined in Data.Colour.Internal Methods affineCombo :: Num a => [(a, AlphaColour a)] -> AlphaColour a -> AlphaColour a #
ColourOps AlphaColour
Instance details Defined in Data.Colour.Internal Methods over :: Num a => AlphaColour a -> AlphaColour a -> AlphaColour a # darken :: Num a => a -> AlphaColour a -> AlphaColour a #
Eq a => Eq (AlphaColour a)
Instance details Defined in Data.Colour.Internal Methods (==) :: AlphaColour a -> AlphaColour a -> Bool # (/=) :: AlphaColour a -> AlphaColour a -> Bool #
Num a => Semigroup (AlphaColour a)	`AlphaColour` forms a monoid with `over` and `transparent`.
Instance details Defined in Data.Colour.Internal Methods (<>) :: AlphaColour a -> AlphaColour a -> AlphaColour a # sconcat :: NonEmpty (AlphaColour a) -> AlphaColour a # stimes :: Integral b => b -> AlphaColour a -> AlphaColour a #
Num a => Monoid (AlphaColour a)
Instance details Defined in Data.Colour.Internal Methods mempty :: AlphaColour a # mappend :: AlphaColour a -> AlphaColour a -> AlphaColour a # mconcat :: [AlphaColour a] -> AlphaColour a #
a ~ Double => Color (AlphaColour a)
Instance details Defined in Diagrams.Attributes Methods toAlphaColour :: AlphaColour a -> AlphaColour Double # fromAlphaColour :: AlphaColour Double -> AlphaColour a #

class ColourOps (f :: Type -> Type) where #

Minimal complete definition

over, darken

Methods

darken :: Num a => a -> f a -> f a #

darken s c blends a colour with black without changing it's opacity.

For Colour, darken s c = blend s c mempty

Instances

ColourOps Colour
Instance details Defined in Data.Colour.Internal Methods over :: Num a => AlphaColour a -> Colour a -> Colour a # darken :: Num a => a -> Colour a -> Colour a #
ColourOps AlphaColour
Instance details Defined in Data.Colour.Internal Methods over :: Num a => AlphaColour a -> AlphaColour a -> AlphaColour a # darken :: Num a => a -> AlphaColour a -> AlphaColour a #

class Default a where #

A class for types with a default value.

Minimal complete definition

Nothing

Methods

def :: a #

The default value for this type.

Instances

Default Double
Instance details Defined in Data.Default.Class Methods def :: Double #
Default Float
Instance details Defined in Data.Default.Class Methods def :: Float #
Default Int
Instance details Defined in Data.Default.Class Methods def :: Int #
Default Int8
Instance details Defined in Data.Default.Class Methods def :: Int8 #
Default Int16
Instance details Defined in Data.Default.Class Methods def :: Int16 #
Default Int32
Instance details Defined in Data.Default.Class Methods def :: Int32 #
Default Int64
Instance details Defined in Data.Default.Class Methods def :: Int64 #
Default Integer
Instance details Defined in Data.Default.Class Methods def :: Integer #
Default Ordering
Instance details Defined in Data.Default.Class Methods def :: Ordering #
Default Word
Instance details Defined in Data.Default.Class Methods def :: Word #
Default Word8
Instance details Defined in Data.Default.Class Methods def :: Word8 #
Default Word16
Instance details Defined in Data.Default.Class Methods def :: Word16 #
Default Word32
Instance details Defined in Data.Default.Class Methods def :: Word32 #
Default Word64
Instance details Defined in Data.Default.Class Methods def :: Word64 #
Default ()
Instance details Defined in Data.Default.Class Methods def :: () #
Default All
Instance details Defined in Data.Default.Class Methods def :: All #
Default Any
Instance details Defined in Data.Default.Class Methods def :: Any #
Default CShort
Instance details Defined in Data.Default.Class Methods def :: CShort #
Default CUShort
Instance details Defined in Data.Default.Class Methods def :: CUShort #
Default CInt
Instance details Defined in Data.Default.Class Methods def :: CInt #
Default CUInt
Instance details Defined in Data.Default.Class Methods def :: CUInt #
Default CLong
Instance details Defined in Data.Default.Class Methods def :: CLong #
Default CULong
Instance details Defined in Data.Default.Class Methods def :: CULong #
Default CLLong
Instance details Defined in Data.Default.Class Methods def :: CLLong #
Default CULLong
Instance details Defined in Data.Default.Class Methods def :: CULLong #
Default CFloat
Instance details Defined in Data.Default.Class Methods def :: CFloat #
Default CDouble
Instance details Defined in Data.Default.Class Methods def :: CDouble #
Default CPtrdiff
Instance details Defined in Data.Default.Class Methods def :: CPtrdiff #
Default CSize
Instance details Defined in Data.Default.Class Methods def :: CSize #
Default CSigAtomic
Instance details Defined in Data.Default.Class Methods def :: CSigAtomic #
Default CClock
Instance details Defined in Data.Default.Class Methods def :: CClock #
Default CTime
Instance details Defined in Data.Default.Class Methods def :: CTime #
Default CUSeconds
Instance details Defined in Data.Default.Class Methods def :: CUSeconds #
Default CSUSeconds
Instance details Defined in Data.Default.Class Methods def :: CSUSeconds #
Default CIntPtr
Instance details Defined in Data.Default.Class Methods def :: CIntPtr #
Default CUIntPtr
Instance details Defined in Data.Default.Class Methods def :: CUIntPtr #
Default CIntMax
Instance details Defined in Data.Default.Class Methods def :: CIntMax #
Default CUIntMax
Instance details Defined in Data.Default.Class Methods def :: CUIntMax #
Default FontSlant
Instance details Defined in Diagrams.TwoD.Text Methods def :: FontSlant #
Default FontWeight
Instance details Defined in Diagrams.TwoD.Text Methods def :: FontWeight #
Default FillRule
Instance details Defined in Diagrams.TwoD.Path Methods def :: FillRule #
Default AdjustSide
Instance details Defined in Diagrams.Parametric.Adjust Methods def :: AdjustSide #
Default LineCap
Instance details Defined in Diagrams.Attributes Methods def :: LineCap #
Default LineJoin
Instance details Defined in Diagrams.Attributes Methods def :: LineJoin #
Default LineMiterLimit
Instance details Defined in Diagrams.Attributes Methods def :: LineMiterLimit #
Default CommonState
Instance details Defined in Text.Pandoc.Class Methods def :: CommonState #
Default PureState
Instance details Defined in Text.Pandoc.Class Methods def :: PureState #
Default ReaderOptions
Instance details Defined in Text.Pandoc.Options Methods def :: ReaderOptions #
Default WriterOptions
Instance details Defined in Text.Pandoc.Options Methods def :: WriterOptions #
Default DEnv
Instance details Defined in Text.Pandoc.Readers.Docx Methods def :: DEnv #
Default DState
Instance details Defined in Text.Pandoc.Readers.Docx Methods def :: DState #
Default HTMLLocal
Instance details Defined in Text.Pandoc.Readers.HTML Methods def :: HTMLLocal #
Default WriterEnv
Instance details Defined in Text.Pandoc.Writers.Markdown Methods def :: WriterEnv #
Default WriterState
Instance details Defined in Text.Pandoc.Writers.Markdown Methods def :: WriterState #
Default [a]
Instance details Defined in Data.Default.Class Methods def :: [a] #
Default (Maybe a)
Instance details Defined in Data.Default.Class Methods def :: Maybe a #
Integral a => Default (Ratio a)
Instance details Defined in Data.Default.Class Methods def :: Ratio a #
Default a => Default (IO a)
Instance details Defined in Data.Default.Class Methods def :: IO a #
(Default a, RealFloat a) => Default (Complex a)
Instance details Defined in Data.Default.Class Methods def :: Complex a #
Default (First a)
Instance details Defined in Data.Default.Class Methods def :: First a #
Default (Last a)
Instance details Defined in Data.Default.Class Methods def :: Last a #
Default a => Default (Dual a)
Instance details Defined in Data.Default.Class Methods def :: Dual a #
Default (Endo a)
Instance details Defined in Data.Default.Class Methods def :: Endo a #
Num a => Default (Sum a)
Instance details Defined in Data.Default.Class Methods def :: Sum a #
Num a => Default (Product a)
Instance details Defined in Data.Default.Class Methods def :: Product a #
Floating n => Default (TraceOpts n)
Instance details Defined in Diagrams.TwoD.Model Methods def :: TraceOpts n #
OrderedField n => Default (EnvelopeOpts n)
Instance details Defined in Diagrams.TwoD.Model Methods def :: EnvelopeOpts n #
Fractional n => Default (OriginOpts n)
Instance details Defined in Diagrams.TwoD.Model Methods def :: OriginOpts n #
TypeableFloat n => Default (ArrowOpts n)
Instance details Defined in Diagrams.TwoD.Arrow Methods def :: ArrowOpts n #
Default (LineTexture n)
Instance details Defined in Diagrams.TwoD.Attributes Methods def :: LineTexture n #
Default (FillTexture n)
Instance details Defined in Diagrams.TwoD.Attributes Methods def :: FillTexture n #
Default (StrokeOpts a)
Instance details Defined in Diagrams.TwoD.Path Methods def :: StrokeOpts a #
Num d => Default (RoundedRectOpts d)
Instance details Defined in Diagrams.TwoD.Shapes Methods def :: RoundedRectOpts d #
Num n => Default (PolygonOpts n)	The default polygon is a regular pentagon of radius 1, centered at the origin, aligned to the x-axis.
Instance details Defined in Diagrams.TwoD.Polygons Methods def :: PolygonOpts n #
Num n => Default (CatOpts n)
Instance details Defined in Diagrams.Combinators Methods def :: CatOpts n #
Fractional n => Default (AdjustMethod n)
Instance details Defined in Diagrams.Parametric.Adjust Methods def :: AdjustMethod n #
Fractional n => Default (AdjustOpts n)
Instance details Defined in Diagrams.Parametric.Adjust Methods def :: AdjustOpts n #
Num n => Default (FontSizeM n)
Instance details Defined in Diagrams.TwoD.Text Methods def :: FontSizeM n #
OrderedField n => Default (LineWidthM n)
Instance details Defined in Diagrams.Attributes Methods def :: LineWidthM n #
Default r => Default (e -> r)
Instance details Defined in Data.Default.Class Methods def :: e -> r #
(Default a, Default b) => Default (a, b)
Instance details Defined in Data.Default.Class Methods def :: (a, b) #
(Default a, Default b, Default c) => Default (a, b, c)
Instance details Defined in Data.Default.Class Methods def :: (a, b, c) #
(Default a, Default b, Default c, Default d) => Default (a, b, c, d)
Instance details Defined in Data.Default.Class Methods def :: (a, b, c, d) #
(Default a, Default b, Default c, Default d, Default e) => Default (a, b, c, d, e)
Instance details Defined in Data.Default.Class Methods def :: (a, b, c, d, e) #
(Default a, Default b, Default c, Default d, Default e, Default f) => Default (a, b, c, d, e, f)
Instance details Defined in Data.Default.Class Methods def :: (a, b, c, d, e, f) #
(Default a, Default b, Default c, Default d, Default e, Default f, Default g) => Default (a, b, c, d, e, f, g)
Instance details Defined in Data.Default.Class Methods def :: (a, b, c, d, e, f, g) #

class Functor f => Additive (f :: Type -> Type) where #

A vector is an additive group with additional structure.

Minimal complete definition

Nothing

Methods

zero :: Num a => f a #

The zero vector

(^+^) :: Num a => f a -> f a -> f a infixl 6 #

Compute the sum of two vectors

>>> V2 1 2 ^+^ V2 3 4
V2 4 6

(^-^) :: Num a => f a -> f a -> f a infixl 6 #

Compute the difference between two vectors

>>> V2 4 5 ^-^ V2 3 1
V2 1 4

lerp :: Num a => a -> f a -> f a -> f a #

Linearly interpolate between two vectors.

liftU2 :: (a -> a -> a) -> f a -> f a -> f a #

Apply a function to merge the 'non-zero' components of two vectors, unioning the rest of the values.

For a dense vector this is equivalent to liftA2.
For a sparse vector this is equivalent to unionWith.

liftI2 :: (a -> b -> c) -> f a -> f b -> f c #

Apply a function to the components of two vectors.

For a dense vector this is equivalent to liftA2.
For a sparse vector this is equivalent to intersectionWith.

Instances

Additive []
Instance details Defined in Linear.Vector Methods zero :: Num a => [a] # (^+^) :: Num a => [a] -> [a] -> [a] # (^-^) :: Num a => [a] -> [a] -> [a] # lerp :: Num a => a -> [a] -> [a] -> [a] # liftU2 :: (a -> a -> a) -> [a] -> [a] -> [a] # liftI2 :: (a -> b -> c) -> [a] -> [b] -> [c] #
Additive Maybe
Instance details Defined in Linear.Vector Methods zero :: Num a => Maybe a # (^+^) :: Num a => Maybe a -> Maybe a -> Maybe a # (^-^) :: Num a => Maybe a -> Maybe a -> Maybe a # lerp :: Num a => a -> Maybe a -> Maybe a -> Maybe a # liftU2 :: (a -> a -> a) -> Maybe a -> Maybe a -> Maybe a # liftI2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c #
Additive Identity
Instance details Defined in Linear.Vector Methods zero :: Num a => Identity a # (^+^) :: Num a => Identity a -> Identity a -> Identity a # (^-^) :: Num a => Identity a -> Identity a -> Identity a # lerp :: Num a => a -> Identity a -> Identity a -> Identity a # liftU2 :: (a -> a -> a) -> Identity a -> Identity a -> Identity a # liftI2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c #
Additive ZipList
Instance details Defined in Linear.Vector Methods zero :: Num a => ZipList a # (^+^) :: Num a => ZipList a -> ZipList a -> ZipList a # (^-^) :: Num a => ZipList a -> ZipList a -> ZipList a # lerp :: Num a => a -> ZipList a -> ZipList a -> ZipList a # liftU2 :: (a -> a -> a) -> ZipList a -> ZipList a -> ZipList a # liftI2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c #
Additive Duration
Instance details Defined in Data.Active Methods zero :: Num a => Duration a # (^+^) :: Num a => Duration a -> Duration a -> Duration a # (^-^) :: Num a => Duration a -> Duration a -> Duration a # lerp :: Num a => a -> Duration a -> Duration a -> Duration a # liftU2 :: (a -> a -> a) -> Duration a -> Duration a -> Duration a # liftI2 :: (a -> b -> c) -> Duration a -> Duration b -> Duration c #
Additive Complex
Instance details Defined in Linear.Vector Methods zero :: Num a => Complex a # (^+^) :: Num a => Complex a -> Complex a -> Complex a # (^-^) :: Num a => Complex a -> Complex a -> Complex a # lerp :: Num a => a -> Complex a -> Complex a -> Complex a # liftU2 :: (a -> a -> a) -> Complex a -> Complex a -> Complex a # liftI2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c #
Additive Vector
Instance details Defined in Linear.Vector Methods zero :: Num a => Vector a # (^+^) :: Num a => Vector a -> Vector a -> Vector a # (^-^) :: Num a => Vector a -> Vector a -> Vector a # lerp :: Num a => a -> Vector a -> Vector a -> Vector a # liftU2 :: (a -> a -> a) -> Vector a -> Vector a -> Vector a # liftI2 :: (a -> b -> c) -> Vector a -> Vector b -> Vector c #
Additive IntMap
Instance details Defined in Linear.Vector Methods zero :: Num a => IntMap a # (^+^) :: Num a => IntMap a -> IntMap a -> IntMap a # (^-^) :: Num a => IntMap a -> IntMap a -> IntMap a # lerp :: Num a => a -> IntMap a -> IntMap a -> IntMap a # liftU2 :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a # liftI2 :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c #
Additive Angle
Instance details Defined in Diagrams.Angle Methods zero :: Num a => Angle a # (^+^) :: Num a => Angle a -> Angle a -> Angle a # (^-^) :: Num a => Angle a -> Angle a -> Angle a # lerp :: Num a => a -> Angle a -> Angle a -> Angle a # liftU2 :: (a -> a -> a) -> Angle a -> Angle a -> Angle a # liftI2 :: (a -> b -> c) -> Angle a -> Angle b -> Angle c #
Additive V2
Instance details Defined in Linear.V2 Methods zero :: Num a => V2 a # (^+^) :: Num a => V2 a -> V2 a -> V2 a # (^-^) :: Num a => V2 a -> V2 a -> V2 a # lerp :: Num a => a -> V2 a -> V2 a -> V2 a # liftU2 :: (a -> a -> a) -> V2 a -> V2 a -> V2 a # liftI2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c #
Additive V3
Instance details Defined in Linear.V3 Methods zero :: Num a => V3 a # (^+^) :: Num a => V3 a -> V3 a -> V3 a # (^-^) :: Num a => V3 a -> V3 a -> V3 a # lerp :: Num a => a -> V3 a -> V3 a -> V3 a # liftU2 :: (a -> a -> a) -> V3 a -> V3 a -> V3 a # liftI2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c #
Additive Plucker
Instance details Defined in Linear.Plucker Methods zero :: Num a => Plucker a # (^+^) :: Num a => Plucker a -> Plucker a -> Plucker a # (^-^) :: Num a => Plucker a -> Plucker a -> Plucker a # lerp :: Num a => a -> Plucker a -> Plucker a -> Plucker a # liftU2 :: (a -> a -> a) -> Plucker a -> Plucker a -> Plucker a # liftI2 :: (a -> b -> c) -> Plucker a -> Plucker b -> Plucker c #
Additive Quaternion
Instance details Defined in Linear.Quaternion Methods zero :: Num a => Quaternion a # (^+^) :: Num a => Quaternion a -> Quaternion a -> Quaternion a # (^-^) :: Num a => Quaternion a -> Quaternion a -> Quaternion a # lerp :: Num a => a -> Quaternion a -> Quaternion a -> Quaternion a # liftU2 :: (a -> a -> a) -> Quaternion a -> Quaternion a -> Quaternion a # liftI2 :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c #
Additive V0
Instance details Defined in Linear.V0 Methods zero :: Num a => V0 a # (^+^) :: Num a => V0 a -> V0 a -> V0 a # (^-^) :: Num a => V0 a -> V0 a -> V0 a # lerp :: Num a => a -> V0 a -> V0 a -> V0 a # liftU2 :: (a -> a -> a) -> V0 a -> V0 a -> V0 a # liftI2 :: (a -> b -> c) -> V0 a -> V0 b -> V0 c #
Additive V4
Instance details Defined in Linear.V4 Methods zero :: Num a => V4 a # (^+^) :: Num a => V4 a -> V4 a -> V4 a # (^-^) :: Num a => V4 a -> V4 a -> V4 a # lerp :: Num a => a -> V4 a -> V4 a -> V4 a # liftU2 :: (a -> a -> a) -> V4 a -> V4 a -> V4 a # liftI2 :: (a -> b -> c) -> V4 a -> V4 b -> V4 c #
Additive V1
Instance details Defined in Linear.V1 Methods zero :: Num a => V1 a # (^+^) :: Num a => V1 a -> V1 a -> V1 a # (^-^) :: Num a => V1 a -> V1 a -> V1 a # lerp :: Num a => a -> V1 a -> V1 a -> V1 a # liftU2 :: (a -> a -> a) -> V1 a -> V1 a -> V1 a # liftI2 :: (a -> b -> c) -> V1 a -> V1 b -> V1 c #
Ord k => Additive (Map k)
Instance details Defined in Linear.Vector Methods zero :: Num a => Map k a # (^+^) :: Num a => Map k a -> Map k a -> Map k a # (^-^) :: Num a => Map k a -> Map k a -> Map k a # lerp :: Num a => a -> Map k a -> Map k a -> Map k a # liftU2 :: (a -> a -> a) -> Map k a -> Map k a -> Map k a # liftI2 :: (a -> b -> c) -> Map k a -> Map k b -> Map k c #
(Eq k, Hashable k) => Additive (HashMap k)
Instance details Defined in Linear.Vector Methods zero :: Num a => HashMap k a # (^+^) :: Num a => HashMap k a -> HashMap k a -> HashMap k a # (^-^) :: Num a => HashMap k a -> HashMap k a -> HashMap k a # lerp :: Num a => a -> HashMap k a -> HashMap k a -> HashMap k a # liftU2 :: (a -> a -> a) -> HashMap k a -> HashMap k a -> HashMap k a # liftI2 :: (a -> b -> c) -> HashMap k a -> HashMap k b -> HashMap k c #
Additive (Measured n)
Instance details Defined in Diagrams.Core.Measure Methods zero :: Num a => Measured n a # (^+^) :: Num a => Measured n a -> Measured n a -> Measured n a # (^-^) :: Num a => Measured n a -> Measured n a -> Measured n a # lerp :: Num a => a -> Measured n a -> Measured n a -> Measured n a # liftU2 :: (a -> a -> a) -> Measured n a -> Measured n a -> Measured n a # liftI2 :: (a -> b -> c) -> Measured n a -> Measured n b -> Measured n c #
Additive f => Additive (Point f)
Instance details Defined in Linear.Affine Methods zero :: Num a => Point f a # (^+^) :: Num a => Point f a -> Point f a -> Point f a # (^-^) :: Num a => Point f a -> Point f a -> Point f a # lerp :: Num a => a -> Point f a -> Point f a -> Point f a # liftU2 :: (a -> a -> a) -> Point f a -> Point f a -> Point f a # liftI2 :: (a -> b -> c) -> Point f a -> Point f b -> Point f c #
Dim n => Additive (V n)
Instance details Defined in Linear.V Methods zero :: Num a => V n a # (^+^) :: Num a => V n a -> V n a -> V n a # (^-^) :: Num a => V n a -> V n a -> V n a # lerp :: Num a => a -> V n a -> V n a -> V n a # liftU2 :: (a -> a -> a) -> V n a -> V n a -> V n a # liftI2 :: (a -> b -> c) -> V n a -> V n b -> V n c #
Additive ((->) b :: Type -> Type)
Instance details Defined in Linear.Vector Methods zero :: Num a => b -> a # (^+^) :: Num a => (b -> a) -> (b -> a) -> b -> a # (^-^) :: Num a => (b -> a) -> (b -> a) -> b -> a # lerp :: Num a => a -> (b -> a) -> (b -> a) -> b -> a # liftU2 :: (a -> a -> a) -> (b -> a) -> (b -> a) -> b -> a # liftI2 :: (a -> b0 -> c) -> (b -> a) -> (b -> b0) -> b -> c #

renderDia :: (Backend b v n, HasLinearMap v, Metric v, Typeable n, OrderedField n, Monoid' m) => b -> Options b v n -> QDiagram b v n m -> Result b v n #

Render a diagram.

renderDiaT :: (Backend b v n, HasLinearMap v, Metric v, Typeable n, OrderedField n, Monoid' m) => b -> Options b v n -> QDiagram b v n m -> (Transformation v n, Result b v n) #

Render a diagram, returning also the transformation which was used to convert the diagram from its ("global") coordinate system into the output coordinate system. The inverse of this transformation can be used, for example, to convert output/screen coordinates back into diagram coordinates. See also adjustDia.

lookupSub :: IsName nm => nm -> SubMap b v n m -> Maybe [Subdiagram b v n m] #

Look for the given name in a name map, returning a list of subdiagrams associated with that name. If no names match the given name exactly, return all the subdiagrams associated with names of which the given name is a suffix.

rememberAs :: IsName a => a -> QDiagram b v n m -> SubMap b v n m -> SubMap b v n m #

Add a name/diagram association to a submap.

fromNames :: IsName a => [(a, Subdiagram b v n m)] -> SubMap b v n m #

Construct a SubMap from a list of associations between names and subdiagrams.

rawSub :: Subdiagram b v n m -> QDiagram b v n m #

Extract the "raw" content of a subdiagram, by throwing away the context.

getSub :: (Metric v, OrderedField n, Semigroup m) => Subdiagram b v n m -> QDiagram b v n m #

Turn a subdiagram into a normal diagram, including the enclosing context. Concretely, a subdiagram is a pair of (1) a diagram and (2) a "context" consisting of an extra transformation and attributes. getSub simply applies the transformation and attributes to the diagram to get the corresponding "top-level" diagram.

location :: (Additive v, Num n) => Subdiagram b v n m -> Point v n #

Get the location of a subdiagram; that is, the location of its local origin with respect to the vector space of its parent diagram. In other words, the point where its local origin "ended up".

subPoint :: (Metric v, OrderedField n) => Point v n -> Subdiagram b v n m #

Create a "point subdiagram", that is, a pointDiagram (with no content and a point envelope) treated as a subdiagram with local origin at the given point. Note this is not the same as mkSubdiagram . pointDiagram, which would result in a subdiagram with local origin at the parent origin, rather than at the given point.

mkSubdiagram :: QDiagram b v n m -> Subdiagram b v n m #

Turn a diagram into a subdiagram with no accumulated context.

atop :: (OrderedField n, Metric v, Semigroup m) => QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m infixl 6 #

A convenient synonym for mappend on diagrams, designed to be used infix (to help remember which diagram goes on top of which when combining them, namely, the first on top of the second).

mkQD :: Prim b v n -> Envelope v n -> Trace v n -> SubMap b v n m -> Query v n m -> QDiagram b v n m #

Create a diagram from a single primitive, along with an envelope, trace, subdiagram map, and query function.

query :: Monoid m => QDiagram b v n m -> Query v n m #

Get the query function associated with a diagram.

localize :: (Metric v, OrderedField n, Semigroup m) => QDiagram b v n m -> QDiagram b v n m #

"Localize" a diagram by hiding all the names, so they are no longer visible to the outside.

withNames :: (IsName nm, Metric v, Semigroup m, OrderedField n) => [nm] -> ([Subdiagram b v n m] -> QDiagram b v n m -> QDiagram b v n m) -> QDiagram b v n m -> QDiagram b v n m #

Given a list of names and a diagram transformation indexed by a list of subdiagrams, perform the transformation using the list of most recent subdiagrams associated with (some qualification of) each name. Do nothing (the identity transformation) if any of the names do not exist.

withNameAll :: (IsName nm, Metric v, Semigroup m, OrderedField n) => nm -> ([Subdiagram b v n m] -> QDiagram b v n m -> QDiagram b v n m) -> QDiagram b v n m -> QDiagram b v n m #

Given a name and a diagram transformation indexed by a list of subdiagrams, perform the transformation using the collection of all such subdiagrams associated with (some qualification of) the given name.

withName :: (IsName nm, Metric v, Semigroup m, OrderedField n) => nm -> (Subdiagram b v n m -> QDiagram b v n m -> QDiagram b v n m) -> QDiagram b v n m -> QDiagram b v n m #

Given a name and a diagram transformation indexed by a subdiagram, perform the transformation using the most recent subdiagram associated with (some qualification of) the name, or perform the identity transformation if the name does not exist.

lookupName :: (IsName nm, Metric v, Semigroup m, OrderedField n) => nm -> QDiagram b v n m -> Maybe (Subdiagram b v n m) #

Lookup the most recent diagram associated with (some qualification of) the given name.

nameSub :: (IsName nm, Metric v, OrderedField n, Semigroup m) => (QDiagram b v n m -> Subdiagram b v n m) -> nm -> QDiagram b v n m -> QDiagram b v n m #

Attach an atomic name to a certain subdiagram, computed from the given diagram /with the mapping from name to subdiagram included/. The upshot of this knot-tying is that if d' = d # named x, then lookupName x d' == Just d' (instead of Just d).

names :: (Metric v, Semigroup m, OrderedField n) => QDiagram b v n m -> [(Name, [Point v n])] #

Get a list of names of subdiagrams and their locations.

subMap :: (Metric v, Semigroup m, OrderedField n) => Lens' (QDiagram b v n m) (SubMap b v n m) #

Lens onto the SubMap of a QDiagram (i.e. an association from names to subdiagrams).

setTrace :: (OrderedField n, Metric v, Semigroup m) => Trace v n -> QDiagram b v n m -> QDiagram b v n m #

Replace the trace of a diagram.

setEnvelope :: (OrderedField n, Metric v, Monoid' m) => Envelope v n -> QDiagram b v n m -> QDiagram b v n m #

Replace the envelope of a diagram.

envelope :: (OrderedField n, Metric v, Monoid' m) => Lens' (QDiagram b v n m) (Envelope v n) #

Lens onto the Envelope of a QDiagram.

pointDiagram :: (Metric v, Fractional n) => Point v n -> QDiagram b v n m #

Create a "point diagram", which has no content, no trace, an empty query, and a point envelope.

groupOpacity :: (Metric v, OrderedField n, Semigroup m) => Double -> QDiagram b v n m -> QDiagram b v n m #

Change the transparency of a Diagram as a group.

opacityGroup :: (Metric v, OrderedField n, Semigroup m) => Double -> QDiagram b v n m -> QDiagram b v n m #

Change the transparency of a Diagram as a group.

href :: (Metric v, OrderedField n, Semigroup m) => String -> QDiagram b v n m -> QDiagram b v n m #

Make a diagram into a hyperlink. Note that only some backends will honor hyperlink annotations.

type TypeableFloat n = (Typeable n, RealFloat n) #

Constraint for numeric types that are RealFloat and Typeable, which often occur together. This is used to shorten shorten type constraint contexts.

data QDiagram b (v :: Type -> Type) n m #

The fundamental diagram type. The type variables are as follows:

b represents the backend, such as SVG or Cairo. Note that each backend also exports a type synonym B for itself, so the type variable b may also typically be instantiated by B, meaning "use whatever backend is in scope".
v represents the vector space of the diagram. Typical instantiations include V2 (for a two-dimensional diagram) or V3 (for a three-dimensional diagram).
n represents the numerical field the diagram uses. Typically this will be a concrete numeric type like Double.
m is the monoidal type of "query annotations": each point in the diagram has a value of type m associated to it, and these values are combined according to the Monoid instance for m. Most often, m is simply instantiated to Any, associating a simple Bool value to each point indicating whether the point is inside the diagram; Diagram is a synonym for QDiagram with m thus instantiated to Any.

Diagrams can be combined via their Monoid instance, transformed via their Transformable instance, and assigned attributes via their HasStyle instance.

Note that the Q in QDiagram stands for "Queriable", as distinguished from Diagram, where m is fixed to Any. This is not really a very good name, but it's probably not worth changing it at this point.

Instances

Functor (QDiagram b v n)
Instance details Defined in Diagrams.Core.Types Methods fmap :: (a -> b0) -> QDiagram b v n a -> QDiagram b v n b0 # (<$) :: a -> QDiagram b v n b0 -> QDiagram b v n a #
(Metric v, OrderedField n, Semigroup m) => Semigroup (QDiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods (<>) :: QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m # sconcat :: NonEmpty (QDiagram b v n m) -> QDiagram b v n m # stimes :: Integral b0 => b0 -> QDiagram b v n m -> QDiagram b v n m #
(Metric v, OrderedField n, Semigroup m) => Monoid (QDiagram b v n m)	Diagrams form a monoid since each of their components do: the empty diagram has no primitives, an empty envelope, an empty trace, no named subdiagrams, and a constantly empty query function. Diagrams compose by aligning their respective local origins. The new diagram has all the primitives and all the names from the two diagrams combined, and query functions are combined pointwise. The first diagram goes on top of the second. "On top of" probably only makes sense in vector spaces of dimension lower than 3, but in theory it could make sense for, say, 3-dimensional diagrams when viewed by 4-dimensional beings.
Instance details Defined in Diagrams.Core.Types Methods mempty :: QDiagram b v n m # mappend :: QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m # mconcat :: [QDiagram b v n m] -> QDiagram b v n m #
(Metric v, OrderedField n, Monoid' m) => Juxtaposable (QDiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods juxtapose :: Vn (QDiagram b v n m) -> QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m #
(Metric v, OrderedField n, Monoid' m) => Enveloped (QDiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods getEnvelope :: QDiagram b v n m -> Envelope (V (QDiagram b v n m)) (N (QDiagram b v n m)) #
(Metric v, OrderedField n, Semigroup m) => Traced (QDiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods getTrace :: QDiagram b v n m -> Trace (V (QDiagram b v n m)) (N (QDiagram b v n m)) #
(Metric v, OrderedField n, Semigroup m) => Qualifiable (QDiagram b v n m)	Diagrams can be qualified so that all their named points can now be referred to using the qualification prefix.
Instance details Defined in Diagrams.Core.Types Methods (.>>) :: IsName a => a -> QDiagram b v n m -> QDiagram b v n m #
(Metric v, OrderedField n, Semigroup m) => HasStyle (QDiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods applyStyle :: Style (V (QDiagram b v n m)) (N (QDiagram b v n m)) -> QDiagram b v n m -> QDiagram b v n m #
(OrderedField n, Metric v, Semigroup m) => Transformable (QDiagram b v n m)	Diagrams can be transformed by transforming each of their components appropriately.
Instance details Defined in Diagrams.Core.Types Methods transform :: Transformation (V (QDiagram b v n m)) (N (QDiagram b v n m)) -> QDiagram b v n m -> QDiagram b v n m #
(Metric v, OrderedField n, Semigroup m) => HasOrigin (QDiagram b v n m)	Every diagram has an intrinsic "local origin" which is the basis for all combining operations.
Instance details Defined in Diagrams.Core.Types Methods moveOriginTo :: Point (V (QDiagram b v n m)) (N (QDiagram b v n m)) -> QDiagram b v n m -> QDiagram b v n m #
(Metric v, OrderedField n, Monoid' m) => Alignable (QDiagram b v n m)
Instance details Defined in Diagrams.Align Methods alignBy' :: (InSpace v0 n0 (QDiagram b v n m), Fractional n0, HasOrigin (QDiagram b v n m)) => (v0 n0 -> QDiagram b v n m -> Point v0 n0) -> v0 n0 -> n0 -> QDiagram b v n m -> QDiagram b v n m # defaultBoundary :: (V (QDiagram b v n m) ~ v0, N (QDiagram b v n m) ~ n0) => v0 n0 -> QDiagram b v n m -> Point v0 n0 # alignBy :: (InSpace v0 n0 (QDiagram b v n m), Fractional n0, HasOrigin (QDiagram b v n m)) => v0 n0 -> n0 -> QDiagram b v n m -> QDiagram b v n m #
Wrapped (QDiagram b v n m)
Instance details Defined in Diagrams.Core.Types Associated Types type Unwrapped (QDiagram b v n m) :: Type # Methods _Wrapped' :: Iso' (QDiagram b v n m) (Unwrapped (QDiagram b v n m)) #
Monoid m => HasQuery (QDiagram b v n m) m
Instance details Defined in Diagrams.Query Methods getQuery :: QDiagram b v n m -> Query (V (QDiagram b v n m)) (N (QDiagram b v n m)) m #
Rewrapped (QDiagram b v n m) (QDiagram b' v' n' m')
Instance details Defined in Diagrams.Core.Types
type V (QDiagram b v n m)
Instance details Defined in Diagrams.Core.Types type V (QDiagram b v n m) = v
type N (QDiagram b v n m)
Instance details Defined in Diagrams.Core.Types type N (QDiagram b v n m) = n
type Unwrapped (QDiagram b v n m)
Instance details Defined in Diagrams.Core.Types type Unwrapped (QDiagram b v n m) = DUALTree (DownAnnots v n) (UpAnnots b v n m) Annotation (QDiaLeaf b v n m)

type Diagram b = QDiagram b (V b) (N b) Any #

Diagram b is a synonym for QDiagram b (V b) (N b) Any. That is, the default sort of diagram is one where querying at a point simply tells you whether the diagram contains that point or not. Transforming a default diagram into one with a more interesting query can be done via the Functor instance of QDiagram b v n or the value function.

data Subdiagram b (v :: Type -> Type) n m #

A Subdiagram represents a diagram embedded within the context of a larger diagram. Essentially, it consists of a diagram paired with any accumulated information from the larger context (transformations, attributes, etc.).

Constructors

Subdiagram (QDiagram b v n m) (DownAnnots v n)

Instances

Functor (Subdiagram b v n)
Instance details Defined in Diagrams.Core.Types Methods fmap :: (a -> b0) -> Subdiagram b v n a -> Subdiagram b v n b0 # (<$) :: a -> Subdiagram b v n b0 -> Subdiagram b v n a #
(OrderedField n, Metric v, Monoid' m) => Enveloped (Subdiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods getEnvelope :: Subdiagram b v n m -> Envelope (V (Subdiagram b v n m)) (N (Subdiagram b v n m)) #
(OrderedField n, Metric v, Semigroup m) => Traced (Subdiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods getTrace :: Subdiagram b v n m -> Trace (V (Subdiagram b v n m)) (N (Subdiagram b v n m)) #
Transformable (Subdiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods transform :: Transformation (V (Subdiagram b v n m)) (N (Subdiagram b v n m)) -> Subdiagram b v n m -> Subdiagram b v n m #
(Metric v, OrderedField n) => HasOrigin (Subdiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods moveOriginTo :: Point (V (Subdiagram b v n m)) (N (Subdiagram b v n m)) -> Subdiagram b v n m -> Subdiagram b v n m #
type V (Subdiagram b v n m)
Instance details Defined in Diagrams.Core.Types type V (Subdiagram b v n m) = v
type N (Subdiagram b v n m)
Instance details Defined in Diagrams.Core.Types type N (Subdiagram b v n m) = n

newtype SubMap b (v :: Type -> Type) n m #

A SubMap is a map associating names to subdiagrams. There can be multiple associations for any given name.

Constructors

SubMap (Map Name [Subdiagram b v n m])

Instances

Action Name (SubMap b v n m)	A name acts on a name map by qualifying every name in it.
Instance details Defined in Diagrams.Core.Types Methods act :: Name -> SubMap b v n m -> SubMap b v n m #
Functor (SubMap b v n)
Instance details Defined in Diagrams.Core.Types Methods fmap :: (a -> b0) -> SubMap b v n a -> SubMap b v n b0 # (<$) :: a -> SubMap b v n b0 -> SubMap b v n a #
Semigroup (SubMap b v n m)
Instance details Defined in Diagrams.Core.Types Methods (<>) :: SubMap b v n m -> SubMap b v n m -> SubMap b v n m # sconcat :: NonEmpty (SubMap b v n m) -> SubMap b v n m # stimes :: Integral b0 => b0 -> SubMap b v n m -> SubMap b v n m #
Monoid (SubMap b v n m)	`SubMap`s form a monoid with the empty map as the identity, and map union as the binary operation. No information is ever lost: if two maps have the same name in their domain, the resulting map will associate that name to the concatenation of the information associated with that name.
Instance details Defined in Diagrams.Core.Types Methods mempty :: SubMap b v n m # mappend :: SubMap b v n m -> SubMap b v n m -> SubMap b v n m # mconcat :: [SubMap b v n m] -> SubMap b v n m #
Qualifiable (SubMap b v n m)	`SubMap`s are qualifiable: if `ns` is a `SubMap`, then `a \|> ns` is the same `SubMap` except with every name qualified by `a`.
Instance details Defined in Diagrams.Core.Types Methods (.>>) :: IsName a => a -> SubMap b v n m -> SubMap b v n m #
Transformable (SubMap b v n m)
Instance details Defined in Diagrams.Core.Types Methods transform :: Transformation (V (SubMap b v n m)) (N (SubMap b v n m)) -> SubMap b v n m -> SubMap b v n m #
(OrderedField n, Metric v) => HasOrigin (SubMap b v n m)
Instance details Defined in Diagrams.Core.Types Methods moveOriginTo :: Point (V (SubMap b v n m)) (N (SubMap b v n m)) -> SubMap b v n m -> SubMap b v n m #
Wrapped (SubMap b v n m)
Instance details Defined in Diagrams.Core.Types Associated Types type Unwrapped (SubMap b v n m) :: Type # Methods _Wrapped' :: Iso' (SubMap b v n m) (Unwrapped (SubMap b v n m)) #
Rewrapped (SubMap b v n m) (SubMap b' v' n' m')
Instance details Defined in Diagrams.Core.Types
type V (SubMap b v n m)
Instance details Defined in Diagrams.Core.Types type V (SubMap b v n m) = v
type N (SubMap b v n m)
Instance details Defined in Diagrams.Core.Types type N (SubMap b v n m) = n
type Unwrapped (SubMap b v n m)
Instance details Defined in Diagrams.Core.Types type Unwrapped (SubMap b v n m) = Map Name [Subdiagram b v n m]

data Prim b (v :: Type -> Type) n where #

A value of type Prim b v n is an opaque (existentially quantified) primitive which backend b knows how to render in vector space v.

Constructors

Prim :: forall b (v :: Type -> Type) n p. (Transformable p, Typeable p, Renderable p b) => p -> Prim b (V p) (N p)

Instances

Transformable (Prim b v n)	The `Transformable` instance for `Prim` just pushes calls to `transform` down through the `Prim` constructor.
Instance details Defined in Diagrams.Core.Types Methods transform :: Transformation (V (Prim b v n)) (N (Prim b v n)) -> Prim b v n -> Prim b v n #
Renderable (Prim b v n) b	The `Renderable` instance for `Prim` just pushes calls to `render` down through the `Prim` constructor.
Instance details Defined in Diagrams.Core.Types Methods render :: b -> Prim b v n -> Render b (V (Prim b v n)) (N (Prim b v n)) #
type V (Prim b v n)
Instance details Defined in Diagrams.Core.Types type V (Prim b v n) = v
type N (Prim b v n)
Instance details Defined in Diagrams.Core.Types type N (Prim b v n) = n

class Backend b (v :: Type -> Type) n where #

Abstract diagrams are rendered to particular formats by backends. Each backend/vector space combination must be an instance of the Backend class.

A minimal complete definition consists of Render, Result, Options, and renderRTree. However, most backends will want to implement adjustDia as well; the default definition does nothing. Some useful standard definitions are provided in the Diagrams.TwoD.Adjust module from the diagrams-lib package.

Minimal complete definition

renderRTree

Associated Types

data Render b (v :: Type -> Type) n :: Type #

An intermediate representation used for rendering primitives. (Typically, this will be some sort of monad, but it need not be.) The Renderable class guarantees that a backend will be able to convert primitives into this type; how these rendered primitives are combined into an ultimate Result is completely up to the backend.

type Result b (v :: Type -> Type) n :: Type #

The result of running/interpreting a rendering operation.

data Options b (v :: Type -> Type) n :: Type #

Backend-specific rendering options.

Methods

adjustDia :: (Additive v, Monoid' m, Num n) => b -> Options b v n -> QDiagram b v n m -> (Options b v n, Transformation v n, QDiagram b v n m) #

adjustDia allows the backend to make adjustments to the final diagram (e.g. to adjust the size based on the options) before rendering it. It returns a modified options record, the transformation applied to the diagram (which can be used to convert attributes whose value is Measure, or transform e.g. screen coordinates back into local diagram coordinates), and the adjusted diagram itself.

See the diagrams-lib package (particularly the Diagrams.TwoD.Adjust module) for some useful implementations.

renderRTree :: b -> Options b v n -> RTree b v n Annotation -> Result b v n #

Given some options, take a representation of a diagram as a tree and render it. The RTree has already been simplified and has all measurements converted to Output units.

Instances

Backend NullBackend v n
Instance details Defined in Diagrams.Core.Types Associated Types data Render NullBackend v n :: Type # type Result NullBackend v n :: Type # data Options NullBackend v n :: Type # Methods adjustDia :: (Additive v, Monoid' m, Num n) => NullBackend -> Options NullBackend v n -> QDiagram NullBackend v n m -> (Options NullBackend v n, Transformation v n, QDiagram NullBackend v n m) # renderRTree :: NullBackend -> Options NullBackend v n -> RTree NullBackend v n Annotation -> Result NullBackend v n #
SVGFloat n => Backend SVG V2 n
Instance details Defined in Diagrams.Backend.SVG Associated Types data Render SVG V2 n :: Type # type Result SVG V2 n :: Type # data Options SVG V2 n :: Type # Methods adjustDia :: (Additive V2, Monoid' m, Num n) => SVG -> Options SVG V2 n -> QDiagram SVG V2 n m -> (Options SVG V2 n, Transformation V2 n, QDiagram SVG V2 n m) # renderRTree :: SVG -> Options SVG V2 n -> RTree SVG V2 n Annotation -> Result SVG V2 n #

type D (v :: Type -> Type) n = QDiagram NullBackend v n Any #

The D type is provided for convenience in situations where you must give a diagram a concrete, monomorphic type, but don't care which one. Such situations arise when you pass a diagram to a function which is polymorphic in its input but monomorphic in its output, such as width, height, phantom, or names. Such functions compute some property of the diagram, or use it to accomplish some other purpose, but do not result in the diagram being rendered. If the diagram does not have a monomorphic type, GHC complains that it cannot determine the diagram's type.

For example, here is the error we get if we try to compute the width of an image (this example requires diagrams-lib):

  ghci> width (image (uncheckedImageRef "foo.png" 200 200))
  <interactive>:11:8:
      No instance for (Renderable (DImage n0 External) b0)
        arising from a use of image
      The type variables n0, b0 are ambiguous
      Possible fix: add a type signature that fixes these type variable(s)
      Note: there is a potential instance available:
        instance Fractional n => Renderable (DImage n a) NullBackend
          -- Defined in Image
      Possible fix:
        add an instance declaration for
        (Renderable (DImage n0 External) b0)
      In the first argument of width, namely
        `(image (uncheckedImageRef "foo.png" 200 200))'
      In the expression:
        width (image (uncheckedImageRef "foo.png" 200 200))
      In an equation for it:
          it = width (image (uncheckedImageRef "foo.png" 200 200))

GHC complains that there is no instance for Renderable (DImage n0 External) b0; what is really going on is that it does not have enough information to decide what backend to use (hence the uninstantiated n0 and b0). This is annoying because we know that the choice of backend cannot possibly affect the width of the image (it's 200! it's right there in the code!); but there is no way for GHC to know that.

The solution is to annotate the call to image with the type D V2 Double, like so:

  ghci> width (image (uncheckedImageRef "foo.png" 200 200) :: D V2 Double)
  200.00000000000006

(It turns out the width wasn't 200 after all...)

As another example, here is the error we get if we try to compute the width of a radius-1 circle:

  ghci> width (circle 1)
  <interactive>:12:1:
      Couldn't match expected type V2 with actual type `V a0'
      The type variable a0 is ambiguous
      Possible fix: add a type signature that fixes these type variable(s)
      In the expression: width (circle 1)
      In an equation for it: it = width (circle 1)

There's even more ambiguity here. Whereas image always returns a Diagram, the circle function can produce any TrailLike type, and the width function can consume any Enveloped type, so GHC has no idea what type to pick to go in the middle. However, the solution is the same:

  ghci> width (circle 1 :: D V2 Double)
  1.9999999999999998

data NullBackend #

A null backend which does no actual rendering. It is provided mainly for convenience in situations where you must give a diagram a concrete, monomorphic type, but don't actually care which one. See D for more explanation and examples.

It is courteous, when defining a new primitive P, to make an instance

instance Renderable P NullBackend where
  render _ _ = mempty

This ensures that the trick with D annotations can be used for diagrams containing your primitive.

Instances

Backend NullBackend v n
Instance details Defined in Diagrams.Core.Types Associated Types data Render NullBackend v n :: Type # type Result NullBackend v n :: Type # data Options NullBackend v n :: Type # Methods adjustDia :: (Additive v, Monoid' m, Num n) => NullBackend -> Options NullBackend v n -> QDiagram NullBackend v n m -> (Options NullBackend v n, Transformation v n, QDiagram NullBackend v n m) # renderRTree :: NullBackend -> Options NullBackend v n -> RTree NullBackend v n Annotation -> Result NullBackend v n #
Floating n => Renderable (Text n) NullBackend
Instance details Defined in Diagrams.TwoD.Text Methods render :: NullBackend -> Text n -> Render NullBackend (V (Text n)) (N (Text n)) #
Fractional n => Renderable (Ellipsoid n) NullBackend
Instance details Defined in Diagrams.ThreeD.Shapes Methods render :: NullBackend -> Ellipsoid n -> Render NullBackend (V (Ellipsoid n)) (N (Ellipsoid n)) #
Fractional n => Renderable (Box n) NullBackend
Instance details Defined in Diagrams.ThreeD.Shapes Methods render :: NullBackend -> Box n -> Render NullBackend (V (Box n)) (N (Box n)) #
Fractional n => Renderable (Frustum n) NullBackend
Instance details Defined in Diagrams.ThreeD.Shapes Methods render :: NullBackend -> Frustum n -> Render NullBackend (V (Frustum n)) (N (Frustum n)) #
Fractional n => Renderable (DImage n a) NullBackend
Instance details Defined in Diagrams.TwoD.Image Methods render :: NullBackend -> DImage n a -> Render NullBackend (V (DImage n a)) (N (DImage n a)) #
(HasLinearMap v, Metric v, OrderedField n) => Renderable (Path v n) NullBackend
Instance details Defined in Diagrams.Path Methods render :: NullBackend -> Path v n -> Render NullBackend (V (Path v n)) (N (Path v n)) #
Num n => Renderable (Camera l n) NullBackend
Instance details Defined in Diagrams.ThreeD.Camera Methods render :: NullBackend -> Camera l n -> Render NullBackend (V (Camera l n)) (N (Camera l n)) #
Semigroup (Render NullBackend v n)
Instance details Defined in Diagrams.Core.Types Methods (<>) :: Render NullBackend v n -> Render NullBackend v n -> Render NullBackend v n # sconcat :: NonEmpty (Render NullBackend v n) -> Render NullBackend v n # stimes :: Integral b => b -> Render NullBackend v n -> Render NullBackend v n #
Monoid (Render NullBackend v n)
Instance details Defined in Diagrams.Core.Types Methods mempty :: Render NullBackend v n # mappend :: Render NullBackend v n -> Render NullBackend v n -> Render NullBackend v n # mconcat :: [Render NullBackend v n] -> Render NullBackend v n #
(HasLinearMap v, Metric v, OrderedField n) => Renderable (Trail' o v n) NullBackend
Instance details Defined in Diagrams.Trail Methods render :: NullBackend -> Trail' o v n -> Render NullBackend (V (Trail' o v n)) (N (Trail' o v n)) #
Renderable (Segment c v n) NullBackend
Instance details Defined in Diagrams.Segment Methods render :: NullBackend -> Segment c v n -> Render NullBackend (V (Segment c v n)) (N (Segment c v n)) #
data Options NullBackend v n
Instance details Defined in Diagrams.Core.Types data Options NullBackend v n
data Render NullBackend v n
Instance details Defined in Diagrams.Core.Types data Render NullBackend v n = NullBackendRender
type Result NullBackend v n
Instance details Defined in Diagrams.Core.Types type Result NullBackend v n = ()

class Transformable t => Renderable t b where #

The Renderable type class connects backends to primitives which they know how to render.

Methods

render :: b -> t -> Render b (V t) (N t) #

Given a token representing the backend and a transformable object, render it in the appropriate rendering context.

Instances

Floating n => Renderable (Text n) NullBackend
Instance details Defined in Diagrams.TwoD.Text Methods render :: NullBackend -> Text n -> Render NullBackend (V (Text n)) (N (Text n)) #
SVGFloat n => Renderable (Text n) SVG
Instance details Defined in Diagrams.Backend.SVG Methods render :: SVG -> Text n -> Render SVG (V (Text n)) (N (Text n)) #
Fractional n => Renderable (Ellipsoid n) NullBackend
Instance details Defined in Diagrams.ThreeD.Shapes Methods render :: NullBackend -> Ellipsoid n -> Render NullBackend (V (Ellipsoid n)) (N (Ellipsoid n)) #
Fractional n => Renderable (Box n) NullBackend
Instance details Defined in Diagrams.ThreeD.Shapes Methods render :: NullBackend -> Box n -> Render NullBackend (V (Box n)) (N (Box n)) #
Fractional n => Renderable (Frustum n) NullBackend
Instance details Defined in Diagrams.ThreeD.Shapes Methods render :: NullBackend -> Frustum n -> Render NullBackend (V (Frustum n)) (N (Frustum n)) #
Fractional n => Renderable (DImage n a) NullBackend
Instance details Defined in Diagrams.TwoD.Image Methods render :: NullBackend -> DImage n a -> Render NullBackend (V (DImage n a)) (N (DImage n a)) #
SVGFloat n => Renderable (DImage n (Native Img)) SVG
Instance details Defined in Diagrams.Backend.SVG Methods render :: SVG -> DImage n (Native Img) -> Render SVG (V (DImage n (Native Img))) (N (DImage n (Native Img))) #
SVGFloat n => Renderable (DImage n Embedded) SVG
Instance details Defined in Diagrams.Backend.SVG Methods render :: SVG -> DImage n Embedded -> Render SVG (V (DImage n Embedded)) (N (DImage n Embedded)) #
(HasLinearMap v, Metric v, OrderedField n) => Renderable (Path v n) NullBackend
Instance details Defined in Diagrams.Path Methods render :: NullBackend -> Path v n -> Render NullBackend (V (Path v n)) (N (Path v n)) #
SVGFloat n => Renderable (Path V2 n) SVG
Instance details Defined in Diagrams.Backend.SVG Methods render :: SVG -> Path V2 n -> Render SVG (V (Path V2 n)) (N (Path V2 n)) #
Num n => Renderable (Camera l n) NullBackend
Instance details Defined in Diagrams.ThreeD.Camera Methods render :: NullBackend -> Camera l n -> Render NullBackend (V (Camera l n)) (N (Camera l n)) #
Renderable (Prim b v n) b	The `Renderable` instance for `Prim` just pushes calls to `render` down through the `Prim` constructor.
Instance details Defined in Diagrams.Core.Types Methods render :: b -> Prim b v n -> Render b (V (Prim b v n)) (N (Prim b v n)) #
(HasLinearMap v, Metric v, OrderedField n) => Renderable (Trail' o v n) NullBackend
Instance details Defined in Diagrams.Trail Methods render :: NullBackend -> Trail' o v n -> Render NullBackend (V (Trail' o v n)) (N (Trail' o v n)) #
Renderable (Segment c v n) NullBackend
Instance details Defined in Diagrams.Segment Methods render :: NullBackend -> Segment c v n -> Render NullBackend (V (Segment c v n)) (N (Segment c v n)) #

juxtaposeDefault :: (Enveloped a, HasOrigin a) => Vn a -> a -> a -> a #

Default implementation of juxtapose for things which are instances of Enveloped and HasOrigin. If either envelope is empty, the second object is returned unchanged.

class Juxtaposable a where #

Class of things which can be placed "next to" other things, for some appropriate notion of "next to".

Methods

juxtapose :: Vn a -> a -> a -> a #

juxtapose v a1 a2 positions a2 next to a1 in the direction of v. In particular, place a2 so that v points from the local origin of a1 towards the old local origin of a2; a1's local origin becomes a2's new local origin. The result is just a translated version of a2. (In particular, this operation does not combine a1 and a2 in any way.)

Instances

(Enveloped b, HasOrigin b) => Juxtaposable [b]
Instance details Defined in Diagrams.Core.Juxtapose Methods juxtapose :: Vn [b] -> [b] -> [b] -> [b] #
(Enveloped b, HasOrigin b, Ord b) => Juxtaposable (Set b)
Instance details Defined in Diagrams.Core.Juxtapose Methods juxtapose :: Vn (Set b) -> Set b -> Set b -> Set b #
Enveloped a => Juxtaposable (Located a)
Instance details Defined in Diagrams.Located Methods juxtapose :: Vn (Located a) -> Located a -> Located a -> Located a #
Juxtaposable a => Juxtaposable (b -> a)
Instance details Defined in Diagrams.Core.Juxtapose Methods juxtapose :: Vn (b -> a) -> (b -> a) -> (b -> a) -> b -> a #
(Enveloped a, HasOrigin a, Enveloped b, HasOrigin b, V a ~ V b, N a ~ N b) => Juxtaposable (a, b)
Instance details Defined in Diagrams.Core.Juxtapose Methods juxtapose :: Vn (a, b) -> (a, b) -> (a, b) -> (a, b) #
(Enveloped b, HasOrigin b) => Juxtaposable (Map k b)
Instance details Defined in Diagrams.Core.Juxtapose Methods juxtapose :: Vn (Map k b) -> Map k b -> Map k b -> Map k b #
(Metric v, OrderedField n) => Juxtaposable (Envelope v n)
Instance details Defined in Diagrams.Core.Juxtapose Methods juxtapose :: Vn (Envelope v n) -> Envelope v n -> Envelope v n -> Envelope v n #
Juxtaposable a => Juxtaposable (Measured n a)
Instance details Defined in Diagrams.Core.Juxtapose Methods juxtapose :: Vn (Measured n a) -> Measured n a -> Measured n a -> Measured n a #
(Metric v, OrderedField n) => Juxtaposable (Path v n)
Instance details Defined in Diagrams.Path Methods juxtapose :: Vn (Path v n) -> Path v n -> Path v n -> Path v n #
(Metric v, OrderedField n, Monoid' m) => Juxtaposable (QDiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods juxtapose :: Vn (QDiagram b v n m) -> QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m #

size :: (V a ~ v, N a ~ n, Enveloped a, HasBasis v) => a -> v n #

The smallest positive axis-parallel vector that bounds the envelope of an object.

radius :: (V a ~ v, N a ~ n, Enveloped a) => v n -> a -> n #

Compute the "radius" (1/2 the diameter) of an enveloped object along a particular vector.

diameter :: (V a ~ v, N a ~ n, Enveloped a) => v n -> a -> n #

Compute the diameter of a enveloped object along a particular vector. Returns zero for the empty envelope.

envelopeP :: (V a ~ v, N a ~ n, Enveloped a) => v n -> a -> Point v n #

Compute the point on a separating hyperplane in the given direction. Returns the origin for the empty envelope.

envelopePMay :: (V a ~ v, N a ~ n, Enveloped a) => v n -> a -> Maybe (Point v n) #

Compute the point on a separating hyperplane in the given direction, or Nothing for the empty envelope.

envelopeV :: Enveloped a => Vn a -> a -> Vn a #

Compute the vector from the local origin to a separating hyperplane in the given direction. Returns the zero vector for the empty envelope.

envelopeVMay :: Enveloped a => Vn a -> a -> Maybe (Vn a) #

Compute the vector from the local origin to a separating hyperplane in the given direction, or Nothing for the empty envelope.

mkEnvelope :: (v n -> n) -> Envelope v n #

Create an envelope from a v n -> n function.

onEnvelope :: ((v n -> n) -> v n -> n) -> Envelope v n -> Envelope v n #

A convenient way to transform an envelope, by specifying a transformation on the underlying v n -> n function. The empty envelope is unaffected.

appEnvelope :: Envelope v n -> Maybe (v n -> n) #

"Apply" an envelope by turning it into a function. Nothing is returned iff the envelope is empty.

newtype Envelope (v :: Type -> Type) n #

Every diagram comes equipped with an envelope. What is an envelope?

Consider first the idea of a bounding box. A bounding box expresses the distance to a bounding plane in every direction parallel to an axis. That is, a bounding box can be thought of as the intersection of a collection of half-planes, two perpendicular to each axis.

More generally, the intersection of half-planes in every direction would give a tight "bounding region", or convex hull. However, representing such a thing intensionally would be impossible; hence bounding boxes are often used as an approximation.

An envelope is an extensional representation of such a "bounding region". Instead of storing some sort of direct representation, we store a function which takes a direction as input and gives a distance to a bounding half-plane as output. The important point is that envelopes can be composed, and transformed by any affine transformation.

Formally, given a vector v, the envelope computes a scalar s such that

for every point u inside the diagram, if the projection of (u - origin) onto v is s' *^ v, then s' <= s.
s is the smallest such scalar.

There is also a special "empty envelope".

The idea for envelopes came from Sebastian Setzer; see http://byorgey.wordpress.com/2009/10/28/collecting-attributes/#comment-2030. See also Brent Yorgey, Monoids: Theme and Variations, published in the 2012 Haskell Symposium: http://ozark.hendrix.edu/~yorgey/pub/monoid-pearl.pdf; video: http://www.youtube.com/watch?v=X-8NCkD2vOw.

Constructors

Envelope (Option (v n -> Max n))

Instances

Show (Envelope v n)
Instance details Defined in Diagrams.Core.Envelope Methods showsPrec :: Int -> Envelope v n -> ShowS # show :: Envelope v n -> String # showList :: [Envelope v n] -> ShowS #
Ord n => Semigroup (Envelope v n)	Envelopes form a semigroup with pointwise maximum as composition. Hence, if `e1` is the envelope for diagram `d1`, and `e2` is the envelope for `d2`, then e1 `mappend` e2 is the envelope for d1 `atop` d2.
Instance details Defined in Diagrams.Core.Envelope Methods (<>) :: Envelope v n -> Envelope v n -> Envelope v n # sconcat :: NonEmpty (Envelope v n) -> Envelope v n # stimes :: Integral b => b -> Envelope v n -> Envelope v n #
Ord n => Monoid (Envelope v n)	The special empty envelope is the identity for the `Monoid` instance.
Instance details Defined in Diagrams.Core.Envelope Methods mempty :: Envelope v n # mappend :: Envelope v n -> Envelope v n -> Envelope v n # mconcat :: [Envelope v n] -> Envelope v n #
(Metric v, OrderedField n) => Juxtaposable (Envelope v n)
Instance details Defined in Diagrams.Core.Juxtapose Methods juxtapose :: Vn (Envelope v n) -> Envelope v n -> Envelope v n -> Envelope v n #
(Metric v, OrderedField n) => Enveloped (Envelope v n)
Instance details Defined in Diagrams.Core.Envelope Methods getEnvelope :: Envelope v n -> Envelope (V (Envelope v n)) (N (Envelope v n)) #
(Metric v, Floating n) => Transformable (Envelope v n)
Instance details Defined in Diagrams.Core.Envelope Methods transform :: Transformation (V (Envelope v n)) (N (Envelope v n)) -> Envelope v n -> Envelope v n #
(Metric v, Fractional n) => HasOrigin (Envelope v n)	The local origin of an envelope is the point with respect to which bounding queries are made, i.e. the point from which the input vectors are taken to originate.
Instance details Defined in Diagrams.Core.Envelope Methods moveOriginTo :: Point (V (Envelope v n)) (N (Envelope v n)) -> Envelope v n -> Envelope v n #
(Metric v, OrderedField n) => Alignable (Envelope v n)
Instance details Defined in Diagrams.Align Methods alignBy' :: (InSpace v0 n0 (Envelope v n), Fractional n0, HasOrigin (Envelope v n)) => (v0 n0 -> Envelope v n -> Point v0 n0) -> v0 n0 -> n0 -> Envelope v n -> Envelope v n # defaultBoundary :: (V (Envelope v n) ~ v0, N (Envelope v n) ~ n0) => v0 n0 -> Envelope v n -> Point v0 n0 # alignBy :: (InSpace v0 n0 (Envelope v n), Fractional n0, HasOrigin (Envelope v n)) => v0 n0 -> n0 -> Envelope v n -> Envelope v n #
Wrapped (Envelope v n)
Instance details Defined in Diagrams.Core.Envelope Associated Types type Unwrapped (Envelope v n) :: Type # Methods _Wrapped' :: Iso' (Envelope v n) (Unwrapped (Envelope v n)) #
Rewrapped (Envelope v n) (Envelope v' n')
Instance details Defined in Diagrams.Core.Envelope
type V (Envelope v n)
Instance details Defined in Diagrams.Core.Envelope type V (Envelope v n) = v
type N (Envelope v n)
Instance details Defined in Diagrams.Core.Envelope type N (Envelope v n) = n
type Unwrapped (Envelope v n)
Instance details Defined in Diagrams.Core.Envelope type Unwrapped (Envelope v n) = Option (v n -> Max n)

type OrderedField s = (Floating s, Ord s) #

When dealing with envelopes we often want scalars to be an ordered field (i.e. support all four arithmetic operations and be totally ordered) so we introduce this constraint as a convenient shorthand.

class (Metric (V a), OrderedField (N a)) => Enveloped a where #

Enveloped abstracts over things which have an envelope.

Methods

getEnvelope :: a -> Envelope (V a) (N a) #

Compute the envelope of an object. For types with an intrinsic notion of "local origin", the envelope will be based there. Other types (e.g. Trail) may have some other default reference point at which the envelope will be based; their instances should document what it is.

Instances

Enveloped b => Enveloped [b]
Instance details Defined in Diagrams.Core.Envelope Methods getEnvelope :: [b] -> Envelope (V [b]) (N [b]) #
Enveloped b => Enveloped (Set b)
Instance details Defined in Diagrams.Core.Envelope Methods getEnvelope :: Set b -> Envelope (V (Set b)) (N (Set b)) #
Enveloped t => Enveloped (TransInv t)
Instance details Defined in Diagrams.Core.Envelope Methods getEnvelope :: TransInv t -> Envelope (V (TransInv t)) (N (TransInv t)) #
Enveloped a => Enveloped (Located a)	The envelope of a `Located a` is the envelope of the `a`, translated to the location.
Instance details Defined in Diagrams.Located Methods getEnvelope :: Located a -> Envelope (V (Located a)) (N (Located a)) #
OrderedField n => Enveloped (Ellipsoid n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods getEnvelope :: Ellipsoid n -> Envelope (V (Ellipsoid n)) (N (Ellipsoid n)) #
OrderedField n => Enveloped (Box n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods getEnvelope :: Box n -> Envelope (V (Box n)) (N (Box n)) #
(OrderedField n, RealFloat n) => Enveloped (Frustum n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods getEnvelope :: Frustum n -> Envelope (V (Frustum n)) (N (Frustum n)) #
RealFloat n => Enveloped (CSG n)	The Envelope for an Intersection or Difference is simply the Envelope of the Union. This is wrong but easy to implement.
Instance details Defined in Diagrams.ThreeD.Shapes Methods getEnvelope :: CSG n -> Envelope (V (CSG n)) (N (CSG n)) #
(Enveloped a, Enveloped b, V a ~ V b, N a ~ N b) => Enveloped (a, b)
Instance details Defined in Diagrams.Core.Envelope Methods getEnvelope :: (a, b) -> Envelope (V (a, b)) (N (a, b)) #
Enveloped b => Enveloped (Map k b)
Instance details Defined in Diagrams.Core.Envelope Methods getEnvelope :: Map k b -> Envelope (V (Map k b)) (N (Map k b)) #
(Metric v, OrderedField n) => Enveloped (Envelope v n)
Instance details Defined in Diagrams.Core.Envelope Methods getEnvelope :: Envelope v n -> Envelope (V (Envelope v n)) (N (Envelope v n)) #
(OrderedField n, Metric v) => Enveloped (Point v n)
Instance details Defined in Diagrams.Core.Envelope Methods getEnvelope :: Point v n -> Envelope (V (Point v n)) (N (Point v n)) #
(Metric v, Traversable v, OrderedField n) => Enveloped (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox Methods getEnvelope :: BoundingBox v n -> Envelope (V (BoundingBox v n)) (N (BoundingBox v n)) #
(Metric v, OrderedField n) => Enveloped (Path v n)
Instance details Defined in Diagrams.Path Methods getEnvelope :: Path v n -> Envelope (V (Path v n)) (N (Path v n)) #
(Metric v, OrderedField n) => Enveloped (Trail v n)
Instance details Defined in Diagrams.Trail Methods getEnvelope :: Trail v n -> Envelope (V (Trail v n)) (N (Trail v n)) #
(Metric v, OrderedField n) => Enveloped (FixedSegment v n)
Instance details Defined in Diagrams.Segment Methods getEnvelope :: FixedSegment v n -> Envelope (V (FixedSegment v n)) (N (FixedSegment v n)) #
(Metric v, OrderedField n) => Enveloped (Trail' l v n)	The envelope for a trail is based at the trail's start.
Instance details Defined in Diagrams.Trail Methods getEnvelope :: Trail' l v n -> Envelope (V (Trail' l v n)) (N (Trail' l v n)) #
(Metric v, OrderedField n) => Enveloped (Segment Closed v n)	The envelope for a segment is based at the segment's start.
Instance details Defined in Diagrams.Segment Methods getEnvelope :: Segment Closed v n -> Envelope (V (Segment Closed v n)) (N (Segment Closed v n)) #
(Metric v, OrderedField n, Monoid' m) => Enveloped (QDiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods getEnvelope :: QDiagram b v n m -> Envelope (V (QDiagram b v n m)) (N (QDiagram b v n m)) #
(OrderedField n, Metric v, Monoid' m) => Enveloped (Subdiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods getEnvelope :: Subdiagram b v n m -> Envelope (V (Subdiagram b v n m)) (N (Subdiagram b v n m)) #

newtype Query (v :: Type -> Type) n m #

A query is a function that maps points in a vector space to values in some monoid. Queries naturally form a monoid, with two queries being combined pointwise.

The idea for annotating diagrams with monoidal queries came from the graphics-drawingcombinators package, http://hackage.haskell.org/package/graphics-drawingcombinators.

Constructors

Query
Fields runQuery :: Point v n -> m

Instances

Functor v => Profunctor (Query v)
Instance details Defined in Diagrams.Core.Query Methods dimap :: (a -> b) -> (c -> d) -> Query v b c -> Query v a d # lmap :: (a -> b) -> Query v b c -> Query v a c # rmap :: (b -> c) -> Query v a b -> Query v a c # (#.) :: Coercible c b => q b c -> Query v a b -> Query v a c # (.#) :: Coercible b a => Query v b c -> q a b -> Query v a c #
Functor v => Corepresentable (Query v)
Instance details Defined in Diagrams.Core.Query Associated Types type Corep (Query v) :: Type -> Type # Methods cotabulate :: (Corep (Query v) d -> c) -> Query v d c #
Functor v => Closed (Query v)
Instance details Defined in Diagrams.Core.Query Methods closed :: Query v a b -> Query v (x -> a) (x -> b) #
Functor v => Costrong (Query v)
Instance details Defined in Diagrams.Core.Query Methods unfirst :: Query v (a, d) (b, d) -> Query v a b # unsecond :: Query v (d, a) (d, b) -> Query v a b #
Functor v => Cosieve (Query v) (Point v)
Instance details Defined in Diagrams.Core.Query Methods cosieve :: Query v a b -> Point v a -> b #
Monad (Query v n)
Instance details Defined in Diagrams.Core.Query Methods (>>=) :: Query v n a -> (a -> Query v n b) -> Query v n b # (>>) :: Query v n a -> Query v n b -> Query v n b # return :: a -> Query v n a # fail :: String -> Query v n a #
Functor (Query v n)
Instance details Defined in Diagrams.Core.Query Methods fmap :: (a -> b) -> Query v n a -> Query v n b # (<$) :: a -> Query v n b -> Query v n a #
Applicative (Query v n)
Instance details Defined in Diagrams.Core.Query Methods pure :: a -> Query v n a # (<>) :: Query v n (a -> b) -> Query v n a -> Query v n b # liftA2 :: (a -> b -> c) -> Query v n a -> Query v n b -> Query v n c # (>) :: Query v n a -> Query v n b -> Query v n b # (<*) :: Query v n a -> Query v n b -> Query v n a #
Distributive (Query v n)
Instance details Defined in Diagrams.Core.Query Methods distribute :: Functor f => f (Query v n a) -> Query v n (f a) # collect :: Functor f => (a -> Query v n b) -> f a -> Query v n (f b) # distributeM :: Monad m => m (Query v n a) -> Query v n (m a) # collectM :: Monad m => (a -> Query v n b) -> m a -> Query v n (m b) #
Representable (Query v n)
Instance details Defined in Diagrams.Core.Query Associated Types type Rep (Query v n) :: Type # Methods tabulate :: (Rep (Query v n) -> a) -> Query v n a # index :: Query v n a -> Rep (Query v n) -> a #
Semigroup m => Semigroup (Query v n m)
Instance details Defined in Diagrams.Core.Query Methods (<>) :: Query v n m -> Query v n m -> Query v n m # sconcat :: NonEmpty (Query v n m) -> Query v n m # stimes :: Integral b => b -> Query v n m -> Query v n m #
Monoid m => Monoid (Query v n m)
Instance details Defined in Diagrams.Core.Query Methods mempty :: Query v n m # mappend :: Query v n m -> Query v n m -> Query v n m # mconcat :: [Query v n m] -> Query v n m #
(Additive v, Num n) => Transformable (Query v n m)
Instance details Defined in Diagrams.Core.Query Methods transform :: Transformation (V (Query v n m)) (N (Query v n m)) -> Query v n m -> Query v n m #
(Additive v, Num n) => HasOrigin (Query v n m)
Instance details Defined in Diagrams.Core.Query Methods moveOriginTo :: Point (V (Query v n m)) (N (Query v n m)) -> Query v n m -> Query v n m #
Wrapped (Query v n m)
Instance details Defined in Diagrams.Core.Query Associated Types type Unwrapped (Query v n m) :: Type # Methods _Wrapped' :: Iso' (Query v n m) (Unwrapped (Query v n m)) #
HasQuery (Query v n m) m
Instance details Defined in Diagrams.Query Methods getQuery :: Query v n m -> Query (V (Query v n m)) (N (Query v n m)) m #
Rewrapped (Query v a m) (Query v' a' m')
Instance details Defined in Diagrams.Core.Query
type Corep (Query v)
Instance details Defined in Diagrams.Core.Query type Corep (Query v) = Point v
type Rep (Query v n)
Instance details Defined in Diagrams.Core.Query type Rep (Query v n) = Point v n
type V (Query v n m)
Instance details Defined in Diagrams.Core.Query type V (Query v n m) = v
type N (Query v n m)
Instance details Defined in Diagrams.Core.Query type N (Query v n m) = n
type Unwrapped (Query v n m)
Instance details Defined in Diagrams.Core.Query type Unwrapped (Query v n m) = Point v n -> m

maxRayTraceP :: (n ~ N a, Traced a, Num n) => Point (V a) n -> V a n -> a -> Maybe (Point (V a) n) #

Like rayTraceP, but computes the "largest" boundary point instead of the smallest. Considers only positive boundary points.

maxRayTraceV :: (n ~ N a, Traced a, Num n) => Point (V a) n -> V a n -> a -> Maybe (V a n) #

Like rayTraceV, but computes a vector to the "largest" boundary point instead of the smallest. Considers only positive boundary points.

rayTraceP :: (n ~ N a, Traced a, Num n) => Point (V a) n -> V a n -> a -> Maybe (Point (V a) n) #

Compute the boundary point on an object which is closest to the given base point in the given direction, or Nothing if there is no such boundary point. Note that unlike traceP, only positive boundary points are considered, i.e. boundary points corresponding to a positive scalar multiple of the direction vector. This is intuitively the "usual" behavior of a raytracer, which only considers intersection points "in front of" the camera.

rayTraceV :: (n ~ N a, Traced a, Num n) => Point (V a) n -> V a n -> a -> Maybe (V a n) #

Compute the vector from the given point to the closest boundary point of the given object in the given direction, or Nothing if there is no such boundary point (as in the third example below). Note that unlike traceV, only positive boundary points are considered, i.e. boundary points corresponding to a positive scalar multiple of the direction vector. This is intuitively the "usual" behavior of a raytracer, which only considers intersections "in front of" the camera. Compare the second example diagram below with the second example shown for traceV.

maxTraceP :: (n ~ N a, Num n, Traced a) => Point (V a) n -> V a n -> a -> Maybe (Point (V a) n) #

Like traceP, but computes the "largest" boundary point instead of the smallest. (Note, however, the "largest" boundary point may still be in the opposite direction from the given vector, if all the boundary points are.)

maxTraceV :: (n ~ N a, Num n, Traced a) => Point (V a) n -> V a n -> a -> Maybe (V a n) #

Like traceV, but computes a vector to the "largest" boundary point instead of the smallest. (Note, however, the "largest" boundary point may still be in the opposite direction from the given vector, if all the boundary points are, as in the third example shown below.)

traceP :: (n ~ N a, Traced a, Num n) => Point (V a) n -> V a n -> a -> Maybe (Point (V a) n) #

Compute the "smallest" boundary point along the line determined by the given point p and vector v. The "smallest" boundary point is defined as the one given by p .+^ (s *^ v) for the smallest (most negative) value of s. Return Nothing if there is no such boundary point. See also traceV.

See also rayTraceP which uses the smallest positive intersection, which is often more intuitive behavior.

traceV :: (n ~ N a, Num n, Traced a) => Point (V a) n -> V a n -> a -> Maybe (V a n) #

Compute the vector from the given point p to the "smallest" boundary intersection along the given vector v. The "smallest" boundary intersection is defined as the one given by p .+^ (s *^ v) for the smallest (most negative) value of s. Return Nothing if there is no intersection. See also traceP.

See also rayTraceV which uses the smallest positive intersection, which is often more intuitive behavior.

mkTrace :: (Point v n -> v n -> SortedList n) -> Trace v n #

getSortedList :: SortedList a -> [a] #

Project the (guaranteed sorted) list out of a SortedList wrapper.

mkSortedList :: Ord a => [a] -> SortedList a #

A smart constructor for the SortedList type, which sorts the input to ensure the SortedList invariant.

data SortedList a #

A newtype wrapper around a list which maintains the invariant that the list is sorted. The constructor is not exported; use the smart constructor mkSortedList (which sorts the given list) instead.

Instances

Ord a => Semigroup (SortedList a)	`SortedList` forms a semigroup with `merge` as composition.
Instance details Defined in Diagrams.Core.Trace Methods (<>) :: SortedList a -> SortedList a -> SortedList a # sconcat :: NonEmpty (SortedList a) -> SortedList a # stimes :: Integral b => b -> SortedList a -> SortedList a #
Ord a => Monoid (SortedList a)	`SortedList` forms a monoid with `merge` and the empty list.
Instance details Defined in Diagrams.Core.Trace Methods mempty :: SortedList a # mappend :: SortedList a -> SortedList a -> SortedList a # mconcat :: [SortedList a] -> SortedList a #

newtype Trace (v :: Type -> Type) n #

Every diagram comes equipped with a trace. Intuitively, the trace for a diagram is like a raytracer: given a line (represented as a base point and a direction vector), the trace computes a sorted list of signed distances from the base point to all intersections of the line with the boundary of the diagram.

Note that the outputs are not absolute distances, but multipliers relative to the input vector. That is, if the base point is p and direction vector is v, and one of the output scalars is s, then there is an intersection at the point p .+^ (s *^ v).

Constructors

Trace
Fields appTrace :: Point v n -> v n -> SortedList n

Instances

Show (Trace v n)
Instance details Defined in Diagrams.Core.Trace Methods showsPrec :: Int -> Trace v n -> ShowS # show :: Trace v n -> String # showList :: [Trace v n] -> ShowS #
Ord n => Semigroup (Trace v n)	Traces form a semigroup with pointwise minimum as composition. Hence, if `t1` is the trace for diagram `d1`, and `e2` is the trace for `d2`, then e1 `mappend` e2 is the trace for d1 `atop` d2.
Instance details Defined in Diagrams.Core.Trace Methods (<>) :: Trace v n -> Trace v n -> Trace v n # sconcat :: NonEmpty (Trace v n) -> Trace v n # stimes :: Integral b => b -> Trace v n -> Trace v n #
Ord n => Monoid (Trace v n)
Instance details Defined in Diagrams.Core.Trace Methods mempty :: Trace v n # mappend :: Trace v n -> Trace v n -> Trace v n # mconcat :: [Trace v n] -> Trace v n #
(Additive v, Ord n) => Traced (Trace v n)
Instance details Defined in Diagrams.Core.Trace Methods getTrace :: Trace v n -> Trace (V (Trace v n)) (N (Trace v n)) #
(Additive v, Num n) => Transformable (Trace v n)
Instance details Defined in Diagrams.Core.Trace Methods transform :: Transformation (V (Trace v n)) (N (Trace v n)) -> Trace v n -> Trace v n #
(Additive v, Num n) => HasOrigin (Trace v n)
Instance details Defined in Diagrams.Core.Trace Methods moveOriginTo :: Point (V (Trace v n)) (N (Trace v n)) -> Trace v n -> Trace v n #
(Metric v, OrderedField n) => Alignable (Trace v n)
Instance details Defined in Diagrams.Align Methods alignBy' :: (InSpace v0 n0 (Trace v n), Fractional n0, HasOrigin (Trace v n)) => (v0 n0 -> Trace v n -> Point v0 n0) -> v0 n0 -> n0 -> Trace v n -> Trace v n # defaultBoundary :: (V (Trace v n) ~ v0, N (Trace v n) ~ n0) => v0 n0 -> Trace v n -> Point v0 n0 # alignBy :: (InSpace v0 n0 (Trace v n), Fractional n0, HasOrigin (Trace v n)) => v0 n0 -> n0 -> Trace v n -> Trace v n #
Wrapped (Trace v n)
Instance details Defined in Diagrams.Core.Trace Associated Types type Unwrapped (Trace v n) :: Type # Methods _Wrapped' :: Iso' (Trace v n) (Unwrapped (Trace v n)) #
Rewrapped (Trace v n) (Trace v' n')
Instance details Defined in Diagrams.Core.Trace
type V (Trace v n)
Instance details Defined in Diagrams.Core.Trace type V (Trace v n) = v
type N (Trace v n)
Instance details Defined in Diagrams.Core.Trace type N (Trace v n) = n
type Unwrapped (Trace v n)
Instance details Defined in Diagrams.Core.Trace type Unwrapped (Trace v n) = Point v n -> v n -> SortedList n

class (Additive (V a), Ord (N a)) => Traced a where #

Traced abstracts over things which have a trace.

Methods

getTrace :: a -> Trace (V a) (N a) #

Compute the trace of an object.

Instances

Traced b => Traced [b]
Instance details Defined in Diagrams.Core.Trace Methods getTrace :: [b] -> Trace (V [b]) (N [b]) #
Traced b => Traced (Set b)
Instance details Defined in Diagrams.Core.Trace Methods getTrace :: Set b -> Trace (V (Set b)) (N (Set b)) #
Traced t => Traced (TransInv t)
Instance details Defined in Diagrams.Core.Trace Methods getTrace :: TransInv t -> Trace (V (TransInv t)) (N (TransInv t)) #
(Traced a, Num (N a)) => Traced (Located a)	The trace of a `Located a` is the trace of the `a`, translated to the location.
Instance details Defined in Diagrams.Located Methods getTrace :: Located a -> Trace (V (Located a)) (N (Located a)) #
OrderedField n => Traced (Ellipsoid n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods getTrace :: Ellipsoid n -> Trace (V (Ellipsoid n)) (N (Ellipsoid n)) #
(Fractional n, Ord n) => Traced (Box n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods getTrace :: Box n -> Trace (V (Box n)) (N (Box n)) #
(RealFloat n, Ord n) => Traced (Frustum n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods getTrace :: Frustum n -> Trace (V (Frustum n)) (N (Frustum n)) #
(RealFloat n, Ord n) => Traced (CSG n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods getTrace :: CSG n -> Trace (V (CSG n)) (N (CSG n)) #
(Traced a, Traced b, SameSpace a b) => Traced (a, b)
Instance details Defined in Diagrams.Core.Trace Methods getTrace :: (a, b) -> Trace (V (a, b)) (N (a, b)) #
Traced b => Traced (Map k b)
Instance details Defined in Diagrams.Core.Trace Methods getTrace :: Map k b -> Trace (V (Map k b)) (N (Map k b)) #
(Additive v, Ord n) => Traced (Trace v n)
Instance details Defined in Diagrams.Core.Trace Methods getTrace :: Trace v n -> Trace (V (Trace v n)) (N (Trace v n)) #
(Additive v, Ord n) => Traced (Point v n)	The trace of a single point is the empty trace, i.e. the one which returns no intersection points for every query. Arguably it should return a single finite distance for vectors aimed directly at the given point, but due to floating-point inaccuracy this is problematic. Note that the envelope for a single point is not the empty envelope (see Diagrams.Core.Envelope).
Instance details Defined in Diagrams.Core.Trace Methods getTrace :: Point v n -> Trace (V (Point v n)) (N (Point v n)) #
RealFloat n => Traced (BoundingBox V2 n)
Instance details Defined in Diagrams.BoundingBox Methods getTrace :: BoundingBox V2 n -> Trace (V (BoundingBox V2 n)) (N (BoundingBox V2 n)) #
TypeableFloat n => Traced (BoundingBox V3 n)
Instance details Defined in Diagrams.BoundingBox Methods getTrace :: BoundingBox V3 n -> Trace (V (BoundingBox V3 n)) (N (BoundingBox V3 n)) #
(Metric v, OrderedField n, Semigroup m) => Traced (QDiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods getTrace :: QDiagram b v n m -> Trace (V (QDiagram b v n m)) (N (QDiagram b v n m)) #
(OrderedField n, Metric v, Semigroup m) => Traced (Subdiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods getTrace :: Subdiagram b v n m -> Trace (V (Subdiagram b v n m)) (N (Subdiagram b v n m)) #

(.>) :: (IsName a1, IsName a2) => a1 -> a2 -> Name infixr 5 #

Convenient operator for writing qualified names with atomic components of different types. Instead of writing toName a1 <> toName a2 <> toName a3 you can just write a1 .> a2 .> a3.

eachName :: (Typeable a, Ord a, Show a) => Traversal' Name a #

Traversal over each name in a Name that matches the target type.

>>> toListOf eachName (a .> False .> b) :: String
"ab"
>>> a .> True .> b & eachName %~ not
a .> False .> b

Note that the type of the name is very important.

>>> sumOf eachName ((1::Int) .> (2 :: Integer) .> (3 :: Int)) :: Int
4
>>> sumOf eachName ((1::Int) .> (2 :: Integer) .> (3 :: Int)) :: Integer
2

class (Typeable a, Ord a, Show a) => IsName a where #

Class for those types which can be used as names. They must support Typeable (to facilitate extracting them from existential wrappers), Ord (for comparison and efficient storage) and Show.

To make an instance of IsName, you need not define any methods, just declare it.

WARNING: it is not recommended to use GeneralizedNewtypeDeriving in conjunction with IsName, since in that case the underlying type and the newtype will be considered equivalent when comparing names. For example:

    newtype WordN = WordN Int deriving (Show, Ord, Eq, Typeable, IsName)

is unlikely to work as intended, since (1 :: Int) and (WordN 1) will be considered equal as names. Instead, use

    newtype WordN = WordN Int deriving (Show, Ord, Eq, Typeable, IsName)
    instance IsName WordN

Minimal complete definition

Nothing

Methods

toName :: a -> Name #

Instances

IsName Bool
Instance details Defined in Diagrams.Core.Names Methods toName :: Bool -> Name #
IsName Char
Instance details Defined in Diagrams.Core.Names Methods toName :: Char -> Name #
IsName Double
Instance details Defined in Diagrams.Core.Names Methods toName :: Double -> Name #
IsName Float
Instance details Defined in Diagrams.Core.Names Methods toName :: Float -> Name #
IsName Int
Instance details Defined in Diagrams.Core.Names Methods toName :: Int -> Name #
IsName Integer
Instance details Defined in Diagrams.Core.Names Methods toName :: Integer -> Name #
IsName ()
Instance details Defined in Diagrams.Core.Names Methods toName :: () -> Name #
IsName AName
Instance details Defined in Diagrams.Core.Names Methods toName :: AName -> Name #
IsName Name
Instance details Defined in Diagrams.Core.Names Methods toName :: Name -> Name #
IsName a => IsName [a]
Instance details Defined in Diagrams.Core.Names Methods toName :: [a] -> Name #
IsName a => IsName (Maybe a)
Instance details Defined in Diagrams.Core.Names Methods toName :: Maybe a -> Name #
(IsName a, IsName b) => IsName (a, b)
Instance details Defined in Diagrams.Core.Names Methods toName :: (a, b) -> Name #
(IsName a, IsName b, IsName c) => IsName (a, b, c)
Instance details Defined in Diagrams.Core.Names Methods toName :: (a, b, c) -> Name #

data AName #

Atomic names. AName is just an existential wrapper around things which are Typeable, Ord and Show.

Instances

Eq AName
Instance details Defined in Diagrams.Core.Names Methods (==) :: AName -> AName -> Bool # (/=) :: AName -> AName -> Bool #
Ord AName
Instance details Defined in Diagrams.Core.Names Methods compare :: AName -> AName -> Ordering # (<) :: AName -> AName -> Bool # (<=) :: AName -> AName -> Bool # (>) :: AName -> AName -> Bool # (>=) :: AName -> AName -> Bool # max :: AName -> AName -> AName # min :: AName -> AName -> AName #
Show AName
Instance details Defined in Diagrams.Core.Names Methods showsPrec :: Int -> AName -> ShowS # show :: AName -> String # showList :: [AName] -> ShowS #
IsName AName
Instance details Defined in Diagrams.Core.Names Methods toName :: AName -> Name #
Each Name Name AName AName
Instance details Defined in Diagrams.Core.Names Methods each :: Traversal Name Name AName AName #

data Name #

A (qualified) name is a (possibly empty) sequence of atomic names.

Instances

Eq Name
Instance details Defined in Diagrams.Core.Names Methods (==) :: Name -> Name -> Bool # (/=) :: Name -> Name -> Bool #
Ord Name
Instance details Defined in Diagrams.Core.Names Methods compare :: Name -> Name -> Ordering # (<) :: Name -> Name -> Bool # (<=) :: Name -> Name -> Bool # (>) :: Name -> Name -> Bool # (>=) :: Name -> Name -> Bool # max :: Name -> Name -> Name # min :: Name -> Name -> Name #
Show Name
Instance details Defined in Diagrams.Core.Names Methods showsPrec :: Int -> Name -> ShowS # show :: Name -> String # showList :: [Name] -> ShowS #
Semigroup Name
Instance details Defined in Diagrams.Core.Names Methods (<>) :: Name -> Name -> Name # sconcat :: NonEmpty Name -> Name # stimes :: Integral b => b -> Name -> Name #
Monoid Name
Instance details Defined in Diagrams.Core.Names Methods mempty :: Name # mappend :: Name -> Name -> Name # mconcat :: [Name] -> Name #
IsName Name
Instance details Defined in Diagrams.Core.Names Methods toName :: Name -> Name #
Qualifiable Name	Of course, names can be qualified using `(.>)`.
Instance details Defined in Diagrams.Core.Names Methods (.>>) :: IsName a => a -> Name -> Name #
Wrapped Name
Instance details Defined in Diagrams.Core.Names Associated Types type Unwrapped Name :: Type # Methods _Wrapped' :: Iso' Name (Unwrapped Name) #
Rewrapped Name Name
Instance details Defined in Diagrams.Core.Names
Each Name Name AName AName
Instance details Defined in Diagrams.Core.Names Methods each :: Traversal Name Name AName AName #
Action Name (SubMap b v n m)	A name acts on a name map by qualifying every name in it.
Instance details Defined in Diagrams.Core.Types Methods act :: Name -> SubMap b v n m -> SubMap b v n m #
type Unwrapped Name
Instance details Defined in Diagrams.Core.Names type Unwrapped Name = [AName]

class Qualifiable q where #

Instances of Qualifiable are things which can be qualified by prefixing them with a name.

Methods

(.>>) :: IsName a => a -> q -> q infixr 5 #

Qualify with the given name.

Instances

Qualifiable Name	Of course, names can be qualified using `(.>)`.
Instance details Defined in Diagrams.Core.Names Methods (.>>) :: IsName a => a -> Name -> Name #
Qualifiable a => Qualifiable [a]
Instance details Defined in Diagrams.Core.Names Methods (.>>) :: IsName a0 => a0 -> [a] -> [a] #
(Ord a, Qualifiable a) => Qualifiable (Set a)
Instance details Defined in Diagrams.Core.Names Methods (.>>) :: IsName a0 => a0 -> Set a -> Set a #
Qualifiable a => Qualifiable (TransInv a)
Instance details Defined in Diagrams.Core.Names Methods (.>>) :: IsName a0 => a0 -> TransInv a -> TransInv a #
Qualifiable a => Qualifiable (Located a)
Instance details Defined in Diagrams.Located Methods (.>>) :: IsName a0 => a0 -> Located a -> Located a #
Qualifiable a => Qualifiable (b -> a)
Instance details Defined in Diagrams.Core.Names Methods (.>>) :: IsName a0 => a0 -> (b -> a) -> b -> a #
(Qualifiable a, Qualifiable b) => Qualifiable (a, b)
Instance details Defined in Diagrams.Core.Names Methods (.>>) :: IsName a0 => a0 -> (a, b) -> (a, b) #
Qualifiable a => Qualifiable (Map k a)
Instance details Defined in Diagrams.Core.Names Methods (.>>) :: IsName a0 => a0 -> Map k a -> Map k a #
Qualifiable a => Qualifiable (Measured n a)
Instance details Defined in Diagrams.Core.Names Methods (.>>) :: IsName a0 => a0 -> Measured n a -> Measured n a #
(Qualifiable a, Qualifiable b, Qualifiable c) => Qualifiable (a, b, c)
Instance details Defined in Diagrams.Core.Names Methods (.>>) :: IsName a0 => a0 -> (a, b, c) -> (a, b, c) #
(Metric v, OrderedField n, Semigroup m) => Qualifiable (QDiagram b v n m)	Diagrams can be qualified so that all their named points can now be referred to using the qualification prefix.
Instance details Defined in Diagrams.Core.Types Methods (.>>) :: IsName a => a -> QDiagram b v n m -> QDiagram b v n m #
Qualifiable (SubMap b v n m)	`SubMap`s are qualifiable: if `ns` is a `SubMap`, then `a \|> ns` is the same `SubMap` except with every name qualified by `a`.
Instance details Defined in Diagrams.Core.Types Methods (.>>) :: IsName a => a -> SubMap b v n m -> SubMap b v n m #

applyTAttr :: (AttributeClass a, Transformable a, V a ~ V d, N a ~ N d, HasStyle d) => a -> d -> d #

Apply a transformable attribute to an instance of HasStyle (such as a diagram or a style). If the object already has an attribute of the same type, the new attribute is combined on the left with the existing attribute, according to their semigroup structure.

applyMAttr :: (AttributeClass a, N d ~ n, HasStyle d) => Measured n a -> d -> d #

Apply a measured attribute to an instance of HasStyle (such as a diagram or a style). If the object already has an attribute of the same type, the new attribute is combined on the left with the existing attribute, according to their semigroup structure.

applyAttr :: (AttributeClass a, HasStyle d) => a -> d -> d #

Apply an attribute to an instance of HasStyle (such as a diagram or a style). If the object already has an attribute of the same type, the new attribute is combined on the left with the existing attribute, according to their semigroup structure.

atTAttr :: (V a ~ v, N a ~ n, AttributeClass a, Transformable a) => Lens' (Style v n) (Maybe a) #

Lens onto a transformable attribute of a style.

atMAttr :: (AttributeClass a, Typeable n) => Lens' (Style v n) (Maybe (Measured n a)) #

Lens onto a measured attribute of a style.

atAttr :: AttributeClass a => Lens' (Style v n) (Maybe a) #

Lens onto a plain attribute of a style.

getAttr :: AttributeClass a => Style v n -> Maybe a #

Extract an attribute from a style of a particular type. If the style contains an attribute of the requested type, it will be returned wrapped in Just; otherwise, Nothing is returned.

Trying to extract a measured attibute will fail. It either has to be unmeasured with unmeasureAttrs or use the atMAttr lens.

class (Typeable a, Semigroup a) => AttributeClass a #

Every attribute must be an instance of AttributeClass, which simply guarantees Typeable and Semigroup constraints. The Semigroup instance for an attribute determines how it will combine with other attributes of the same type.

Instances

AttributeClass Font
Instance details Defined in Diagrams.TwoD.Text
AttributeClass FontSlant
Instance details Defined in Diagrams.TwoD.Text
AttributeClass FontWeight
Instance details Defined in Diagrams.TwoD.Text
AttributeClass FillRule
Instance details Defined in Diagrams.TwoD.Path
AttributeClass Highlight
Instance details Defined in Diagrams.ThreeD.Attributes
AttributeClass SurfaceColor
Instance details Defined in Diagrams.ThreeD.Attributes
AttributeClass Diffuse
Instance details Defined in Diagrams.ThreeD.Attributes
AttributeClass Ambient
Instance details Defined in Diagrams.ThreeD.Attributes
AttributeClass Opacity
Instance details Defined in Diagrams.Attributes
AttributeClass FillOpacity
Instance details Defined in Diagrams.Attributes
AttributeClass StrokeOpacity
Instance details Defined in Diagrams.Attributes
AttributeClass LineCap
Instance details Defined in Diagrams.Attributes
AttributeClass LineJoin
Instance details Defined in Diagrams.Attributes
AttributeClass LineMiterLimit
Instance details Defined in Diagrams.Attributes
Typeable n => AttributeClass (FontSize n)
Instance details Defined in Diagrams.TwoD.Text
Typeable n => AttributeClass (LineTexture n)
Instance details Defined in Diagrams.TwoD.Attributes
Typeable n => AttributeClass (FillTexture n)
Instance details Defined in Diagrams.TwoD.Attributes
Typeable n => AttributeClass (Clip n)
Instance details Defined in Diagrams.TwoD.Path
Typeable n => AttributeClass (LineWidth n)
Instance details Defined in Diagrams.Attributes
Typeable n => AttributeClass (Dashing n)
Instance details Defined in Diagrams.Attributes

data Attribute (v :: Type -> Type) n where #

An existential wrapper type to hold attributes. Some attributes are simply inert/static; some are affected by transformations; and some are affected by transformations and can be modified generically.

Constructors

Attribute :: forall (v :: Type -> Type) n a. AttributeClass a => a -> Attribute v n
MAttribute :: forall (v :: Type -> Type) n a. AttributeClass a => Measured n a -> Attribute v n
TAttribute :: forall (v :: Type -> Type) n a. (AttributeClass a, Transformable a, V a ~ v, N a ~ n) => a -> Attribute v n

Instances

Show (Attribute v n)	Shows the kind of attribute and the type contained in the attribute.
Instance details Defined in Diagrams.Core.Style Methods showsPrec :: Int -> Attribute v n -> ShowS # show :: Attribute v n -> String # showList :: [Attribute v n] -> ShowS #
Typeable n => Semigroup (Attribute v n)	Attributes form a semigroup, where the semigroup operation simply returns the right-hand attribute when the types do not match, and otherwise uses the semigroup operation specific to the (matching) types.
Instance details Defined in Diagrams.Core.Style Methods (<>) :: Attribute v n -> Attribute v n -> Attribute v n # sconcat :: NonEmpty (Attribute v n) -> Attribute v n # stimes :: Integral b => b -> Attribute v n -> Attribute v n #
(Additive v, Traversable v, Floating n) => Transformable (Attribute v n)	`TAttribute`s are transformed directly, `MAttribute`s have their local scale multiplied by the average scale of the transform. Plain `Attribute`s are unaffected.
Instance details Defined in Diagrams.Core.Style Methods transform :: Transformation (V (Attribute v n)) (N (Attribute v n)) -> Attribute v n -> Attribute v n #
Each (Style v n) (Style v' n') (Attribute v n) (Attribute v' n')
Instance details Defined in Diagrams.Core.Style Methods each :: Traversal (Style v n) (Style v' n') (Attribute v n) (Attribute v' n') #
type V (Attribute v n)
Instance details Defined in Diagrams.Core.Style type V (Attribute v n) = v
type N (Attribute v n)
Instance details Defined in Diagrams.Core.Style type N (Attribute v n) = n

data Style (v :: Type -> Type) n #

A Style is a heterogeneous collection of attributes, containing at most one attribute of any given type.

Instances

Show (Style v n)	Show the attributes in the style.
Instance details Defined in Diagrams.Core.Style Methods showsPrec :: Int -> Style v n -> ShowS # show :: Style v n -> String # showList :: [Style v n] -> ShowS #
Typeable n => Semigroup (Style v n)	Combine a style by combining the attributes; if the two styles have attributes of the same type they are combined according to their semigroup structure.
Instance details Defined in Diagrams.Core.Style Methods (<>) :: Style v n -> Style v n -> Style v n # sconcat :: NonEmpty (Style v n) -> Style v n # stimes :: Integral b => b -> Style v n -> Style v n #
Typeable n => Monoid (Style v n)	The empty style contains no attributes.
Instance details Defined in Diagrams.Core.Style Methods mempty :: Style v n # mappend :: Style v n -> Style v n -> Style v n # mconcat :: [Style v n] -> Style v n #
Typeable n => HasStyle (Style v n)
Instance details Defined in Diagrams.Core.Style Methods applyStyle :: Style (V (Style v n)) (N (Style v n)) -> Style v n -> Style v n #
(Additive v, Traversable v, Floating n) => Transformable (Style v n)
Instance details Defined in Diagrams.Core.Style Methods transform :: Transformation (V (Style v n)) (N (Style v n)) -> Style v n -> Style v n #
Wrapped (Style v n)
Instance details Defined in Diagrams.Core.Style Associated Types type Unwrapped (Style v n) :: Type # Methods _Wrapped' :: Iso' (Style v n) (Unwrapped (Style v n)) #
At (Style v n)
Instance details Defined in Diagrams.Core.Style Methods at :: Index (Style v n) -> Lens' (Style v n) (Maybe (IxValue (Style v n))) #
Ixed (Style v n)
Instance details Defined in Diagrams.Core.Style Methods ix :: Index (Style v n) -> Traversal' (Style v n) (IxValue (Style v n)) #
Action (Style v n) m	Styles have no action on other monoids.
Instance details Defined in Diagrams.Core.Style Methods act :: Style v n -> m -> m #
Rewrapped (Style v n) (Style v' n')
Instance details Defined in Diagrams.Core.Style
Each (Style v n) (Style v' n') (Attribute v n) (Attribute v' n')
Instance details Defined in Diagrams.Core.Style Methods each :: Traversal (Style v n) (Style v' n') (Attribute v n) (Attribute v' n') #
type V (Style v n)
Instance details Defined in Diagrams.Core.Style type V (Style v n) = v
type N (Style v n)
Instance details Defined in Diagrams.Core.Style type N (Style v n) = n
type Unwrapped (Style v n)
Instance details Defined in Diagrams.Core.Style type Unwrapped (Style v n) = HashMap TypeRep (Attribute v n)
type IxValue (Style v n)
Instance details Defined in Diagrams.Core.Style type IxValue (Style v n) = Attribute v n
type Index (Style v n)
Instance details Defined in Diagrams.Core.Style type Index (Style v n) = TypeRep

class HasStyle a where #

Type class for things which have a style.

Methods

applyStyle :: Style (V a) (N a) -> a -> a #

Apply a style by combining it (on the left) with the existing style.

Instances

HasStyle a => HasStyle [a]
Instance details Defined in Diagrams.Core.Style Methods applyStyle :: Style (V [a]) (N [a]) -> [a] -> [a] #
(HasStyle a, Ord a) => HasStyle (Set a)
Instance details Defined in Diagrams.Core.Style Methods applyStyle :: Style (V (Set a)) (N (Set a)) -> Set a -> Set a #
HasStyle b => HasStyle (a -> b)
Instance details Defined in Diagrams.Core.Style Methods applyStyle :: Style (V (a -> b)) (N (a -> b)) -> (a -> b) -> a -> b #
(HasStyle a, HasStyle b, V a ~ V b, N a ~ N b) => HasStyle (a, b)
Instance details Defined in Diagrams.Core.Style Methods applyStyle :: Style (V (a, b)) (N (a, b)) -> (a, b) -> (a, b) #
HasStyle a => HasStyle (Map k a)
Instance details Defined in Diagrams.Core.Style Methods applyStyle :: Style (V (Map k a)) (N (Map k a)) -> Map k a -> Map k a #
Typeable n => HasStyle (Style v n)
Instance details Defined in Diagrams.Core.Style Methods applyStyle :: Style (V (Style v n)) (N (Style v n)) -> Style v n -> Style v n #
HasStyle b => HasStyle (Measured n b)
Instance details Defined in Diagrams.Core.Style Methods applyStyle :: Style (V (Measured n b)) (N (Measured n b)) -> Measured n b -> Measured n b #
(Metric v, OrderedField n, Semigroup m) => HasStyle (QDiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods applyStyle :: Style (V (QDiagram b v n m)) (N (QDiagram b v n m)) -> QDiagram b v n m -> QDiagram b v n m #

scale :: (InSpace v n a, Eq n, Fractional n, Transformable a) => n -> a -> a #

Scale uniformly in every dimension by the given scalar.

scaling :: (Additive v, Fractional n) => n -> Transformation v n #

Create a uniform scaling transformation.

translate :: Transformable t => Vn t -> t -> t #

Translate by a vector.

translation :: v n -> Transformation v n #

Create a translation.

avgScale :: (Additive v, Traversable v, Floating n) => Transformation v n -> n #

Compute the "average" amount of scaling performed by a transformation. Satisfies the properties

  avgScale (scaling k) == k
  avgScale (t1 <> t2)  == avgScale t1 * avgScale t2

isReflection :: (Additive v, Traversable v, Num n, Ord n) => Transformation v n -> Bool #

Determine whether a Transformation includes a reflection component, that is, whether it reverses orientation.

determinant :: (Additive v, Traversable v, Num n) => Transformation v n -> n #

The determinant of (the linear part of) a Transformation.

dimension :: (Additive (V a), Traversable (V a)) => a -> Int #

Get the dimension of an object whose vector space is an instance of HasLinearMap, e.g. transformations, paths, diagrams, etc.

fromLinear :: (Additive v, Num n) => (v n :-: v n) -> (v n :-: v n) -> Transformation v n #

Create a general affine transformation from an invertible linear transformation and its transpose. The translational component is assumed to be zero.

papply :: (Additive v, Num n) => Transformation v n -> Point v n -> Point v n #

Apply a transformation to a point.

apply :: Transformation v n -> v n -> v n #

Apply a transformation to a vector. Note that any translational component of the transformation will not affect the vector, since vectors are invariant under translation.

dropTransl :: (Additive v, Num n) => Transformation v n -> Transformation v n #

Drop the translational component of a transformation, leaving only the linear part.

transl :: Transformation v n -> v n #

Get the translational component of a transformation.

transp :: Transformation v n -> v n :-: v n #

Get the transpose of a transformation (ignoring the translation component).

inv :: (Functor v, Num n) => Transformation v n -> Transformation v n #

Invert a transformation.

eye :: (HasBasis v, Num n) => v (v n) #

Identity matrix.

lapp :: (u :-: v) -> u -> v #

Apply a linear map to a vector.

linv :: (u :-: v) -> v :-: u #

Invert a linear map.

(<->) :: (u -> v) -> (v -> u) -> u :-: v #

Create an invertible linear map from two functions which are assumed to be linear inverses.

data u :-: v infixr 7 #

(v1 :-: v2) is a linear map paired with its inverse.

Instances

Semigroup (a :-: a)
Instance details Defined in Diagrams.Core.Transform Methods (<>) :: (a :-: a) -> (a :-: a) -> a :-: a # sconcat :: NonEmpty (a :-: a) -> a :-: a # stimes :: Integral b => b -> (a :-: a) -> a :-: a #
Monoid (v :-: v)	Invertible linear maps from a vector space to itself form a monoid under composition.
Instance details Defined in Diagrams.Core.Transform Methods mempty :: v :-: v # mappend :: (v :-: v) -> (v :-: v) -> v :-: v # mconcat :: [v :-: v] -> v :-: v #

data Transformation (v :: Type -> Type) n #

General (affine) transformations, represented by an invertible linear map, its transpose, and a vector representing a translation component.

By the transpose of a linear map we mean simply the linear map corresponding to the transpose of the map's matrix representation. For example, any scale is its own transpose, since scales are represented by matrices with zeros everywhere except the diagonal. The transpose of a rotation is the same as its inverse.

The reason we need to keep track of transposes is because it turns out that when transforming a shape according to some linear map L, the shape's normal vectors transform according to L's inverse transpose. (For a more detailed explanation and proof, see https://wiki.haskell.org/Diagrams/Dev/Transformations.) This is exactly what we need when transforming bounding functions, which are defined in terms of perpendicular (i.e. normal) hyperplanes.

For more general, non-invertible transformations, see Diagrams.Deform (in diagrams-lib).

Instances

(Additive v, Num n) => Semigroup (Transformation v n)	Transformations are closed under composition; `t1 <> t2` is the transformation which performs first `t2`, then `t1`.
Instance details Defined in Diagrams.Core.Transform Methods (<>) :: Transformation v n -> Transformation v n -> Transformation v n # sconcat :: NonEmpty (Transformation v n) -> Transformation v n # stimes :: Integral b => b -> Transformation v n -> Transformation v n #
(Additive v, Num n) => Monoid (Transformation v n)
Instance details Defined in Diagrams.Core.Transform Methods mempty :: Transformation v n # mappend :: Transformation v n -> Transformation v n -> Transformation v n # mconcat :: [Transformation v n] -> Transformation v n #
(Additive v, Num n) => Transformable (Transformation v n)
Instance details Defined in Diagrams.Core.Transform Methods transform :: Transformation (V (Transformation v n)) (N (Transformation v n)) -> Transformation v n -> Transformation v n #
(Additive v, Num n) => HasOrigin (Transformation v n)
Instance details Defined in Diagrams.Core.Transform Methods moveOriginTo :: Point (V (Transformation v n)) (N (Transformation v n)) -> Transformation v n -> Transformation v n #
(Transformable a, V a ~ v, N a ~ n) => Action (Transformation v n) a	Transformations can act on transformable things.
Instance details Defined in Diagrams.Core.Transform Methods act :: Transformation v n -> a -> a #
type V (Transformation v n)
Instance details Defined in Diagrams.Core.Transform type V (Transformation v n) = v
type N (Transformation v n)
Instance details Defined in Diagrams.Core.Transform type N (Transformation v n) = n

type HasLinearMap (v :: Type -> Type) = (HasBasis v, Traversable v) #

HasLinearMap is a constraint synonym, just to help shorten some of the ridiculously long constraint sets.

type HasBasis (v :: Type -> Type) = (Additive v, Representable v, Rep v ~ E v) #

An Additive vector space whose representation is made up of basis elements.

class Transformable t where #

Type class for things t which can be transformed.

Methods

transform :: Transformation (V t) (N t) -> t -> t #

Apply a transformation to an object.

Instances

Transformable t => Transformable [t]
Instance details Defined in Diagrams.Core.Transform Methods transform :: Transformation (V [t]) (N [t]) -> [t] -> [t] #
(Transformable t, Ord t) => Transformable (Set t)
Instance details Defined in Diagrams.Core.Transform Methods transform :: Transformation (V (Set t)) (N (Set t)) -> Set t -> Set t #
(Num (N t), Additive (V t), Transformable t) => Transformable (TransInv t)
Instance details Defined in Diagrams.Core.Transform Methods transform :: Transformation (V (TransInv t)) (N (TransInv t)) -> TransInv t -> TransInv t #
Floating n => Transformable (Text n)
Instance details Defined in Diagrams.TwoD.Text Methods transform :: Transformation (V (Text n)) (N (Text n)) -> Text n -> Text n #
Floating n => Transformable (LineTexture n)
Instance details Defined in Diagrams.TwoD.Attributes Methods transform :: Transformation (V (LineTexture n)) (N (LineTexture n)) -> LineTexture n -> LineTexture n #
Floating n => Transformable (FillTexture n)
Instance details Defined in Diagrams.TwoD.Attributes Methods transform :: Transformation (V (FillTexture n)) (N (FillTexture n)) -> FillTexture n -> FillTexture n #
Floating n => Transformable (Texture n)
Instance details Defined in Diagrams.TwoD.Attributes Methods transform :: Transformation (V (Texture n)) (N (Texture n)) -> Texture n -> Texture n #
Fractional n => Transformable (RGradient n)
Instance details Defined in Diagrams.TwoD.Attributes Methods transform :: Transformation (V (RGradient n)) (N (RGradient n)) -> RGradient n -> RGradient n #
Fractional n => Transformable (LGradient n)
Instance details Defined in Diagrams.TwoD.Attributes Methods transform :: Transformation (V (LGradient n)) (N (LGradient n)) -> LGradient n -> LGradient n #
OrderedField n => Transformable (Clip n)
Instance details Defined in Diagrams.TwoD.Path Methods transform :: Transformation (V (Clip n)) (N (Clip n)) -> Clip n -> Clip n #
(Additive (V a), Num (N a), Transformable a) => Transformable (Located a)	Applying a transformation `t` to a `Located a` results in the transformation being applied to the location, and the linear portion of `t` being applied to the value of type `a` (i.e. it is not translated).
Instance details Defined in Diagrams.Located Methods transform :: Transformation (V (Located a)) (N (Located a)) -> Located a -> Located a #
Fractional n => Transformable (Ellipsoid n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods transform :: Transformation (V (Ellipsoid n)) (N (Ellipsoid n)) -> Ellipsoid n -> Ellipsoid n #
Fractional n => Transformable (Box n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods transform :: Transformation (V (Box n)) (N (Box n)) -> Box n -> Box n #
Fractional n => Transformable (Frustum n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods transform :: Transformation (V (Frustum n)) (N (Frustum n)) -> Frustum n -> Frustum n #
Fractional n => Transformable (CSG n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods transform :: Transformation (V (CSG n)) (N (CSG n)) -> CSG n -> CSG n #
Fractional n => Transformable (PointLight n)
Instance details Defined in Diagrams.ThreeD.Light Methods transform :: Transformation (V (PointLight n)) (N (PointLight n)) -> PointLight n -> PointLight n #
Transformable (ParallelLight n)
Instance details Defined in Diagrams.ThreeD.Light Methods transform :: Transformation (V (ParallelLight n)) (N (ParallelLight n)) -> ParallelLight n -> ParallelLight n #
Transformable m => Transformable (Deletable m)
Instance details Defined in Diagrams.Core.Transform Methods transform :: Transformation (V (Deletable m)) (N (Deletable m)) -> Deletable m -> Deletable m #
(V t ~ v, N t ~ n, V t ~ V s, N t ~ N s, Functor v, Num n, Transformable t, Transformable s) => Transformable (s -> t)
Instance details Defined in Diagrams.Core.Transform Methods transform :: Transformation (V (s -> t)) (N (s -> t)) -> (s -> t) -> s -> t #
(Transformable t, Transformable s, V t ~ V s, N t ~ N s) => Transformable (t, s)
Instance details Defined in Diagrams.Core.Transform Methods transform :: Transformation (V (t, s)) (N (t, s)) -> (t, s) -> (t, s) #
Transformable t => Transformable (Map k t)
Instance details Defined in Diagrams.Core.Transform Methods transform :: Transformation (V (Map k t)) (N (Map k t)) -> Map k t -> Map k t #
(Metric v, Floating n) => Transformable (Envelope v n)
Instance details Defined in Diagrams.Core.Envelope Methods transform :: Transformation (V (Envelope v n)) (N (Envelope v n)) -> Envelope v n -> Envelope v n #
(Additive v, Num n) => Transformable (Trace v n)
Instance details Defined in Diagrams.Core.Trace Methods transform :: Transformation (V (Trace v n)) (N (Trace v n)) -> Trace v n -> Trace v n #
(Additive v, Traversable v, Floating n) => Transformable (Attribute v n)	`TAttribute`s are transformed directly, `MAttribute`s have their local scale multiplied by the average scale of the transform. Plain `Attribute`s are unaffected.
Instance details Defined in Diagrams.Core.Style Methods transform :: Transformation (V (Attribute v n)) (N (Attribute v n)) -> Attribute v n -> Attribute v n #
(Additive v, Traversable v, Floating n) => Transformable (Style v n)
Instance details Defined in Diagrams.Core.Style Methods transform :: Transformation (V (Style v n)) (N (Style v n)) -> Style v n -> Style v n #
(Additive v, Num n) => Transformable (Transformation v n)
Instance details Defined in Diagrams.Core.Transform Methods transform :: Transformation (V (Transformation v n)) (N (Transformation v n)) -> Transformation v n -> Transformation v n #
(InSpace v n t, Transformable t, HasLinearMap v, Floating n) => Transformable (Measured n t)
Instance details Defined in Diagrams.Core.Transform Methods transform :: Transformation (V (Measured n t)) (N (Measured n t)) -> Measured n t -> Measured n t #
(Additive v, Num n) => Transformable (Point v n)
Instance details Defined in Diagrams.Core.Transform Methods transform :: Transformation (V (Point v n)) (N (Point v n)) -> Point v n -> Point v n #
Fractional n => Transformable (DImage n a)
Instance details Defined in Diagrams.TwoD.Image Methods transform :: Transformation (V (DImage n a)) (N (DImage n a)) -> DImage n a -> DImage n a #
(HasLinearMap v, Metric v, OrderedField n) => Transformable (Path v n)
Instance details Defined in Diagrams.Path Methods transform :: Transformation (V (Path v n)) (N (Path v n)) -> Path v n -> Path v n #
(Floating n, Ord n, Metric v) => Transformable (SegTree v n)
Instance details Defined in Diagrams.Trail Methods transform :: Transformation (V (SegTree v n)) (N (SegTree v n)) -> SegTree v n -> SegTree v n #
(HasLinearMap v, Metric v, OrderedField n) => Transformable (Trail v n)
Instance details Defined in Diagrams.Trail Methods transform :: Transformation (V (Trail v n)) (N (Trail v n)) -> Trail v n -> Trail v n #
(Additive v, Num n) => Transformable (FixedSegment v n)
Instance details Defined in Diagrams.Segment Methods transform :: Transformation (V (FixedSegment v n)) (N (FixedSegment v n)) -> FixedSegment v n -> FixedSegment v n #
Num n => Transformable (Camera l n)
Instance details Defined in Diagrams.ThreeD.Camera Methods transform :: Transformation (V (Camera l n)) (N (Camera l n)) -> Camera l n -> Camera l n #
(V (v n) ~ v, N (v n) ~ n, Transformable (v n)) => Transformable (Direction v n)
Instance details Defined in Diagrams.Direction Methods transform :: Transformation (V (Direction v n)) (N (Direction v n)) -> Direction v n -> Direction v n #
(Transformable t, Transformable s, Transformable u, V s ~ V t, N s ~ N t, V s ~ V u, N s ~ N u) => Transformable (t, s, u)
Instance details Defined in Diagrams.Core.Transform Methods transform :: Transformation (V (t, s, u)) (N (t, s, u)) -> (t, s, u) -> (t, s, u) #
Transformable (Prim b v n)	The `Transformable` instance for `Prim` just pushes calls to `transform` down through the `Prim` constructor.
Instance details Defined in Diagrams.Core.Types Methods transform :: Transformation (V (Prim b v n)) (N (Prim b v n)) -> Prim b v n -> Prim b v n #
(Additive v, Num n) => Transformable (Query v n m)
Instance details Defined in Diagrams.Core.Query Methods transform :: Transformation (V (Query v n m)) (N (Query v n m)) -> Query v n m -> Query v n m #
(HasLinearMap v, Metric v, OrderedField n) => Transformable (Trail' l v n)
Instance details Defined in Diagrams.Trail Methods transform :: Transformation (V (Trail' l v n)) (N (Trail' l v n)) -> Trail' l v n -> Trail' l v n #
Transformable (Offset c v n)
Instance details Defined in Diagrams.Segment Methods transform :: Transformation (V (Offset c v n)) (N (Offset c v n)) -> Offset c v n -> Offset c v n #
Transformable (Segment c v n)
Instance details Defined in Diagrams.Segment Methods transform :: Transformation (V (Segment c v n)) (N (Segment c v n)) -> Segment c v n -> Segment c v n #
(OrderedField n, Metric v, Semigroup m) => Transformable (QDiagram b v n m)	Diagrams can be transformed by transforming each of their components appropriately.
Instance details Defined in Diagrams.Core.Types Methods transform :: Transformation (V (QDiagram b v n m)) (N (QDiagram b v n m)) -> QDiagram b v n m -> QDiagram b v n m #
Transformable (Subdiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods transform :: Transformation (V (Subdiagram b v n m)) (N (Subdiagram b v n m)) -> Subdiagram b v n m -> Subdiagram b v n m #
Transformable (SubMap b v n m)
Instance details Defined in Diagrams.Core.Types Methods transform :: Transformation (V (SubMap b v n m)) (N (SubMap b v n m)) -> SubMap b v n m -> SubMap b v n m #

newtype TransInv t #

TransInv is a wrapper which makes a transformable type translationally invariant; the translational component of transformations will no longer affect things wrapped in TransInv.

Constructors

TransInv t

Instances

Eq t => Eq (TransInv t)
Instance details Defined in Diagrams.Core.Transform Methods (==) :: TransInv t -> TransInv t -> Bool # (/=) :: TransInv t -> TransInv t -> Bool #
Ord t => Ord (TransInv t)
Instance details Defined in Diagrams.Core.Transform Methods compare :: TransInv t -> TransInv t -> Ordering # (<) :: TransInv t -> TransInv t -> Bool # (<=) :: TransInv t -> TransInv t -> Bool # (>) :: TransInv t -> TransInv t -> Bool # (>=) :: TransInv t -> TransInv t -> Bool # max :: TransInv t -> TransInv t -> TransInv t # min :: TransInv t -> TransInv t -> TransInv t #
Show t => Show (TransInv t)
Instance details Defined in Diagrams.Core.Transform Methods showsPrec :: Int -> TransInv t -> ShowS # show :: TransInv t -> String # showList :: [TransInv t] -> ShowS #
Semigroup t => Semigroup (TransInv t)
Instance details Defined in Diagrams.Core.Transform Methods (<>) :: TransInv t -> TransInv t -> TransInv t # sconcat :: NonEmpty (TransInv t) -> TransInv t # stimes :: Integral b => b -> TransInv t -> TransInv t #
Monoid t => Monoid (TransInv t)
Instance details Defined in Diagrams.Core.Transform Methods mempty :: TransInv t # mappend :: TransInv t -> TransInv t -> TransInv t # mconcat :: [TransInv t] -> TransInv t #
Enveloped t => Enveloped (TransInv t)
Instance details Defined in Diagrams.Core.Envelope Methods getEnvelope :: TransInv t -> Envelope (V (TransInv t)) (N (TransInv t)) #
Traced t => Traced (TransInv t)
Instance details Defined in Diagrams.Core.Trace Methods getTrace :: TransInv t -> Trace (V (TransInv t)) (N (TransInv t)) #
Qualifiable a => Qualifiable (TransInv a)
Instance details Defined in Diagrams.Core.Names Methods (.>>) :: IsName a0 => a0 -> TransInv a -> TransInv a #
(Num (N t), Additive (V t), Transformable t) => Transformable (TransInv t)
Instance details Defined in Diagrams.Core.Transform Methods transform :: Transformation (V (TransInv t)) (N (TransInv t)) -> TransInv t -> TransInv t #
HasOrigin (TransInv t)
Instance details Defined in Diagrams.Core.Transform Methods moveOriginTo :: Point (V (TransInv t)) (N (TransInv t)) -> TransInv t -> TransInv t #
TrailLike t => TrailLike (TransInv t)	Translationally invariant things are trail-like as long as the underlying type is.
Instance details Defined in Diagrams.TrailLike Methods trailLike :: Located (Trail (V (TransInv t)) (N (TransInv t))) -> TransInv t #
Wrapped (TransInv t)
Instance details Defined in Diagrams.Core.Transform Associated Types type Unwrapped (TransInv t) :: Type # Methods _Wrapped' :: Iso' (TransInv t) (Unwrapped (TransInv t)) #
Rewrapped (TransInv t) (TransInv t')
Instance details Defined in Diagrams.Core.Transform
type V (TransInv t)
Instance details Defined in Diagrams.Core.Transform type V (TransInv t) = V t
type N (TransInv t)
Instance details Defined in Diagrams.Core.Transform type N (TransInv t) = N t
type Unwrapped (TransInv t)
Instance details Defined in Diagrams.Core.Transform type Unwrapped (TransInv t) = t

place :: (InSpace v n t, HasOrigin t) => t -> Point v n -> t #

A flipped variant of moveTo, provided for convenience. Useful when writing a function which takes a point as an argument, such as when using withName and friends.

moveTo :: (InSpace v n t, HasOrigin t) => Point v n -> t -> t #

Translate the object by the translation that sends the origin to the given point. Note that this is dual to moveOriginTo, i.e. we should have

  moveTo (origin .^+ v) === moveOriginTo (origin .^- v)

For types which are also Transformable, this is essentially the same as translate, i.e.

  moveTo (origin .^+ v) === translate v

moveOriginBy :: (V t ~ v, N t ~ n, HasOrigin t) => v n -> t -> t #

Move the local origin by a relative vector.

class HasOrigin t where #

Class of types which have an intrinsic notion of a "local origin", i.e. things which are not invariant under translation, and which allow the origin to be moved.

One might wonder why not just use Transformable instead of having a separate class for HasOrigin; indeed, for types which are instances of both we should have the identity

  moveOriginTo (origin .^+ v) === translate (negated v)

The reason is that some things (e.g. vectors, Trails) are transformable but are translationally invariant, i.e. have no origin.

Methods

moveOriginTo :: Point (V t) (N t) -> t -> t #

Move the local origin to another point.

Note that this function is in some sense dual to translate (for types which are also Transformable); moving the origin itself while leaving the object "fixed" is dual to fixing the origin and translating the diagram.

Instances

HasOrigin t => HasOrigin [t]
Instance details Defined in Diagrams.Core.HasOrigin Methods moveOriginTo :: Point (V [t]) (N [t]) -> [t] -> [t] #
(HasOrigin t, Ord t) => HasOrigin (Set t)
Instance details Defined in Diagrams.Core.HasOrigin Methods moveOriginTo :: Point (V (Set t)) (N (Set t)) -> Set t -> Set t #
HasOrigin (TransInv t)
Instance details Defined in Diagrams.Core.Transform Methods moveOriginTo :: Point (V (TransInv t)) (N (TransInv t)) -> TransInv t -> TransInv t #
Floating n => HasOrigin (Text n)
Instance details Defined in Diagrams.TwoD.Text Methods moveOriginTo :: Point (V (Text n)) (N (Text n)) -> Text n -> Text n #
(Num (N a), Additive (V a)) => HasOrigin (Located a)	`Located a` is an instance of `HasOrigin` whether `a` is or not. In particular, translating a `Located a` simply translates the associated point (and does not affect the value of type `a`).
Instance details Defined in Diagrams.Located Methods moveOriginTo :: Point (V (Located a)) (N (Located a)) -> Located a -> Located a #
(HasOrigin t, HasOrigin s, SameSpace s t) => HasOrigin (s, t)
Instance details Defined in Diagrams.Core.HasOrigin Methods moveOriginTo :: Point (V (s, t)) (N (s, t)) -> (s, t) -> (s, t) #
HasOrigin t => HasOrigin (Map k t)
Instance details Defined in Diagrams.Core.HasOrigin Methods moveOriginTo :: Point (V (Map k t)) (N (Map k t)) -> Map k t -> Map k t #
(Metric v, Fractional n) => HasOrigin (Envelope v n)	The local origin of an envelope is the point with respect to which bounding queries are made, i.e. the point from which the input vectors are taken to originate.
Instance details Defined in Diagrams.Core.Envelope Methods moveOriginTo :: Point (V (Envelope v n)) (N (Envelope v n)) -> Envelope v n -> Envelope v n #
(Additive v, Num n) => HasOrigin (Trace v n)
Instance details Defined in Diagrams.Core.Trace Methods moveOriginTo :: Point (V (Trace v n)) (N (Trace v n)) -> Trace v n -> Trace v n #
(Additive v, Num n) => HasOrigin (Transformation v n)
Instance details Defined in Diagrams.Core.Transform Methods moveOriginTo :: Point (V (Transformation v n)) (N (Transformation v n)) -> Transformation v n -> Transformation v n #
HasOrigin t => HasOrigin (Measured n t)
Instance details Defined in Diagrams.Core.HasOrigin Methods moveOriginTo :: Point (V (Measured n t)) (N (Measured n t)) -> Measured n t -> Measured n t #
(Additive v, Num n) => HasOrigin (Point v n)
Instance details Defined in Diagrams.Core.HasOrigin Methods moveOriginTo :: Point (V (Point v n)) (N (Point v n)) -> Point v n -> Point v n #
(Additive v, Num n) => HasOrigin (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox Methods moveOriginTo :: Point (V (BoundingBox v n)) (N (BoundingBox v n)) -> BoundingBox v n -> BoundingBox v n #
Fractional n => HasOrigin (DImage n a)
Instance details Defined in Diagrams.TwoD.Image Methods moveOriginTo :: Point (V (DImage n a)) (N (DImage n a)) -> DImage n a -> DImage n a #
(Additive v, Num n) => HasOrigin (Path v n)
Instance details Defined in Diagrams.Path Methods moveOriginTo :: Point (V (Path v n)) (N (Path v n)) -> Path v n -> Path v n #
(Additive v, Num n) => HasOrigin (FixedSegment v n)
Instance details Defined in Diagrams.Segment Methods moveOriginTo :: Point (V (FixedSegment v n)) (N (FixedSegment v n)) -> FixedSegment v n -> FixedSegment v n #
(Additive v, Num n) => HasOrigin (Query v n m)
Instance details Defined in Diagrams.Core.Query Methods moveOriginTo :: Point (V (Query v n m)) (N (Query v n m)) -> Query v n m -> Query v n m #
(Metric v, OrderedField n, Semigroup m) => HasOrigin (QDiagram b v n m)	Every diagram has an intrinsic "local origin" which is the basis for all combining operations.
Instance details Defined in Diagrams.Core.Types Methods moveOriginTo :: Point (V (QDiagram b v n m)) (N (QDiagram b v n m)) -> QDiagram b v n m -> QDiagram b v n m #
(Metric v, OrderedField n) => HasOrigin (Subdiagram b v n m)
Instance details Defined in Diagrams.Core.Types Methods moveOriginTo :: Point (V (Subdiagram b v n m)) (N (Subdiagram b v n m)) -> Subdiagram b v n m -> Subdiagram b v n m #
(OrderedField n, Metric v) => HasOrigin (SubMap b v n m)
Instance details Defined in Diagrams.Core.Types Methods moveOriginTo :: Point (V (SubMap b v n m)) (N (SubMap b v n m)) -> SubMap b v n m -> SubMap b v n m #

atMost :: Ord n => Measure n -> Measure n -> Measure n #

Calculate the larger of two measures.

atLeast :: Ord n => Measure n -> Measure n -> Measure n #

Calculate the smaller of two measures.

scaleLocal :: Num n => n -> Measured n a -> Measured n a #

Scale the local units of a Measured thing.

normalized :: Num n => n -> Measure n #

Normalized units get scaled so that one normalized unit is the size of the final diagram.

global :: Num n => n -> Measure n #

Global units are scaled so that they are interpreted relative to the size of the final rendered diagram.

local :: Num n => n -> Measure n #

Local units are scaled by the average scale of a transform.

output :: n -> Measure n #

Output units don't change.

fromMeasured :: Num n => n -> n -> Measured n a -> a #

fromMeasured globalScale normalizedScale measure -> a

data Measured n a #

'Measured n a' is an object that depends on local, normalized and global scales. The normalized and global scales are calculated when rendering a diagram.

For attributes, the local scale gets multiplied by the average scale of the transform.

Instances

Profunctor Measured
Instance details Defined in Diagrams.Core.Measure Methods dimap :: (a -> b) -> (c -> d) -> Measured b c -> Measured a d # lmap :: (a -> b) -> Measured b c -> Measured a c # rmap :: (b -> c) -> Measured a b -> Measured a c # (#.) :: Coercible c b => q b c -> Measured a b -> Measured a c # (.#) :: Coercible b a => Measured b c -> q a b -> Measured a c #
Monad (Measured n)
Instance details Defined in Diagrams.Core.Measure Methods (>>=) :: Measured n a -> (a -> Measured n b) -> Measured n b # (>>) :: Measured n a -> Measured n b -> Measured n b # return :: a -> Measured n a # fail :: String -> Measured n a #
Functor (Measured n)
Instance details Defined in Diagrams.Core.Measure Methods fmap :: (a -> b) -> Measured n a -> Measured n b # (<$) :: a -> Measured n b -> Measured n a #
Applicative (Measured n)
Instance details Defined in Diagrams.Core.Measure Methods pure :: a -> Measured n a # (<>) :: Measured n (a -> b) -> Measured n a -> Measured n b # liftA2 :: (a -> b -> c) -> Measured n a -> Measured n b -> Measured n c # (>) :: Measured n a -> Measured n b -> Measured n b # (<*) :: Measured n a -> Measured n b -> Measured n a #
Distributive (Measured n)
Instance details Defined in Diagrams.Core.Measure Methods distribute :: Functor f => f (Measured n a) -> Measured n (f a) # collect :: Functor f => (a -> Measured n b) -> f a -> Measured n (f b) # distributeM :: Monad m => m (Measured n a) -> Measured n (m a) # collectM :: Monad m => (a -> Measured n b) -> m a -> Measured n (m b) #
Representable (Measured n)
Instance details Defined in Diagrams.Core.Measure Associated Types type Rep (Measured n) :: Type # Methods tabulate :: (Rep (Measured n) -> a) -> Measured n a # index :: Measured n a -> Rep (Measured n) -> a #
Num n => Default (FontSizeM n)
Instance details Defined in Diagrams.TwoD.Text Methods def :: FontSizeM n #
OrderedField n => Default (LineWidthM n)
Instance details Defined in Diagrams.Attributes Methods def :: LineWidthM n #
Additive (Measured n)
Instance details Defined in Diagrams.Core.Measure Methods zero :: Num a => Measured n a # (^+^) :: Num a => Measured n a -> Measured n a -> Measured n a # (^-^) :: Num a => Measured n a -> Measured n a -> Measured n a # lerp :: Num a => a -> Measured n a -> Measured n a -> Measured n a # liftU2 :: (a -> a -> a) -> Measured n a -> Measured n a -> Measured n a # liftI2 :: (a -> b -> c) -> Measured n a -> Measured n b -> Measured n c #
Floating a => Floating (Measured n a)
Instance details Defined in Diagrams.Core.Measure Methods pi :: Measured n a # exp :: Measured n a -> Measured n a # log :: Measured n a -> Measured n a # sqrt :: Measured n a -> Measured n a # (**) :: Measured n a -> Measured n a -> Measured n a # logBase :: Measured n a -> Measured n a -> Measured n a # sin :: Measured n a -> Measured n a # cos :: Measured n a -> Measured n a # tan :: Measured n a -> Measured n a # asin :: Measured n a -> Measured n a # acos :: Measured n a -> Measured n a # atan :: Measured n a -> Measured n a # sinh :: Measured n a -> Measured n a # cosh :: Measured n a -> Measured n a # tanh :: Measured n a -> Measured n a # asinh :: Measured n a -> Measured n a # acosh :: Measured n a -> Measured n a # atanh :: Measured n a -> Measured n a # log1p :: Measured n a -> Measured n a # expm1 :: Measured n a -> Measured n a # log1pexp :: Measured n a -> Measured n a # log1mexp :: Measured n a -> Measured n a #
Fractional a => Fractional (Measured n a)
Instance details Defined in Diagrams.Core.Measure Methods (/) :: Measured n a -> Measured n a -> Measured n a # recip :: Measured n a -> Measured n a # fromRational :: Rational -> Measured n a #
Num a => Num (Measured n a)
Instance details Defined in Diagrams.Core.Measure Methods (+) :: Measured n a -> Measured n a -> Measured n a # (-) :: Measured n a -> Measured n a -> Measured n a # (*) :: Measured n a -> Measured n a -> Measured n a # negate :: Measured n a -> Measured n a # abs :: Measured n a -> Measured n a # signum :: Measured n a -> Measured n a # fromInteger :: Integer -> Measured n a #
Semigroup a => Semigroup (Measured n a)
Instance details Defined in Diagrams.Core.Measure Methods (<>) :: Measured n a -> Measured n a -> Measured n a # sconcat :: NonEmpty (Measured n a) -> Measured n a # stimes :: Integral b => b -> Measured n a -> Measured n a #
Monoid a => Monoid (Measured n a)
Instance details Defined in Diagrams.Core.Measure Methods mempty :: Measured n a # mappend :: Measured n a -> Measured n a -> Measured n a # mconcat :: [Measured n a] -> Measured n a #
Juxtaposable a => Juxtaposable (Measured n a)
Instance details Defined in Diagrams.Core.Juxtapose Methods juxtapose :: Vn (Measured n a) -> Measured n a -> Measured n a -> Measured n a #
Qualifiable a => Qualifiable (Measured n a)
Instance details Defined in Diagrams.Core.Names Methods (.>>) :: IsName a0 => a0 -> Measured n a -> Measured n a #
HasStyle b => HasStyle (Measured n b)
Instance details Defined in Diagrams.Core.Style Methods applyStyle :: Style (V (Measured n b)) (N (Measured n b)) -> Measured n b -> Measured n b #
(InSpace v n t, Transformable t, HasLinearMap v, Floating n) => Transformable (Measured n t)
Instance details Defined in Diagrams.Core.Transform Methods transform :: Transformation (V (Measured n t)) (N (Measured n t)) -> Measured n t -> Measured n t #
HasOrigin t => HasOrigin (Measured n t)
Instance details Defined in Diagrams.Core.HasOrigin Methods moveOriginTo :: Point (V (Measured n t)) (N (Measured n t)) -> Measured n t -> Measured n t #
MonadReader (n, n, n) (Measured n)
Instance details Defined in Diagrams.Core.Measure Methods ask :: Measured n (n, n, n) # local :: ((n, n, n) -> (n, n, n)) -> Measured n a -> Measured n a # reader :: ((n, n, n) -> a) -> Measured n a #
type Rep (Measured n)
Instance details Defined in Diagrams.Core.Measure type Rep (Measured n) = (n, n, n)
type V (Measured n a)
Instance details Defined in Diagrams.Core.Measure type V (Measured n a) = V a
type N (Measured n a)
Instance details Defined in Diagrams.Core.Measure type N (Measured n a) = N a

type Measure n = Measured n n #

A measure is a Measured number.

(*.) :: (Functor v, Num n) => n -> Point v n -> Point v n #

Scale a point by a scalar. Specialized version of '(*^)'.

type family V a :: Type -> Type #

Many sorts of objects have an associated vector space in which they "live". The type function V maps from object types to the associated vector space. The resulting vector space has kind * -> * which means it takes another value (a number) and returns a concrete vector. For example V2 has kind * -> * and V2 Double is a vector.

Instances

type V SVG
Instance details Defined in Diagrams.Backend.SVG type V SVG = V2
type V [a]
Instance details Defined in Diagrams.Core.V type V [a] = V a
type V (Set a)
Instance details Defined in Diagrams.Core.V type V (Set a) = V a
type V (Active a)
Instance details Defined in Diagrams.Animation.Active type V (Active a) = V a
type V (Option a)
Instance details Defined in Diagrams.Core.V type V (Option a) = V a
type V (TransInv t)
Instance details Defined in Diagrams.Core.Transform type V (TransInv t) = V t
type V (Text n)
Instance details Defined in Diagrams.TwoD.Text type V (Text n) = V2
type V (LineTexture n)
Instance details Defined in Diagrams.TwoD.Attributes type V (LineTexture n) = V2
type V (FillTexture n)
Instance details Defined in Diagrams.TwoD.Attributes type V (FillTexture n) = V2
type V (Texture n)
Instance details Defined in Diagrams.TwoD.Attributes type V (Texture n) = V2
type V (RGradient n)
Instance details Defined in Diagrams.TwoD.Attributes type V (RGradient n) = V2
type V (LGradient n)
Instance details Defined in Diagrams.TwoD.Attributes type V (LGradient n) = V2
type V (Clip n)
Instance details Defined in Diagrams.TwoD.Path type V (Clip n) = V2
type V (GetSegment t)
Instance details Defined in Diagrams.Trail type V (GetSegment t) = V t
type V (Tangent t)
Instance details Defined in Diagrams.Tangent type V (Tangent t) = V t
type V (Located a)
Instance details Defined in Diagrams.Located type V (Located a) = V a
type V (OrthoLens n)
Instance details Defined in Diagrams.ThreeD.Camera type V (OrthoLens n) = V3
type V (PerspectiveLens n)
Instance details Defined in Diagrams.ThreeD.Camera type V (PerspectiveLens n) = V3
type V (Ellipsoid n)
Instance details Defined in Diagrams.ThreeD.Shapes type V (Ellipsoid n) = V3
type V (Box n)
Instance details Defined in Diagrams.ThreeD.Shapes type V (Box n) = V3
type V (Frustum n)
Instance details Defined in Diagrams.ThreeD.Shapes type V (Frustum n) = V3
type V (CSG n)
Instance details Defined in Diagrams.ThreeD.Shapes type V (CSG n) = V3
type V (PointLight n)
Instance details Defined in Diagrams.ThreeD.Light type V (PointLight n) = V3
type V (ParallelLight n)
Instance details Defined in Diagrams.ThreeD.Light type V (ParallelLight n) = V3
type V (BernsteinPoly n)
Instance details Defined in Diagrams.TwoD.Segment.Bernstein type V (BernsteinPoly n) = V1
type V (V2 n)
Instance details Defined in Diagrams.TwoD.Types type V (V2 n) = V2
type V (V3 n)
Instance details Defined in Diagrams.ThreeD.Types type V (V3 n) = V3
type V (Split m)
Instance details Defined in Diagrams.Core.V type V (Split m) = V m
type V (Deletable m)
Instance details Defined in Diagrams.Core.V type V (Deletable m) = V m
type V (a -> b)
Instance details Defined in Diagrams.Core.V type V (a -> b) = V b
type V (a, b)
Instance details Defined in Diagrams.Core.V type V (a, b) = V a
type V (Map k a)
Instance details Defined in Diagrams.Core.V type V (Map k a) = V a
type V (Envelope v n)
Instance details Defined in Diagrams.Core.Envelope type V (Envelope v n) = v
type V (Trace v n)
Instance details Defined in Diagrams.Core.Trace type V (Trace v n) = v
type V (Attribute v n)
Instance details Defined in Diagrams.Core.Style type V (Attribute v n) = v
type V (Style v n)
Instance details Defined in Diagrams.Core.Style type V (Style v n) = v
type V (Transformation v n)
Instance details Defined in Diagrams.Core.Transform type V (Transformation v n) = v
type V (Measured n a)
Instance details Defined in Diagrams.Core.Measure type V (Measured n a) = V a
type V (Point v n)
Instance details Defined in Diagrams.Core.Points type V (Point v n) = v
type V (SizeSpec v n)
Instance details Defined in Diagrams.Size type V (SizeSpec v n) = v
type V (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox type V (BoundingBox v n) = v
type V (DImage n a)
Instance details Defined in Diagrams.TwoD.Image type V (DImage n a) = V2
type V (Path v n)
Instance details Defined in Diagrams.Path type V (Path v n) = v
type V (SegTree v n)
Instance details Defined in Diagrams.Trail type V (SegTree v n) = v
type V (Trail v n)
Instance details Defined in Diagrams.Trail type V (Trail v n) = v
type V (FixedSegment v n)
Instance details Defined in Diagrams.Segment type V (FixedSegment v n) = v
type V (Camera l n)
Instance details Defined in Diagrams.ThreeD.Camera type V (Camera l n) = V3
type V (Direction v n)
Instance details Defined in Diagrams.Direction type V (Direction v n) = v
type V (FingerTree m a)
Instance details Defined in Diagrams.Trail type V (FingerTree m a) = V a
type V (m :+: n)
Instance details Defined in Diagrams.Core.V type V (m :+: n) = V m
type V (NonEmptyBoundingBox v n)
Instance details Defined in Diagrams.BoundingBox type V (NonEmptyBoundingBox v n) = v
type V (a, b, c)
Instance details Defined in Diagrams.Core.V type V (a, b, c) = V a
type V (Prim b v n)
Instance details Defined in Diagrams.Core.Types type V (Prim b v n) = v
type V (Query v n m)
Instance details Defined in Diagrams.Core.Query type V (Query v n m) = v
type V (Trail' l v n)
Instance details Defined in Diagrams.Trail type V (Trail' l v n) = v
type V (Offset c v n)
Instance details Defined in Diagrams.Segment type V (Offset c v n) = v
type V (Segment c v n)
Instance details Defined in Diagrams.Segment type V (Segment c v n) = v
type V (QDiagram b v n m)
Instance details Defined in Diagrams.Core.Types type V (QDiagram b v n m) = v
type V (Subdiagram b v n m)
Instance details Defined in Diagrams.Core.Types type V (Subdiagram b v n m) = v
type V (SubMap b v n m)
Instance details Defined in Diagrams.Core.Types type V (SubMap b v n m) = v

type family N a :: Type #

The numerical field for the object, the number type used for calculations.

Instances

type N SVG
Instance details Defined in Diagrams.Backend.SVG type N SVG = Double
type N [a]
Instance details Defined in Diagrams.Core.V type N [a] = N a
type N (Set a)
Instance details Defined in Diagrams.Core.V type N (Set a) = N a
type N (Active a)
Instance details Defined in Diagrams.Animation.Active type N (Active a) = N a
type N (Option a)
Instance details Defined in Diagrams.Core.V type N (Option a) = N a
type N (TransInv t)
Instance details Defined in Diagrams.Core.Transform type N (TransInv t) = N t
type N (Text n)
Instance details Defined in Diagrams.TwoD.Text type N (Text n) = n
type N (LineTexture n)
Instance details Defined in Diagrams.TwoD.Attributes type N (LineTexture n) = n
type N (FillTexture n)
Instance details Defined in Diagrams.TwoD.Attributes type N (FillTexture n) = n
type N (Texture n)
Instance details Defined in Diagrams.TwoD.Attributes type N (Texture n) = n
type N (RGradient n)
Instance details Defined in Diagrams.TwoD.Attributes type N (RGradient n) = n
type N (LGradient n)
Instance details Defined in Diagrams.TwoD.Attributes type N (LGradient n) = n
type N (Clip n)
Instance details Defined in Diagrams.TwoD.Path type N (Clip n) = n
type N (GetSegment t)
Instance details Defined in Diagrams.Trail type N (GetSegment t) = N t
type N (Tangent t)
Instance details Defined in Diagrams.Tangent type N (Tangent t) = N t
type N (Located a)
Instance details Defined in Diagrams.Located type N (Located a) = N a
type N (OrthoLens n)
Instance details Defined in Diagrams.ThreeD.Camera type N (OrthoLens n) = n
type N (PerspectiveLens n)
Instance details Defined in Diagrams.ThreeD.Camera type N (PerspectiveLens n) = n
type N (Ellipsoid n)
Instance details Defined in Diagrams.ThreeD.Shapes type N (Ellipsoid n) = n
type N (Box n)
Instance details Defined in Diagrams.ThreeD.Shapes type N (Box n) = n
type N (Frustum n)
Instance details Defined in Diagrams.ThreeD.Shapes type N (Frustum n) = n
type N (CSG n)
Instance details Defined in Diagrams.ThreeD.Shapes type N (CSG n) = n
type N (PointLight n)
Instance details Defined in Diagrams.ThreeD.Light type N (PointLight n) = n
type N (ParallelLight n)
Instance details Defined in Diagrams.ThreeD.Light type N (ParallelLight n) = n
type N (BernsteinPoly n)
Instance details Defined in Diagrams.TwoD.Segment.Bernstein type N (BernsteinPoly n) = n
type N (Angle n)
Instance details Defined in Diagrams.Angle type N (Angle n) = n
type N (V2 n)
Instance details Defined in Diagrams.TwoD.Types type N (V2 n) = n
type N (V3 n)
Instance details Defined in Diagrams.ThreeD.Types type N (V3 n) = n
type N (Split m)
Instance details Defined in Diagrams.Core.V type N (Split m) = N m
type N (Deletable m)
Instance details Defined in Diagrams.Core.V type N (Deletable m) = N m
type N (a -> b)
Instance details Defined in Diagrams.Core.V type N (a -> b) = N b
type N (a, b)
Instance details Defined in Diagrams.Core.V type N (a, b) = N a
type N (Map k a)
Instance details Defined in Diagrams.Core.V type N (Map k a) = N a
type N (Envelope v n)
Instance details Defined in Diagrams.Core.Envelope type N (Envelope v n) = n
type N (Trace v n)
Instance details Defined in Diagrams.Core.Trace type N (Trace v n) = n
type N (Attribute v n)
Instance details Defined in Diagrams.Core.Style type N (Attribute v n) = n
type N (Style v n)
Instance details Defined in Diagrams.Core.Style type N (Style v n) = n
type N (Transformation v n)
Instance details Defined in Diagrams.Core.Transform type N (Transformation v n) = n
type N (Measured n a)
Instance details Defined in Diagrams.Core.Measure type N (Measured n a) = N a
type N (Point v n)
Instance details Defined in Diagrams.Core.Points type N (Point v n) = n
type N (SizeSpec v n)
Instance details Defined in Diagrams.Size type N (SizeSpec v n) = n
type N (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox type N (BoundingBox v n) = n
type N (DImage n a)
Instance details Defined in Diagrams.TwoD.Image type N (DImage n a) = n
type N (Path v n)
Instance details Defined in Diagrams.Path type N (Path v n) = n
type N (SegTree v n)
Instance details Defined in Diagrams.Trail type N (SegTree v n) = n
type N (Trail v n)
Instance details Defined in Diagrams.Trail type N (Trail v n) = n
type N (FixedSegment v n)
Instance details Defined in Diagrams.Segment type N (FixedSegment v n) = n
type N (Camera l n)
Instance details Defined in Diagrams.ThreeD.Camera type N (Camera l n) = n
type N (Direction v n)
Instance details Defined in Diagrams.Direction type N (Direction v n) = n
type N (FingerTree m a)
Instance details Defined in Diagrams.Trail type N (FingerTree m a) = N a
type N (m :+: n)
Instance details Defined in Diagrams.Core.V type N (m :+: n) = N m
type N (NonEmptyBoundingBox v n)
Instance details Defined in Diagrams.BoundingBox type N (NonEmptyBoundingBox v n) = n
type N (a, b, c)
Instance details Defined in Diagrams.Core.V type N (a, b, c) = N a
type N (Prim b v n)
Instance details Defined in Diagrams.Core.Types type N (Prim b v n) = n
type N (Query v n m)
Instance details Defined in Diagrams.Core.Query type N (Query v n m) = n
type N (Trail' l v n)
Instance details Defined in Diagrams.Trail type N (Trail' l v n) = n
type N (Offset c v n)
Instance details Defined in Diagrams.Segment type N (Offset c v n) = n
type N (Segment c v n)
Instance details Defined in Diagrams.Segment type N (Segment c v n) = n
type N (QDiagram b v n m)
Instance details Defined in Diagrams.Core.Types type N (QDiagram b v n m) = n
type N (Subdiagram b v n m)
Instance details Defined in Diagrams.Core.Types type N (Subdiagram b v n m) = n
type N (SubMap b v n m)
Instance details Defined in Diagrams.Core.Types type N (SubMap b v n m) = n

type Vn a = V a (N a) #

Conveient type alias to retrieve the vector type associated with an object's vector space. This is usually used as Vn a ~ v n where v is the vector space and n is the numerical field.

type InSpace (v :: Type -> Type) n a = (V a ~ v, N a ~ n, Additive v, Num n) #

InSpace v n a means the type a belongs to the vector space v n, where v is Additive and n is a Num.

type SameSpace a b = (V a ~ V b, N a ~ N b) #

SameSpace a b means the types a and b belong to the same vector space v n.

type Monoid' = Monoid #

For base < 4.11, the Monoid' constraint is a synonym for things which are instances of both Semigroup and Monoid. For base version 4.11 and onwards, Monoid has Semigroup as a superclass already, so for backwards compatibility Monoid' is provided as a synonym for Monoid.

basis :: (Additive t, Traversable t, Num a) => [t a] #

Produce a default basis for a vector space. If the dimensionality of the vector space is not statically known, see basisFor.

newtype Point (f :: Type -> Type) a #

A handy wrapper to help distinguish points from vectors at the type level

Constructors

P (f a)

Instances

Unbox (f a) => Vector Vector (Point f a)
Instance details Defined in Linear.Affine Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Point f a) -> m (Vector (Point f a)) # basicUnsafeThaw :: PrimMonad m => Vector (Point f a) -> m (Mutable Vector (PrimState m) (Point f a)) # basicLength :: Vector (Point f a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Point f a) -> Vector (Point f a) # basicUnsafeIndexM :: Monad m => Vector (Point f a) -> Int -> m (Point f a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Point f a) -> Vector (Point f a) -> m () # elemseq :: Vector (Point f a) -> Point f a -> b -> b #
Unbox (f a) => MVector MVector (Point f a)
Instance details Defined in Linear.Affine Methods basicLength :: MVector s (Point f a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Point f a) -> MVector s (Point f a) # basicOverlaps :: MVector s (Point f a) -> MVector s (Point f a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Point f a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (Point f a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Point f a -> m (MVector (PrimState m) (Point f a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Point f a) -> Int -> m (Point f a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Point f a) -> Int -> Point f a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (Point f a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (Point f a) -> Point f a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Point f a) -> MVector (PrimState m) (Point f a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Point f a) -> MVector (PrimState m) (Point f a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Point f a) -> Int -> m (MVector (PrimState m) (Point f a)) #
Monad f => Monad (Point f)
Instance details Defined in Linear.Affine Methods (>>=) :: Point f a -> (a -> Point f b) -> Point f b # (>>) :: Point f a -> Point f b -> Point f b # return :: a -> Point f a # fail :: String -> Point f a #
Functor f => Functor (Point f)
Instance details Defined in Linear.Affine Methods fmap :: (a -> b) -> Point f a -> Point f b # (<$) :: a -> Point f b -> Point f a #
Applicative f => Applicative (Point f)
Instance details Defined in Linear.Affine Methods pure :: a -> Point f a # (<>) :: Point f (a -> b) -> Point f a -> Point f b # liftA2 :: (a -> b -> c) -> Point f a -> Point f b -> Point f c # (>) :: Point f a -> Point f b -> Point f b # (<*) :: Point f a -> Point f b -> Point f a #
Foldable f => Foldable (Point f)
Instance details Defined in Linear.Affine Methods fold :: Monoid m => Point f m -> m # foldMap :: Monoid m => (a -> m) -> Point f a -> m # foldr :: (a -> b -> b) -> b -> Point f a -> b # foldr' :: (a -> b -> b) -> b -> Point f a -> b # foldl :: (b -> a -> b) -> b -> Point f a -> b # foldl' :: (b -> a -> b) -> b -> Point f a -> b # foldr1 :: (a -> a -> a) -> Point f a -> a # foldl1 :: (a -> a -> a) -> Point f a -> a # toList :: Point f a -> [a] # null :: Point f a -> Bool # length :: Point f a -> Int # elem :: Eq a => a -> Point f a -> Bool # maximum :: Ord a => Point f a -> a # minimum :: Ord a => Point f a -> a # sum :: Num a => Point f a -> a # product :: Num a => Point f a -> a #
Traversable f => Traversable (Point f)
Instance details Defined in Linear.Affine Methods traverse :: Applicative f0 => (a -> f0 b) -> Point f a -> f0 (Point f b) # sequenceA :: Applicative f0 => Point f (f0 a) -> f0 (Point f a) # mapM :: Monad m => (a -> m b) -> Point f a -> m (Point f b) # sequence :: Monad m => Point f (m a) -> m (Point f a) #
Apply f => Apply (Point f)
Instance details Defined in Linear.Affine Methods (<.>) :: Point f (a -> b) -> Point f a -> Point f b # (.>) :: Point f a -> Point f b -> Point f b # (<.) :: Point f a -> Point f b -> Point f a # liftF2 :: (a -> b -> c) -> Point f a -> Point f b -> Point f c #
Distributive f => Distributive (Point f)
Instance details Defined in Linear.Affine Methods distribute :: Functor f0 => f0 (Point f a) -> Point f (f0 a) # collect :: Functor f0 => (a -> Point f b) -> f0 a -> Point f (f0 b) # distributeM :: Monad m => m (Point f a) -> Point f (m a) # collectM :: Monad m => (a -> Point f b) -> m a -> Point f (m b) #
Representable f => Representable (Point f)
Instance details Defined in Linear.Affine Associated Types type Rep (Point f) :: Type # Methods tabulate :: (Rep (Point f) -> a) -> Point f a # index :: Point f a -> Rep (Point f) -> a #
Eq1 f => Eq1 (Point f)
Instance details Defined in Linear.Affine Methods liftEq :: (a -> b -> Bool) -> Point f a -> Point f b -> Bool #
Ord1 f => Ord1 (Point f)
Instance details Defined in Linear.Affine Methods liftCompare :: (a -> b -> Ordering) -> Point f a -> Point f b -> Ordering #
Read1 f => Read1 (Point f)
Instance details Defined in Linear.Affine Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Point f a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Point f a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Point f a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Point f a] #
Show1 f => Show1 (Point f)
Instance details Defined in Linear.Affine Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Point f a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Point f a] -> ShowS #
Serial1 f => Serial1 (Point f)
Instance details Defined in Linear.Affine Methods serializeWith :: MonadPut m => (a -> m ()) -> Point f a -> m () # deserializeWith :: MonadGet m => m a -> m (Point f a) #
Additive f => Additive (Point f)
Instance details Defined in Linear.Affine Methods zero :: Num a => Point f a # (^+^) :: Num a => Point f a -> Point f a -> Point f a # (^-^) :: Num a => Point f a -> Point f a -> Point f a # lerp :: Num a => a -> Point f a -> Point f a -> Point f a # liftU2 :: (a -> a -> a) -> Point f a -> Point f a -> Point f a # liftI2 :: (a -> b -> c) -> Point f a -> Point f b -> Point f c #
Metric f => Metric (Point f)
Instance details Defined in Linear.Affine Methods dot :: Num a => Point f a -> Point f a -> a # quadrance :: Num a => Point f a -> a # qd :: Num a => Point f a -> Point f a -> a # distance :: Floating a => Point f a -> Point f a -> a # norm :: Floating a => Point f a -> a # signorm :: Floating a => Point f a -> Point f a #
Additive f => Affine (Point f)
Instance details Defined in Linear.Affine Associated Types type Diff (Point f) :: Type -> Type # Methods (.-.) :: Num a => Point f a -> Point f a -> Diff (Point f) a # (.+^) :: Num a => Point f a -> Diff (Point f) a -> Point f a # (.-^) :: Num a => Point f a -> Diff (Point f) a -> Point f a #
(Metric v, OrderedField n) => TrailLike [Point v n]	A list of points is trail-like; this instance simply computes the vertices of the trail, using `trailPoints`.
Instance details Defined in Diagrams.TrailLike Methods trailLike :: Located (Trail (V [Point v n]) (N [Point v n])) -> [Point v n] #
HasR v => HasR (Point v)
Instance details Defined in Diagrams.TwoD.Types Methods _r :: RealFloat n => Lens' (Point v n) n #
HasTheta v => HasTheta (Point v)
Instance details Defined in Diagrams.Angle Methods _theta :: RealFloat n => Lens' (Point v n) (Angle n) #
HasPhi v => HasPhi (Point v)
Instance details Defined in Diagrams.Angle Methods _phi :: RealFloat n => Lens' (Point v n) (Angle n) #
R1 f => R1 (Point f)
Instance details Defined in Linear.Affine Methods _x :: Lens' (Point f a) a #
R2 f => R2 (Point f)
Instance details Defined in Linear.Affine Methods _y :: Lens' (Point f a) a # _xy :: Lens' (Point f a) (V2 a) #
R3 f => R3 (Point f)
Instance details Defined in Linear.Affine Methods _z :: Lens' (Point f a) a # _xyz :: Lens' (Point f a) (V3 a) #
Hashable1 f => Hashable1 (Point f)
Instance details Defined in Linear.Affine Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> Point f a -> Int #
R4 f => R4 (Point f)
Instance details Defined in Linear.Affine Methods _w :: Lens' (Point f a) a # _xyzw :: Lens' (Point f a) (V4 a) #
Finite f => Finite (Point f)
Instance details Defined in Linear.Affine Associated Types type Size (Point f) :: Nat # Methods toV :: Point f a -> V (Size (Point f)) a # fromV :: V (Size (Point f)) a -> Point f a #
Bind f => Bind (Point f)
Instance details Defined in Linear.Affine Methods (>>-) :: Point f a -> (a -> Point f b) -> Point f b # join :: Point f (Point f a) -> Point f a #
Generic1 (Point f :: Type -> Type)
Instance details Defined in Linear.Affine Associated Types type Rep1 (Point f) :: k -> Type # Methods from1 :: Point f a -> Rep1 (Point f) a # to1 :: Rep1 (Point f) a -> Point f a #
Functor v => Cosieve (Query v) (Point v)
Instance details Defined in Diagrams.Core.Query Methods cosieve :: Query v a b -> Point v a -> b #
Eq (f a) => Eq (Point f a)
Instance details Defined in Linear.Affine Methods (==) :: Point f a -> Point f a -> Bool # (/=) :: Point f a -> Point f a -> Bool #
Fractional (f a) => Fractional (Point f a)
Instance details Defined in Linear.Affine Methods (/) :: Point f a -> Point f a -> Point f a # recip :: Point f a -> Point f a # fromRational :: Rational -> Point f a #
(Typeable f, Typeable a, Data (f a)) => Data (Point f a)
Instance details Defined in Linear.Affine Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Point f a -> c (Point f a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Point f a) # toConstr :: Point f a -> Constr # dataTypeOf :: Point f a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Point f a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Point f a)) # gmapT :: (forall b. Data b => b -> b) -> Point f a -> Point f a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Point f a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Point f a -> r # gmapQ :: (forall d. Data d => d -> u) -> Point f a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Point f a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Point f a -> m (Point f a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Point f a -> m (Point f a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Point f a -> m (Point f a) #
Num (f a) => Num (Point f a)
Instance details Defined in Linear.Affine Methods (+) :: Point f a -> Point f a -> Point f a # (-) :: Point f a -> Point f a -> Point f a # (*) :: Point f a -> Point f a -> Point f a # negate :: Point f a -> Point f a # abs :: Point f a -> Point f a # signum :: Point f a -> Point f a # fromInteger :: Integer -> Point f a #
Ord (f a) => Ord (Point f a)
Instance details Defined in Linear.Affine Methods compare :: Point f a -> Point f a -> Ordering # (<) :: Point f a -> Point f a -> Bool # (<=) :: Point f a -> Point f a -> Bool # (>) :: Point f a -> Point f a -> Bool # (>=) :: Point f a -> Point f a -> Bool # max :: Point f a -> Point f a -> Point f a # min :: Point f a -> Point f a -> Point f a #
Read (f a) => Read (Point f a)
Instance details Defined in Linear.Affine Methods readsPrec :: Int -> ReadS (Point f a) # readList :: ReadS [Point f a] # readPrec :: ReadPrec (Point f a) # readListPrec :: ReadPrec [Point f a] #
Show (f a) => Show (Point f a)
Instance details Defined in Linear.Affine Methods showsPrec :: Int -> Point f a -> ShowS # show :: Point f a -> String # showList :: [Point f a] -> ShowS #
Ix (f a) => Ix (Point f a)
Instance details Defined in Linear.Affine Methods range :: (Point f a, Point f a) -> [Point f a] # index :: (Point f a, Point f a) -> Point f a -> Int # unsafeIndex :: (Point f a, Point f a) -> Point f a -> Int inRange :: (Point f a, Point f a) -> Point f a -> Bool # rangeSize :: (Point f a, Point f a) -> Int # unsafeRangeSize :: (Point f a, Point f a) -> Int
Generic (Point f a)
Instance details Defined in Linear.Affine Associated Types type Rep (Point f a) :: Type -> Type # Methods from :: Point f a -> Rep (Point f a) x # to :: Rep (Point f a) x -> Point f a #
Hashable (f a) => Hashable (Point f a)
Instance details Defined in Linear.Affine Methods hashWithSalt :: Int -> Point f a -> Int # hash :: Point f a -> Int #
Storable (f a) => Storable (Point f a)
Instance details Defined in Linear.Affine Methods sizeOf :: Point f a -> Int # alignment :: Point f a -> Int # peekElemOff :: Ptr (Point f a) -> Int -> IO (Point f a) # pokeElemOff :: Ptr (Point f a) -> Int -> Point f a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Point f a) # pokeByteOff :: Ptr b -> Int -> Point f a -> IO () # peek :: Ptr (Point f a) -> IO (Point f a) # poke :: Ptr (Point f a) -> Point f a -> IO () #
Binary (f a) => Binary (Point f a)
Instance details Defined in Linear.Affine Methods put :: Point f a -> Put # get :: Get (Point f a) # putList :: [Point f a] -> Put #
Serial (f a) => Serial (Point f a)
Instance details Defined in Linear.Affine Methods serialize :: MonadPut m => Point f a -> m () # deserialize :: MonadGet m => m (Point f a) #
Serialize (f a) => Serialize (Point f a)
Instance details Defined in Linear.Affine Methods put :: Putter (Point f a) # get :: Get (Point f a) #
NFData (f a) => NFData (Point f a)
Instance details Defined in Linear.Affine Methods rnf :: Point f a -> () #
(OrderedField n, Metric v) => Enveloped (Point v n)
Instance details Defined in Diagrams.Core.Envelope Methods getEnvelope :: Point v n -> Envelope (V (Point v n)) (N (Point v n)) #
(Additive v, Ord n) => Traced (Point v n)	The trace of a single point is the empty trace, i.e. the one which returns no intersection points for every query. Arguably it should return a single finite distance for vectors aimed directly at the given point, but due to floating-point inaccuracy this is problematic. Note that the envelope for a single point is not the empty envelope (see Diagrams.Core.Envelope).
Instance details Defined in Diagrams.Core.Trace Methods getTrace :: Point v n -> Trace (V (Point v n)) (N (Point v n)) #
(Additive v, Num n) => Transformable (Point v n)
Instance details Defined in Diagrams.Core.Transform Methods transform :: Transformation (V (Point v n)) (N (Point v n)) -> Point v n -> Point v n #
(Additive v, Num n) => HasOrigin (Point v n)
Instance details Defined in Diagrams.Core.HasOrigin Methods moveOriginTo :: Point (V (Point v n)) (N (Point v n)) -> Point v n -> Point v n #
Coordinates (v n) => Coordinates (Point v n)
Instance details Defined in Diagrams.Coordinates Associated Types type FinalCoord (Point v n) :: Type # type PrevDim (Point v n) :: Type # type Decomposition (Point v n) :: Type # Methods (^&) :: PrevDim (Point v n) -> FinalCoord (Point v n) -> Point v n # pr :: PrevDim (Point v n) -> FinalCoord (Point v n) -> Point v n # coords :: Point v n -> Decomposition (Point v n) #
Wrapped (Point f a)
Instance details Defined in Linear.Affine Associated Types type Unwrapped (Point f a) :: Type # Methods _Wrapped' :: Iso' (Point f a) (Unwrapped (Point f a)) #
Ixed (f a) => Ixed (Point f a)
Instance details Defined in Linear.Affine Methods ix :: Index (Point f a) -> Traversal' (Point f a) (IxValue (Point f a)) #
Unbox (f a) => Unbox (Point f a)
Instance details Defined in Linear.Affine
Epsilon (f a) => Epsilon (Point f a)
Instance details Defined in Linear.Affine Methods nearZero :: Point f a -> Bool #
r ~ Point u n => Deformable (Point v n) r
Instance details Defined in Diagrams.Deform Methods deform' :: N (Point v n) -> Deformation (V (Point v n)) (V r) (N (Point v n)) -> Point v n -> r # deform :: Deformation (V (Point v n)) (V r) (N (Point v n)) -> Point v n -> r #
t ~ Point g b => Rewrapped (Point f a) t
Instance details Defined in Linear.Affine
Traversable f => Each (Point f a) (Point f b) a b
Instance details Defined in Linear.Affine Methods each :: Traversal (Point f a) (Point f b) a b #
(Additive v', Foldable v', Ord n') => Each (BoundingBox v n) (BoundingBox v' n') (Point v n) (Point v' n')	Only valid if the second point is not smaller than the first.
Instance details Defined in Diagrams.BoundingBox Methods each :: Traversal (BoundingBox v n) (BoundingBox v' n') (Point v n) (Point v' n') #
Each (FixedSegment v n) (FixedSegment v' n') (Point v n) (Point v' n')
Instance details Defined in Diagrams.Segment Methods each :: Traversal (FixedSegment v n) (FixedSegment v' n') (Point v n) (Point v' n') #
newtype MVector s (Point f a)
Instance details Defined in Linear.Affine newtype MVector s (Point f a) = MV_P (MVector s (f a))
type Rep (Point f)
Instance details Defined in Linear.Affine type Rep (Point f) = Rep f
type Diff (Point f)
Instance details Defined in Linear.Affine type Diff (Point f) = f
type Size (Point f)
Instance details Defined in Linear.Affine type Size (Point f) = Size f
type Rep1 (Point f :: Type -> Type)
Instance details Defined in Linear.Affine type Rep1 (Point f :: Type -> Type) = D1 (MetaData "Point" "Linear.Affine" "linear-1.20.9-27UQiD0kWRO59L1Ww4Df0c" True) (C1 (MetaCons "P" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 f)))
type Rep (Point f a)
Instance details Defined in Linear.Affine type Rep (Point f a) = D1 (MetaData "Point" "Linear.Affine" "linear-1.20.9-27UQiD0kWRO59L1Ww4Df0c" True) (C1 (MetaCons "P" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f a))))
type V (Point v n)
Instance details Defined in Diagrams.Core.Points type V (Point v n) = v
type N (Point v n)
Instance details Defined in Diagrams.Core.Points type N (Point v n) = n
newtype Vector (Point f a)
Instance details Defined in Linear.Affine newtype Vector (Point f a) = V_P (Vector (f a))
type Decomposition (Point v n)
Instance details Defined in Diagrams.Coordinates type Decomposition (Point v n) = Decomposition (v n)
type PrevDim (Point v n)
Instance details Defined in Diagrams.Coordinates type PrevDim (Point v n) = PrevDim (v n)
type FinalCoord (Point v n)
Instance details Defined in Diagrams.Coordinates type FinalCoord (Point v n) = FinalCoord (v n)
type Unwrapped (Point f a)
Instance details Defined in Linear.Affine type Unwrapped (Point f a) = f a
type IxValue (Point f a)
Instance details Defined in Linear.Affine type IxValue (Point f a) = IxValue (f a)
type Index (Point f a)
Instance details Defined in Linear.Affine type Index (Point f a) = Index (f a)

_Point :: Iso' (Point f a) (f a) #

origin :: (Additive f, Num a) => Point f a #

Vector spaces have origins.

relative :: (Additive f, Num a) => Point f a -> Iso' (Point f a) (f a) #

An isomorphism between points and vectors, given a reference point.

newtype E (t :: Type -> Type) #

Basis element

Constructors

E
Fields el :: forall x. Lens' (t x) x

Instances

TraversableWithIndex (E V2) V2
Instance details Defined in Linear.V2 Methods itraverse :: Applicative f => (E V2 -> a -> f b) -> V2 a -> f (V2 b) # itraversed :: IndexedTraversal (E V2) (V2 a) (V2 b) a b #
TraversableWithIndex (E V3) V3
Instance details Defined in Linear.V3 Methods itraverse :: Applicative f => (E V3 -> a -> f b) -> V3 a -> f (V3 b) # itraversed :: IndexedTraversal (E V3) (V3 a) (V3 b) a b #
TraversableWithIndex (E Plucker) Plucker
Instance details Defined in Linear.Plucker Methods itraverse :: Applicative f => (E Plucker -> a -> f b) -> Plucker a -> f (Plucker b) # itraversed :: IndexedTraversal (E Plucker) (Plucker a) (Plucker b) a b #
TraversableWithIndex (E Quaternion) Quaternion
Instance details Defined in Linear.Quaternion Methods itraverse :: Applicative f => (E Quaternion -> a -> f b) -> Quaternion a -> f (Quaternion b) # itraversed :: IndexedTraversal (E Quaternion) (Quaternion a) (Quaternion b) a b #
TraversableWithIndex (E V0) V0
Instance details Defined in Linear.V0 Methods itraverse :: Applicative f => (E V0 -> a -> f b) -> V0 a -> f (V0 b) # itraversed :: IndexedTraversal (E V0) (V0 a) (V0 b) a b #
TraversableWithIndex (E V4) V4
Instance details Defined in Linear.V4 Methods itraverse :: Applicative f => (E V4 -> a -> f b) -> V4 a -> f (V4 b) # itraversed :: IndexedTraversal (E V4) (V4 a) (V4 b) a b #
TraversableWithIndex (E V1) V1
Instance details Defined in Linear.V1 Methods itraverse :: Applicative f => (E V1 -> a -> f b) -> V1 a -> f (V1 b) # itraversed :: IndexedTraversal (E V1) (V1 a) (V1 b) a b #
FoldableWithIndex (E V2) V2
Instance details Defined in Linear.V2 Methods ifoldMap :: Monoid m => (E V2 -> a -> m) -> V2 a -> m # ifolded :: IndexedFold (E V2) (V2 a) a # ifoldr :: (E V2 -> a -> b -> b) -> b -> V2 a -> b # ifoldl :: (E V2 -> b -> a -> b) -> b -> V2 a -> b # ifoldr' :: (E V2 -> a -> b -> b) -> b -> V2 a -> b # ifoldl' :: (E V2 -> b -> a -> b) -> b -> V2 a -> b #
FoldableWithIndex (E V3) V3
Instance details Defined in Linear.V3 Methods ifoldMap :: Monoid m => (E V3 -> a -> m) -> V3 a -> m # ifolded :: IndexedFold (E V3) (V3 a) a # ifoldr :: (E V3 -> a -> b -> b) -> b -> V3 a -> b # ifoldl :: (E V3 -> b -> a -> b) -> b -> V3 a -> b # ifoldr' :: (E V3 -> a -> b -> b) -> b -> V3 a -> b # ifoldl' :: (E V3 -> b -> a -> b) -> b -> V3 a -> b #
FoldableWithIndex (E Plucker) Plucker
Instance details Defined in Linear.Plucker Methods ifoldMap :: Monoid m => (E Plucker -> a -> m) -> Plucker a -> m # ifolded :: IndexedFold (E Plucker) (Plucker a) a # ifoldr :: (E Plucker -> a -> b -> b) -> b -> Plucker a -> b # ifoldl :: (E Plucker -> b -> a -> b) -> b -> Plucker a -> b # ifoldr' :: (E Plucker -> a -> b -> b) -> b -> Plucker a -> b # ifoldl' :: (E Plucker -> b -> a -> b) -> b -> Plucker a -> b #
FoldableWithIndex (E Quaternion) Quaternion
Instance details Defined in Linear.Quaternion Methods ifoldMap :: Monoid m => (E Quaternion -> a -> m) -> Quaternion a -> m # ifolded :: IndexedFold (E Quaternion) (Quaternion a) a # ifoldr :: (E Quaternion -> a -> b -> b) -> b -> Quaternion a -> b # ifoldl :: (E Quaternion -> b -> a -> b) -> b -> Quaternion a -> b # ifoldr' :: (E Quaternion -> a -> b -> b) -> b -> Quaternion a -> b # ifoldl' :: (E Quaternion -> b -> a -> b) -> b -> Quaternion a -> b #
FoldableWithIndex (E V0) V0
Instance details Defined in Linear.V0 Methods ifoldMap :: Monoid m => (E V0 -> a -> m) -> V0 a -> m # ifolded :: IndexedFold (E V0) (V0 a) a # ifoldr :: (E V0 -> a -> b -> b) -> b -> V0 a -> b # ifoldl :: (E V0 -> b -> a -> b) -> b -> V0 a -> b # ifoldr' :: (E V0 -> a -> b -> b) -> b -> V0 a -> b # ifoldl' :: (E V0 -> b -> a -> b) -> b -> V0 a -> b #
FoldableWithIndex (E V4) V4
Instance details Defined in Linear.V4 Methods ifoldMap :: Monoid m => (E V4 -> a -> m) -> V4 a -> m # ifolded :: IndexedFold (E V4) (V4 a) a # ifoldr :: (E V4 -> a -> b -> b) -> b -> V4 a -> b # ifoldl :: (E V4 -> b -> a -> b) -> b -> V4 a -> b # ifoldr' :: (E V4 -> a -> b -> b) -> b -> V4 a -> b # ifoldl' :: (E V4 -> b -> a -> b) -> b -> V4 a -> b #
FoldableWithIndex (E V1) V1
Instance details Defined in Linear.V1 Methods ifoldMap :: Monoid m => (E V1 -> a -> m) -> V1 a -> m # ifolded :: IndexedFold (E V1) (V1 a) a # ifoldr :: (E V1 -> a -> b -> b) -> b -> V1 a -> b # ifoldl :: (E V1 -> b -> a -> b) -> b -> V1 a -> b # ifoldr' :: (E V1 -> a -> b -> b) -> b -> V1 a -> b # ifoldl' :: (E V1 -> b -> a -> b) -> b -> V1 a -> b #
FunctorWithIndex (E V2) V2
Instance details Defined in Linear.V2 Methods imap :: (E V2 -> a -> b) -> V2 a -> V2 b # imapped :: IndexedSetter (E V2) (V2 a) (V2 b) a b #
FunctorWithIndex (E V3) V3
Instance details Defined in Linear.V3 Methods imap :: (E V3 -> a -> b) -> V3 a -> V3 b # imapped :: IndexedSetter (E V3) (V3 a) (V3 b) a b #
FunctorWithIndex (E Plucker) Plucker
Instance details Defined in Linear.Plucker Methods imap :: (E Plucker -> a -> b) -> Plucker a -> Plucker b # imapped :: IndexedSetter (E Plucker) (Plucker a) (Plucker b) a b #
FunctorWithIndex (E Quaternion) Quaternion
Instance details Defined in Linear.Quaternion Methods imap :: (E Quaternion -> a -> b) -> Quaternion a -> Quaternion b # imapped :: IndexedSetter (E Quaternion) (Quaternion a) (Quaternion b) a b #
FunctorWithIndex (E V0) V0
Instance details Defined in Linear.V0 Methods imap :: (E V0 -> a -> b) -> V0 a -> V0 b # imapped :: IndexedSetter (E V0) (V0 a) (V0 b) a b #
FunctorWithIndex (E V4) V4
Instance details Defined in Linear.V4 Methods imap :: (E V4 -> a -> b) -> V4 a -> V4 b # imapped :: IndexedSetter (E V4) (V4 a) (V4 b) a b #
FunctorWithIndex (E V1) V1
Instance details Defined in Linear.V1 Methods imap :: (E V1 -> a -> b) -> V1 a -> V1 b # imapped :: IndexedSetter (E V1) (V1 a) (V1 b) a b #

negated :: (Functor f, Num a) => f a -> f a #

Compute the negation of a vector

>>> negated (V2 2 4)
V2 (-2) (-4)

sumV :: (Foldable f, Additive v, Num a) => f (v a) -> v a #

Sum over multiple vectors

>>> sumV [V2 1 1, V2 3 4]
V2 4 5

(*^) :: (Functor f, Num a) => a -> f a -> f a infixl 7 #

Compute the left scalar product

>>> 2 *^ V2 3 4
V2 6 8

(^*) :: (Functor f, Num a) => f a -> a -> f a infixl 7 #

Compute the right scalar product

>>> V2 3 4 ^* 2
V2 6 8

(^/) :: (Functor f, Fractional a) => f a -> a -> f a infixl 7 #

Compute division by a scalar on the right.

basisFor :: (Traversable t, Num a) => t b -> [t a] #

Produce a default basis for a vector space from which the argument is drawn.

scaled :: (Traversable t, Num a) => t a -> t (t a) #

Produce a diagonal (scale) matrix from a vector.

>>> scaled (V2 2 3)
V2 (V2 2 0) (V2 0 3)

unit :: (Additive t, Num a) => ASetter' (t a) a -> t a #

Create a unit vector.

>>> unit _x :: V2 Int
V2 1 0

outer :: (Functor f, Functor g, Num a) => f a -> g a -> f (g a) #

Outer (tensor) product of two vectors

class Additive f => Metric (f :: Type -> Type) where #

Free and sparse inner product/metric spaces.

Minimal complete definition

Nothing

Methods

dot :: Num a => f a -> f a -> a #

Compute the inner product of two vectors or (equivalently) convert a vector f a into a covector f a -> a.

>>> V2 1 2 `dot` V2 3 4
11

quadrance :: Num a => f a -> a #

Compute the squared norm. The name quadrance arises from Norman J. Wildberger's rational trigonometry.

qd :: Num a => f a -> f a -> a #

Compute the quadrance of the difference

distance :: Floating a => f a -> f a -> a #

Compute the distance between two vectors in a metric space

norm :: Floating a => f a -> a #

Compute the norm of a vector in a metric space

signorm :: Floating a => f a -> f a #

Convert a non-zero vector to unit vector.

Instances

Metric []
Instance details Defined in Linear.Metric Methods dot :: Num a => [a] -> [a] -> a # quadrance :: Num a => [a] -> a # qd :: Num a => [a] -> [a] -> a # distance :: Floating a => [a] -> [a] -> a # norm :: Floating a => [a] -> a # signorm :: Floating a => [a] -> [a] #
Metric Maybe
Instance details Defined in Linear.Metric Methods dot :: Num a => Maybe a -> Maybe a -> a # quadrance :: Num a => Maybe a -> a # qd :: Num a => Maybe a -> Maybe a -> a # distance :: Floating a => Maybe a -> Maybe a -> a # norm :: Floating a => Maybe a -> a # signorm :: Floating a => Maybe a -> Maybe a #
Metric Identity
Instance details Defined in Linear.Metric Methods dot :: Num a => Identity a -> Identity a -> a # quadrance :: Num a => Identity a -> a # qd :: Num a => Identity a -> Identity a -> a # distance :: Floating a => Identity a -> Identity a -> a # norm :: Floating a => Identity a -> a # signorm :: Floating a => Identity a -> Identity a #
Metric ZipList
Instance details Defined in Linear.Metric Methods dot :: Num a => ZipList a -> ZipList a -> a # quadrance :: Num a => ZipList a -> a # qd :: Num a => ZipList a -> ZipList a -> a # distance :: Floating a => ZipList a -> ZipList a -> a # norm :: Floating a => ZipList a -> a # signorm :: Floating a => ZipList a -> ZipList a #
Metric Vector
Instance details Defined in Linear.Metric Methods dot :: Num a => Vector a -> Vector a -> a # quadrance :: Num a => Vector a -> a # qd :: Num a => Vector a -> Vector a -> a # distance :: Floating a => Vector a -> Vector a -> a # norm :: Floating a => Vector a -> a # signorm :: Floating a => Vector a -> Vector a #
Metric IntMap
Instance details Defined in Linear.Metric Methods dot :: Num a => IntMap a -> IntMap a -> a # quadrance :: Num a => IntMap a -> a # qd :: Num a => IntMap a -> IntMap a -> a # distance :: Floating a => IntMap a -> IntMap a -> a # norm :: Floating a => IntMap a -> a # signorm :: Floating a => IntMap a -> IntMap a #
Metric V2
Instance details Defined in Linear.V2 Methods dot :: Num a => V2 a -> V2 a -> a # quadrance :: Num a => V2 a -> a # qd :: Num a => V2 a -> V2 a -> a # distance :: Floating a => V2 a -> V2 a -> a # norm :: Floating a => V2 a -> a # signorm :: Floating a => V2 a -> V2 a #
Metric V3
Instance details Defined in Linear.V3 Methods dot :: Num a => V3 a -> V3 a -> a # quadrance :: Num a => V3 a -> a # qd :: Num a => V3 a -> V3 a -> a # distance :: Floating a => V3 a -> V3 a -> a # norm :: Floating a => V3 a -> a # signorm :: Floating a => V3 a -> V3 a #
Metric Plucker
Instance details Defined in Linear.Plucker Methods dot :: Num a => Plucker a -> Plucker a -> a # quadrance :: Num a => Plucker a -> a # qd :: Num a => Plucker a -> Plucker a -> a # distance :: Floating a => Plucker a -> Plucker a -> a # norm :: Floating a => Plucker a -> a # signorm :: Floating a => Plucker a -> Plucker a #
Metric Quaternion
Instance details Defined in Linear.Quaternion Methods dot :: Num a => Quaternion a -> Quaternion a -> a # quadrance :: Num a => Quaternion a -> a # qd :: Num a => Quaternion a -> Quaternion a -> a # distance :: Floating a => Quaternion a -> Quaternion a -> a # norm :: Floating a => Quaternion a -> a # signorm :: Floating a => Quaternion a -> Quaternion a #
Metric V0
Instance details Defined in Linear.V0 Methods dot :: Num a => V0 a -> V0 a -> a # quadrance :: Num a => V0 a -> a # qd :: Num a => V0 a -> V0 a -> a # distance :: Floating a => V0 a -> V0 a -> a # norm :: Floating a => V0 a -> a # signorm :: Floating a => V0 a -> V0 a #
Metric V4
Instance details Defined in Linear.V4 Methods dot :: Num a => V4 a -> V4 a -> a # quadrance :: Num a => V4 a -> a # qd :: Num a => V4 a -> V4 a -> a # distance :: Floating a => V4 a -> V4 a -> a # norm :: Floating a => V4 a -> a # signorm :: Floating a => V4 a -> V4 a #
Metric V1
Instance details Defined in Linear.V1 Methods dot :: Num a => V1 a -> V1 a -> a # quadrance :: Num a => V1 a -> a # qd :: Num a => V1 a -> V1 a -> a # distance :: Floating a => V1 a -> V1 a -> a # norm :: Floating a => V1 a -> a # signorm :: Floating a => V1 a -> V1 a #
Ord k => Metric (Map k)
Instance details Defined in Linear.Metric Methods dot :: Num a => Map k a -> Map k a -> a # quadrance :: Num a => Map k a -> a # qd :: Num a => Map k a -> Map k a -> a # distance :: Floating a => Map k a -> Map k a -> a # norm :: Floating a => Map k a -> a # signorm :: Floating a => Map k a -> Map k a #
(Hashable k, Eq k) => Metric (HashMap k)
Instance details Defined in Linear.Metric Methods dot :: Num a => HashMap k a -> HashMap k a -> a # quadrance :: Num a => HashMap k a -> a # qd :: Num a => HashMap k a -> HashMap k a -> a # distance :: Floating a => HashMap k a -> HashMap k a -> a # norm :: Floating a => HashMap k a -> a # signorm :: Floating a => HashMap k a -> HashMap k a #
Metric f => Metric (Point f)
Instance details Defined in Linear.Affine Methods dot :: Num a => Point f a -> Point f a -> a # quadrance :: Num a => Point f a -> a # qd :: Num a => Point f a -> Point f a -> a # distance :: Floating a => Point f a -> Point f a -> a # norm :: Floating a => Point f a -> a # signorm :: Floating a => Point f a -> Point f a #
Dim n => Metric (V n)
Instance details Defined in Linear.V Methods dot :: Num a => V n a -> V n a -> a # quadrance :: Num a => V n a -> a # qd :: Num a => V n a -> V n a -> a # distance :: Floating a => V n a -> V n a -> a # norm :: Floating a => V n a -> a # signorm :: Floating a => V n a -> V n a #

normalize :: (Floating a, Metric f, Epsilon a) => f a -> f a #

Normalize a Metric functor to have unit norm. This function does not change the functor if its norm is 0 or 1.

class Additive (Diff p) => Affine (p :: Type -> Type) where #

An affine space is roughly a vector space in which we have forgotten or at least pretend to have forgotten the origin.

a .+^ (b .-. a)  =  b@
(a .+^ u) .+^ v  =  a .+^ (u ^+^ v)@
(a .-. b) ^+^ v  =  (a .+^ v) .-. q@

Minimal complete definition

(.-.), (.+^)

Associated Types

type Diff (p :: Type -> Type) :: Type -> Type #

Methods

(.-.) :: Num a => p a -> p a -> Diff p a infixl 6 #

Get the difference between two points as a vector offset.

(.+^) :: Num a => p a -> Diff p a -> p a infixl 6 #

Add a vector offset to a point.

(.-^) :: Num a => p a -> Diff p a -> p a infixl 6 #

Subtract a vector offset from a point.

Instances

Affine []
Instance details Defined in Linear.Affine Associated Types type Diff [] :: Type -> Type # Methods (.-.) :: Num a => [a] -> [a] -> Diff [] a # (.+^) :: Num a => [a] -> Diff [] a -> [a] # (.-^) :: Num a => [a] -> Diff [] a -> [a] #
Affine Maybe
Instance details Defined in Linear.Affine Associated Types type Diff Maybe :: Type -> Type # Methods (.-.) :: Num a => Maybe a -> Maybe a -> Diff Maybe a # (.+^) :: Num a => Maybe a -> Diff Maybe a -> Maybe a # (.-^) :: Num a => Maybe a -> Diff Maybe a -> Maybe a #
Affine Identity
Instance details Defined in Linear.Affine Associated Types type Diff Identity :: Type -> Type # Methods (.-.) :: Num a => Identity a -> Identity a -> Diff Identity a # (.+^) :: Num a => Identity a -> Diff Identity a -> Identity a # (.-^) :: Num a => Identity a -> Diff Identity a -> Identity a #
Affine ZipList
Instance details Defined in Linear.Affine Associated Types type Diff ZipList :: Type -> Type # Methods (.-.) :: Num a => ZipList a -> ZipList a -> Diff ZipList a # (.+^) :: Num a => ZipList a -> Diff ZipList a -> ZipList a # (.-^) :: Num a => ZipList a -> Diff ZipList a -> ZipList a #
Affine Time
Instance details Defined in Data.Active Associated Types type Diff Time :: Type -> Type # Methods (.-.) :: Num a => Time a -> Time a -> Diff Time a # (.+^) :: Num a => Time a -> Diff Time a -> Time a # (.-^) :: Num a => Time a -> Diff Time a -> Time a #
Affine Complex
Instance details Defined in Linear.Affine Associated Types type Diff Complex :: Type -> Type # Methods (.-.) :: Num a => Complex a -> Complex a -> Diff Complex a # (.+^) :: Num a => Complex a -> Diff Complex a -> Complex a # (.-^) :: Num a => Complex a -> Diff Complex a -> Complex a #
Affine Vector
Instance details Defined in Linear.Affine Associated Types type Diff Vector :: Type -> Type # Methods (.-.) :: Num a => Vector a -> Vector a -> Diff Vector a # (.+^) :: Num a => Vector a -> Diff Vector a -> Vector a # (.-^) :: Num a => Vector a -> Diff Vector a -> Vector a #
Affine IntMap
Instance details Defined in Linear.Affine Associated Types type Diff IntMap :: Type -> Type # Methods (.-.) :: Num a => IntMap a -> IntMap a -> Diff IntMap a # (.+^) :: Num a => IntMap a -> Diff IntMap a -> IntMap a # (.-^) :: Num a => IntMap a -> Diff IntMap a -> IntMap a #
Affine V2
Instance details Defined in Linear.Affine Associated Types type Diff V2 :: Type -> Type # Methods (.-.) :: Num a => V2 a -> V2 a -> Diff V2 a # (.+^) :: Num a => V2 a -> Diff V2 a -> V2 a # (.-^) :: Num a => V2 a -> Diff V2 a -> V2 a #
Affine V3
Instance details Defined in Linear.Affine Associated Types type Diff V3 :: Type -> Type # Methods (.-.) :: Num a => V3 a -> V3 a -> Diff V3 a # (.+^) :: Num a => V3 a -> Diff V3 a -> V3 a # (.-^) :: Num a => V3 a -> Diff V3 a -> V3 a #
Affine Plucker
Instance details Defined in Linear.Affine Associated Types type Diff Plucker :: Type -> Type # Methods (.-.) :: Num a => Plucker a -> Plucker a -> Diff Plucker a # (.+^) :: Num a => Plucker a -> Diff Plucker a -> Plucker a # (.-^) :: Num a => Plucker a -> Diff Plucker a -> Plucker a #
Affine Quaternion
Instance details Defined in Linear.Affine Associated Types type Diff Quaternion :: Type -> Type # Methods (.-.) :: Num a => Quaternion a -> Quaternion a -> Diff Quaternion a # (.+^) :: Num a => Quaternion a -> Diff Quaternion a -> Quaternion a # (.-^) :: Num a => Quaternion a -> Diff Quaternion a -> Quaternion a #
Affine V0
Instance details Defined in Linear.Affine Associated Types type Diff V0 :: Type -> Type # Methods (.-.) :: Num a => V0 a -> V0 a -> Diff V0 a # (.+^) :: Num a => V0 a -> Diff V0 a -> V0 a # (.-^) :: Num a => V0 a -> Diff V0 a -> V0 a #
Affine V4
Instance details Defined in Linear.Affine Associated Types type Diff V4 :: Type -> Type # Methods (.-.) :: Num a => V4 a -> V4 a -> Diff V4 a # (.+^) :: Num a => V4 a -> Diff V4 a -> V4 a # (.-^) :: Num a => V4 a -> Diff V4 a -> V4 a #
Affine V1
Instance details Defined in Linear.Affine Associated Types type Diff V1 :: Type -> Type # Methods (.-.) :: Num a => V1 a -> V1 a -> Diff V1 a # (.+^) :: Num a => V1 a -> Diff V1 a -> V1 a # (.-^) :: Num a => V1 a -> Diff V1 a -> V1 a #
Ord k => Affine (Map k)
Instance details Defined in Linear.Affine Associated Types type Diff (Map k) :: Type -> Type # Methods (.-.) :: Num a => Map k a -> Map k a -> Diff (Map k) a # (.+^) :: Num a => Map k a -> Diff (Map k) a -> Map k a # (.-^) :: Num a => Map k a -> Diff (Map k) a -> Map k a #
(Eq k, Hashable k) => Affine (HashMap k)
Instance details Defined in Linear.Affine Associated Types type Diff (HashMap k) :: Type -> Type # Methods (.-.) :: Num a => HashMap k a -> HashMap k a -> Diff (HashMap k) a # (.+^) :: Num a => HashMap k a -> Diff (HashMap k) a -> HashMap k a # (.-^) :: Num a => HashMap k a -> Diff (HashMap k) a -> HashMap k a #
Additive f => Affine (Point f)
Instance details Defined in Linear.Affine Associated Types type Diff (Point f) :: Type -> Type # Methods (.-.) :: Num a => Point f a -> Point f a -> Diff (Point f) a # (.+^) :: Num a => Point f a -> Diff (Point f) a -> Point f a # (.-^) :: Num a => Point f a -> Diff (Point f) a -> Point f a #
Dim n => Affine (V n)
Instance details Defined in Linear.Affine Associated Types type Diff (V n) :: Type -> Type # Methods (.-.) :: Num a => V n a -> V n a -> Diff (V n) a # (.+^) :: Num a => V n a -> Diff (V n) a -> V n a # (.-^) :: Num a => V n a -> Diff (V n) a -> V n a #
Affine ((->) b :: Type -> Type)
Instance details Defined in Linear.Affine Associated Types type Diff ((->) b) :: Type -> Type # Methods (.-.) :: Num a => (b -> a) -> (b -> a) -> Diff ((->) b) a # (.+^) :: Num a => (b -> a) -> Diff ((->) b) a -> b -> a # (.-^) :: Num a => (b -> a) -> Diff ((->) b) a -> b -> a #

qdA :: (Affine p, Foldable (Diff p), Num a) => p a -> p a -> a #

Compute the quadrance of the difference (the square of the distance)

distanceA :: (Floating a, Foldable (Diff p), Affine p) => p a -> p a -> a #

Distance between two points in an affine space

(.#) :: Coercible b a => (b -> c) -> (a -> b) -> a -> c #

(#.) :: Coercible c b => (b -> c) -> (a -> b) -> a -> c #

unP :: Point f a -> f a #

data family MVector s a :: Type #

Instances

MVector MVector Bool
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Bool -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Bool -> MVector s Bool # basicOverlaps :: MVector s Bool -> MVector s Bool -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Bool) # basicInitialize :: PrimMonad m => MVector (PrimState m) Bool -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Bool -> m (MVector (PrimState m) Bool) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Bool -> Int -> m Bool # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Bool -> Int -> Bool -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Bool -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Bool -> Bool -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Bool -> MVector (PrimState m) Bool -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Bool -> MVector (PrimState m) Bool -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Bool -> Int -> m (MVector (PrimState m) Bool) #
MVector MVector Char
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Char -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Char -> MVector s Char # basicOverlaps :: MVector s Char -> MVector s Char -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Char) # basicInitialize :: PrimMonad m => MVector (PrimState m) Char -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Char -> m (MVector (PrimState m) Char) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Char -> Int -> m Char # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Char -> Int -> Char -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Char -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Char -> Char -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Char -> MVector (PrimState m) Char -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Char -> MVector (PrimState m) Char -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Char -> Int -> m (MVector (PrimState m) Char) #
MVector MVector Double
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Double -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Double -> MVector s Double # basicOverlaps :: MVector s Double -> MVector s Double -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Double) # basicInitialize :: PrimMonad m => MVector (PrimState m) Double -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Double -> m (MVector (PrimState m) Double) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Double -> Int -> m Double # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Double -> Int -> Double -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Double -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Double -> Double -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Double -> MVector (PrimState m) Double -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Double -> MVector (PrimState m) Double -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Double -> Int -> m (MVector (PrimState m) Double) #
MVector MVector Float
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Float -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Float -> MVector s Float # basicOverlaps :: MVector s Float -> MVector s Float -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Float) # basicInitialize :: PrimMonad m => MVector (PrimState m) Float -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Float -> m (MVector (PrimState m) Float) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Float -> Int -> m Float # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Float -> Int -> Float -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Float -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Float -> Float -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Float -> MVector (PrimState m) Float -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Float -> MVector (PrimState m) Float -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Float -> Int -> m (MVector (PrimState m) Float) #
MVector MVector Int
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Int -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Int -> MVector s Int # basicOverlaps :: MVector s Int -> MVector s Int -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Int) # basicInitialize :: PrimMonad m => MVector (PrimState m) Int -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Int -> m (MVector (PrimState m) Int) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Int -> Int -> m Int # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Int -> Int -> Int -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Int -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Int -> Int -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Int -> MVector (PrimState m) Int -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Int -> MVector (PrimState m) Int -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Int -> Int -> m (MVector (PrimState m) Int) #
MVector MVector Int8
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Int8 -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Int8 -> MVector s Int8 # basicOverlaps :: MVector s Int8 -> MVector s Int8 -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Int8) # basicInitialize :: PrimMonad m => MVector (PrimState m) Int8 -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Int8 -> m (MVector (PrimState m) Int8) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Int8 -> Int -> m Int8 # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Int8 -> Int -> Int8 -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Int8 -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Int8 -> Int8 -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Int8 -> MVector (PrimState m) Int8 -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Int8 -> MVector (PrimState m) Int8 -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Int8 -> Int -> m (MVector (PrimState m) Int8) #
MVector MVector Int16
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Int16 -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Int16 -> MVector s Int16 # basicOverlaps :: MVector s Int16 -> MVector s Int16 -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Int16) # basicInitialize :: PrimMonad m => MVector (PrimState m) Int16 -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Int16 -> m (MVector (PrimState m) Int16) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Int16 -> Int -> m Int16 # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Int16 -> Int -> Int16 -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Int16 -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Int16 -> Int16 -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Int16 -> MVector (PrimState m) Int16 -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Int16 -> MVector (PrimState m) Int16 -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Int16 -> Int -> m (MVector (PrimState m) Int16) #
MVector MVector Int32
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Int32 -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Int32 -> MVector s Int32 # basicOverlaps :: MVector s Int32 -> MVector s Int32 -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Int32) # basicInitialize :: PrimMonad m => MVector (PrimState m) Int32 -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Int32 -> m (MVector (PrimState m) Int32) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Int32 -> Int -> m Int32 # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Int32 -> Int -> Int32 -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Int32 -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Int32 -> Int32 -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Int32 -> MVector (PrimState m) Int32 -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Int32 -> MVector (PrimState m) Int32 -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Int32 -> Int -> m (MVector (PrimState m) Int32) #
MVector MVector Int64
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Int64 -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Int64 -> MVector s Int64 # basicOverlaps :: MVector s Int64 -> MVector s Int64 -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Int64) # basicInitialize :: PrimMonad m => MVector (PrimState m) Int64 -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Int64 -> m (MVector (PrimState m) Int64) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Int64 -> Int -> m Int64 # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Int64 -> Int -> Int64 -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Int64 -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Int64 -> Int64 -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Int64 -> MVector (PrimState m) Int64 -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Int64 -> MVector (PrimState m) Int64 -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Int64 -> Int -> m (MVector (PrimState m) Int64) #
MVector MVector Word
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Word -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Word -> MVector s Word # basicOverlaps :: MVector s Word -> MVector s Word -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Word) # basicInitialize :: PrimMonad m => MVector (PrimState m) Word -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Word -> m (MVector (PrimState m) Word) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Word -> Int -> m Word # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Word -> Int -> Word -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Word -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Word -> Word -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Word -> MVector (PrimState m) Word -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Word -> MVector (PrimState m) Word -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Word -> Int -> m (MVector (PrimState m) Word) #
MVector MVector Word8
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Word8 -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Word8 -> MVector s Word8 # basicOverlaps :: MVector s Word8 -> MVector s Word8 -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Word8) # basicInitialize :: PrimMonad m => MVector (PrimState m) Word8 -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Word8 -> m (MVector (PrimState m) Word8) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Word8 -> Int -> m Word8 # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Word8 -> Int -> Word8 -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Word8 -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Word8 -> Word8 -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Word8 -> MVector (PrimState m) Word8 -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Word8 -> MVector (PrimState m) Word8 -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Word8 -> Int -> m (MVector (PrimState m) Word8) #
MVector MVector Word16
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Word16 -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Word16 -> MVector s Word16 # basicOverlaps :: MVector s Word16 -> MVector s Word16 -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Word16) # basicInitialize :: PrimMonad m => MVector (PrimState m) Word16 -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Word16 -> m (MVector (PrimState m) Word16) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Word16 -> Int -> m Word16 # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Word16 -> Int -> Word16 -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Word16 -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Word16 -> Word16 -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Word16 -> MVector (PrimState m) Word16 -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Word16 -> MVector (PrimState m) Word16 -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Word16 -> Int -> m (MVector (PrimState m) Word16) #
MVector MVector Word32
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Word32 -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Word32 -> MVector s Word32 # basicOverlaps :: MVector s Word32 -> MVector s Word32 -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Word32) # basicInitialize :: PrimMonad m => MVector (PrimState m) Word32 -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Word32 -> m (MVector (PrimState m) Word32) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Word32 -> Int -> m Word32 # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Word32 -> Int -> Word32 -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Word32 -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Word32 -> Word32 -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Word32 -> MVector (PrimState m) Word32 -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Word32 -> MVector (PrimState m) Word32 -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Word32 -> Int -> m (MVector (PrimState m) Word32) #
MVector MVector Word64
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Word64 -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Word64 -> MVector s Word64 # basicOverlaps :: MVector s Word64 -> MVector s Word64 -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Word64) # basicInitialize :: PrimMonad m => MVector (PrimState m) Word64 -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Word64 -> m (MVector (PrimState m) Word64) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Word64 -> Int -> m Word64 # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Word64 -> Int -> Word64 -> m () # basicClear :: PrimMonad m => MVector (PrimState m) Word64 -> m () # basicSet :: PrimMonad m => MVector (PrimState m) Word64 -> Word64 -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Word64 -> MVector (PrimState m) Word64 -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Word64 -> MVector (PrimState m) Word64 -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Word64 -> Int -> m (MVector (PrimState m) Word64) #
MVector MVector ()
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s () -> Int # basicUnsafeSlice :: Int -> Int -> MVector s () -> MVector s () # basicOverlaps :: MVector s () -> MVector s () -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) ()) # basicInitialize :: PrimMonad m => MVector (PrimState m) () -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> () -> m (MVector (PrimState m) ()) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) () -> Int -> m () # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) () -> Int -> () -> m () # basicClear :: PrimMonad m => MVector (PrimState m) () -> m () # basicSet :: PrimMonad m => MVector (PrimState m) () -> () -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) () -> MVector (PrimState m) () -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) () -> MVector (PrimState m) () -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) () -> Int -> m (MVector (PrimState m) ()) #
Unbox a => MVector MVector (Complex a)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s (Complex a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Complex a) -> MVector s (Complex a) # basicOverlaps :: MVector s (Complex a) -> MVector s (Complex a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Complex a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (Complex a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Complex a -> m (MVector (PrimState m) (Complex a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Complex a) -> Int -> m (Complex a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Complex a) -> Int -> Complex a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (Complex a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (Complex a) -> Complex a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Complex a) -> MVector (PrimState m) (Complex a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Complex a) -> MVector (PrimState m) (Complex a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Complex a) -> Int -> m (MVector (PrimState m) (Complex a)) #
Unbox a => MVector MVector (V2 a)
Instance details Defined in Linear.V2 Methods basicLength :: MVector s (V2 a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (V2 a) -> MVector s (V2 a) # basicOverlaps :: MVector s (V2 a) -> MVector s (V2 a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V2 a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (V2 a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V2 a -> m (MVector (PrimState m) (V2 a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> m (V2 a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> V2 a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (V2 a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (V2 a) -> V2 a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V2 a) -> MVector (PrimState m) (V2 a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V2 a) -> MVector (PrimState m) (V2 a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> m (MVector (PrimState m) (V2 a)) #
Unbox a => MVector MVector (V3 a)
Instance details Defined in Linear.V3 Methods basicLength :: MVector s (V3 a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (V3 a) -> MVector s (V3 a) # basicOverlaps :: MVector s (V3 a) -> MVector s (V3 a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V3 a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (V3 a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V3 a -> m (MVector (PrimState m) (V3 a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (V3 a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> V3 a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (V3 a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (V3 a) -> V3 a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (MVector (PrimState m) (V3 a)) #
Unbox a => MVector MVector (Plucker a)
Instance details Defined in Linear.Plucker Methods basicLength :: MVector s (Plucker a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Plucker a) -> MVector s (Plucker a) # basicOverlaps :: MVector s (Plucker a) -> MVector s (Plucker a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Plucker a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (Plucker a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Plucker a -> m (MVector (PrimState m) (Plucker a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Plucker a) -> Int -> m (Plucker a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Plucker a) -> Int -> Plucker a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (Plucker a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (Plucker a) -> Plucker a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Plucker a) -> MVector (PrimState m) (Plucker a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Plucker a) -> MVector (PrimState m) (Plucker a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Plucker a) -> Int -> m (MVector (PrimState m) (Plucker a)) #
Unbox a => MVector MVector (Quaternion a)
Instance details Defined in Linear.Quaternion Methods basicLength :: MVector s (Quaternion a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Quaternion a) -> MVector s (Quaternion a) # basicOverlaps :: MVector s (Quaternion a) -> MVector s (Quaternion a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Quaternion a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Quaternion a -> m (MVector (PrimState m) (Quaternion a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Int -> m (Quaternion a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Int -> Quaternion a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Quaternion a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> MVector (PrimState m) (Quaternion a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> MVector (PrimState m) (Quaternion a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Quaternion a) -> Int -> m (MVector (PrimState m) (Quaternion a)) #
MVector MVector (V0 a)
Instance details Defined in Linear.V0 Methods basicLength :: MVector s (V0 a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (V0 a) -> MVector s (V0 a) # basicOverlaps :: MVector s (V0 a) -> MVector s (V0 a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V0 a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (V0 a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V0 a -> m (MVector (PrimState m) (V0 a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V0 a) -> Int -> m (V0 a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V0 a) -> Int -> V0 a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (V0 a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (V0 a) -> V0 a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V0 a) -> MVector (PrimState m) (V0 a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V0 a) -> MVector (PrimState m) (V0 a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V0 a) -> Int -> m (MVector (PrimState m) (V0 a)) #
Unbox a => MVector MVector (V4 a)
Instance details Defined in Linear.V4 Methods basicLength :: MVector s (V4 a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (V4 a) -> MVector s (V4 a) # basicOverlaps :: MVector s (V4 a) -> MVector s (V4 a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V4 a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (V4 a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V4 a -> m (MVector (PrimState m) (V4 a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V4 a) -> Int -> m (V4 a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V4 a) -> Int -> V4 a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (V4 a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (V4 a) -> V4 a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V4 a) -> MVector (PrimState m) (V4 a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V4 a) -> MVector (PrimState m) (V4 a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V4 a) -> Int -> m (MVector (PrimState m) (V4 a)) #
Unbox a => MVector MVector (V1 a)
Instance details Defined in Linear.V1 Methods basicLength :: MVector s (V1 a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (V1 a) -> MVector s (V1 a) # basicOverlaps :: MVector s (V1 a) -> MVector s (V1 a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V1 a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (V1 a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V1 a -> m (MVector (PrimState m) (V1 a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V1 a) -> Int -> m (V1 a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V1 a) -> Int -> V1 a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (V1 a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (V1 a) -> V1 a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V1 a) -> MVector (PrimState m) (V1 a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V1 a) -> MVector (PrimState m) (V1 a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V1 a) -> Int -> m (MVector (PrimState m) (V1 a)) #
(Unbox a, Unbox b) => MVector MVector (a, b)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s (a, b) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (a, b) -> MVector s (a, b) # basicOverlaps :: MVector s (a, b) -> MVector s (a, b) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (a, b)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (a, b) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> (a, b) -> m (MVector (PrimState m) (a, b)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (a, b) -> Int -> m (a, b) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (a, b) -> Int -> (a, b) -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (a, b) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (a, b) -> (a, b) -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (a, b) -> MVector (PrimState m) (a, b) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (a, b) -> MVector (PrimState m) (a, b) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (a, b) -> Int -> m (MVector (PrimState m) (a, b)) #
Unbox (f a) => MVector MVector (Point f a)
Instance details Defined in Linear.Affine Methods basicLength :: MVector s (Point f a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Point f a) -> MVector s (Point f a) # basicOverlaps :: MVector s (Point f a) -> MVector s (Point f a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Point f a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (Point f a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> Point f a -> m (MVector (PrimState m) (Point f a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Point f a) -> Int -> m (Point f a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Point f a) -> Int -> Point f a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (Point f a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (Point f a) -> Point f a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Point f a) -> MVector (PrimState m) (Point f a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Point f a) -> MVector (PrimState m) (Point f a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Point f a) -> Int -> m (MVector (PrimState m) (Point f a)) #
(Unbox a, Unbox b, Unbox c) => MVector MVector (a, b, c)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s (a, b, c) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (a, b, c) -> MVector s (a, b, c) # basicOverlaps :: MVector s (a, b, c) -> MVector s (a, b, c) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (a, b, c)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (a, b, c) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> (a, b, c) -> m (MVector (PrimState m) (a, b, c)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (a, b, c) -> Int -> m (a, b, c) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (a, b, c) -> Int -> (a, b, c) -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (a, b, c) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (a, b, c) -> (a, b, c) -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (a, b, c) -> MVector (PrimState m) (a, b, c) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (a, b, c) -> MVector (PrimState m) (a, b, c) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (a, b, c) -> Int -> m (MVector (PrimState m) (a, b, c)) #
(Dim n, Unbox a) => MVector MVector (V n a)
Instance details Defined in Linear.V Methods basicLength :: MVector s (V n a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (V n a) -> MVector s (V n a) # basicOverlaps :: MVector s (V n a) -> MVector s (V n a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V n a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (V n a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V n a -> m (MVector (PrimState m) (V n a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V n a) -> Int -> m (V n a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V n a) -> Int -> V n a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (V n a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (V n a) -> V n a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V n a) -> MVector (PrimState m) (V n a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V n a) -> MVector (PrimState m) (V n a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V n a) -> Int -> m (MVector (PrimState m) (V n a)) #
(Unbox a, Unbox b, Unbox c, Unbox d) => MVector MVector (a, b, c, d)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s (a, b, c, d) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (a, b, c, d) -> MVector s (a, b, c, d) # basicOverlaps :: MVector s (a, b, c, d) -> MVector s (a, b, c, d) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (a, b, c, d)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (a, b, c, d) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> (a, b, c, d) -> m (MVector (PrimState m) (a, b, c, d)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (a, b, c, d) -> Int -> m (a, b, c, d) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (a, b, c, d) -> Int -> (a, b, c, d) -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (a, b, c, d) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (a, b, c, d) -> (a, b, c, d) -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (a, b, c, d) -> MVector (PrimState m) (a, b, c, d) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (a, b, c, d) -> MVector (PrimState m) (a, b, c, d) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (a, b, c, d) -> Int -> m (MVector (PrimState m) (a, b, c, d)) #
(Unbox a, Unbox b, Unbox c, Unbox d, Unbox e) => MVector MVector (a, b, c, d, e)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s (a, b, c, d, e) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (a, b, c, d, e) -> MVector s (a, b, c, d, e) # basicOverlaps :: MVector s (a, b, c, d, e) -> MVector s (a, b, c, d, e) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (a, b, c, d, e)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (a, b, c, d, e) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> (a, b, c, d, e) -> m (MVector (PrimState m) (a, b, c, d, e)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (a, b, c, d, e) -> Int -> m (a, b, c, d, e) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (a, b, c, d, e) -> Int -> (a, b, c, d, e) -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (a, b, c, d, e) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (a, b, c, d, e) -> (a, b, c, d, e) -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (a, b, c, d, e) -> MVector (PrimState m) (a, b, c, d, e) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (a, b, c, d, e) -> MVector (PrimState m) (a, b, c, d, e) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (a, b, c, d, e) -> Int -> m (MVector (PrimState m) (a, b, c, d, e)) #
(Unbox a, Unbox b, Unbox c, Unbox d, Unbox e, Unbox f) => MVector MVector (a, b, c, d, e, f)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s (a, b, c, d, e, f) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (a, b, c, d, e, f) -> MVector s (a, b, c, d, e, f) # basicOverlaps :: MVector s (a, b, c, d, e, f) -> MVector s (a, b, c, d, e, f) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (a, b, c, d, e, f)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (a, b, c, d, e, f) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> (a, b, c, d, e, f) -> m (MVector (PrimState m) (a, b, c, d, e, f)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (a, b, c, d, e, f) -> Int -> m (a, b, c, d, e, f) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (a, b, c, d, e, f) -> Int -> (a, b, c, d, e, f) -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (a, b, c, d, e, f) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (a, b, c, d, e, f) -> MVector (PrimState m) (a, b, c, d, e, f) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (a, b, c, d, e, f) -> MVector (PrimState m) (a, b, c, d, e, f) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (a, b, c, d, e, f) -> Int -> m (MVector (PrimState m) (a, b, c, d, e, f)) #
NFData (MVector s a)
Instance details Defined in Data.Vector.Unboxed.Base Methods rnf :: MVector s a -> () #
newtype MVector s Bool
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Bool = MV_Bool (MVector s Word8)
newtype MVector s Char
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Char = MV_Char (MVector s Char)
newtype MVector s Double
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Double = MV_Double (MVector s Double)
newtype MVector s Float
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Float = MV_Float (MVector s Float)
newtype MVector s Word64
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Word64 = MV_Word64 (MVector s Word64)
newtype MVector s Word32
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Word32 = MV_Word32 (MVector s Word32)
newtype MVector s Word16
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Word16 = MV_Word16 (MVector s Word16)
newtype MVector s Word8
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Word8 = MV_Word8 (MVector s Word8)
newtype MVector s Word
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Word = MV_Word (MVector s Word)
newtype MVector s Int64
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Int64 = MV_Int64 (MVector s Int64)
newtype MVector s Int32
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Int32 = MV_Int32 (MVector s Int32)
newtype MVector s Int16
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Int16 = MV_Int16 (MVector s Int16)
newtype MVector s Int8
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Int8 = MV_Int8 (MVector s Int8)
newtype MVector s Int
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s Int = MV_Int (MVector s Int)
newtype MVector s ()
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s () = MV_Unit Int
data MVector s (V4 a)
Instance details Defined in Linear.V4 data MVector s (V4 a) = MV_V4 !Int !(MVector s a)
data MVector s (V3 a)
Instance details Defined in Linear.V3 data MVector s (V3 a) = MV_V3 !Int !(MVector s a)
data MVector s (V2 a)
Instance details Defined in Linear.V2 data MVector s (V2 a) = MV_V2 !Int !(MVector s a)
newtype MVector s (V1 a)
Instance details Defined in Linear.V1 newtype MVector s (V1 a) = MV_V1 (MVector s a)
newtype MVector s (V0 a)
Instance details Defined in Linear.V0 newtype MVector s (V0 a) = MV_V0 Int
data MVector s (Quaternion a)
Instance details Defined in Linear.Quaternion data MVector s (Quaternion a) = MV_Quaternion !Int (MVector s a)
data MVector s (Plucker a)
Instance details Defined in Linear.Plucker data MVector s (Plucker a) = MV_Plucker !Int (MVector s a)
newtype MVector s (Complex a)
Instance details Defined in Data.Vector.Unboxed.Base newtype MVector s (Complex a) = MV_Complex (MVector s (a, a))
newtype MVector s (Point f a)
Instance details Defined in Linear.Affine newtype MVector s (Point f a) = MV_P (MVector s (f a))
data MVector s (a, b)
Instance details Defined in Data.Vector.Unboxed.Base data MVector s (a, b) = MV_2 !Int !(MVector s a) !(MVector s b)
data MVector s (V n a)
Instance details Defined in Linear.V data MVector s (V n a) = MV_VN !Int !(MVector s a)
data MVector s (a, b, c)
Instance details Defined in Data.Vector.Unboxed.Base data MVector s (a, b, c) = MV_3 !Int !(MVector s a) !(MVector s b) !(MVector s c)
data MVector s (a, b, c, d)
Instance details Defined in Data.Vector.Unboxed.Base data MVector s (a, b, c, d) = MV_4 !Int !(MVector s a) !(MVector s b) !(MVector s c) !(MVector s d)
data MVector s (a, b, c, d, e)
Instance details Defined in Data.Vector.Unboxed.Base data MVector s (a, b, c, d, e) = MV_5 !Int !(MVector s a) !(MVector s b) !(MVector s c) !(MVector s d) !(MVector s e)
data MVector s (a, b, c, d, e, f)
Instance details Defined in Data.Vector.Unboxed.Base data MVector s (a, b, c, d, e, f) = MV_6 !Int !(MVector s a) !(MVector s b) !(MVector s c) !(MVector s d) !(MVector s e) !(MVector s f)

data family Vector a :: Type #

Instances

Vector Vector Bool
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Bool -> m (Vector Bool) # basicUnsafeThaw :: PrimMonad m => Vector Bool -> m (Mutable Vector (PrimState m) Bool) # basicLength :: Vector Bool -> Int # basicUnsafeSlice :: Int -> Int -> Vector Bool -> Vector Bool # basicUnsafeIndexM :: Monad m => Vector Bool -> Int -> m Bool # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Bool -> Vector Bool -> m () # elemseq :: Vector Bool -> Bool -> b -> b #
Vector Vector Char
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Char -> m (Vector Char) # basicUnsafeThaw :: PrimMonad m => Vector Char -> m (Mutable Vector (PrimState m) Char) # basicLength :: Vector Char -> Int # basicUnsafeSlice :: Int -> Int -> Vector Char -> Vector Char # basicUnsafeIndexM :: Monad m => Vector Char -> Int -> m Char # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Char -> Vector Char -> m () # elemseq :: Vector Char -> Char -> b -> b #
Vector Vector Double
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Double -> m (Vector Double) # basicUnsafeThaw :: PrimMonad m => Vector Double -> m (Mutable Vector (PrimState m) Double) # basicLength :: Vector Double -> Int # basicUnsafeSlice :: Int -> Int -> Vector Double -> Vector Double # basicUnsafeIndexM :: Monad m => Vector Double -> Int -> m Double # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Double -> Vector Double -> m () # elemseq :: Vector Double -> Double -> b -> b #
Vector Vector Float
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Float -> m (Vector Float) # basicUnsafeThaw :: PrimMonad m => Vector Float -> m (Mutable Vector (PrimState m) Float) # basicLength :: Vector Float -> Int # basicUnsafeSlice :: Int -> Int -> Vector Float -> Vector Float # basicUnsafeIndexM :: Monad m => Vector Float -> Int -> m Float # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Float -> Vector Float -> m () # elemseq :: Vector Float -> Float -> b -> b #
Vector Vector Int
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Int -> m (Vector Int) # basicUnsafeThaw :: PrimMonad m => Vector Int -> m (Mutable Vector (PrimState m) Int) # basicLength :: Vector Int -> Int # basicUnsafeSlice :: Int -> Int -> Vector Int -> Vector Int # basicUnsafeIndexM :: Monad m => Vector Int -> Int -> m Int # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Int -> Vector Int -> m () # elemseq :: Vector Int -> Int -> b -> b #
Vector Vector Int8
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Int8 -> m (Vector Int8) # basicUnsafeThaw :: PrimMonad m => Vector Int8 -> m (Mutable Vector (PrimState m) Int8) # basicLength :: Vector Int8 -> Int # basicUnsafeSlice :: Int -> Int -> Vector Int8 -> Vector Int8 # basicUnsafeIndexM :: Monad m => Vector Int8 -> Int -> m Int8 # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Int8 -> Vector Int8 -> m () # elemseq :: Vector Int8 -> Int8 -> b -> b #
Vector Vector Int16
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Int16 -> m (Vector Int16) # basicUnsafeThaw :: PrimMonad m => Vector Int16 -> m (Mutable Vector (PrimState m) Int16) # basicLength :: Vector Int16 -> Int # basicUnsafeSlice :: Int -> Int -> Vector Int16 -> Vector Int16 # basicUnsafeIndexM :: Monad m => Vector Int16 -> Int -> m Int16 # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Int16 -> Vector Int16 -> m () # elemseq :: Vector Int16 -> Int16 -> b -> b #
Vector Vector Int32
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Int32 -> m (Vector Int32) # basicUnsafeThaw :: PrimMonad m => Vector Int32 -> m (Mutable Vector (PrimState m) Int32) # basicLength :: Vector Int32 -> Int # basicUnsafeSlice :: Int -> Int -> Vector Int32 -> Vector Int32 # basicUnsafeIndexM :: Monad m => Vector Int32 -> Int -> m Int32 # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Int32 -> Vector Int32 -> m () # elemseq :: Vector Int32 -> Int32 -> b -> b #
Vector Vector Int64
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Int64 -> m (Vector Int64) # basicUnsafeThaw :: PrimMonad m => Vector Int64 -> m (Mutable Vector (PrimState m) Int64) # basicLength :: Vector Int64 -> Int # basicUnsafeSlice :: Int -> Int -> Vector Int64 -> Vector Int64 # basicUnsafeIndexM :: Monad m => Vector Int64 -> Int -> m Int64 # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Int64 -> Vector Int64 -> m () # elemseq :: Vector Int64 -> Int64 -> b -> b #
Vector Vector Word
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Word -> m (Vector Word) # basicUnsafeThaw :: PrimMonad m => Vector Word -> m (Mutable Vector (PrimState m) Word) # basicLength :: Vector Word -> Int # basicUnsafeSlice :: Int -> Int -> Vector Word -> Vector Word # basicUnsafeIndexM :: Monad m => Vector Word -> Int -> m Word # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Word -> Vector Word -> m () # elemseq :: Vector Word -> Word -> b -> b #
Vector Vector Word8
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Word8 -> m (Vector Word8) # basicUnsafeThaw :: PrimMonad m => Vector Word8 -> m (Mutable Vector (PrimState m) Word8) # basicLength :: Vector Word8 -> Int # basicUnsafeSlice :: Int -> Int -> Vector Word8 -> Vector Word8 # basicUnsafeIndexM :: Monad m => Vector Word8 -> Int -> m Word8 # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Word8 -> Vector Word8 -> m () # elemseq :: Vector Word8 -> Word8 -> b -> b #
Vector Vector Word16
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Word16 -> m (Vector Word16) # basicUnsafeThaw :: PrimMonad m => Vector Word16 -> m (Mutable Vector (PrimState m) Word16) # basicLength :: Vector Word16 -> Int # basicUnsafeSlice :: Int -> Int -> Vector Word16 -> Vector Word16 # basicUnsafeIndexM :: Monad m => Vector Word16 -> Int -> m Word16 # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Word16 -> Vector Word16 -> m () # elemseq :: Vector Word16 -> Word16 -> b -> b #
Vector Vector Word32
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Word32 -> m (Vector Word32) # basicUnsafeThaw :: PrimMonad m => Vector Word32 -> m (Mutable Vector (PrimState m) Word32) # basicLength :: Vector Word32 -> Int # basicUnsafeSlice :: Int -> Int -> Vector Word32 -> Vector Word32 # basicUnsafeIndexM :: Monad m => Vector Word32 -> Int -> m Word32 # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Word32 -> Vector Word32 -> m () # elemseq :: Vector Word32 -> Word32 -> b -> b #
Vector Vector Word64
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Word64 -> m (Vector Word64) # basicUnsafeThaw :: PrimMonad m => Vector Word64 -> m (Mutable Vector (PrimState m) Word64) # basicLength :: Vector Word64 -> Int # basicUnsafeSlice :: Int -> Int -> Vector Word64 -> Vector Word64 # basicUnsafeIndexM :: Monad m => Vector Word64 -> Int -> m Word64 # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Word64 -> Vector Word64 -> m () # elemseq :: Vector Word64 -> Word64 -> b -> b #
Vector Vector ()
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) () -> m (Vector ()) # basicUnsafeThaw :: PrimMonad m => Vector () -> m (Mutable Vector (PrimState m) ()) # basicLength :: Vector () -> Int # basicUnsafeSlice :: Int -> Int -> Vector () -> Vector () # basicUnsafeIndexM :: Monad m => Vector () -> Int -> m () # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) () -> Vector () -> m () # elemseq :: Vector () -> () -> b -> b #
Unbox a => Vector Vector (Complex a)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Complex a) -> m (Vector (Complex a)) # basicUnsafeThaw :: PrimMonad m => Vector (Complex a) -> m (Mutable Vector (PrimState m) (Complex a)) # basicLength :: Vector (Complex a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Complex a) -> Vector (Complex a) # basicUnsafeIndexM :: Monad m => Vector (Complex a) -> Int -> m (Complex a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Complex a) -> Vector (Complex a) -> m () # elemseq :: Vector (Complex a) -> Complex a -> b -> b #
Unbox a => Vector Vector (V2 a)
Instance details Defined in Linear.V2 Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V2 a) -> m (Vector (V2 a)) # basicUnsafeThaw :: PrimMonad m => Vector (V2 a) -> m (Mutable Vector (PrimState m) (V2 a)) # basicLength :: Vector (V2 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V2 a) -> Vector (V2 a) # basicUnsafeIndexM :: Monad m => Vector (V2 a) -> Int -> m (V2 a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V2 a) -> Vector (V2 a) -> m () # elemseq :: Vector (V2 a) -> V2 a -> b -> b #
Unbox a => Vector Vector (V3 a)
Instance details Defined in Linear.V3 Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> m (Vector (V3 a)) # basicUnsafeThaw :: PrimMonad m => Vector (V3 a) -> m (Mutable Vector (PrimState m) (V3 a)) # basicLength :: Vector (V3 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V3 a) -> Vector (V3 a) # basicUnsafeIndexM :: Monad m => Vector (V3 a) -> Int -> m (V3 a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> Vector (V3 a) -> m () # elemseq :: Vector (V3 a) -> V3 a -> b -> b #
Unbox a => Vector Vector (Plucker a)
Instance details Defined in Linear.Plucker Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Plucker a) -> m (Vector (Plucker a)) # basicUnsafeThaw :: PrimMonad m => Vector (Plucker a) -> m (Mutable Vector (PrimState m) (Plucker a)) # basicLength :: Vector (Plucker a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Plucker a) -> Vector (Plucker a) # basicUnsafeIndexM :: Monad m => Vector (Plucker a) -> Int -> m (Plucker a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Plucker a) -> Vector (Plucker a) -> m () # elemseq :: Vector (Plucker a) -> Plucker a -> b -> b #
Unbox a => Vector Vector (Quaternion a)
Instance details Defined in Linear.Quaternion Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Quaternion a) -> m (Vector (Quaternion a)) # basicUnsafeThaw :: PrimMonad m => Vector (Quaternion a) -> m (Mutable Vector (PrimState m) (Quaternion a)) # basicLength :: Vector (Quaternion a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Quaternion a) -> Vector (Quaternion a) # basicUnsafeIndexM :: Monad m => Vector (Quaternion a) -> Int -> m (Quaternion a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Quaternion a) -> Vector (Quaternion a) -> m () # elemseq :: Vector (Quaternion a) -> Quaternion a -> b -> b #
Vector Vector (V0 a)
Instance details Defined in Linear.V0 Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V0 a) -> m (Vector (V0 a)) # basicUnsafeThaw :: PrimMonad m => Vector (V0 a) -> m (Mutable Vector (PrimState m) (V0 a)) # basicLength :: Vector (V0 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V0 a) -> Vector (V0 a) # basicUnsafeIndexM :: Monad m => Vector (V0 a) -> Int -> m (V0 a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V0 a) -> Vector (V0 a) -> m () # elemseq :: Vector (V0 a) -> V0 a -> b -> b #
Unbox a => Vector Vector (V4 a)
Instance details Defined in Linear.V4 Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V4 a) -> m (Vector (V4 a)) # basicUnsafeThaw :: PrimMonad m => Vector (V4 a) -> m (Mutable Vector (PrimState m) (V4 a)) # basicLength :: Vector (V4 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V4 a) -> Vector (V4 a) # basicUnsafeIndexM :: Monad m => Vector (V4 a) -> Int -> m (V4 a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V4 a) -> Vector (V4 a) -> m () # elemseq :: Vector (V4 a) -> V4 a -> b -> b #
Unbox a => Vector Vector (V1 a)
Instance details Defined in Linear.V1 Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V1 a) -> m (Vector (V1 a)) # basicUnsafeThaw :: PrimMonad m => Vector (V1 a) -> m (Mutable Vector (PrimState m) (V1 a)) # basicLength :: Vector (V1 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V1 a) -> Vector (V1 a) # basicUnsafeIndexM :: Monad m => Vector (V1 a) -> Int -> m (V1 a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V1 a) -> Vector (V1 a) -> m () # elemseq :: Vector (V1 a) -> V1 a -> b -> b #
(Unbox a, Unbox b) => Vector Vector (a, b)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (a, b) -> m (Vector (a, b)) # basicUnsafeThaw :: PrimMonad m => Vector (a, b) -> m (Mutable Vector (PrimState m) (a, b)) # basicLength :: Vector (a, b) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (a, b) -> Vector (a, b) # basicUnsafeIndexM :: Monad m => Vector (a, b) -> Int -> m (a, b) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (a, b) -> Vector (a, b) -> m () # elemseq :: Vector (a, b) -> (a, b) -> b0 -> b0 #
Unbox (f a) => Vector Vector (Point f a)
Instance details Defined in Linear.Affine Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Point f a) -> m (Vector (Point f a)) # basicUnsafeThaw :: PrimMonad m => Vector (Point f a) -> m (Mutable Vector (PrimState m) (Point f a)) # basicLength :: Vector (Point f a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Point f a) -> Vector (Point f a) # basicUnsafeIndexM :: Monad m => Vector (Point f a) -> Int -> m (Point f a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Point f a) -> Vector (Point f a) -> m () # elemseq :: Vector (Point f a) -> Point f a -> b -> b #
(Unbox a, Unbox b, Unbox c) => Vector Vector (a, b, c)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c) -> m (Vector (a, b, c)) # basicUnsafeThaw :: PrimMonad m => Vector (a, b, c) -> m (Mutable Vector (PrimState m) (a, b, c)) # basicLength :: Vector (a, b, c) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (a, b, c) -> Vector (a, b, c) # basicUnsafeIndexM :: Monad m => Vector (a, b, c) -> Int -> m (a, b, c) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c) -> Vector (a, b, c) -> m () # elemseq :: Vector (a, b, c) -> (a, b, c) -> b0 -> b0 #
(Dim n, Unbox a) => Vector Vector (V n a)
Instance details Defined in Linear.V Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V n a) -> m (Vector (V n a)) # basicUnsafeThaw :: PrimMonad m => Vector (V n a) -> m (Mutable Vector (PrimState m) (V n a)) # basicLength :: Vector (V n a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V n a) -> Vector (V n a) # basicUnsafeIndexM :: Monad m => Vector (V n a) -> Int -> m (V n a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V n a) -> Vector (V n a) -> m () # elemseq :: Vector (V n a) -> V n a -> b -> b #
(Unbox a, Unbox b, Unbox c, Unbox d) => Vector Vector (a, b, c, d)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d) -> m (Vector (a, b, c, d)) # basicUnsafeThaw :: PrimMonad m => Vector (a, b, c, d) -> m (Mutable Vector (PrimState m) (a, b, c, d)) # basicLength :: Vector (a, b, c, d) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (a, b, c, d) -> Vector (a, b, c, d) # basicUnsafeIndexM :: Monad m => Vector (a, b, c, d) -> Int -> m (a, b, c, d) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d) -> Vector (a, b, c, d) -> m () # elemseq :: Vector (a, b, c, d) -> (a, b, c, d) -> b0 -> b0 #
(Unbox a, Unbox b, Unbox c, Unbox d, Unbox e) => Vector Vector (a, b, c, d, e)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d, e) -> m (Vector (a, b, c, d, e)) # basicUnsafeThaw :: PrimMonad m => Vector (a, b, c, d, e) -> m (Mutable Vector (PrimState m) (a, b, c, d, e)) # basicLength :: Vector (a, b, c, d, e) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (a, b, c, d, e) -> Vector (a, b, c, d, e) # basicUnsafeIndexM :: Monad m => Vector (a, b, c, d, e) -> Int -> m (a, b, c, d, e) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d, e) -> Vector (a, b, c, d, e) -> m () # elemseq :: Vector (a, b, c, d, e) -> (a, b, c, d, e) -> b0 -> b0 #
(Unbox a, Unbox b, Unbox c, Unbox d, Unbox e, Unbox f) => Vector Vector (a, b, c, d, e, f)
Instance details Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d, e, f) -> m (Vector (a, b, c, d, e, f)) # basicUnsafeThaw :: PrimMonad m => Vector (a, b, c, d, e, f) -> m (Mutable Vector (PrimState m) (a, b, c, d, e, f)) # basicLength :: Vector (a, b, c, d, e, f) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (a, b, c, d, e, f) -> Vector (a, b, c, d, e, f) # basicUnsafeIndexM :: Monad m => Vector (a, b, c, d, e, f) -> Int -> m (a, b, c, d, e, f) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d, e, f) -> Vector (a, b, c, d, e, f) -> m () # elemseq :: Vector (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> b0 -> b0 #
(Data a, Unbox a) => Data (Vector a)
Instance details Defined in Data.Vector.Unboxed.Base Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Vector a -> c (Vector a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Vector a) # toConstr :: Vector a -> Constr # dataTypeOf :: Vector a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Vector a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Vector a)) # gmapT :: (forall b. Data b => b -> b) -> Vector a -> Vector a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Vector a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Vector a -> r # gmapQ :: (forall d. Data d => d -> u) -> Vector a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Vector a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Vector a -> m (Vector a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector a -> m (Vector a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector a -> m (Vector a) #
(Vector Vector a, ToJSON a) => ToJSON (Vector a)
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSON :: Vector a -> Value # toEncoding :: Vector a -> Encoding # toJSONList :: [Vector a] -> Value # toEncodingList :: [Vector a] -> Encoding #
NFData (Vector a)
Instance details Defined in Data.Vector.Unboxed.Base Methods rnf :: Vector a -> () #
Unbox a => Reversing (Vector a)
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Vector a -> Vector a #
Unbox a => AsEmpty (Vector a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Vector a) () #
Unbox a => Wrapped (Vector a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Vector a) :: Type # Methods _Wrapped' :: Iso' (Vector a) (Unwrapped (Vector a)) #
Unbox a => Ixed (Vector a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a)) #
(Unbox a, t ~ Vector a') => Rewrapped (Vector a) t
Instance details Defined in Control.Lens.Wrapped
(Unbox a, Unbox b) => Snoc (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b) #
(Unbox a, Unbox b) => Cons (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b) #
(Unbox a, Unbox b) => Each (Vector a) (Vector b) a b	`each` :: (`Unbox` a, `Unbox` b) => `Traversal` (`Vector` a) (`Vector` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Vector a) (Vector b) a b #
newtype Vector Bool
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Bool = V_Bool (Vector Word8)
newtype Vector Char
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Char = V_Char (Vector Char)
newtype Vector Double
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Double = V_Double (Vector Double)
newtype Vector Float
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Float = V_Float (Vector Float)
newtype Vector Int
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Int = V_Int (Vector Int)
newtype Vector Int8
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Int8 = V_Int8 (Vector Int8)
newtype Vector Int16
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Int16 = V_Int16 (Vector Int16)
newtype Vector Int32
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Int32 = V_Int32 (Vector Int32)
newtype Vector Int64
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Int64 = V_Int64 (Vector Int64)
newtype Vector Word
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Word = V_Word (Vector Word)
newtype Vector Word8
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Word8 = V_Word8 (Vector Word8)
newtype Vector Word16
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Word16 = V_Word16 (Vector Word16)
newtype Vector Word32
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Word32 = V_Word32 (Vector Word32)
newtype Vector Word64
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector Word64 = V_Word64 (Vector Word64)
newtype Vector ()
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector () = V_Unit Int
type Mutable Vector
Instance details Defined in Data.Vector.Unboxed.Base type Mutable Vector = MVector
type Item (Vector e)
Instance details Defined in Data.Vector.Unboxed type Item (Vector e) = e
newtype Vector (Complex a)
Instance details Defined in Data.Vector.Unboxed.Base newtype Vector (Complex a) = V_Complex (Vector (a, a))
data Vector (V2 a)
Instance details Defined in Linear.V2 data Vector (V2 a) = V_V2 !Int !(Vector a)
data Vector (V3 a)
Instance details Defined in Linear.V3 data Vector (V3 a) = V_V3 !Int !(Vector a)
data Vector (Plucker a)
Instance details Defined in Linear.Plucker data Vector (Plucker a) = V_Plucker !Int (Vector a)
data Vector (Quaternion a)
Instance details Defined in Linear.Quaternion data Vector (Quaternion a) = V_Quaternion !Int (Vector a)
newtype Vector (V0 a)
Instance details Defined in Linear.V0 newtype Vector (V0 a) = V_V0 Int
data Vector (V4 a)
Instance details Defined in Linear.V4 data Vector (V4 a) = V_V4 !Int !(Vector a)
newtype Vector (V1 a)
Instance details Defined in Linear.V1 newtype Vector (V1 a) = V_V1 (Vector a)
type Unwrapped (Vector a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (Vector a) = [a]
type IxValue (Vector a)
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type Index (Vector a)
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
data Vector (a, b)
Instance details Defined in Data.Vector.Unboxed.Base data Vector (a, b) = V_2 !Int !(Vector a) !(Vector b)
newtype Vector (Point f a)
Instance details Defined in Linear.Affine newtype Vector (Point f a) = V_P (Vector (f a))
data Vector (a, b, c)
Instance details Defined in Data.Vector.Unboxed.Base data Vector (a, b, c) = V_3 !Int !(Vector a) !(Vector b) !(Vector c)
data Vector (V n a)
Instance details Defined in Linear.V data Vector (V n a) = V_VN !Int !(Vector a)
data Vector (a, b, c, d)
Instance details Defined in Data.Vector.Unboxed.Base data Vector (a, b, c, d) = V_4 !Int !(Vector a) !(Vector b) !(Vector c) !(Vector d)
data Vector (a, b, c, d, e)
Instance details Defined in Data.Vector.Unboxed.Base data Vector (a, b, c, d, e) = V_5 !Int !(Vector a) !(Vector b) !(Vector c) !(Vector d) !(Vector e)
data Vector (a, b, c, d, e, f)
Instance details Defined in Data.Vector.Unboxed.Base data Vector (a, b, c, d, e, f) = V_6 !Int !(Vector a) !(Vector b) !(Vector c) !(Vector d) !(Vector e) !(Vector f)

animRect' :: (InSpace V2 n t, Monoid' m, TrailLike t, Enveloped t, Transformable t, Monoid t) => Rational -> QAnimation b V2 n m -> t #

Like animRect, but with an adjustible sample rate. The first parameter is the number of samples per time unit to use. Lower rates will be faster but less accurate; higher rates are more accurate but slower.

animRect :: (InSpace V2 n t, Monoid' m, TrailLike t, Enveloped t, Transformable t, Monoid t) => QAnimation b V2 n m -> t #

animRect works similarly to animEnvelope for 2D diagrams, but instead of adjusting the envelope, simply returns the smallest bounding rectangle which encloses the entire animation. Useful for e.g. creating a background to go behind an animation.

Uses 30 samples per time unit by default; to adjust this number see animRect'.

animEnvelope' :: (OrderedField n, Metric v, Monoid' m) => Rational -> QAnimation b v n m -> QAnimation b v n m #

Like animEnvelope, but with an adjustible sample rate. The first parameter is the number of samples per time unit to use. Lower rates will be faster but less accurate; higher rates are more accurate but slower.

animEnvelope :: (OrderedField n, Metric v, Monoid' m) => QAnimation b v n m -> QAnimation b v n m #

Automatically assign fixed a envelope to the entirety of an animation by sampling the envelope at a number of points in time and taking the union of all the sampled envelopes to form the "hull". This hull is then used uniformly throughout the animation.

This is useful when you have an animation that grows and shrinks in size or shape over time, but you want it to take up a fixed amount of space, e.g. so that the final rendered movie does not zoom in and out, or so that it occupies a fixed location with respect to another animation, when combining animations with something like |||.

By default, 30 samples per time unit are used; to adjust this number see animEnvelope'.

See also animRect for help constructing a background to go behind an animation.

type QAnimation b (v :: Type -> Type) n m = Active (QDiagram b v n m) #

A value of type QAnimation b v m is an animation (a time-varying diagram with start and end times) that can be rendered by backend b, with vector space v and monoidal annotations of type m.

type Animation b (v :: Type -> Type) n = QAnimation b v n Any #

A value of type Animation b v is an animation (a time-varying diagram with start and end times) in vector space v that can be rendered by backspace b.

Note that Animation is actually a synonym for QAnimation where the type of the monoidal annotations has been fixed to Any (the default).

mkHeight :: Num n => n -> SizeSpec V2 n #

Make a SizeSpec with only height defined.

mkWidth :: Num n => n -> SizeSpec V2 n #

Make a SizeSpec with only width defined.

dims2D :: n -> n -> SizeSpec V2 n #

Make a SizeSpec from a width and height.

mkSizeSpec2D :: Num n => Maybe n -> Maybe n -> SizeSpec V2 n #

Make a SizeSpec from possibly-specified width and height.

extentY :: (InSpace v n a, R2 v, Enveloped a) => a -> Maybe (n, n) #

Compute the absolute y-coordinate range of an enveloped object in the form (lo,hi). Return Nothing for objects with an empty envelope.

extentX :: (InSpace v n a, R1 v, Enveloped a) => a -> Maybe (n, n) #

Compute the absolute x-coordinate range of an enveloped object in the form (lo,hi). Return Nothing for objects with an empty envelope.

Note this is just extent unitX.

height :: (InSpace V2 n a, Enveloped a) => a -> n #

Compute the height of an enveloped object.

width :: (InSpace V2 n a, Enveloped a) => a -> n #

Compute the width of an enveloped object.

Note this is just diameter unitX.

sizeAdjustment :: (Additive v, Foldable v, OrderedField n) => SizeSpec v n -> BoundingBox v n -> (v n, Transformation v n) #

Get the adjustment to fit a BoundingBox in the given SizeSpec. The vector is the new size and the transformation to position the lower corner at the origin and scale to the size spec.

sizedAs :: (InSpace v n a, SameSpace a b, HasLinearMap v, Transformable a, Enveloped a, Enveloped b) => b -> a -> a #

Uniformly scale an enveloped object so that it "has the same size as" (fits within the width and height of) some other object.

sized :: (InSpace v n a, HasLinearMap v, Transformable a, Enveloped a) => SizeSpec v n -> a -> a #

Uniformly scale any enveloped object so that it fits within the given size. For non-uniform scaling see boxFit.

requiredScaling :: (Additive v, Foldable v, Fractional n, Ord n) => SizeSpec v n -> v n -> Transformation v n #

Return the Transformation calcuated from requiredScale.

requiredScale :: (Additive v, Foldable v, Fractional n, Ord n) => SizeSpec v n -> v n -> n #

requiredScale spec sz returns the largest scaling factor to make something of size sz fit the requested size spec without changing the aspect ratio. sz should be non-zero (otherwise a scale of 1 is returned). For non-uniform scaling see boxFit.

specToSize :: (Foldable v, Functor v, Num n, Ord n) => n -> SizeSpec v n -> v n #

specToSize n spec extracts a size from a SizeSpec sz. Any values not specified in the spec are replaced by the smallest of the values that are specified. If there are no specified values (i.e. absolute) then n is used.

absolute :: (Additive v, Num n) => SizeSpec v n #

A size spec with no hints to the size.

dims :: v n -> SizeSpec v n #

Make a SizeSpec from a vector. Any negative values will be ignored.

mkSizeSpec :: (Functor v, Num n) => v (Maybe n) -> SizeSpec v n #

Make a SizeSpec from a vector of maybe values. Any negative values will be ignored. For 2D SizeSpecs see mkWidth and mkHeight from Diagrams.TwoD.Size.

getSpec :: (Functor v, Num n, Ord n) => SizeSpec v n -> v (Maybe n) #

Retrieve a size spec as a vector of maybe values. Only positive sizes are returned.

data SizeSpec (v :: Type -> Type) n #

A SizeSpec is a way of specifying a size without needed lengths for all the dimensions.

Instances

Functor v => Functor (SizeSpec v)
Instance details Defined in Diagrams.Size Methods fmap :: (a -> b) -> SizeSpec v a -> SizeSpec v b # (<$) :: a -> SizeSpec v b -> SizeSpec v a #
Show (v n) => Show (SizeSpec v n)
Instance details Defined in Diagrams.Size Methods showsPrec :: Int -> SizeSpec v n -> ShowS # show :: SizeSpec v n -> String # showList :: [SizeSpec v n] -> ShowS #
Generic (SizeSpec v n)
Instance details Defined in Diagrams.Size Associated Types type Rep (SizeSpec v n) :: Type -> Type # Methods from :: SizeSpec v n -> Rep (SizeSpec v n) x # to :: Rep (SizeSpec v n) x -> SizeSpec v n #
Hashable (v n) => Hashable (SizeSpec v n)
Instance details Defined in Diagrams.Size Methods hashWithSalt :: Int -> SizeSpec v n -> Int # hash :: SizeSpec v n -> Int #
type Rep (SizeSpec v n)
Instance details Defined in Diagrams.Size type Rep (SizeSpec v n) = D1 (MetaData "SizeSpec" "Diagrams.Size" "diagrams-lib-1.4.2.3-4IkVVBmK9qBElHMtgqeLQ1" True) (C1 (MetaCons "SizeSpec" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (v n))))
type V (SizeSpec v n)
Instance details Defined in Diagrams.Size type V (SizeSpec v n) = v
type N (SizeSpec v n)
Instance details Defined in Diagrams.Size type N (SizeSpec v n) = n

bgFrame :: (TypeableFloat n, Renderable (Path V2 n) b) => n -> Colour Double -> QDiagram b V2 n Any -> QDiagram b V2 n Any #

Similar to bg but makes the colored background rectangle larger than the diagram. The first parameter is used to set how far the background extends beyond the diagram.

bg :: (TypeableFloat n, Renderable (Path V2 n) b) => Colour Double -> QDiagram b V2 n Any -> QDiagram b V2 n Any #

"Set the background color" of a diagram. That is, place a diagram atop a bounding rectangle of the given color.

boundingRect :: (InSpace V2 n a, SameSpace a t, Enveloped t, Transformable t, TrailLike t, Monoid t, Enveloped a) => a -> t #

Construct a bounding rectangle for an enveloped object, that is, the smallest axis-aligned rectangle which encloses the object.

rectEnvelope :: (OrderedField n, Monoid' m) => Point V2 n -> V2 n -> QDiagram b V2 n m -> QDiagram b V2 n m #

rectEnvelope p v sets the envelope of a diagram to a rectangle whose lower-left corner is at p and whose upper-right corner is at p .+^ v. Useful for selecting the rectangular portion of a diagram which should actually be "viewed" in the final render, if you don't want to see the entire diagram.

extrudeTop :: (OrderedField n, Monoid' m) => n -> QDiagram b V2 n m -> QDiagram b V2 n m #

extrudeTop s "extrudes" a diagram in the positive y-direction, offsetting its envelope by the provided distance. When s < 0 , the envelope is inset instead.

See the documentation for extrudeEnvelope for more information.

extrudeBottom :: (OrderedField n, Monoid' m) => n -> QDiagram b V2 n m -> QDiagram b V2 n m #

extrudeBottom s "extrudes" a diagram in the negative y-direction, offsetting its envelope by the provided distance. When s < 0 , the envelope is inset instead.

See the documentation for extrudeEnvelope for more information.

extrudeRight :: (OrderedField n, Monoid' m) => n -> QDiagram b V2 n m -> QDiagram b V2 n m #

extrudeRight s "extrudes" a diagram in the positive x-direction, offsetting its envelope by the provided distance. When s < 0 , the envelope is inset instead.

See the documentation for extrudeEnvelope for more information.

extrudeLeft :: (OrderedField n, Monoid' m) => n -> QDiagram b V2 n m -> QDiagram b V2 n m #

extrudeLeft s "extrudes" a diagram in the negative x-direction, offsetting its envelope by the provided distance. When s < 0 , the envelope is inset instead.

See the documentation for extrudeEnvelope for more information.

padY :: (Metric v, R2 v, Monoid' m, OrderedField n) => n -> QDiagram b v n m -> QDiagram b v n m #

padY s "pads" a diagram in the y-direction, expanding its envelope vertically by a factor of s (factors between 0 and 1 can be used to shrink the envelope). Note that the envelope will expand with respect to the local origin, so if the origin is not centered vertically the padding may appear "uneven". If this is not desired, the origin can be centered (using centerY) before applying padY.

padX :: (Metric v, R2 v, OrderedField n, Monoid' m) => n -> QDiagram b v n m -> QDiagram b v n m #

padX s "pads" a diagram in the x-direction, expanding its envelope horizontally by a factor of s (factors between 0 and 1 can be used to shrink the envelope). Note that the envelope will expand with respect to the local origin, so if the origin is not centered horizontally the padding may appear "uneven". If this is not desired, the origin can be centered (using centerX) before applying padX.

strutY :: (Metric v, R2 v, OrderedField n) => n -> QDiagram b v n m #

strutY h is an empty diagram with height h, width 0, and a centered local origin. Note that strutY (-h) behaves the same as strutY h.

strutX :: (Metric v, R1 v, OrderedField n) => n -> QDiagram b v n m #

strutX w is an empty diagram with width w, height 0, and a centered local origin. Note that strutX (-w) behaves the same as strutX w.

vsep :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a) => n -> [a] -> a #

A convenient synonym for vertical concatenation with separation: vsep s === vcat' (with & sep .~ s).

vcat' :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a) => CatOpts n -> [a] -> a #

A variant of vcat taking an extra CatOpts record to control the spacing. See the cat' documentation for a description of the possibilities. For the common case of setting just a separation amount, see vsep.

vcat :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a) => [a] -> a #

Lay out a list of juxtaposable objects in a column from top to bottom, so that their local origins lie along a single vertical line, with successive envelopes tangent to one another.

For more control over the spacing, see vcat'.
To align the diagrams horizontally (or otherwise), use alignment combinators (such as alignL or alignR) from Diagrams.TwoD.Align before applying vcat.
For non-axis-aligned layout, see cat.

hsep :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a) => n -> [a] -> a #

A convenient synonym for horizontal concatenation with separation: hsep s === hcat' (with & sep .~ s).

hcat' :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a) => CatOpts n -> [a] -> a #

A variant of hcat taking an extra CatOpts record to control the spacing. See the cat' documentation for a description of the possibilities. For the common case of setting just a separation amount, see hsep.

hcat :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a) => [a] -> a #

Lay out a list of juxtaposable objects in a row from left to right, so that their local origins lie along a single horizontal line, with successive envelopes tangent to one another.

For more control over the spacing, see hcat'.
To align the diagrams vertically (or otherwise), use alignment combinators (such as alignT or alignB) from Diagrams.TwoD.Align before applying hcat.
For non-axis-aligned layout, see cat.

(|||) :: (InSpace V2 n a, Juxtaposable a, Semigroup a) => a -> a -> a infixl 6 #

Place two diagrams (or other juxtaposable objects) horizontally adjacent to one another, with the first diagram to the left of the second. The local origin of the resulting combined diagram is the same as the local origin of the first. (|||) is associative and has mempty as an identity. See the documentation of beside for more information.

(===) :: (InSpace V2 n a, Juxtaposable a, Semigroup a) => a -> a -> a infixl 6 #

Place two diagrams (or other objects) vertically adjacent to one another, with the first diagram above the second. Since Haskell ignores whitespace in expressions, one can thus write

      c
     ===
      d

to place c above d. The local origin of the resulting combined diagram is the same as the local origin of the first. (===) is associative and has mempty as an identity. See the documentation of beside for more information.

boxGrid :: (Traversable v, Additive v, Num n, Enum n) => n -> BoundingBox v n -> [Point v n] #

boxGrid f box returns a grid of regularly spaced points inside the box, such that there are (1/f) points along each dimension. For example, for a 3D box with corners at (0,0,0) and (2,2,2), boxGrid 0.1 would yield a grid of approximately 1000 points (it might actually be 11^3 instead of 10^3) spaced 0.2 units apart.

outside' :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> BoundingBox v n -> Bool #

Test whether the first bounding box lies strictly outside the second (they do not intersect at all).

inside' :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> BoundingBox v n -> Bool #

Test whether the first bounding box is strictly contained inside the second.

contains' :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> Point v n -> Bool #

Check whether a point is strictly contained in a bounding box.

boxFit :: (InSpace v n a, HasBasis v, Enveloped a, Transformable a, Monoid a) => BoundingBox v n -> a -> a #

Transforms an enveloped thing to fit within a BoundingBox. If the bounding box is empty, then the result is also mempty.

boxTransform :: (Additive v, Fractional n) => BoundingBox v n -> BoundingBox v n -> Maybe (Transformation v n) #

Create a transformation mapping points from one bounding box to the other. Returns Nothing if either of the boxes are empty.

centerPoint :: (InSpace v n a, HasBasis v, Enveloped a) => a -> Point v n #

Get the center of a the bounding box of an enveloped object, return the origin for object with empty envelope.

mCenterPoint :: (InSpace v n a, HasBasis v, Enveloped a) => a -> Maybe (Point v n) #

Get the center of a the bounding box of an enveloped object, return Nothing for object with empty envelope.

boxCenter :: (Additive v, Fractional n) => BoundingBox v n -> Maybe (Point v n) #

Get the center point in a bounding box.

boxExtents :: (Additive v, Num n) => BoundingBox v n -> v n #

Get the size of the bounding box - the vector from the (component-wise) lesser point to the greater point.

getAllCorners :: (Additive v, Traversable v) => BoundingBox v n -> [Point v n] #

Computes all of the corners of the bounding box.

getCorners :: BoundingBox v n -> Maybe (Point v n, Point v n) #

Gets the lower and upper corners that define the bounding box.

isEmptyBox :: BoundingBox v n -> Bool #

Queries whether the BoundingBox is empty.

boundingBox :: (InSpace v n a, HasBasis v, Enveloped a) => a -> BoundingBox v n #

Create a bounding box for any enveloped object (such as a diagram or path).

fromPoints :: (Additive v, Ord n) => [Point v n] -> BoundingBox v n #

Create the smallest bounding box containing all the given points.

fromPoint :: Point v n -> BoundingBox v n #

Create a degenerate bounding "box" containing only a single point.

fromCorners :: (Additive v, Foldable v, Ord n) => Point v n -> Point v n -> BoundingBox v n #

Create a bounding box from a point that is component-wise (<=) than the other. If this is not the case, then mempty is returned.

emptyBox :: BoundingBox v n #

An empty bounding box. This is the same thing as mempty, but it doesn't require the same type constraints that the Monoid instance does.

data BoundingBox (v :: Type -> Type) n #

A bounding box is an axis-aligned region determined by two points indicating its "lower" and "upper" corners. It can also represent an empty bounding box - the points are wrapped in Maybe.

Instances

Functor v => Functor (BoundingBox v)
Instance details Defined in Diagrams.BoundingBox Methods fmap :: (a -> b) -> BoundingBox v a -> BoundingBox v b # (<$) :: a -> BoundingBox v b -> BoundingBox v a #
Eq (v n) => Eq (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox Methods (==) :: BoundingBox v n -> BoundingBox v n -> Bool # (/=) :: BoundingBox v n -> BoundingBox v n -> Bool #
Read (v n) => Read (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox Methods readsPrec :: Int -> ReadS (BoundingBox v n) # readList :: ReadS [BoundingBox v n] # readPrec :: ReadPrec (BoundingBox v n) # readListPrec :: ReadPrec [BoundingBox v n] #
Show (v n) => Show (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox Methods showsPrec :: Int -> BoundingBox v n -> ShowS # show :: BoundingBox v n -> String # showList :: [BoundingBox v n] -> ShowS #
(Additive v, Ord n) => Semigroup (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox Methods (<>) :: BoundingBox v n -> BoundingBox v n -> BoundingBox v n # sconcat :: NonEmpty (BoundingBox v n) -> BoundingBox v n # stimes :: Integral b => b -> BoundingBox v n -> BoundingBox v n #
(Additive v, Ord n) => Monoid (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox Methods mempty :: BoundingBox v n # mappend :: BoundingBox v n -> BoundingBox v n -> BoundingBox v n # mconcat :: [BoundingBox v n] -> BoundingBox v n #
(Metric v, Traversable v, OrderedField n) => Enveloped (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox Methods getEnvelope :: BoundingBox v n -> Envelope (V (BoundingBox v n)) (N (BoundingBox v n)) #
RealFloat n => Traced (BoundingBox V2 n)
Instance details Defined in Diagrams.BoundingBox Methods getTrace :: BoundingBox V2 n -> Trace (V (BoundingBox V2 n)) (N (BoundingBox V2 n)) #
TypeableFloat n => Traced (BoundingBox V3 n)
Instance details Defined in Diagrams.BoundingBox Methods getTrace :: BoundingBox V3 n -> Trace (V (BoundingBox V3 n)) (N (BoundingBox V3 n)) #
(Additive v, Num n) => HasOrigin (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox Methods moveOriginTo :: Point (V (BoundingBox v n)) (N (BoundingBox v n)) -> BoundingBox v n -> BoundingBox v n #
(Metric v, Traversable v, OrderedField n) => Alignable (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox Methods alignBy' :: (InSpace v0 n0 (BoundingBox v n), Fractional n0, HasOrigin (BoundingBox v n)) => (v0 n0 -> BoundingBox v n -> Point v0 n0) -> v0 n0 -> n0 -> BoundingBox v n -> BoundingBox v n # defaultBoundary :: (V (BoundingBox v n) ~ v0, N (BoundingBox v n) ~ n0) => v0 n0 -> BoundingBox v n -> Point v0 n0 # alignBy :: (InSpace v0 n0 (BoundingBox v n), Fractional n0, HasOrigin (BoundingBox v n)) => v0 n0 -> n0 -> BoundingBox v n -> BoundingBox v n #
AsEmpty (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox Methods _Empty :: Prism' (BoundingBox v n) () #
(Additive v, Foldable v, Ord n) => HasQuery (BoundingBox v n) Any
Instance details Defined in Diagrams.BoundingBox Methods getQuery :: BoundingBox v n -> Query (V (BoundingBox v n)) (N (BoundingBox v n)) Any #
(Additive v', Foldable v', Ord n') => Each (BoundingBox v n) (BoundingBox v' n') (Point v n) (Point v' n')	Only valid if the second point is not smaller than the first.
Instance details Defined in Diagrams.BoundingBox Methods each :: Traversal (BoundingBox v n) (BoundingBox v' n') (Point v n) (Point v' n') #
type V (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox type V (BoundingBox v n) = v
type N (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox type N (BoundingBox v n) = n

showLabels :: (TypeableFloat n, Renderable (Text n) b, Semigroup m) => QDiagram b V2 n m -> QDiagram b V2 n Any #

showTrace :: (Enum n, TypeableFloat n, Renderable (Path V2 n) b) => QDiagram b V2 n Any -> QDiagram b V2 n Any #

Mark the trace of a diagram by placing 64 red dots 1/100th its size along the trace.

showTrace' :: (Enum n, TypeableFloat n, Renderable (Path V2 n) b) => TraceOpts n -> QDiagram b V2 n Any -> QDiagram b V2 n Any #

Mark the trace of a diagram, with control over colour and scale of marker dot and the number of points on the trace.

showEnvelope :: (Enum n, TypeableFloat n, Renderable (Path V2 n) b) => QDiagram b V2 n Any -> QDiagram b V2 n Any #

Mark the envelope with an approximating cubic spline using 32 points, medium line width and red line color.

showEnvelope' :: (Enum n, TypeableFloat n, Renderable (Path V2 n) b) => EnvelopeOpts n -> QDiagram b V2 n Any -> QDiagram b V2 n Any #

Mark the envelope with an approximating cubic spline with control over the color, line width and number of points.

showOrigin' :: (TypeableFloat n, Renderable (Path V2 n) b, Monoid' m) => OriginOpts n -> QDiagram b V2 n m -> QDiagram b V2 n m #

Mark the origin of a diagram, with control over colour and scale of marker dot.

showOrigin :: (TypeableFloat n, Renderable (Path V2 n) b, Monoid' m) => QDiagram b V2 n m -> QDiagram b V2 n m #

Mark the origin of a diagram by placing a red dot 1/50th its size.

tScale :: Lens' (TraceOpts n) n #

tPoints :: Lens' (TraceOpts n) Int #

tMinSize :: Lens' (TraceOpts n) n #

tColor :: Lens' (TraceOpts n) (Colour Double) #

ePoints :: Lens' (EnvelopeOpts n) Int #

eLineWidth :: Lens (EnvelopeOpts n1) (EnvelopeOpts n2) (Measure n1) (Measure n2) #

eColor :: Lens' (EnvelopeOpts n) (Colour Double) #

data TraceOpts n #

Constructors

TraceOpts
Fields _tColor :: Colour Double _tScale :: n _tMinSize :: n _tPoints :: Int

Instances

Floating n => Default (TraceOpts n)
Instance details Defined in Diagrams.TwoD.Model Methods def :: TraceOpts n #

oScale :: Lens' (OriginOpts n) n #

oMinSize :: Lens' (OriginOpts n) n #

oColor :: Lens' (OriginOpts n) (Colour Double) #

data EnvelopeOpts n #

Constructors

EnvelopeOpts
Fields _eColor :: Colour Double _eLineWidth :: Measure n _ePoints :: Int

Instances

OrderedField n => Default (EnvelopeOpts n)
Instance details Defined in Diagrams.TwoD.Model Methods def :: EnvelopeOpts n #

data OriginOpts n #

Constructors

OriginOpts
Fields _oColor :: Colour Double _oScale :: n _oMinSize :: n

Instances

Fractional n => Default (OriginOpts n)
Instance details Defined in Diagrams.TwoD.Model Methods def :: OriginOpts n #

cubicSpline :: (V t ~ v, N t ~ n, TrailLike t, Fractional (v n)) => Bool -> [Point v n] -> t #

Construct a spline path-like thing of cubic segments from a list of vertices, with the first vertex as the starting point. The first argument specifies whether the path should be closed.

pts = map p2 [(0,0), (2,3), (5,-2), (-4,1), (0,3)]
spot = circle 0.2 # fc blue # lw none
mkPath closed = position (zip pts (repeat spot))
             <> cubicSpline closed pts
cubicSplineEx = (mkPath False ||| strutX 2 ||| mkPath True)
              # centerXY # pad 1.1

For more information, see http://mathworld.wolfram.com/CubicSpline.html.

bspline :: (TrailLike t, V t ~ v, N t ~ n) => BSpline v n -> t #

Generate a uniform cubic B-spline from the given control points. The spline starts and ends at the first and last control points, and is tangent to the line to the second(-to-last) control point. It does not necessarily pass through any of the other control points.

pts = map p2 [(0,0), (2,3), (5,-2), (-4,1), (0,3)]
spot = circle 0.2 # fc blue # lw none
bsplineEx = mconcat
  [ position (zip pts (repeat spot))
  , bspline pts
  ]
  # frame 0.5

type BSpline (v :: Type -> Type) n = [Point v n] #

facingZ :: (R3 v, Functor v, Fractional n) => Deformation v v n #

perspectiveZ1 :: (R3 v, Functor v, Fractional n) => Deformation v v n #

The perspective division onto the plane z=1 along lines going through the origin.

parallelZ0 :: (R3 v, Num n) => Deformation v v n #

The parallel projection onto the plane z=0

facingY :: (R2 v, Functor v, Fractional n) => Deformation v v n #

facingX :: (R1 v, Functor v, Fractional n) => Deformation v v n #

The viewing transform for a viewer facing along the positive X axis. X coördinates stay fixed, while Y coördinates are compressed with increasing distance. asDeformation (translation unitX) <> parallelX0 <> frustrumX = perspectiveX1

perspectiveY1 :: (R2 v, Functor v, Floating n) => Deformation v v n #

The perspective division onto the plane y=1 along lines going through the origin.

parallelY0 :: (R2 v, Num n) => Deformation v v n #

The parallel projection onto the plane y=0

perspectiveX1 :: (R1 v, Functor v, Fractional n) => Deformation v v n #

The perspective division onto the plane x=1 along lines going through the origin.

parallelX0 :: (R1 v, Num n) => Deformation v v n #

The parallel projection onto the plane x=0

asDeformation :: (Additive v, Num n) => Transformation v n -> Deformation v v n #

asDeformation converts a Transformation to a Deformation by discarding the inverse transform. This allows reusing Transformations in the construction of Deformations.

newtype Deformation (v :: Type -> Type) (u :: Type -> Type) n #

Deformations are a superset of the affine transformations represented by the Transformation type. In general they are not invertible. Deformations include projective transformations. Deformation can represent other functions from points to points which are "well-behaved", in that they do not introduce small wiggles.

Constructors

Deformation (Point v n -> Point u n)

Instances

Semigroup (Deformation v v n)
Instance details Defined in Diagrams.Deform Methods (<>) :: Deformation v v n -> Deformation v v n -> Deformation v v n # sconcat :: NonEmpty (Deformation v v n) -> Deformation v v n # stimes :: Integral b => b -> Deformation v v n -> Deformation v v n #
Monoid (Deformation v v n)
Instance details Defined in Diagrams.Deform Methods mempty :: Deformation v v n # mappend :: Deformation v v n -> Deformation v v n -> Deformation v v n # mconcat :: [Deformation v v n] -> Deformation v v n #

class Deformable a b where #

Methods

deform' :: N a -> Deformation (V a) (V b) (N a) -> a -> b #

deform' epsilon d a transforms a by the deformation d. If the type of a is not closed under projection, approximate to accuracy epsilon.

deform :: Deformation (V a) (V b) (N a) -> a -> b #

deform d a transforms a by the deformation d. If the type of a is not closed under projection, deform should call deform' with some reasonable default value of epsilon.

Instances

(Metric v, Metric u, OrderedField n, r ~ Located (Trail u n)) => Deformable (Located (Trail v n)) r
Instance details Defined in Diagrams.Deform Methods deform' :: N (Located (Trail v n)) -> Deformation (V (Located (Trail v n))) (V r) (N (Located (Trail v n))) -> Located (Trail v n) -> r # deform :: Deformation (V (Located (Trail v n))) (V r) (N (Located (Trail v n))) -> Located (Trail v n) -> r #
r ~ Point u n => Deformable (Point v n) r
Instance details Defined in Diagrams.Deform Methods deform' :: N (Point v n) -> Deformation (V (Point v n)) (V r) (N (Point v n)) -> Point v n -> r # deform :: Deformation (V (Point v n)) (V r) (N (Point v n)) -> Point v n -> r #
(Metric v, Metric u, OrderedField n, r ~ Path u n) => Deformable (Path v n) r
Instance details Defined in Diagrams.Deform Methods deform' :: N (Path v n) -> Deformation (V (Path v n)) (V r) (N (Path v n)) -> Path v n -> r # deform :: Deformation (V (Path v n)) (V r) (N (Path v n)) -> Path v n -> r #

connectOutside' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2) => ArrowOpts n -> n1 -> n2 -> QDiagram b V2 n Any -> QDiagram b V2 n Any #

connectOutside :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2) => n1 -> n2 -> QDiagram b V2 n Any -> QDiagram b V2 n Any #

Draw an arrow from diagram named "n1" to diagram named "n2". The arrow lies on the line between the centres of the diagrams, but is drawn so that it stops at the boundaries of the diagrams, using traces to find the intersection points.

connectPerim' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2) => ArrowOpts n -> n1 -> n2 -> Angle n -> Angle n -> QDiagram b V2 n Any -> QDiagram b V2 n Any #

connectPerim :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2) => n1 -> n2 -> Angle n -> Angle n -> QDiagram b V2 n Any -> QDiagram b V2 n Any #

Connect two diagrams at point on the perimeter of the diagrams, choosen by angle.

connect' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2) => ArrowOpts n -> n1 -> n2 -> QDiagram b V2 n Any -> QDiagram b V2 n Any #

Connect two diagrams with an arbitrary arrow.

connect :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2) => n1 -> n2 -> QDiagram b V2 n Any -> QDiagram b V2 n Any #

Connect two diagrams with a straight arrow.

arrowV' :: (TypeableFloat n, Renderable (Path V2 n) b) => ArrowOpts n -> V2 n -> QDiagram b V2 n Any #

arrowV' v creates an arrow with the direction and norm of the vector v (with its tail at the origin).

arrowV :: (TypeableFloat n, Renderable (Path V2 n) b) => V2 n -> QDiagram b V2 n Any #

arrowV v creates an arrow with the direction and norm of the vector v (with its tail at the origin), using default parameters.

arrowAt' :: (TypeableFloat n, Renderable (Path V2 n) b) => ArrowOpts n -> Point V2 n -> V2 n -> QDiagram b V2 n Any #

arrowAt :: (TypeableFloat n, Renderable (Path V2 n) b) => Point V2 n -> V2 n -> QDiagram b V2 n Any #

Create an arrow starting at s with length and direction determined by the vector v.

arrowBetween' :: (TypeableFloat n, Renderable (Path V2 n) b) => ArrowOpts n -> Point V2 n -> Point V2 n -> QDiagram b V2 n Any #

arrowBetween' opts s e creates an arrow pointing from s to e using the given options. In particular, it scales and rotates arrowShaft to go between s and e, taking head, tail, and gaps into account.

arrowBetween :: (TypeableFloat n, Renderable (Path V2 n) b) => Point V2 n -> Point V2 n -> QDiagram b V2 n Any #

arrowBetween s e creates an arrow pointing from s to e with default parameters.

arrow' :: (TypeableFloat n, Renderable (Path V2 n) b) => ArrowOpts n -> n -> QDiagram b V2 n Any #

arrow' opts len creates an arrow of length len using the given options, starting at the origin and ending at the point (len,0). In particular, it scales the given arrowShaft so that the entire arrow has length len.

arrow :: (TypeableFloat n, Renderable (Path V2 n) b) => n -> QDiagram b V2 n Any #

arrow len creates an arrow of length len with default parameters, starting at the origin and ending at the point (len,0).

shaftTexture :: TypeableFloat n => Lens' (ArrowOpts n) (Texture n) #

A lens for setting or modifying the texture of an arrow shaft.

tailTexture :: TypeableFloat n => Lens' (ArrowOpts n) (Texture n) #

A lens for setting or modifying the texture of an arrow tail. This is *not* a valid lens (see committed).

headTexture :: TypeableFloat n => Lens' (ArrowOpts n) (Texture n) #

A lens for setting or modifying the texture of an arrowhead. For example, one may write ... (with & headTexture .~ grad) to get an arrow with a head filled with a gradient, assuming grad has been defined. Or ... (with & headTexture .~ solid blue to set the head color to blue. For more general control over the style of arrowheads, see headStyle.

lengths :: Traversal' (ArrowOpts n) (Measure n) #

Set both the headLength and tailLength simultaneously.

gap :: Traversal' (ArrowOpts n) (Measure n) #

Same as gaps, provided for backward compatiiblity.

gaps :: Traversal' (ArrowOpts n) (Measure n) #

Set both the headGap and tailGap simultaneously.

tailStyle :: Lens' (ArrowOpts n) (Style V2 n) #

Style to apply to the tail. See headStyle.

tailLength :: Lens' (ArrowOpts n) (Measure n) #

The length of the tail plus its joint.

tailGap :: Lens' (ArrowOpts n) (Measure n) #

Distance to leave between the starting point and the tail.

shaftStyle :: Lens' (ArrowOpts n) (Style V2 n) #

Style to apply to the shaft. See headStyle.

headStyle :: Lens' (ArrowOpts n) (Style V2 n) #

Style to apply to the head. headStyle is modified by using the lens combinator %~ to change the current style. For example, to change an opaque black arrowhead to translucent orange: (with & headStyle %~ fc orange . opacity 0.75).

headLength :: Lens' (ArrowOpts n) (Measure n) #

The length from the start of the joint to the tip of the head.

headGap :: Lens' (ArrowOpts n) (Measure n) #

Distance to leave between the head and the target point.

arrowTail :: Lens' (ArrowOpts n) (ArrowHT n) #

A shape to place at the tail of the arrow.

arrowShaft :: Lens' (ArrowOpts n) (Trail V2 n) #

The trail to use for the arrow shaft.

arrowHead :: Lens' (ArrowOpts n) (ArrowHT n) #

A shape to place at the head of the arrow.

straightShaft :: OrderedField n => Trail V2 n #

Straight line arrow shaft.

data ArrowOpts n #

Constructors

ArrowOpts
Fields _arrowHead :: ArrowHT n _arrowTail :: ArrowHT n _arrowShaft :: Trail V2 n _headGap :: Measure n _tailGap :: Measure n _headStyle :: Style V2 n _headLength :: Measure n _tailStyle :: Style V2 n _tailLength :: Measure n _shaftStyle :: Style V2 n

Instances

TypeableFloat n => Default (ArrowOpts n)
Instance details Defined in Diagrams.TwoD.Arrow Methods def :: ArrowOpts n #

block :: RealFloat n => ArrowHT n #

quill :: (Floating n, Ord n) => ArrowHT n #

halfDart' :: RealFloat n => ArrowHT n #

dart' :: RealFloat n => ArrowHT n #

thorn' :: RealFloat n => ArrowHT n #

spike' :: RealFloat n => ArrowHT n #

tri' :: RealFloat n => ArrowHT n #

noTail :: ArrowHT n #

lineTail :: RealFloat n => ArrowHT n #

A line the same width as the shaft.

arrowtailQuill :: OrderedField n => Angle n -> ArrowHT n #

The angle is where the top left corner intersects the circle.

arrowtailBlock :: RealFloat n => Angle n -> ArrowHT n #

halfDart :: RealFloat n => ArrowHT n #

dart :: RealFloat n => ArrowHT n #

thorn :: RealFloat n => ArrowHT n #

spike :: RealFloat n => ArrowHT n #

tri :: RealFloat n => ArrowHT n #

noHead :: ArrowHT n #

lineHead :: RealFloat n => ArrowHT n #

A line the same width as the shaft.

arrowheadThorn :: RealFloat n => Angle n -> ArrowHT n #

Curved sides, linear concave base. Illustrator CS5 #3

arrowheadSpike :: RealFloat n => Angle n -> ArrowHT n #

Isoceles triangle with curved concave base. Inkscape type 2.

arrowheadHalfDart :: RealFloat n => Angle n -> ArrowHT n #

Top half of an arrowheadDart.

arrowheadDart :: RealFloat n => Angle n -> ArrowHT n #

Isoceles triangle with linear concave base. Inkscape type 1 - dart like.

arrowheadTriangle :: RealFloat n => Angle n -> ArrowHT n #

Isoceles triangle style. The above example specifies an angle of `2/5 Turn`.

type ArrowHT n = n -> n -> (Path V2 n, Path V2 n) #

lighter :: HasStyle a => a -> a #

Set all text to be lighter than the inherited font weight.

bolder :: HasStyle a => a -> a #

Set all text to be bolder than the inherited font weight.

heavy :: HasStyle a => a -> a #

Set all text using a heavy/black font weight.

ultraBold :: HasStyle a => a -> a #

Set all text using an ultra-bold font weight.

semiBold :: HasStyle a => a -> a #

Set all text using a semi-bold font weight.

mediumWeight :: HasStyle a => a -> a #

Set all text using a medium font weight.

light :: HasStyle a => a -> a #

Set all text using a light font weight.

ultraLight :: HasStyle a => a -> a #

Set all text using a extra light font weight.

thinWeight :: HasStyle a => a -> a #

Set all text using a thin font weight.

bold :: HasStyle a => a -> a #

Set all text using a bold font weight.

oblique :: HasStyle a => a -> a #

Set all text using an oblique slant.

italic :: HasStyle a => a -> a #

Set all text in italics.

_fontSize :: (Typeable n, OrderedField n) => Lens' (Style v n) (Measure n) #

Lens to commit a font size. This is *not* a valid lens (see commited.

_fontSizeR :: (Typeable n, OrderedField n) => Lens' (Style v n) (Measured n (Recommend n)) #

fontSizeL :: (N a ~ n, Typeable n, Num n, HasStyle a) => n -> a -> a #

A convenient sysnonym for 'fontSize (Local w)'.

fontSizeO :: (N a ~ n, Typeable n, HasStyle a) => n -> a -> a #

A convenient synonym for 'fontSize (Output w)'.

fontSizeN :: (N a ~ n, Typeable n, Num n, HasStyle a) => n -> a -> a #

A convenient synonym for 'fontSize (Normalized w)'.

fontSizeG :: (N a ~ n, Typeable n, Num n, HasStyle a) => n -> a -> a #

A convenient synonym for 'fontSize (Global w)'.

fontSize :: (N a ~ n, Typeable n, HasStyle a) => Measure n -> a -> a #

Set the font size, that is, the size of the font's em-square as measured within the current local vector space. The default size is local 1 (which is applied by recommendFontSize).

_font :: Lens' (Style v n) (Maybe String) #

Lens onto the font name of a style.

font :: HasStyle a => String -> a -> a #

Specify a font family to be used for all text within a diagram.

baselineText :: (TypeableFloat n, Renderable (Text n) b) => String -> QDiagram b V2 n Any #

Create a primitive text diagram from the given string, with the origin set to be on the baseline, at the beginning (although not bounding). This is the reference point of showText in the Cairo graphics library.

Note that it takes up no space.

alignedText :: (TypeableFloat n, Renderable (Text n) b) => n -> n -> String -> QDiagram b V2 n Any #

Create a primitive text diagram from the given string, with the origin set to a point interpolated within the bounding box. The first parameter varies from 0 (left) to 1 (right), and the second parameter from 0 (bottom) to 1 (top). Some backends do not implement this and instead snap to closest corner or the center.

The height of this box is determined by the font's potential ascent and descent, rather than the height of the particular string.

Note that it takes up no space.

topLeftText :: (TypeableFloat n, Renderable (Text n) b) => String -> QDiagram b V2 n Any #

Create a primitive text diagram from the given string, origin at the top left corner of the text's bounding box, equivalent to alignedText 0 1.

Note that it takes up no space.

text :: (TypeableFloat n, Renderable (Text n) b) => String -> QDiagram b V2 n Any #

Create a primitive text diagram from the given string, with center alignment, equivalent to alignedText 0.5 0.5.

Note that it takes up no space, as text size information is not available.

fcA :: (InSpace V2 n a, Floating n, Typeable n, HasStyle a) => AlphaColour Double -> a -> a #

A synonym for fillColor, specialized to AlphaColour Double (i.e. colors with transparency). See comment after fillColor about backends.

fc :: (InSpace V2 n a, Floating n, Typeable n, HasStyle a) => Colour Double -> a -> a #

A synonym for fillColor, specialized to Colour Double (i.e. opaque colors). See comment after fillColor about backends.

recommendFillColor :: (InSpace V2 n a, Color c, Typeable n, Floating n, HasStyle a) => c -> a -> a #

Set a "recommended" fill color, to be used only if no explicit calls to fillColor (or fc, or fcA) are used. See comment after fillColor about backends.

fillColor :: (InSpace V2 n a, Color c, Typeable n, Floating n, HasStyle a) => c -> a -> a #

Set the fill color. This function is polymorphic in the color type (so it can be used with either Colour or AlphaColour), but this can sometimes create problems for type inference, so the fc and fcA variants are provided with more concrete types.

_fillTexture :: (Typeable n, Floating n) => Lens' (Style V2 n) (Texture n) #

Commit a fill texture in a style. This is not a valid setter because it doesn't abide the functor law (see committed).

fillTexture :: (InSpace V2 n a, Typeable n, Floating n, HasStyle a) => Texture n -> a -> a #

getFillTexture :: FillTexture n -> Texture n #

_FillTexture :: Iso' (FillTexture n) (Recommend (Texture n)) #

lcA :: (InSpace V2 n a, Typeable n, Floating n, HasStyle a) => AlphaColour Double -> a -> a #

A synonym for lineColor, specialized to AlphaColour Double (i.e. colors with transparency). See comment in lineColor about backends.

lc :: (InSpace V2 n a, Typeable n, Floating n, HasStyle a) => Colour Double -> a -> a #

A synonym for lineColor, specialized to Colour Double (i.e. opaque colors). See comment in lineColor about backends.

lineColor :: (InSpace V2 n a, Color c, Typeable n, Floating n, HasStyle a) => c -> a -> a #

Set the line (stroke) color. This function is polymorphic in the color type (so it can be used with either Colour or AlphaColour), but this can sometimes create problems for type inference, so the lc and lcA variants are provided with more concrete types.

_lineTexture :: (Floating n, Typeable n) => Lens' (Style V2 n) (Texture n) #

lineTextureA :: (InSpace V2 n a, Typeable n, Floating n, HasStyle a) => LineTexture n -> a -> a #

lineTexture :: (InSpace V2 n a, Typeable n, Floating n, HasStyle a) => Texture n -> a -> a #

getLineTexture :: LineTexture n -> Texture n #

_LineTexture :: Iso (LineTexture n) (LineTexture n') (Texture n) (Texture n') #

mkRadialGradient :: Num n => [GradientStop n] -> Point V2 n -> n -> Point V2 n -> n -> SpreadMethod -> Texture n #

Make a radial gradient texture from a stop list, radius, start point, end point, and SpreadMethod. The rGradTrans field is set to the identity transfrom, to change it use the rGradTrans lens.

mkLinearGradient :: Num n => [GradientStop n] -> Point V2 n -> Point V2 n -> SpreadMethod -> Texture n #

Make a linear gradient texture from a stop list, start point, end point, and SpreadMethod. The lGradTrans field is set to the identity transfrom, to change it use the lGradTrans lens.

mkStops :: [(Colour Double, d, Double)] -> [GradientStop d] #

A convenient function for making gradient stops from a list of triples. (An opaque color, a stop fraction, an opacity).

defaultRG :: Fractional n => Texture n #

A default is provided so that radial gradients can easily be created using lenses. For example, rg = defaultRG & rGradRadius1 .~ 0.25. Note that no default value is provided for rGradStops, this must be set before the gradient value is used, otherwise the object will appear transparent.

defaultLG :: Fractional n => Texture n #

A default is provided so that linear gradients can easily be created using lenses. For example, lg = defaultLG & lGradStart .~ (0.25 ^& 0.33). Note that no default value is provided for lGradStops, this must be set before the gradient value is used, otherwise the object will appear transparent.

solid :: Color a => a -> Texture n #

Convert a solid colour into a texture.

_AC :: Prism' (Texture n) (AlphaColour Double) #

Prism onto an AlphaColour Double of a SC texture.

_RG :: Prism' (Texture n) (RGradient n) #

_LG :: Prism' (Texture n) (LGradient n) #

_SC :: Prism' (Texture n) SomeColor #

rGradTrans :: Lens' (RGradient n) (Transformation V2 n) #

A transformation to be applied to the gradient. Usually this field will start as the identity transform and capture the transforms that are applied to the gradient.

rGradStops :: Lens' (RGradient n) [GradientStop n] #

A list of stops (colors and fractions).

rGradSpreadMethod :: Lens' (RGradient n) SpreadMethod #

For setting the spread method.

rGradRadius1 :: Lens' (RGradient n) n #

The radius of the outer circle in local coordinates.

rGradRadius0 :: Lens' (RGradient n) n #

The radius of the inner cirlce in local coordinates.

rGradCenter1 :: Lens' (RGradient n) (Point V2 n) #

The center of the outer circle.

rGradCenter0 :: Lens' (RGradient n) (Point V2 n) #

The center point of the inner circle.

data Texture n #

A Texture is either a color SC, linear gradient LG, or radial gradient RG. An object can have only one texture which is determined by the Last semigroup structure.

Constructors

SC SomeColor
LG (LGradient n)
RG (RGradient n)

Instances

Floating n => Transformable (Texture n)
Instance details Defined in Diagrams.TwoD.Attributes Methods transform :: Transformation (V (Texture n)) (N (Texture n)) -> Texture n -> Texture n #
type V (Texture n)
Instance details Defined in Diagrams.TwoD.Attributes type V (Texture n) = V2
type N (Texture n)
Instance details Defined in Diagrams.TwoD.Attributes type N (Texture n) = n

lGradTrans :: Lens' (LGradient n) (Transformation V2 n) #

A transformation to be applied to the gradient. Usually this field will start as the identity transform and capture the transforms that are applied to the gradient.

lGradStops :: Lens' (LGradient n) [GradientStop n] #

A list of stops (colors and fractions).

lGradStart :: Lens' (LGradient n) (Point V2 n) #

The starting point for the first gradient stop. The coordinates are in local units and the default is (-0.5, 0).

lGradSpreadMethod :: Lens' (LGradient n) SpreadMethod #

For setting the spread method.

lGradEnd :: Lens' (LGradient n) (Point V2 n) #

The ending point for the last gradient stop.The coordinates are in local units and the default is (0.5, 0).

data RGradient n #

Radial Gradient

Constructors

RGradient
Fields _rGradStops :: [GradientStop n] _rGradCenter0 :: Point V2 n _rGradRadius0 :: n _rGradCenter1 :: Point V2 n _rGradRadius1 :: n _rGradTrans :: Transformation V2 n _rGradSpreadMethod :: SpreadMethod

Instances

Fractional n => Transformable (RGradient n)
Instance details Defined in Diagrams.TwoD.Attributes Methods transform :: Transformation (V (RGradient n)) (N (RGradient n)) -> RGradient n -> RGradient n #
type V (RGradient n)
Instance details Defined in Diagrams.TwoD.Attributes type V (RGradient n) = V2
type N (RGradient n)
Instance details Defined in Diagrams.TwoD.Attributes type N (RGradient n) = n

stopFraction :: Lens' (GradientStop n) n #

The fraction for stop.

stopColor :: Lens' (GradientStop n) SomeColor #

A color for the stop.

data SpreadMethod #

The SpreadMethod determines what happens before lGradStart and after lGradEnd. GradPad fills the space before the start of the gradient with the color of the first stop and the color after end of the gradient with the color of the last stop. GradRepeat restarts the gradient and GradReflect restarts the gradient with the stops in reverse order.

Constructors

GradPad
GradReflect
GradRepeat

data LGradient n #

Linear Gradient

Constructors

LGradient
Fields _lGradStops :: [GradientStop n] _lGradStart :: Point V2 n _lGradEnd :: Point V2 n _lGradTrans :: Transformation V2 n _lGradSpreadMethod :: SpreadMethod

Instances

Fractional n => Transformable (LGradient n)
Instance details Defined in Diagrams.TwoD.Attributes Methods transform :: Transformation (V (LGradient n)) (N (LGradient n)) -> LGradient n -> LGradient n #
type V (LGradient n)
Instance details Defined in Diagrams.TwoD.Attributes type V (LGradient n) = V2
type N (LGradient n)
Instance details Defined in Diagrams.TwoD.Attributes type N (LGradient n) = n

data GradientStop d #

A gradient stop contains a color and fraction (usually between 0 and 1)

Constructors

GradientStop
Fields _stopColor :: SomeColor _stopFraction :: d

raster :: Num n => (Int -> Int -> AlphaColour Double) -> Int -> Int -> DImage n Embedded #

Create an image "from scratch" by specifying the pixel data

rasterDia :: (TypeableFloat n, Renderable (DImage n Embedded) b) => (Int -> Int -> AlphaColour Double) -> Int -> Int -> QDiagram b V2 n Any #

Crate a diagram from raw raster data.

uncheckedImageRef :: Num n => FilePath -> Int -> Int -> DImage n External #

Make an "unchecked" image reference; have to specify a width and height. Unless the aspect ratio of the external image is the w :: h, then the image will be distorted.

loadImageExt :: Num n => FilePath -> IO (Either String (DImage n External)) #

Check that a file exists, and use JuicyPixels to figure out the right size, but save a reference to the image instead of the raster data

loadImageEmb :: Num n => FilePath -> IO (Either String (DImage n Embedded)) #

Use JuicyPixels to read a file in any format and wrap it in a DImage. The width and height of the image are set to their actual values.

image :: (TypeableFloat n, Typeable a, Renderable (DImage n a) b) => DImage n a -> QDiagram b V2 n Any #

Make a DImage into a Diagram.

data Embedded #

Instances

SVGFloat n => Renderable (DImage n Embedded) SVG
Instance details Defined in Diagrams.Backend.SVG Methods render :: SVG -> DImage n Embedded -> Render SVG (V (DImage n Embedded)) (N (DImage n Embedded)) #

data External #

data Native t #

Instances

SVGFloat n => Renderable (DImage n (Native Img)) SVG
Instance details Defined in Diagrams.Backend.SVG Methods render :: SVG -> DImage n (Native Img) -> Render SVG (V (DImage n (Native Img))) (N (DImage n (Native Img))) #

data ImageData a where #

ImageData is either a JuicyPixels DynamicImage tagged as Embedded or a reference tagged as External. Additionally Native is provided for external libraries to hook into.

Constructors

ImageRaster :: forall a. DynamicImage -> ImageData Embedded
ImageRef :: forall a. FilePath -> ImageData External
ImageNative :: forall a t. t -> ImageData (Native t)

data DImage a b #

An image primitive, the two ints are width followed by height. Will typically be created by loadImageEmb or loadImageExt which, will handle setting the width and height to the actual width and height of the image.

Constructors

DImage (ImageData b) Int Int (Transformation V2 a)

Instances

Fractional n => Transformable (DImage n a)
Instance details Defined in Diagrams.TwoD.Image Methods transform :: Transformation (V (DImage n a)) (N (DImage n a)) -> DImage n a -> DImage n a #
Fractional n => HasOrigin (DImage n a)
Instance details Defined in Diagrams.TwoD.Image Methods moveOriginTo :: Point (V (DImage n a)) (N (DImage n a)) -> DImage n a -> DImage n a #
Fractional n => Renderable (DImage n a) NullBackend
Instance details Defined in Diagrams.TwoD.Image Methods render :: NullBackend -> DImage n a -> Render NullBackend (V (DImage n a)) (N (DImage n a)) #
SVGFloat n => Renderable (DImage n (Native Img)) SVG
Instance details Defined in Diagrams.Backend.SVG Methods render :: SVG -> DImage n (Native Img) -> Render SVG (V (DImage n (Native Img))) (N (DImage n (Native Img))) #
SVGFloat n => Renderable (DImage n Embedded) SVG
Instance details Defined in Diagrams.Backend.SVG Methods render :: SVG -> DImage n Embedded -> Render SVG (V (DImage n Embedded)) (N (DImage n Embedded)) #
RealFloat n => HasQuery (DImage n a) Any
Instance details Defined in Diagrams.TwoD.Image Methods getQuery :: DImage n a -> Query (V (DImage n a)) (N (DImage n a)) Any #
type V (DImage n a)
Instance details Defined in Diagrams.TwoD.Image type V (DImage n a) = V2
type N (DImage n a)
Instance details Defined in Diagrams.TwoD.Image type N (DImage n a) = n

intersectPointsT' :: OrderedField n => n -> Located (Trail V2 n) -> Located (Trail V2 n) -> [P2 n] #

Compute the intersect points between two located trails within the given tolerance.

intersectPointsT :: OrderedField n => Located (Trail V2 n) -> Located (Trail V2 n) -> [P2 n] #

Compute the intersect points between two located trails.

intersectPointsP' :: OrderedField n => n -> Path V2 n -> Path V2 n -> [P2 n] #

Compute the intersect points between two paths within given tolerance.

intersectPointsP :: OrderedField n => Path V2 n -> Path V2 n -> [P2 n] #

Compute the intersect points between two paths.

intersectPoints' :: (InSpace V2 n t, SameSpace t s, ToPath t, ToPath s, OrderedField n) => n -> t -> s -> [P2 n] #

Find the intersect points of two objects that can be converted to a path within the given tolerance.

intersectPoints :: (InSpace V2 n t, SameSpace t s, ToPath t, ToPath s, OrderedField n) => t -> s -> [P2 n] #

Find the intersect points of two objects that can be converted to a path.

clipped :: TypeableFloat n => Path V2 n -> QDiagram b V2 n Any -> QDiagram b V2 n Any #

Clip a diagram to the clip path taking the envelope and trace of the clip path.

clipTo :: TypeableFloat n => Path V2 n -> QDiagram b V2 n Any -> QDiagram b V2 n Any #

Clip a diagram to the given path setting its envelope to the pointwise minimum of the envelopes of the diagram and path. The trace consists of those parts of the original diagram's trace which fall within the clipping path, or parts of the path's trace within the original diagram.

clipBy :: (HasStyle a, V a ~ V2, N a ~ n, TypeableFloat n) => Path V2 n -> a -> a #

Clip a diagram by the given path:

Only the parts of the diagram which lie in the interior of the path will be drawn.
The envelope of the diagram is unaffected.

_clip :: (Typeable n, OrderedField n) => Lens' (Style V2 n) [Path V2 n] #

Lens onto the Clip in a style. An empty list means no clipping.

_Clip :: Iso (Clip n) (Clip n') [Path V2 n] [Path V2 n'] #

_fillRule :: Lens' (Style V2 n) FillRule #

Lens onto the fill rule of a style.

fillRule :: HasStyle a => FillRule -> a -> a #

Specify the fill rule that should be used for determining which points are inside a path.

strokeLocLoop :: (TypeableFloat n, Renderable (Path V2 n) b) => Located (Trail' Loop V2 n) -> QDiagram b V2 n Any #

A convenience function for converting a Located loop directly into a diagram; strokeLocLoop = stroke . trailLike . mapLoc wrapLoop.

strokeLocLine :: (TypeableFloat n, Renderable (Path V2 n) b) => Located (Trail' Line V2 n) -> QDiagram b V2 n Any #

A convenience function for converting a Located line directly into a diagram; strokeLocLine = stroke . trailLike . mapLoc wrapLine.

strokeLocT :: (TypeableFloat n, Renderable (Path V2 n) b) => Located (Trail V2 n) -> QDiagram b V2 n Any #

Deprecated synonym for strokeLocTrail.

strokeLocTrail :: (TypeableFloat n, Renderable (Path V2 n) b) => Located (Trail V2 n) -> QDiagram b V2 n Any #

A convenience function for converting a Located Trail directly into a diagram; strokeLocTrail = stroke . trailLike.

strokeLoop :: (TypeableFloat n, Renderable (Path V2 n) b) => Trail' Loop V2 n -> QDiagram b V2 n Any #

A composition of strokeT and wrapLoop for conveniently converting a loop directly into a diagram.

strokeLine :: (TypeableFloat n, Renderable (Path V2 n) b) => Trail' Line V2 n -> QDiagram b V2 n Any #

A composition of strokeT and wrapLine for conveniently converting a line directly into a diagram.

strokeT' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName a) => StrokeOpts a -> Trail V2 n -> QDiagram b V2 n Any #

Deprecated synonym for strokeTrail'.

strokeTrail' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName a) => StrokeOpts a -> Trail V2 n -> QDiagram b V2 n Any #

A composition of stroke' and pathFromTrail for conveniently converting a trail directly into a diagram.

strokeT :: (TypeableFloat n, Renderable (Path V2 n) b) => Trail V2 n -> QDiagram b V2 n Any #

stroke specialised to Trail.

strokeTrail :: (TypeableFloat n, Renderable (Path V2 n) b) => Trail V2 n -> QDiagram b V2 n Any #

stroke specialised to Trail.

strokePath' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName a) => StrokeOpts a -> Path V2 n -> QDiagram b V2 n Any #

stroke' specialised to Path.

strokeP' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName a) => StrokeOpts a -> Path V2 n -> QDiagram b V2 n Any #

stroke' specialised to Path.

strokePath :: (TypeableFloat n, Renderable (Path V2 n) b) => Path V2 n -> QDiagram b V2 n Any #

stroke specialised to Path.

strokeP :: (TypeableFloat n, Renderable (Path V2 n) b) => Path V2 n -> QDiagram b V2 n Any #

stroke specialised to Path.

stroke' :: (InSpace V2 n t, ToPath t, TypeableFloat n, Renderable (Path V2 n) b, IsName a) => StrokeOpts a -> t -> QDiagram b V2 n Any #

A variant of stroke that takes an extra record of options to customize its behaviour. In particular:

Names can be assigned to the path's vertices

StrokeOpts is an instance of Default, so stroke' (with & ... ) syntax may be used.

stroke :: (InSpace V2 n t, ToPath t, TypeableFloat n, Renderable (Path V2 n) b) => t -> QDiagram b V2 n Any #

Convert a ToPath object into a diagram. The resulting diagram has the names 0, 1, ... assigned to each of the path's vertices.

See also stroke', which takes an extra options record allowing its behaviour to be customized.

stroke :: Path V2 Double                  -> Diagram b
stroke :: Located (Trail V2 Double)       -> Diagram b
stroke :: Located (Trail' Loop V2 Double) -> Diagram b
stroke :: Located (Trail' Line V2 Double) -> Diagram b

vertexNames :: Lens (StrokeOpts a) (StrokeOpts a') [[a]] [[a']] #

Atomic names that should be assigned to the vertices of the path so that they can be referenced later. If there are not enough names, the extra vertices are not assigned names; if there are too many, the extra names are ignored. Note that this is a list of lists of names, since paths can consist of multiple trails. The first list of names are assigned to the vertices of the first trail, the second list to the second trail, and so on.

The default value is the empty list.

queryFillRule :: Lens' (StrokeOpts a) FillRule #

The fill rule used for determining which points are inside the path. The default is Winding. NOTE: for now, this only affects the resulting diagram's Query, not how it will be drawn! To set the fill rule determining how it is to be drawn, use the fillRule function.

data FillRule #

Enumeration of algorithms or "rules" for determining which points lie in the interior of a (possibly self-intersecting) path.

Constructors

Winding	Interior points are those with a nonzero winding number. See http://en.wikipedia.org/wiki/Nonzero-rule.
EvenOdd	Interior points are those where a ray extended infinitely in a particular direction crosses the path an odd number of times. See http://en.wikipedia.org/wiki/Even-odd_rule.

Instances

Eq FillRule
Instance details Defined in Diagrams.TwoD.Path Methods (==) :: FillRule -> FillRule -> Bool # (/=) :: FillRule -> FillRule -> Bool #
Ord FillRule
Instance details Defined in Diagrams.TwoD.Path Methods compare :: FillRule -> FillRule -> Ordering # (<) :: FillRule -> FillRule -> Bool # (<=) :: FillRule -> FillRule -> Bool # (>) :: FillRule -> FillRule -> Bool # (>=) :: FillRule -> FillRule -> Bool # max :: FillRule -> FillRule -> FillRule # min :: FillRule -> FillRule -> FillRule #
Show FillRule
Instance details Defined in Diagrams.TwoD.Path Methods showsPrec :: Int -> FillRule -> ShowS # show :: FillRule -> String # showList :: [FillRule] -> ShowS #
Semigroup FillRule
Instance details Defined in Diagrams.TwoD.Path Methods (<>) :: FillRule -> FillRule -> FillRule # sconcat :: NonEmpty FillRule -> FillRule # stimes :: Integral b => b -> FillRule -> FillRule #
Default FillRule
Instance details Defined in Diagrams.TwoD.Path Methods def :: FillRule #
AttributeClass FillRule
Instance details Defined in Diagrams.TwoD.Path

data StrokeOpts a #

A record of options that control how a path is stroked. StrokeOpts is an instance of Default, so a StrokeOpts records can be created using with { ... } notation.

Constructors

StrokeOpts
Fields _vertexNames :: [[a]] _queryFillRule :: FillRule

Instances

Default (StrokeOpts a)
Instance details Defined in Diagrams.TwoD.Path Methods def :: StrokeOpts a #

roundedRect' :: (InSpace V2 n t, TrailLike t, RealFloat n) => n -> n -> RoundedRectOpts n -> t #

roundedRect' works like roundedRect but allows you to set the radius of each corner indivually, using RoundedRectOpts. The default corner radius is 0. Each radius can also be negative, which results in the curves being reversed to be inward instead of outward.

roundedRect :: (InSpace V2 n t, TrailLike t, RealFloat n) => n -> n -> n -> t #

roundedRect w h r generates a closed trail, or closed path centered at the origin, of an axis-aligned rectangle with width w, height h, and circular rounded corners of radius r. If r is negative the corner will be cut out in a reverse arc. If the size of r is larger than half the smaller dimension of w and h, then it will be reduced to fit in that range, to prevent the corners from overlapping. The trail or path begins with the right edge and proceeds counterclockwise. If you need to specify a different radius for each corner individually, use roundedRect' instead.

roundedRectEx = pad 1.1 . centerXY $ hcat' (with & sep .~ 0.2)
  [ roundedRect  0.5 0.4 0.1
  , roundedRect  0.5 0.4 (-0.1)
  , roundedRect' 0.7 0.4 (with & radiusTL .~ 0.2
                               & radiusTR .~ -0.2
                               & radiusBR .~ 0.1)
  ]

radiusTR :: Lens' (RoundedRectOpts d) d #

radiusTL :: Lens' (RoundedRectOpts d) d #

radiusBR :: Lens' (RoundedRectOpts d) d #

radiusBL :: Lens' (RoundedRectOpts d) d #

dodecagon :: (InSpace V2 n t, TrailLike t) => n -> t #

A regular dodecagon, with sides of the given length and base parallel to the x-axis.

hendecagon :: (InSpace V2 n t, TrailLike t) => n -> t #

A regular hendecagon, with sides of the given length and base parallel to the x-axis.

decagon :: (InSpace V2 n t, TrailLike t) => n -> t #

A regular decagon, with sides of the given length and base parallel to the x-axis.

nonagon :: (InSpace V2 n t, TrailLike t) => n -> t #

A regular nonagon, with sides of the given length and base parallel to the x-axis.

octagon :: (InSpace V2 n t, TrailLike t) => n -> t #

A regular octagon, with sides of the given length and base parallel to the x-axis.

septagon :: (InSpace V2 n t, TrailLike t) => n -> t #

A synonym for heptagon. It is, however, completely inferior, being a base admixture of the Latin septum (seven) and the Greek γωνία (angle).

heptagon :: (InSpace V2 n t, TrailLike t) => n -> t #

A regular heptagon, with sides of the given length and base parallel to the x-axis.

hexagon :: (InSpace V2 n t, TrailLike t) => n -> t #

A regular hexagon, with sides of the given length and base parallel to the x-axis.

pentagon :: (InSpace V2 n t, TrailLike t) => n -> t #

A regular pentagon, with sides of the given length and base parallel to the x-axis.

triangle :: (InSpace V2 n t, TrailLike t) => n -> t #

An equilateral triangle, with sides of the given length and base parallel to the x-axis.

eqTriangle :: (InSpace V2 n t, TrailLike t) => n -> t #

A synonym for triangle, provided for backwards compatibility.

regPoly :: (InSpace V2 n t, TrailLike t) => Int -> n -> t #

Create a regular polygon. The first argument is the number of sides, and the second is the length of the sides. (Compare to the polygon function with a PolyRegular option, which produces polygons of a given radius).

The polygon will be oriented with one edge parallel to the x-axis.

rect :: (InSpace V2 n t, TrailLike t) => n -> n -> t #

rect w h is an axis-aligned rectangle of width w and height h, centered at the origin.

square :: (InSpace V2 n t, TrailLike t) => n -> t #

A square with its center at the origin and sides of the given length, oriented parallel to the axes.

unitSquare :: (InSpace V2 n t, TrailLike t) => t #

A square with its center at the origin and sides of length 1, oriented parallel to the axes.

vrule :: (InSpace V2 n t, TrailLike t) => n -> t #

Create a centered vertical (T-B) line of the given length.

vruleEx = hcat' (with & sep .~ 0.2) (map vrule [1, 1.2 .. 2])
        # centerXY # pad 1.1

hrule :: (InSpace V2 n t, TrailLike t) => n -> t #

Create a centered horizontal (L-R) line of the given length.

hruleEx = vcat' (with & sep .~ 0.2) (map hrule [1..5])
        # centerXY # pad 1.1

data RoundedRectOpts d #

Constructors

RoundedRectOpts
Fields _radiusTL :: d _radiusTR :: d _radiusBL :: d _radiusBR :: d

Instances

Num d => Default (RoundedRectOpts d)
Instance details Defined in Diagrams.TwoD.Shapes Methods def :: RoundedRectOpts d #

star :: OrderedField n => StarOpts -> [Point V2 n] -> Path V2 n #

Create a generalized star polygon. The StarOpts are used to determine in which order the given vertices should be connected. The intention is that the second argument of type [Point v] could be generated by a call to polygon, regPoly, or the like, since a list of vertices is TrailLike. But of course the list can be generated any way you like. A Path v is returned (instead of any TrailLike) because the resulting path may have more than one component, for example if the vertices are to be connected in several disjoint cycles.

polygon :: (InSpace V2 n t, TrailLike t) => PolygonOpts n -> t #

Generate the polygon described by the given options.

polyTrail :: OrderedField n => PolygonOpts n -> Located (Trail V2 n) #

Generate a polygon. See PolygonOpts for more information.

polyType :: Lens' (PolygonOpts n) (PolyType n) #

Specification for the polygon's vertices.

polyOrient :: Lens' (PolygonOpts n) (PolyOrientation n) #

Should a rotation be applied to the polygon in order to orient it in a particular way?

polyCenter :: Lens' (PolygonOpts n) (Point V2 n) #

Should a translation be applied to the polygon in order to place the center at a particular location?

data StarOpts #

Options for creating "star" polygons, where the edges connect possibly non-adjacent vertices.

Constructors

StarFun (Int -> Int)	Specify the order in which the vertices should be connected by a function that maps each vertex index to the index of the vertex that should come next. Indexing of vertices begins at 0.
StarSkip Int	Specify a star polygon by a "skip". A skip of 1 indicates a normal polygon, where edges go between successive vertices. A skip of 2 means that edges will connect every second vertex, skipping one in between. Generally, a skip of n means that edges will connect every nth vertex.

data PolyType n #

Method used to determine the vertices of a polygon.

Constructors

PolyPolar [Angle n] [n]

A "polar" polygon.

The first argument is a list of central angles from each vertex to the next.
The second argument is a list of radii from the origin to each successive vertex.

To construct an n-gon, use a list of n-1 angles and n radii. Extra angles or radii are ignored.

Cyclic polygons (with all vertices lying on a circle) can be constructed using a second argument of (repeat r).

PolySides [Angle n] [n]

A polygon determined by the distance between successive vertices and the external angles formed by each three successive vertices. In other words, a polygon specified by "turtle graphics": go straight ahead x1 units; turn by external angle a1; go straight ahead x2 units; turn by external angle a2; etc. The polygon will be centered at the centroid of its vertices.

The first argument is a list of vertex angles, giving the external angle at each vertex from the previous vertex to the next. The first angle in the list is the external angle at the second vertex; the first edge always starts out heading in the positive y direction from the first vertex.
The second argument is a list of distances between successive vertices.

To construct an n-gon, use a list of n-2 angles and n-1 edge lengths. Extra angles or lengths are ignored.

PolyRegular Int n

A regular polygon with the given number of sides (first argument) and the given radius (second argument).

data PolyOrientation n #

Determine how a polygon should be oriented.

Constructors

NoOrient	No special orientation; the first vertex will be at (1,0).
OrientH	Orient horizontally, so the bottommost edge is parallel to the x-axis. This is the default.
OrientV	Orient vertically, so the leftmost edge is parallel to the y-axis.
OrientTo (V2 n)	Orient so some edge is facing in the direction of, that is, perpendicular to, the given vector.

Instances

Eq n => Eq (PolyOrientation n)
Instance details Defined in Diagrams.TwoD.Polygons Methods (==) :: PolyOrientation n -> PolyOrientation n -> Bool # (/=) :: PolyOrientation n -> PolyOrientation n -> Bool #
Ord n => Ord (PolyOrientation n)
Instance details Defined in Diagrams.TwoD.Polygons Methods compare :: PolyOrientation n -> PolyOrientation n -> Ordering # (<) :: PolyOrientation n -> PolyOrientation n -> Bool # (<=) :: PolyOrientation n -> PolyOrientation n -> Bool # (>) :: PolyOrientation n -> PolyOrientation n -> Bool # (>=) :: PolyOrientation n -> PolyOrientation n -> Bool # max :: PolyOrientation n -> PolyOrientation n -> PolyOrientation n # min :: PolyOrientation n -> PolyOrientation n -> PolyOrientation n #
Read n => Read (PolyOrientation n)
Instance details Defined in Diagrams.TwoD.Polygons Methods readsPrec :: Int -> ReadS (PolyOrientation n) # readList :: ReadS [PolyOrientation n] # readPrec :: ReadPrec (PolyOrientation n) # readListPrec :: ReadPrec [PolyOrientation n] #
Show n => Show (PolyOrientation n)
Instance details Defined in Diagrams.TwoD.Polygons Methods showsPrec :: Int -> PolyOrientation n -> ShowS # show :: PolyOrientation n -> String # showList :: [PolyOrientation n] -> ShowS #

data PolygonOpts n #

Options for specifying a polygon.

Constructors

PolygonOpts
Fields _polyType :: PolyType n _polyOrient :: PolyOrientation n _polyCenter :: Point V2 n

Instances

Num n => Default (PolygonOpts n)	The default polygon is a regular pentagon of radius 1, centered at the origin, aligned to the x-axis.
Instance details Defined in Diagrams.TwoD.Polygons Methods def :: PolygonOpts n #

reversePath :: (Metric v, OrderedField n) => Path v n -> Path v n #

Reverse all the component trails of a path.

scalePath :: (HasLinearMap v, Metric v, OrderedField n) => n -> Path v n -> Path v n #

Scale a path using its centroid (see pathCentroid) as the base point for the scale.

partitionPath :: (Located (Trail v n) -> Bool) -> Path v n -> (Path v n, Path v n) #

Partition a path into two paths based on a predicate on trails: the first containing all the trails for which the predicate returns True, and the second containing the remaining trails.

explodePath :: (V t ~ v, N t ~ n, TrailLike t) => Path v n -> [[t]] #

"Explode" a path by exploding every component trail (see explodeTrail).

fixPath :: (Metric v, OrderedField n) => Path v n -> [[FixedSegment v n]] #

Convert a path into a list of lists of FixedSegments.

pathLocSegments :: (Metric v, OrderedField n) => Path v n -> [[Located (Segment Closed v n)]] #

Convert a path into a list of lists of located segments.

pathCentroid :: (Metric v, OrderedField n) => Path v n -> Point v n #

Compute the centroid of a path (i.e. the average location of its vertices; see pathVertices).

pathOffsets :: (Metric v, OrderedField n) => Path v n -> [v n] #

Compute the total offset of each trail comprising a path (see trailOffset).

pathVertices :: (Metric v, OrderedField n) => Path v n -> [[Point v n]] #

Like pathVertices', with a default tolerance.

pathVertices' :: (Metric v, OrderedField n) => n -> Path v n -> [[Point v n]] #

Extract the vertices of a path, resulting in a separate list of vertices for each component trail. Here a vertex is defined as a non-differentiable point on the trail, i.e. a sharp corner. (Vertices are thus a subset of the places where segments join; if you want all joins between segments, see pathPoints.) The tolerance determines how close the tangents of two segments must be at their endpoints to consider the transition point to be differentiable. See trailVertices for more information.

pathFromLocTrail :: (Metric v, OrderedField n) => Located (Trail v n) -> Path v n #

Convert a located trail to a singleton path. This is equivalent to trailLike, but provided with a more specific name and type for convenience.

pathFromTrailAt :: (Metric v, OrderedField n) => Trail v n -> Point v n -> Path v n #

Convert a trail to a path with a particular starting point.

pathFromTrail :: (Metric v, OrderedField n) => Trail v n -> Path v n #

Convert a trail to a path beginning at the origin.

pathTrails :: Path v n -> [Located (Trail v n)] #

Extract the located trails making up a Path.

newtype Path (v :: Type -> Type) n #

A path is a (possibly empty) list of Located Trails. Hence, unlike trails, paths are not translationally invariant, and they form a monoid under superposition (placing one path on top of another) rather than concatenation.

Constructors

Path [Located (Trail v n)]

Instances

Eq (v n) => Eq (Path v n)
Instance details Defined in Diagrams.Path Methods (==) :: Path v n -> Path v n -> Bool # (/=) :: Path v n -> Path v n -> Bool #
Ord (v n) => Ord (Path v n)
Instance details Defined in Diagrams.Path Methods compare :: Path v n -> Path v n -> Ordering # (<) :: Path v n -> Path v n -> Bool # (<=) :: Path v n -> Path v n -> Bool # (>) :: Path v n -> Path v n -> Bool # (>=) :: Path v n -> Path v n -> Bool # max :: Path v n -> Path v n -> Path v n # min :: Path v n -> Path v n -> Path v n #
Show (v n) => Show (Path v n)
Instance details Defined in Diagrams.Path Methods showsPrec :: Int -> Path v n -> ShowS # show :: Path v n -> String # showList :: [Path v n] -> ShowS #
Generic (Path v n)
Instance details Defined in Diagrams.Path Associated Types type Rep (Path v n) :: Type -> Type # Methods from :: Path v n -> Rep (Path v n) x # to :: Rep (Path v n) x -> Path v n #
Semigroup (Path v n)
Instance details Defined in Diagrams.Path Methods (<>) :: Path v n -> Path v n -> Path v n # sconcat :: NonEmpty (Path v n) -> Path v n # stimes :: Integral b => b -> Path v n -> Path v n #
Monoid (Path v n)
Instance details Defined in Diagrams.Path Methods mempty :: Path v n # mappend :: Path v n -> Path v n -> Path v n # mconcat :: [Path v n] -> Path v n #
(OrderedField n, Metric v, Serialize (v n), Serialize (V (v n) (N (v n)))) => Serialize (Path v n)
Instance details Defined in Diagrams.Path Methods put :: Putter (Path v n) # get :: Get (Path v n) #
(Metric v, OrderedField n) => Juxtaposable (Path v n)
Instance details Defined in Diagrams.Path Methods juxtapose :: Vn (Path v n) -> Path v n -> Path v n -> Path v n #
(Metric v, OrderedField n) => Enveloped (Path v n)
Instance details Defined in Diagrams.Path Methods getEnvelope :: Path v n -> Envelope (V (Path v n)) (N (Path v n)) #
(HasLinearMap v, Metric v, OrderedField n) => Transformable (Path v n)
Instance details Defined in Diagrams.Path Methods transform :: Transformation (V (Path v n)) (N (Path v n)) -> Path v n -> Path v n #
(Additive v, Num n) => HasOrigin (Path v n)
Instance details Defined in Diagrams.Path Methods moveOriginTo :: Point (V (Path v n)) (N (Path v n)) -> Path v n -> Path v n #
ToPath (Path v n)
Instance details Defined in Diagrams.Path Methods toPath :: Path v n -> Path (V (Path v n)) (N (Path v n)) #
(Metric v, OrderedField n) => TrailLike (Path v n)	Paths are trail-like; a trail can be used to construct a singleton path.
Instance details Defined in Diagrams.Path Methods trailLike :: Located (Trail (V (Path v n)) (N (Path v n))) -> Path v n #
(Metric v, OrderedField n) => Alignable (Path v n)
Instance details Defined in Diagrams.Path Methods alignBy' :: (InSpace v0 n0 (Path v n), Fractional n0, HasOrigin (Path v n)) => (v0 n0 -> Path v n -> Point v0 n0) -> v0 n0 -> n0 -> Path v n -> Path v n # defaultBoundary :: (V (Path v n) ~ v0, N (Path v n) ~ n0) => v0 n0 -> Path v n -> Point v0 n0 # alignBy :: (InSpace v0 n0 (Path v n), Fractional n0, HasOrigin (Path v n)) => v0 n0 -> n0 -> Path v n -> Path v n #
(Metric v, OrderedField n) => Reversing (Path v n)	Same as `reversePath`.
Instance details Defined in Diagrams.Path Methods reversing :: Path v n -> Path v n #
AsEmpty (Path v n)
Instance details Defined in Diagrams.Path Methods _Empty :: Prism' (Path v n) () #
Wrapped (Path v n)
Instance details Defined in Diagrams.Path Associated Types type Unwrapped (Path v n) :: Type # Methods _Wrapped' :: Iso' (Path v n) (Unwrapped (Path v n)) #
(HasLinearMap v, Metric v, OrderedField n) => Renderable (Path v n) NullBackend
Instance details Defined in Diagrams.Path Methods render :: NullBackend -> Path v n -> Render NullBackend (V (Path v n)) (N (Path v n)) #
SVGFloat n => Renderable (Path V2 n) SVG
Instance details Defined in Diagrams.Backend.SVG Methods render :: SVG -> Path V2 n -> Render SVG (V (Path V2 n)) (N (Path V2 n)) #
(Metric v, Metric u, OrderedField n, r ~ Path u n) => Deformable (Path v n) r
Instance details Defined in Diagrams.Deform Methods deform' :: N (Path v n) -> Deformation (V (Path v n)) (V r) (N (Path v n)) -> Path v n -> r # deform :: Deformation (V (Path v n)) (V r) (N (Path v n)) -> Path v n -> r #
Rewrapped (Path v n) (Path v' n')
Instance details Defined in Diagrams.Path
Snoc (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))
Instance details Defined in Diagrams.Path Methods _Snoc :: Prism (Path v n) (Path v' n') (Path v n, Located (Trail v n)) (Path v' n', Located (Trail v' n')) #
Cons (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))
Instance details Defined in Diagrams.Path Methods _Cons :: Prism (Path v n) (Path v' n') (Located (Trail v n), Path v n) (Located (Trail v' n'), Path v' n') #
Each (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))
Instance details Defined in Diagrams.Path Methods each :: Traversal (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n')) #
type Rep (Path v n)
Instance details Defined in Diagrams.Path type Rep (Path v n) = D1 (MetaData "Path" "Diagrams.Path" "diagrams-lib-1.4.2.3-4IkVVBmK9qBElHMtgqeLQ1" True) (C1 (MetaCons "Path" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [Located (Trail v n)])))
type V (Path v n)
Instance details Defined in Diagrams.Path type V (Path v n) = v
type N (Path v n)
Instance details Defined in Diagrams.Path type N (Path v n) = n
type Unwrapped (Path v n)
Instance details Defined in Diagrams.Path type Unwrapped (Path v n) = [Located (Trail v n)]

class ToPath t where #

Type class for things that can be converted to a Path.

Note that this class is very different from TrailLike. TrailLike is usually the result of a library function to give you a convenient, polymorphic result (Path, Diagram etc.).

Methods

toPath :: t -> Path (V t) (N t) #

toPath takes something that can be converted to Path and returns the Path.

Instances

ToPath a => ToPath [a]
Instance details Defined in Diagrams.Path Methods toPath :: [a] -> Path (V [a]) (N [a]) #
ToPath (Located [Segment Closed v n])
Instance details Defined in Diagrams.Path Methods toPath :: Located [Segment Closed v n] -> Path (V (Located [Segment Closed v n])) (N (Located [Segment Closed v n])) #
ToPath (Located (Trail' l v n))
Instance details Defined in Diagrams.Path Methods toPath :: Located (Trail' l v n) -> Path (V (Located (Trail' l v n))) (N (Located (Trail' l v n))) #
ToPath (Located (Trail v n))
Instance details Defined in Diagrams.Path Methods toPath :: Located (Trail v n) -> Path (V (Located (Trail v n))) (N (Located (Trail v n))) #
ToPath (Located (Segment Closed v n))
Instance details Defined in Diagrams.Path Methods toPath :: Located (Segment Closed v n) -> Path (V (Located (Segment Closed v n))) (N (Located (Segment Closed v n))) #
ToPath (Path v n)
Instance details Defined in Diagrams.Path Methods toPath :: Path v n -> Path (V (Path v n)) (N (Path v n)) #
ToPath (Trail v n)
Instance details Defined in Diagrams.Path Methods toPath :: Trail v n -> Path (V (Trail v n)) (N (Trail v n)) #
ToPath (FixedSegment v n)
Instance details Defined in Diagrams.Path Methods toPath :: FixedSegment v n -> Path (V (FixedSegment v n)) (N (FixedSegment v n)) #
ToPath (Trail' l v n)
Instance details Defined in Diagrams.Path Methods toPath :: Trail' l v n -> Path (V (Trail' l v n)) (N (Trail' l v n)) #

boundaryFromMay :: (Metric v, OrderedField n, Semigroup m) => Subdiagram b v n m -> v n -> Maybe (Point v n) #

Compute the furthest point on the boundary of a subdiagram, beginning from the location (local origin) of the subdiagram and moving in the direction of the given vector, or Nothing if there is no such point.

boundaryFrom :: (OrderedField n, Metric v, Semigroup m) => Subdiagram b v n m -> v n -> Point v n #

Compute the furthest point on the boundary of a subdiagram, beginning from the location (local origin) of the subdiagram and moving in the direction of the given vector. If there is no such point, the origin is returned; see also boundaryFromMay.

composeAligned #

Arguments

:: (Monoid' m, Floating n, Ord n, Metric v)
=> (QDiagram b v n m -> QDiagram b v n m)	Alignment function
-> ([QDiagram b v n m] -> QDiagram b v n m)	Composition function
-> [QDiagram b v n m]
-> QDiagram b v n m

Compose a list of diagrams using the given composition function, first aligning them all according to the given alignment, but retain the local origin of the first diagram, as it would be if the composition function were applied directly. That is, composeAligned algn comp is equivalent to translate v . comp . map algn for some appropriate translation vector v.

Unfortunately, this only works for diagrams (and not, say, paths) because there is no most general type for alignment functions, and no generic way to find out what an alignment function does to the origin of things. (However, it should be possible to make a version of this function that works specifically on paths, if such a thing were deemed useful.)

alignedEx1 = (hsep 2 # composeAligned alignT) (map circle [1,3,5,2])
           # showOrigin
           # frame 0.5

alignedEx2 = (mconcat # composeAligned alignTL) [circle 1, square 1, triangle 1, pentagon 1]
           # showOrigin
           # frame 0.1

cat' :: (InSpace v n a, Metric v, Floating n, Juxtaposable a, Monoid' a, HasOrigin a) => v n -> CatOpts n -> [a] -> a #

Like cat, but taking an extra CatOpts arguments allowing the user to specify

The spacing method: catenation (uniform spacing between envelopes) or distribution (uniform spacing between local origins). The default is catenation.
The amount of separation between successive diagram envelopes/origins (depending on the spacing method). The default is 0.

CatOpts is an instance of Default, so with may be used for the second argument, as in cat' (1,2) (with & sep .~ 2).

Note that cat' v (with & catMethod .~ Distrib) === mconcat (distributing with a separation of 0 is the same as superimposing).

cat :: (InSpace v n a, Metric v, Floating n, Juxtaposable a, Monoid' a, HasOrigin a) => v n -> [a] -> a #

cat v positions a list of objects so that their local origins lie along a line in the direction of v. Successive objects will have their envelopes just touching. The local origin of the result will be the same as the local origin of the first object.

See also cat', which takes an extra options record allowing certain aspects of the operation to be tweaked.

sep :: Lens' (CatOpts n) n #

How much separation should be used between successive diagrams (default: 0)? When catMethod = Cat, this is the distance between envelopes; when catMethod = Distrib, this is the distance between origins.

catMethod :: Lens' (CatOpts n) CatMethod #

Which CatMethod should be used: normal catenation (default), or distribution?

atPoints :: (InSpace v n a, HasOrigin a, Monoid' a) => [Point v n] -> [a] -> a #

Curried version of position, takes a list of points and a list of objects.

position :: (InSpace v n a, HasOrigin a, Monoid' a) => [(Point v n, a)] -> a #

Position things absolutely: combine a list of objects (e.g. diagrams or paths) by assigning them absolute positions in the vector space of the combined object.

positionEx = position (zip (map mkPoint [-3, -2.8 .. 3]) (repeat spot))
  where spot      = circle 0.2 # fc black
        mkPoint :: Double -> P2 Double
        mkPoint x = p2 (x,x*x)

appends :: (Juxtaposable a, Monoid' a) => a -> [(Vn a, a)] -> a #

appends x ys appends each of the objects in ys to the object x in the corresponding direction. Note that each object in ys is positioned beside x without reference to the other objects in ys, so this is not the same as iterating beside.

appendsEx = appends c (zip (iterateN 6 (rotateBy (1/6)) unitX) (repeat c))
            # centerXY # pad 1.1
  where c = circle 1

atDirection :: (InSpace v n a, Metric v, Floating n, Juxtaposable a, Semigroup a) => Direction v n -> a -> a -> a #

Place two diagrams (or other juxtaposable objects) adjacent to one another, with the second diagram placed in the direction d from the first. The local origin of the resulting combined diagram is the same as the local origin of the first. See the documentation of beside for more information.

beside :: (Juxtaposable a, Semigroup a) => Vn a -> a -> a -> a #

Place two monoidal objects (i.e. diagrams, paths, animations...) next to each other along the given vector. In particular, place the second object so that the vector points from the local origin of the first object to the local origin of the second object, at a distance so that their envelopes are just tangent. The local origin of the new, combined object is the local origin of the first object (unless the first object is the identity element, in which case the second object is returned unchanged).

besideEx = beside (r2 (20,30))
                  (circle 1 # fc orange)
                  (circle 1.5 # fc purple)
           # showOrigin
           # centerXY # pad 1.1

Note that beside v is associative, so objects under beside v form a semigroup for any given vector v. In fact, they also form a monoid: mempty is clearly a right identity (beside v d1 mempty === d1), and there should also be a special case to make it a left identity, as described above.

In older versions of diagrams, beside put the local origin of the result at the point of tangency between the two inputs. That semantics can easily be recovered by performing an alignment on the first input before combining. That is, if beside' denotes the old semantics,

beside' v x1 x2 = beside v (x1 # align v) x2

To get something like beside v x1 x2 whose local origin is identified with that of x2 instead of x1, use beside (negateV v) x2 x1.

beneath :: (Metric v, OrderedField n, Monoid' m) => QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m infixl 6 #

beneath is just a convenient synonym for flip atop; that is, d1 `beneath` d2 is the diagram with d2 superimposed on top of d1.

intrudeEnvelope :: (Metric v, OrderedField n, Monoid' m) => v n -> QDiagram b v n m -> QDiagram b v n m #

intrudeEnvelope v d asymmetrically "intrudes" the envelope of a diagram away from the given direction. All parts of the envelope within 90 degrees of this direction are modified, offset inwards by the magnitude of the vector.

Note that this could create strange inverted envelopes, where diameter v d < 0 .

extrudeEnvelope :: (Metric v, OrderedField n, Monoid' m) => v n -> QDiagram b v n m -> QDiagram b v n m #

extrudeEnvelope v d asymmetrically "extrudes" the envelope of a diagram in the given direction. All parts of the envelope within 90 degrees of this direction are modified, offset outwards by the magnitude of the vector.

This works by offsetting the envelope distance proportionally to the cosine of the difference in angle, and leaving it unchanged when this factor is negative.

strut :: (Metric v, OrderedField n) => v n -> QDiagram b v n m #

strut v is a diagram which produces no output, but with respect to alignment and envelope acts like a 1-dimensional segment oriented along the vector v, with local origin at its center. (Note, however, that it has an empty trace; for 2D struts with a nonempty trace see strutR2 from Diagrams.TwoD.Combinators.) Useful for manually creating separation between two diagrams.

strutEx = (circle 1 ||| strut unitX ||| circle 1) # centerXY # pad 1.1

frame :: (Metric v, OrderedField n, Monoid' m) => n -> QDiagram b v n m -> QDiagram b v n m #

frame s increases the envelope of a diagram by and absolute amount s, s is in the local units of the diagram. This function is similar to pad, only it takes an absolute quantity and pre-centering should not be necessary.

pad :: (Metric v, OrderedField n, Monoid' m) => n -> QDiagram b v n m -> QDiagram b v n m #

pad s "pads" a diagram, expanding its envelope by a factor of s (factors between 0 and 1 can be used to shrink the envelope). Note that the envelope will expand with respect to the local origin, so if the origin is not centered the padding may appear "uneven". If this is not desired, the origin can be centered (using, e.g., centerXY for 2D diagrams) before applying pad.

phantom :: (InSpace v n a, Monoid' m, Enveloped a, Traced a) => a -> QDiagram b v n m #

phantom x produces a "phantom" diagram, which has the same envelope and trace as x but produces no output.

withTrace :: (InSpace v n a, Metric v, OrderedField n, Monoid' m, Traced a) => a -> QDiagram b v n m -> QDiagram b v n m #

Use the trace from some object as the trace for a diagram, in place of the diagram's default trace.

withEnvelope :: (InSpace v n a, Monoid' m, Enveloped a) => a -> QDiagram b v n m -> QDiagram b v n m #

Use the envelope from some object as the envelope for a diagram, in place of the diagram's default envelope.

sqNewEnv =
    circle 1 # fc green
    |||
    (    c # dashingG [0.1,0.1] 0 # lc white
      <> square 2 # withEnvelope (c :: D V2 Double) # fc blue
    )
c = circle 0.8
withEnvelopeEx = sqNewEnv # centerXY # pad 1.5

data CatMethod #

Methods for concatenating diagrams.

Constructors

Cat	Normal catenation: simply put diagrams next to one another (possibly with a certain distance in between each). The distance between successive diagram envelopes will be consistent; the distance between origins may vary if the diagrams are of different sizes.
Distrib	Distribution: place the local origins of diagrams at regular intervals. With this method, the distance between successive origins will be consistent but the distance between envelopes may not be. Indeed, depending on the amount of separation, diagrams may overlap.

data CatOpts n #

Options for cat'.

Instances

Num n => Default (CatOpts n)
Instance details Defined in Diagrams.Combinators Methods def :: CatOpts n #

ellipseXY :: (TrailLike t, V t ~ V2, N t ~ n, Transformable t) => n -> n -> t #

ellipseXY x y creates an axis-aligned ellipse, centered at the origin, with radius x along the x-axis and radius y along the y-axis.

ellipse :: (TrailLike t, V t ~ V2, N t ~ n, Transformable t) => n -> t #

ellipse e constructs an ellipse with eccentricity e by scaling the unit circle in the X direction. The eccentricity must be within the interval [0,1).

circle :: (TrailLike t, V t ~ V2, N t ~ n, Transformable t) => n -> t #

A circle of the given radius, centered at the origin. As a path, it begins at (r,0).

unitCircle :: (TrailLike t, V t ~ V2, N t ~ n) => t #

A circle of radius 1, with center at the origin.

annularWedge :: (TrailLike t, V t ~ V2, N t ~ n, RealFloat n) => n -> n -> Direction V2 n -> Angle n -> t #

Create an annular wedge of the given radii, beginning at the first direction and extending through the given sweep angle. The radius of the outer circle is given first.

annularWedgeEx = hsep 0.50
  [ annularWedge 1 0.5 xDir (1/4 @@ turn)
  , annularWedge 1 0.3 (rotate (7/30 @@ turn) xDir) (4/30 @@ turn)
  , annularWedge 1 0.7 (rotate (1/8 @@ turn) xDir) (3/4 @@ turn)
  ]
  # fc blue
  # centerXY # pad 1.1

arcBetween :: (TrailLike t, V t ~ V2, N t ~ n, RealFloat n) => Point V2 n -> Point V2 n -> n -> t #

arcBetween p q height creates an arc beginning at p and ending at q, with its midpoint at a distance of abs height away from the straight line from p to q. A positive value of height results in an arc to the left of the line from p to q; a negative value yields one to the right.

arcBetweenEx = mconcat
  [ arcBetween origin (p2 (2,1)) ht | ht <- [-0.2, -0.1 .. 0.2] ]
  # centerXY # pad 1.1

wedge :: (InSpace V2 n t, OrderedField n, TrailLike t) => n -> Direction V2 n -> Angle n -> t #

Create a circular wedge of the given radius, beginning at the given direction and extending through the given angle.

wedgeEx = hcat' (with & sep .~ 0.5)
  [ wedge 1 xDir (1/4 @@ turn)
  , wedge 1 (rotate (7/30 @@ turn) xDir) (4/30 @@ turn)
  , wedge 1 (rotate (1/8 @@ turn) xDir) (3/4 @@ turn)
  ]
  # fc blue
  # centerXY # pad 1.1

arcCW :: (InSpace V2 n t, RealFloat n, TrailLike t) => Direction V2 n -> Direction V2 n -> t #

Like arcAngleCCW but clockwise.

arcCCW :: (InSpace V2 n t, RealFloat n, TrailLike t) => Direction V2 n -> Direction V2 n -> t #

Given a start direction s and end direction e, arcCCW s e is the path of a radius one arc counterclockwise between the two directions. The origin of the arc is its center.

arc' :: (InSpace V2 n t, OrderedField n, TrailLike t) => n -> Direction V2 n -> Angle n -> t #

Given a radus r, a start direction d and an angle s, arc' r d s is the path of a radius (abs r) arc starting at d and sweeping out the angle s counterclockwise (for positive s). The origin of the arc is its center.

arc'Ex = mconcat [ arc' r xDir (1/4 @@ turn) | r <- [0.5,-1,1.5] ]
       # centerXY # pad 1.1

arc :: (InSpace V2 n t, OrderedField n, TrailLike t) => Direction V2 n -> Angle n -> t #

Given a start direction d and a sweep angle s, arc d s is the path of a radius one arc starting at d and sweeping out the angle s counterclockwise (for positive s). The resulting Trail is allowed to wrap around and overlap itself.

explodeTrail :: (V t ~ v, N t ~ n, TrailLike t) => Located (Trail v n) -> [t] #

Given a concretely located trail, "explode" it by turning each segment into its own separate trail. Useful for (say) applying a different style to each segment.

explodeTrailEx
  = pentagon 1
  # explodeTrail  -- generate a list of diagrams
  # zipWith lc [orange, green, yellow, red, blue]
  # mconcat # centerXY # pad 1.1

(~~) :: (V t ~ v, N t ~ n, TrailLike t) => Point v n -> Point v n -> t #

Create a linear trail between two given points.

twiddleEx
  = mconcat ((~~) <$> hexagon 1 <*> hexagon 1)
  # centerXY # pad 1.1

fromVertices :: TrailLike t => [Point (V t) (N t)] -> t #

Construct a trail-like thing connecting the given vertices with linear segments, with the first vertex as the location. If no vertices are given, the empty trail is used with the origin as the location.

import Data.List (transpose)

fromVerticesEx =
  ( [ pentagon 1
    , pentagon 1.3 # rotateBy (1/15)
    , pentagon 1.5 # rotateBy (2/15)
    ]
    # transpose
    # concat
  )
  # fromVertices
  # closeTrail # strokeTrail
  # centerXY # pad 1.1

fromLocOffsets :: (V t ~ v, N t ~ n, V (v n) ~ v, N (v n) ~ n, TrailLike t) => Located [v n] -> t #

Construct a trail-like thing of linear segments from a located list of offsets.

fromOffsets :: TrailLike t => [Vn t] -> t #

Construct a trail-like thing of linear segments from a list of offsets, with the origin as the location.

fromOffsetsEx = fromOffsets
  [ unitX
  , unitX # rotateBy (1/6)
  , unitX # rotateBy (-1/6)
  , unitX
  ]
  # centerXY # pad 1.1

fromLocSegments :: TrailLike t => Located [Segment Closed (V t) (N t)] -> t #

Construct a trail-like thing from a located list of segments.

fromSegments :: TrailLike t => [Segment Closed (V t) (N t)] -> t #

Construct a trail-like thing from a list of segments, with the origin as the location.

fromSegmentsEx = fromSegments
  [ straight (r2 (1,1))
  , bézier3  (r2 (1,1)) unitX unit_Y
  , straight unit_X
  ]
  # centerXY # pad 1.1

class (Metric (V t), OrderedField (N t)) => TrailLike t where #

A type class for trail-like things, i.e. things which can be constructed from a concretely located Trail. Instances include lines, loops, trails, paths, lists of vertices, two-dimensional Diagrams, and Located variants of all the above.

Usually, type variables with TrailLike constraints are used as the output types of functions, like

  foo :: (TrailLike t) => ... -> t

Functions with such a type can be used to construct trails, paths, diagrams, lists of points, and so on, depending on the context.

To write a function with a signature like the above, you can of course call trailLike directly; more typically, one would use one of the provided functions like fromOffsets, fromVertices, fromSegments, or ~~.

Methods

trailLike #

Arguments

:: Located (Trail (V t) (N t))	The concretely located trail. Note that some trail-like things (e.g. `Trail`s) may ignore the location.
-> t

Instances

(Metric v, OrderedField n) => TrailLike [Point v n]	A list of points is trail-like; this instance simply computes the vertices of the trail, using `trailPoints`.
Instance details Defined in Diagrams.TrailLike Methods trailLike :: Located (Trail (V [Point v n]) (N [Point v n])) -> [Point v n] #
TrailLike t => TrailLike (TransInv t)	Translationally invariant things are trail-like as long as the underlying type is.
Instance details Defined in Diagrams.TrailLike Methods trailLike :: Located (Trail (V (TransInv t)) (N (TransInv t))) -> TransInv t #
TrailLike t => TrailLike (Located t)	`Located` things are trail-like as long as the underlying type is. The location is taken to be the location of the input located trail.
Instance details Defined in Diagrams.TrailLike Methods trailLike :: Located (Trail (V (Located t)) (N (Located t))) -> Located t #
(Metric v, OrderedField n) => TrailLike (Path v n)	Paths are trail-like; a trail can be used to construct a singleton path.
Instance details Defined in Diagrams.Path Methods trailLike :: Located (Trail (V (Path v n)) (N (Path v n))) -> Path v n #
(Metric v, OrderedField n) => TrailLike (Trail v n)	`Trail`s are trail-like; the location is simply ignored.
Instance details Defined in Diagrams.TrailLike Methods trailLike :: Located (Trail (V (Trail v n)) (N (Trail v n))) -> Trail v n #
(Metric v, OrderedField n) => TrailLike (Trail' Line v n)	Lines are trail-like. If given a `Trail` which contains a loop, the loop will be cut with `cutLoop`. The location is ignored.
Instance details Defined in Diagrams.TrailLike Methods trailLike :: Located (Trail (V (Trail' Line v n)) (N (Trail' Line v n))) -> Trail' Line v n #
(Metric v, OrderedField n) => TrailLike (Trail' Loop v n)	Loops are trail-like. If given a `Trail` containing a line, the line will be turned into a loop using `glueLine`. The location is ignored.
Instance details Defined in Diagrams.TrailLike Methods trailLike :: Located (Trail (V (Trail' Loop v n)) (N (Trail' Loop v n))) -> Trail' Loop v n #

reverseLocLoop :: (Metric v, OrderedField n) => Located (Trail' Loop v n) -> Located (Trail' Loop v n) #

Reverse a concretely located loop. See reverseLocTrail. Note that this is guaranteed to preserve the location.

reverseLoop :: (Metric v, OrderedField n) => Trail' Loop v n -> Trail' Loop v n #

Reverse a loop. See reverseTrail.

reverseLocLine :: (Metric v, OrderedField n) => Located (Trail' Line v n) -> Located (Trail' Line v n) #

Reverse a concretely located line. See reverseLocTrail.

reverseLine :: (Metric v, OrderedField n) => Trail' Line v n -> Trail' Line v n #

Reverse a line. See reverseTrail.

reverseLocTrail :: (Metric v, OrderedField n) => Located (Trail v n) -> Located (Trail v n) #

Reverse a concretely located trail. The endpoint of the original trail becomes the starting point of the reversed trail, so the original and reversed trails comprise exactly the same set of points. reverseLocTrail is an involution, i.e.

  reverseLocTrail . reverseLocTrail === id

reverseTrail :: (Metric v, OrderedField n) => Trail v n -> Trail v n #

Reverse a trail. Semantically, if a trail given by a function t from [0,1] to vectors, then the reverse of t is given by t'(s) = t(1-s). reverseTrail is an involution, that is,

  reverseTrail . reverseTrail === id

trailLocSegments :: (Metric v, OrderedField n) => Located (Trail v n) -> [Located (Segment Closed v n)] #

Convert a concretely located trail into a list of located segments.

unfixTrail :: (Metric v, Ord n, Floating n) => [FixedSegment v n] -> Located (Trail v n) #

Convert a list of fixed segments into a located trail. Note that this may lose information: it throws away the locations of all but the first FixedSegment. This does not matter precisely when each FixedSegment begins where the previous one ends.

This is almost left inverse to fixTrail, that is, unfixTrail . fixTrail == id, except for the fact that unfixTrail will never yield a Loop. In the case of a loop, we instead have glueTrail . unfixTrail . fixTrail == id. On the other hand, it is not the case that fixTrail . unfixTrail == id since unfixTrail may lose information.

fixTrail :: (Metric v, OrderedField n) => Located (Trail v n) -> [FixedSegment v n] #

Convert a concretely located trail into a list of fixed segments. unfixTrail is almost its left inverse.

loopVertices :: (Metric v, OrderedField n) => Located (Trail' Loop v n) -> [Point v n] #

Same as loopVertices', with a default tolerance.

loopVertices' :: (Metric v, OrderedField n) => n -> Located (Trail' Loop v n) -> [Point v n] #

Extract the vertices of a concretely located loop. Note that the initial vertex is not repeated at the end. See trailVertices for more information.

lineVertices :: (Metric v, OrderedField n) => Located (Trail' Line v n) -> [Point v n] #

Like lineVertices', with a default tolerance.

lineVertices' :: (Metric v, OrderedField n) => n -> Located (Trail' Line v n) -> [Point v n] #

Extract the vertices of a concretely located line. See trailVertices for more information.

trailVertices :: (Metric v, OrderedField n) => Located (Trail v n) -> [Point v n] #

Like trailVertices', with a default tolerance.

trailVertices' :: (Metric v, OrderedField n) => n -> Located (Trail v n) -> [Point v n] #

Extract the vertices of a concretely located trail. Here a vertex is defined as a non-differentiable point on the trail, i.e. a sharp corner. (Vertices are thus a subset of the places where segments join; if you want all joins between segments, see trailPoints.) The tolerance determines how close the tangents of two segments must be at their endpoints to consider the transition point to be differentiable.

Note that for loops, the starting vertex will not be repeated at the end. If you want this behavior, you can use cutTrail to make the loop into a line first, which happens to repeat the same vertex at the start and end, e.g. with trailVertices . mapLoc cutTrail.

It does not make sense to ask for the vertices of a Trail by itself; if you want the vertices of a trail with the first vertex at, say, the origin, you can use trailVertices . (`at` origin).

lineOffset :: (Metric v, OrderedField n) => Trail' Line v n -> v n #

Compute the offset from the start of a line to the end. (Note, there is no corresponding loopOffset function because by definition it would be constantly zero.)

loopOffsets :: (Metric v, OrderedField n) => Trail' Loop v n -> [v n] #

Extract the offsets of the segments of a loop.

lineOffsets :: Trail' Line v n -> [v n] #

Extract the offsets of the segments of a line.

trailOffset :: (Metric v, OrderedField n) => Trail v n -> v n #

Compute the offset from the start of a trail to the end. Satisfies

  trailOffset === sumV . trailOffsets

but is more efficient.

trailOffsetEx = (strokeLine almostClosed <> showOffset) # centerXY # pad 1.1
  where showOffset = fromOffsets [trailOffset (wrapLine almostClosed)]
                   # strokeP # lc red

trailOffsets :: (Metric v, OrderedField n) => Trail v n -> [v n] #

Extract the offsets of the segments of a trail.

trailSegments :: (Metric v, OrderedField n) => Trail v n -> [Segment Closed v n] #

Extract the segments of a trail. If the trail is a loop it will first have cutLoop applied.

loopSegments :: Trail' Loop v n -> ([Segment Closed v n], Segment Open v n) #

Extract the segments comprising a loop: a list of closed segments, and one final open segment.

onLineSegments :: (Metric v, OrderedField n) => ([Segment Closed v n] -> [Segment Closed v n]) -> Trail' Line v n -> Trail' Line v n #

Modify a line by applying a function to its list of segments.

lineSegments :: Trail' Line v n -> [Segment Closed v n] #

Extract the segments comprising a line.

isLoop :: Trail v n -> Bool #

Determine whether a trail is a loop.

isLine :: Trail v n -> Bool #

Determine whether a trail is a line.

isTrailEmpty :: (Metric v, OrderedField n) => Trail v n -> Bool #

Test whether a trail is empty. Note that loops are never empty.

isLineEmpty :: (Metric v, OrderedField n) => Trail' Line v n -> Bool #

Test whether a line is empty.

cutTrail :: (Metric v, OrderedField n) => Trail v n -> Trail v n #

cutTrail is a variant of cutLoop for Trail; it is the is the identity on lines and performs cutLoop on loops.

cutLoop :: (Metric v, OrderedField n) => Trail' Loop v n -> Trail' Line v n #

Turn a loop into a line by "cutting" it at the common start/end point, resulting in a line which just happens to start and end at the same place.

cutLoop is right inverse to glueLine, that is,

  glueLine . cutLoop === id

closeTrail :: Trail v n -> Trail v n #

closeTrail is a variant of closeLine for Trail, which performs closeLine on lines and is the identity on loops.

closeLine :: Trail' Line v n -> Trail' Loop v n #

Make a line into a loop by adding a new linear segment from the line's end to its start.

closeLine does not have any particularly nice theoretical properties, but can be useful e.g. when you want to make a closed polygon out of a list of points where the initial point is not repeated at the end. To use glueLine, one would first have to duplicate the initial vertex, like

glueLine . lineFromVertices $ ps ++ [head ps]

Using closeLine, however, one can simply

closeLine . lineFromVertices $ ps

closeLineEx = pad 1.1 . centerXY . hcat' (with & sep .~ 1)
  $ [almostClosed # strokeLine, almostClosed # closeLine # strokeLoop]

glueTrail :: (Metric v, OrderedField n) => Trail v n -> Trail v n #

glueTrail is a variant of glueLine which works on Trails. It performs glueLine on lines and is the identity on loops.

glueLine :: (Metric v, OrderedField n) => Trail' Line v n -> Trail' Loop v n #

Make a line into a loop by "gluing" the endpoint to the starting point. In particular, the offset of the final segment is modified so that it ends at the starting point of the entire trail. Typically, you would first construct a line which you know happens to end where it starts, and then call glueLine to turn it into a loop.

glueLineEx = pad 1.1 . hsep 1
  $ [almostClosed # strokeLine, almostClosed # glueLine # strokeLoop]

almostClosed :: Trail' Line V2 Double
almostClosed = fromOffsets $ map r2 [(2, -1), (-3, -0.5), (-2, 1), (1, 0.5)]

glueLine is left inverse to cutLoop, that is,

  glueLine . cutLoop === id

trailFromVertices :: (Metric v, OrderedField n) => [Point v n] -> Trail v n #

trailFromVertices === wrapTrail . lineFromVertices, for conveniently constructing a Trail instead of a Trail' Line.

lineFromVertices :: (Metric v, OrderedField n) => [Point v n] -> Trail' Line v n #

Construct a line containing only linear segments from a list of vertices. Note that only the relative offsets between the vertices matters; the information about their absolute position will be discarded. That is, for all vectors v,

lineFromVertices === lineFromVertices . translate v

If you want to retain the position information, you should instead use the more general fromVertices function to construct, say, a Located (Trail' Line v) or a Located (Trail v).

import Diagrams.Coordinates
lineFromVerticesEx = pad 1.1 . centerXY . strokeLine
  $ lineFromVertices [origin, 0 ^& 1, 1 ^& 2, 5 ^& 1]

trailFromOffsets :: (Metric v, OrderedField n) => [v n] -> Trail v n #

trailFromOffsets === wrapTrail . lineFromOffsets, for conveniently constructing a Trail instead of a Trail' Line.

lineFromOffsets :: (Metric v, OrderedField n) => [v n] -> Trail' Line v n #

Construct a line containing only linear segments from a list of vectors, where each vector represents the offset from one vertex to the next. See also fromOffsets.

import Diagrams.Coordinates
lineFromOffsetsEx = strokeLine $ lineFromOffsets [ 2 ^& 1, 2 ^& (-1), 2 ^& 0.5 ]

trailFromSegments :: (Metric v, OrderedField n) => [Segment Closed v n] -> Trail v n #

trailFromSegments === wrapTrail . lineFromSegments, for conveniently constructing a Trail instead of a Trail'.

loopFromSegments :: (Metric v, OrderedField n) => [Segment Closed v n] -> Segment Open v n -> Trail' Loop v n #

Construct a loop from a list of closed segments and an open segment that completes the loop.

lineFromSegments :: (Metric v, OrderedField n) => [Segment Closed v n] -> Trail' Line v n #

Construct a line from a list of closed segments.

emptyTrail :: (Metric v, OrderedField n) => Trail v n #

A wrapped variant of emptyLine.

emptyLine :: (Metric v, OrderedField n) => Trail' Line v n #

The empty line, which is the identity for concatenation of lines.

wrapLoop :: Trail' Loop v n -> Trail v n #

Convert a loop into a Trail. This is the same as wrapTrail, but with a more specific type, which can occasionally be convenient for fixing the type of a polymorphic expression.

wrapLine :: Trail' Line v n -> Trail v n #

Convert a line into a Trail. This is the same as wrapTrail, but with a more specific type, which can occasionally be convenient for fixing the type of a polymorphic expression.

wrapTrail :: Trail' l v n -> Trail v n #

Convert a Trail' into a Trail, hiding the type-level distinction between lines and loops.

onLine :: (Metric v, OrderedField n) => (Trail' Line v n -> Trail' Line v n) -> Trail v n -> Trail v n #

Modify a Trail by specifying a transformation on lines. If the trail is a line, the transformation will be applied directly. If it is a loop, it will first be cut using cutLoop, the transformation applied, and then glued back into a loop with glueLine. That is,

  onLine f === onTrail f (glueLine . f . cutLoop)

Note that there is no corresponding onLoop function, because there is no nice way in general to convert a line into a loop, operate on it, and then convert back.

withLine :: (Metric v, OrderedField n) => (Trail' Line v n -> r) -> Trail v n -> r #

An eliminator for Trail based on eliminating lines: if the trail is a line, the given function is applied; if it is a loop, it is first converted to a line with cutLoop. That is,

withLine f === withTrail f (f . cutLoop)

onTrail :: (Trail' Line v n -> Trail' l1 v n) -> (Trail' Loop v n -> Trail' l2 v n) -> Trail v n -> Trail v n #

Modify a Trail, specifying two separate transformations for the cases of a line or a loop.

withTrail :: (Trail' Line v n -> r) -> (Trail' Loop v n -> r) -> Trail v n -> r #

A generic eliminator for Trail, taking functions specifying what to do in the case of a line or a loop.

_LocLoop :: Prism' (Located (Trail v n)) (Located (Trail' Loop v n)) #

Prism onto a Located Loop.

_LocLine :: Prism' (Located (Trail v n)) (Located (Trail' Line v n)) #

Prism onto a Located Line.

_Loop :: Prism' (Trail v n) (Trail' Loop v n) #

Prism onto a Loop.

_Line :: Prism' (Trail v n) (Trail' Line v n) #

Prism onto a Line.

getSegment :: t -> GetSegment t #

Create a GetSegment wrapper around a trail, after which you can call atParam, atStart, or atEnd to extract a segment.

withTrail' :: (Trail' Line v n -> r) -> (Trail' Loop v n -> r) -> Trail' l v n -> r #

A generic eliminator for Trail', taking functions specifying what to do in the case of a line or a loop.

offset :: (OrderedField n, Metric v, Measured (SegMeasure v n) t) => t -> v n #

Compute the total offset of anything measured by SegMeasure.

numSegs :: (Num c, Measured (SegMeasure v n) a) => a -> c #

Compute the number of segments of anything measured by SegMeasure (e.g. SegMeasure itself, Segment, SegTree, Trails...)

trailMeasure :: (SegMeasure v n :>: m, Measured (SegMeasure v n) t) => a -> (m -> a) -> t -> a #

Given a default result (to be used in the case of an empty trail), and a function to map a single measure to a result, extract the given measure for a trail and use it to compute a result. Put another way, lift a function on a single measure (along with a default value) to a function on an entire trail.

newtype SegTree (v :: Type -> Type) n #

A SegTree represents a sequence of closed segments, stored in a fingertree so we can easily recover various monoidal measures of the segments (number of segments, arc length, envelope...) and also easily slice and dice them according to the measures (e.g., split off the smallest number of segments from the beginning which have a combined arc length of at least 5).

Constructors

SegTree (FingerTree (SegMeasure v n) (Segment Closed v n))

Instances

Eq (v n) => Eq (SegTree v n)
Instance details Defined in Diagrams.Trail Methods (==) :: SegTree v n -> SegTree v n -> Bool # (/=) :: SegTree v n -> SegTree v n -> Bool #
Ord (v n) => Ord (SegTree v n)
Instance details Defined in Diagrams.Trail Methods compare :: SegTree v n -> SegTree v n -> Ordering # (<) :: SegTree v n -> SegTree v n -> Bool # (<=) :: SegTree v n -> SegTree v n -> Bool # (>) :: SegTree v n -> SegTree v n -> Bool # (>=) :: SegTree v n -> SegTree v n -> Bool # max :: SegTree v n -> SegTree v n -> SegTree v n # min :: SegTree v n -> SegTree v n -> SegTree v n #
Show (v n) => Show (SegTree v n)
Instance details Defined in Diagrams.Trail Methods showsPrec :: Int -> SegTree v n -> ShowS # show :: SegTree v n -> String # showList :: [SegTree v n] -> ShowS #
(Ord n, Floating n, Metric v) => Semigroup (SegTree v n)
Instance details Defined in Diagrams.Trail Methods (<>) :: SegTree v n -> SegTree v n -> SegTree v n # sconcat :: NonEmpty (SegTree v n) -> SegTree v n # stimes :: Integral b => b -> SegTree v n -> SegTree v n #
(Floating n, Ord n, Metric v) => Monoid (SegTree v n)
Instance details Defined in Diagrams.Trail Methods mempty :: SegTree v n # mappend :: SegTree v n -> SegTree v n -> SegTree v n # mconcat :: [SegTree v n] -> SegTree v n #
(OrderedField n, Metric v, Serialize (v n)) => Serialize (SegTree v n)
Instance details Defined in Diagrams.Trail Methods put :: Putter (SegTree v n) # get :: Get (SegTree v n) #
(Floating n, Ord n, Metric v) => Transformable (SegTree v n)
Instance details Defined in Diagrams.Trail Methods transform :: Transformation (V (SegTree v n)) (N (SegTree v n)) -> SegTree v n -> SegTree v n #
(Metric v, OrderedField n, Real n) => Parametric (SegTree v n)
Instance details Defined in Diagrams.Trail Methods atParam :: SegTree v n -> N (SegTree v n) -> Codomain (SegTree v n) (N (SegTree v n)) #
Num n => DomainBounds (SegTree v n)
Instance details Defined in Diagrams.Trail Methods domainLower :: SegTree v n -> N (SegTree v n) # domainUpper :: SegTree v n -> N (SegTree v n) #
(Metric v, OrderedField n, Real n) => EndValues (SegTree v n)
Instance details Defined in Diagrams.Trail Methods atStart :: SegTree v n -> Codomain (SegTree v n) (N (SegTree v n)) # atEnd :: SegTree v n -> Codomain (SegTree v n) (N (SegTree v n)) #
(Metric v, OrderedField n, Real n) => Sectionable (SegTree v n)
Instance details Defined in Diagrams.Trail Methods splitAtParam :: SegTree v n -> N (SegTree v n) -> (SegTree v n, SegTree v n) # section :: SegTree v n -> N (SegTree v n) -> N (SegTree v n) -> SegTree v n # reverseDomain :: SegTree v n -> SegTree v n #
(Metric v, OrderedField n, Real n) => HasArcLength (SegTree v n)
Instance details Defined in Diagrams.Trail Methods arcLengthBounded :: N (SegTree v n) -> SegTree v n -> Interval (N (SegTree v n)) # arcLength :: N (SegTree v n) -> SegTree v n -> N (SegTree v n) # stdArcLength :: SegTree v n -> N (SegTree v n) # arcLengthToParam :: N (SegTree v n) -> SegTree v n -> N (SegTree v n) -> N (SegTree v n) # stdArcLengthToParam :: SegTree v n -> N (SegTree v n) -> N (SegTree v n) #
Wrapped (SegTree v n)
Instance details Defined in Diagrams.Trail Associated Types type Unwrapped (SegTree v n) :: Type # Methods _Wrapped' :: Iso' (SegTree v n) (Unwrapped (SegTree v n)) #
Rewrapped (SegTree v n) (SegTree v' n')
Instance details Defined in Diagrams.Trail
(Floating n, Ord n, Metric v) => Measured (SegMeasure v n) (SegTree v n)
Instance details Defined in Diagrams.Trail Methods measure :: SegTree v n -> SegMeasure v n #
(Metric v, OrderedField n, Metric u, OrderedField n') => Snoc (SegTree v n) (SegTree u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Snoc :: Prism (SegTree v n) (SegTree u n') (SegTree v n, Segment Closed v n) (SegTree u n', Segment Closed u n') #
(Metric v, OrderedField n, Metric u, OrderedField n') => Cons (SegTree v n) (SegTree u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Cons :: Prism (SegTree v n) (SegTree u n') (Segment Closed v n, SegTree v n) (Segment Closed u n', SegTree u n') #
type V (SegTree v n)
Instance details Defined in Diagrams.Trail type V (SegTree v n) = v
type N (SegTree v n)
Instance details Defined in Diagrams.Trail type N (SegTree v n) = n
type Codomain (SegTree v n)
Instance details Defined in Diagrams.Trail type Codomain (SegTree v n) = v
type Unwrapped (SegTree v n)
Instance details Defined in Diagrams.Trail type Unwrapped (SegTree v n) = FingerTree (SegMeasure v n) (Segment Closed v n)

data Line #

Type tag for trails with distinct endpoints.

Instances

(Metric v, OrderedField n) => Parametric (GetSegment (Trail' Line v n))	Parameters less than 0 yield the first segment; parameters greater than 1 yield the last. A parameter exactly at the junction of two segments yields the second segment (i.e. the one with higher parameter values).
Instance details Defined in Diagrams.Trail Methods atParam :: GetSegment (Trail' Line v n) -> N (GetSegment (Trail' Line v n)) -> Codomain (GetSegment (Trail' Line v n)) (N (GetSegment (Trail' Line v n))) #
(Metric v, OrderedField n) => EndValues (GetSegment (Trail' Line v n))
Instance details Defined in Diagrams.Trail Methods atStart :: GetSegment (Trail' Line v n) -> Codomain (GetSegment (Trail' Line v n)) (N (GetSegment (Trail' Line v n))) # atEnd :: GetSegment (Trail' Line v n) -> Codomain (GetSegment (Trail' Line v n)) (N (GetSegment (Trail' Line v n))) #
(OrderedField n, Metric v) => Semigroup (Trail' Line v n)
Instance details Defined in Diagrams.Trail Methods (<>) :: Trail' Line v n -> Trail' Line v n -> Trail' Line v n # sconcat :: NonEmpty (Trail' Line v n) -> Trail' Line v n # stimes :: Integral b => b -> Trail' Line v n -> Trail' Line v n #
(Metric v, OrderedField n) => Monoid (Trail' Line v n)	The empty trail is constantly the zero vector. Trails are composed via concatenation. Note that only lines have a monoid instance (and not loops).
Instance details Defined in Diagrams.Trail Methods mempty :: Trail' Line v n # mappend :: Trail' Line v n -> Trail' Line v n -> Trail' Line v n # mconcat :: [Trail' Line v n] -> Trail' Line v n #
(Metric v, OrderedField n) => TrailLike (Trail' Line v n)	Lines are trail-like. If given a `Trail` which contains a loop, the loop will be cut with `cutLoop`. The location is ignored.
Instance details Defined in Diagrams.TrailLike Methods trailLike :: Located (Trail (V (Trail' Line v n)) (N (Trail' Line v n))) -> Trail' Line v n #
(Metric v, OrderedField n, Real n) => Sectionable (Trail' Line v n)
Instance details Defined in Diagrams.Trail Methods splitAtParam :: Trail' Line v n -> N (Trail' Line v n) -> (Trail' Line v n, Trail' Line v n) # section :: Trail' Line v n -> N (Trail' Line v n) -> N (Trail' Line v n) -> Trail' Line v n # reverseDomain :: Trail' Line v n -> Trail' Line v n #
(Metric v, OrderedField n) => AsEmpty (Trail' Line v n)
Instance details Defined in Diagrams.Trail Methods _Empty :: Prism' (Trail' Line v n) () #
Wrapped (Trail' Line v n)
Instance details Defined in Diagrams.Trail Associated Types type Unwrapped (Trail' Line v n) :: Type # Methods _Wrapped' :: Iso' (Trail' Line v n) (Unwrapped (Trail' Line v n)) #
Rewrapped (Trail' Line v n) (Trail' Line v' n')
Instance details Defined in Diagrams.Trail
(Metric v, OrderedField n, Metric u, OrderedField n') => Snoc (Trail' Line v n) (Trail' Line u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Snoc :: Prism (Trail' Line v n) (Trail' Line u n') (Trail' Line v n, Segment Closed v n) (Trail' Line u n', Segment Closed u n') #
(Metric v, OrderedField n, Metric u, OrderedField n') => Cons (Trail' Line v n) (Trail' Line u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Cons :: Prism (Trail' Line v n) (Trail' Line u n') (Segment Closed v n, Trail' Line v n) (Segment Closed u n', Trail' Line u n') #
type Unwrapped (Trail' Line v n)
Instance details Defined in Diagrams.Trail type Unwrapped (Trail' Line v n) = SegTree v n

data Loop #

Type tag for "loopy" trails which return to their starting point.

Instances

(Metric v, OrderedField n, Real n) => Parametric (GetSegment (Trail' Loop v n))	The parameterization for loops wraps around, i.e. parameters are first reduced "mod 1".
Instance details Defined in Diagrams.Trail Methods atParam :: GetSegment (Trail' Loop v n) -> N (GetSegment (Trail' Loop v n)) -> Codomain (GetSegment (Trail' Loop v n)) (N (GetSegment (Trail' Loop v n))) #
(Metric v, OrderedField n, Real n) => EndValues (GetSegment (Trail' Loop v n))
Instance details Defined in Diagrams.Trail Methods atStart :: GetSegment (Trail' Loop v n) -> Codomain (GetSegment (Trail' Loop v n)) (N (GetSegment (Trail' Loop v n))) # atEnd :: GetSegment (Trail' Loop v n) -> Codomain (GetSegment (Trail' Loop v n)) (N (GetSegment (Trail' Loop v n))) #
(Metric v, OrderedField n) => TrailLike (Trail' Loop v n)	Loops are trail-like. If given a `Trail` containing a line, the line will be turned into a loop using `glueLine`. The location is ignored.
Instance details Defined in Diagrams.TrailLike Methods trailLike :: Located (Trail (V (Trail' Loop v n)) (N (Trail' Loop v n))) -> Trail' Loop v n #

data Trail' l (v :: Type -> Type) n where #

Intuitively, a trail is a single, continuous path through space. However, a trail has no fixed starting point; it merely specifies how to move through space, not where. For example, "take three steps forward, then turn right twenty degrees and take two more steps" is an intuitive analog of a trail; these instructions specify a path through space from any given starting location. To be precise, trails are translation-invariant; applying a translation to a trail has no effect.

A Located Trail, on the other hand, is a trail paired with some concrete starting location ("start at the big tree on the corner, then take three steps forward, ..."). See the Diagrams.Located module for help working with Located values.

Formally, the semantics of a trail is a continuous (though not necessarily differentiable) function from the real interval [0,1] to vectors in some vector space. (In contrast, a Located trail is a continuous function from [0,1] to points in some affine space.)

There are two types of trails:

A "line" (think of the "train", "subway", or "bus" variety, rather than the "straight" variety...) is a trail with two distinct endpoints. Actually, a line can have the same start and end points, but it is still drawn as if it had distinct endpoints: the two endpoints will have the appropriate end caps, and the trail will not be filled. Lines have a Monoid instance where mappend corresponds to concatenation, i.e. chaining one line after the other.
A "loop" is required to end in the same place it starts (that is, t(0) = t(1)). Loops are filled and are drawn as one continuous loop, with the appropriate join at the start/endpoint rather than end caps. Loops do not have a Monoid instance.

To convert between lines and loops, see glueLine, closeLine, and cutLoop.

To construct trails, see emptyTrail, trailFromSegments, trailFromVertices, trailFromOffsets, and friends. You can also get any type of trail from any function which returns a TrailLike (e.g. functions in Diagrams.TwoD.Shapes, and many others; see Diagrams.TrailLike).

To extract information from trails, see withLine, isLoop, trailSegments, trailOffsets, trailVertices, and friends.

Constructors

Line :: forall l (v :: Type -> Type) n. SegTree v n -> Trail' Line v n
Loop :: forall l (v :: Type -> Type) n. SegTree v n -> Segment Open v n -> Trail' Loop v n

Instances

ToPath (Located (Trail' l v n))
Instance details Defined in Diagrams.Path Methods toPath :: Located (Trail' l v n) -> Path (V (Located (Trail' l v n))) (N (Located (Trail' l v n))) #
(Metric v, OrderedField n) => Parametric (GetSegment (Trail' Line v n))	Parameters less than 0 yield the first segment; parameters greater than 1 yield the last. A parameter exactly at the junction of two segments yields the second segment (i.e. the one with higher parameter values).
Instance details Defined in Diagrams.Trail Methods atParam :: GetSegment (Trail' Line v n) -> N (GetSegment (Trail' Line v n)) -> Codomain (GetSegment (Trail' Line v n)) (N (GetSegment (Trail' Line v n))) #
(Metric v, OrderedField n, Real n) => Parametric (GetSegment (Trail' Loop v n))	The parameterization for loops wraps around, i.e. parameters are first reduced "mod 1".
Instance details Defined in Diagrams.Trail Methods atParam :: GetSegment (Trail' Loop v n) -> N (GetSegment (Trail' Loop v n)) -> Codomain (GetSegment (Trail' Loop v n)) (N (GetSegment (Trail' Loop v n))) #
(Parametric (GetSegment (Trail' c v n)), Additive v, Num n) => Parametric (Tangent (Trail' c v n))
Instance details Defined in Diagrams.Trail Methods atParam :: Tangent (Trail' c v n) -> N (Tangent (Trail' c v n)) -> Codomain (Tangent (Trail' c v n)) (N (Tangent (Trail' c v n))) #
(Metric v, OrderedField n) => EndValues (GetSegment (Trail' Line v n))
Instance details Defined in Diagrams.Trail Methods atStart :: GetSegment (Trail' Line v n) -> Codomain (GetSegment (Trail' Line v n)) (N (GetSegment (Trail' Line v n))) # atEnd :: GetSegment (Trail' Line v n) -> Codomain (GetSegment (Trail' Line v n)) (N (GetSegment (Trail' Line v n))) #
(Metric v, OrderedField n, Real n) => EndValues (GetSegment (Trail' Loop v n))
Instance details Defined in Diagrams.Trail Methods atStart :: GetSegment (Trail' Loop v n) -> Codomain (GetSegment (Trail' Loop v n)) (N (GetSegment (Trail' Loop v n))) # atEnd :: GetSegment (Trail' Loop v n) -> Codomain (GetSegment (Trail' Loop v n)) (N (GetSegment (Trail' Loop v n))) #
(Parametric (GetSegment (Trail' c v n)), EndValues (GetSegment (Trail' c v n)), Additive v, Num n) => EndValues (Tangent (Trail' c v n))
Instance details Defined in Diagrams.Trail Methods atStart :: Tangent (Trail' c v n) -> Codomain (Tangent (Trail' c v n)) (N (Tangent (Trail' c v n))) # atEnd :: Tangent (Trail' c v n) -> Codomain (Tangent (Trail' c v n)) (N (Tangent (Trail' c v n))) #
(Metric v, OrderedField n) => Reversing (Located (Trail' l v n))	Same as `reverseLocLine` or `reverseLocLoop`.
Instance details Defined in Diagrams.Trail Methods reversing :: Located (Trail' l v n) -> Located (Trail' l v n) #
Eq (v n) => Eq (Trail' l v n)
Instance details Defined in Diagrams.Trail Methods (==) :: Trail' l v n -> Trail' l v n -> Bool # (/=) :: Trail' l v n -> Trail' l v n -> Bool #
Ord (v n) => Ord (Trail' l v n)
Instance details Defined in Diagrams.Trail Methods compare :: Trail' l v n -> Trail' l v n -> Ordering # (<) :: Trail' l v n -> Trail' l v n -> Bool # (<=) :: Trail' l v n -> Trail' l v n -> Bool # (>) :: Trail' l v n -> Trail' l v n -> Bool # (>=) :: Trail' l v n -> Trail' l v n -> Bool # max :: Trail' l v n -> Trail' l v n -> Trail' l v n # min :: Trail' l v n -> Trail' l v n -> Trail' l v n #
Show (v n) => Show (Trail' l v n)
Instance details Defined in Diagrams.Trail Methods showsPrec :: Int -> Trail' l v n -> ShowS # show :: Trail' l v n -> String # showList :: [Trail' l v n] -> ShowS #
(OrderedField n, Metric v) => Semigroup (Trail' Line v n)
Instance details Defined in Diagrams.Trail Methods (<>) :: Trail' Line v n -> Trail' Line v n -> Trail' Line v n # sconcat :: NonEmpty (Trail' Line v n) -> Trail' Line v n # stimes :: Integral b => b -> Trail' Line v n -> Trail' Line v n #
(Metric v, OrderedField n) => Monoid (Trail' Line v n)	The empty trail is constantly the zero vector. Trails are composed via concatenation. Note that only lines have a monoid instance (and not loops).
Instance details Defined in Diagrams.Trail Methods mempty :: Trail' Line v n # mappend :: Trail' Line v n -> Trail' Line v n -> Trail' Line v n # mconcat :: [Trail' Line v n] -> Trail' Line v n #
(Metric v, OrderedField n) => Enveloped (Trail' l v n)	The envelope for a trail is based at the trail's start.
Instance details Defined in Diagrams.Trail Methods getEnvelope :: Trail' l v n -> Envelope (V (Trail' l v n)) (N (Trail' l v n)) #
(HasLinearMap v, Metric v, OrderedField n) => Transformable (Trail' l v n)
Instance details Defined in Diagrams.Trail Methods transform :: Transformation (V (Trail' l v n)) (N (Trail' l v n)) -> Trail' l v n -> Trail' l v n #
ToPath (Trail' l v n)
Instance details Defined in Diagrams.Path Methods toPath :: Trail' l v n -> Path (V (Trail' l v n)) (N (Trail' l v n)) #
(Metric v, OrderedField n) => TrailLike (Trail' Line v n)	Lines are trail-like. If given a `Trail` which contains a loop, the loop will be cut with `cutLoop`. The location is ignored.
Instance details Defined in Diagrams.TrailLike Methods trailLike :: Located (Trail (V (Trail' Line v n)) (N (Trail' Line v n))) -> Trail' Line v n #
(Metric v, OrderedField n) => TrailLike (Trail' Loop v n)	Loops are trail-like. If given a `Trail` containing a line, the line will be turned into a loop using `glueLine`. The location is ignored.
Instance details Defined in Diagrams.TrailLike Methods trailLike :: Located (Trail (V (Trail' Loop v n)) (N (Trail' Loop v n))) -> Trail' Loop v n #
(Metric v, OrderedField n, Real n) => Parametric (Trail' l v n)
Instance details Defined in Diagrams.Trail Methods atParam :: Trail' l v n -> N (Trail' l v n) -> Codomain (Trail' l v n) (N (Trail' l v n)) #
Num n => DomainBounds (Trail' l v n)
Instance details Defined in Diagrams.Trail Methods domainLower :: Trail' l v n -> N (Trail' l v n) # domainUpper :: Trail' l v n -> N (Trail' l v n) #
(Metric v, OrderedField n, Real n) => EndValues (Trail' l v n)
Instance details Defined in Diagrams.Trail Methods atStart :: Trail' l v n -> Codomain (Trail' l v n) (N (Trail' l v n)) # atEnd :: Trail' l v n -> Codomain (Trail' l v n) (N (Trail' l v n)) #
(Metric v, OrderedField n, Real n) => Sectionable (Trail' Line v n)
Instance details Defined in Diagrams.Trail Methods splitAtParam :: Trail' Line v n -> N (Trail' Line v n) -> (Trail' Line v n, Trail' Line v n) # section :: Trail' Line v n -> N (Trail' Line v n) -> N (Trail' Line v n) -> Trail' Line v n # reverseDomain :: Trail' Line v n -> Trail' Line v n #
(Metric v, OrderedField n, Real n) => HasArcLength (Trail' l v n)
Instance details Defined in Diagrams.Trail Methods arcLengthBounded :: N (Trail' l v n) -> Trail' l v n -> Interval (N (Trail' l v n)) # arcLength :: N (Trail' l v n) -> Trail' l v n -> N (Trail' l v n) # stdArcLength :: Trail' l v n -> N (Trail' l v n) # arcLengthToParam :: N (Trail' l v n) -> Trail' l v n -> N (Trail' l v n) -> N (Trail' l v n) # stdArcLengthToParam :: Trail' l v n -> N (Trail' l v n) -> N (Trail' l v n) #
(Metric v, OrderedField n) => Reversing (Trail' l v n)	Same as `reverseLine` or `reverseLoop`.
Instance details Defined in Diagrams.Trail Methods reversing :: Trail' l v n -> Trail' l v n #
(Metric v, OrderedField n) => AsEmpty (Trail' Line v n)
Instance details Defined in Diagrams.Trail Methods _Empty :: Prism' (Trail' Line v n) () #
Wrapped (Trail' Line v n)
Instance details Defined in Diagrams.Trail Associated Types type Unwrapped (Trail' Line v n) :: Type # Methods _Wrapped' :: Iso' (Trail' Line v n) (Unwrapped (Trail' Line v n)) #
(HasLinearMap v, Metric v, OrderedField n) => Renderable (Trail' o v n) NullBackend
Instance details Defined in Diagrams.Trail Methods render :: NullBackend -> Trail' o v n -> Render NullBackend (V (Trail' o v n)) (N (Trail' o v n)) #
Rewrapped (Trail' Line v n) (Trail' Line v' n')
Instance details Defined in Diagrams.Trail
(Metric v, OrderedField n, Metric u, OrderedField n') => Snoc (Trail' Line v n) (Trail' Line u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Snoc :: Prism (Trail' Line v n) (Trail' Line u n') (Trail' Line v n, Segment Closed v n) (Trail' Line u n', Segment Closed u n') #
(Metric v, OrderedField n, Metric u, OrderedField n') => Cons (Trail' Line v n) (Trail' Line u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Cons :: Prism (Trail' Line v n) (Trail' Line u n') (Segment Closed v n, Trail' Line v n) (Segment Closed u n', Trail' Line u n') #
type V (Trail' l v n)
Instance details Defined in Diagrams.Trail type V (Trail' l v n) = v
type N (Trail' l v n)
Instance details Defined in Diagrams.Trail type N (Trail' l v n) = n
type Codomain (Trail' l v n)
Instance details Defined in Diagrams.Trail type Codomain (Trail' l v n) = v
type Unwrapped (Trail' Line v n)
Instance details Defined in Diagrams.Trail type Unwrapped (Trail' Line v n) = SegTree v n

newtype GetSegment t #

A newtype wrapper around trails which exists solely for its Parametric, DomainBounds and EndValues instances. The idea is that if tr is a trail, you can write, e.g.

  getSegment tr atParam 0.6

or

  atStart (getSegment tr)

to get the segment at parameter 0.6 or the first segment in the trail, respectively.

The codomain for GetSegment, i.e. the result you get from calling atParam, atStart, or atEnd, is GetSegmentCodomain, which is a newtype wrapper around Maybe (v, Segment Closed v, AnIso' n n). Nothing results if the trail is empty; otherwise, you get:

the offset from the start of the trail to the beginning of the segment,
the segment itself, and
a reparameterization isomorphism: in the forward direction, it translates from parameters on the whole trail to a parameters on the segment. Note that for technical reasons you have to call cloneIso on the AnIso' value to get a real isomorphism you can use.

Constructors

GetSegment t

Instances

(Metric v, OrderedField n) => Parametric (GetSegment (Trail' Line v n))	Parameters less than 0 yield the first segment; parameters greater than 1 yield the last. A parameter exactly at the junction of two segments yields the second segment (i.e. the one with higher parameter values).
Instance details Defined in Diagrams.Trail Methods atParam :: GetSegment (Trail' Line v n) -> N (GetSegment (Trail' Line v n)) -> Codomain (GetSegment (Trail' Line v n)) (N (GetSegment (Trail' Line v n))) #
(Metric v, OrderedField n, Real n) => Parametric (GetSegment (Trail' Loop v n))	The parameterization for loops wraps around, i.e. parameters are first reduced "mod 1".
Instance details Defined in Diagrams.Trail Methods atParam :: GetSegment (Trail' Loop v n) -> N (GetSegment (Trail' Loop v n)) -> Codomain (GetSegment (Trail' Loop v n)) (N (GetSegment (Trail' Loop v n))) #
(Metric v, OrderedField n, Real n) => Parametric (GetSegment (Trail v n))
Instance details Defined in Diagrams.Trail Methods atParam :: GetSegment (Trail v n) -> N (GetSegment (Trail v n)) -> Codomain (GetSegment (Trail v n)) (N (GetSegment (Trail v n))) #
DomainBounds t => DomainBounds (GetSegment t)
Instance details Defined in Diagrams.Trail Methods domainLower :: GetSegment t -> N (GetSegment t) # domainUpper :: GetSegment t -> N (GetSegment t) #
(Metric v, OrderedField n) => EndValues (GetSegment (Trail' Line v n))
Instance details Defined in Diagrams.Trail Methods atStart :: GetSegment (Trail' Line v n) -> Codomain (GetSegment (Trail' Line v n)) (N (GetSegment (Trail' Line v n))) # atEnd :: GetSegment (Trail' Line v n) -> Codomain (GetSegment (Trail' Line v n)) (N (GetSegment (Trail' Line v n))) #
(Metric v, OrderedField n, Real n) => EndValues (GetSegment (Trail' Loop v n))
Instance details Defined in Diagrams.Trail Methods atStart :: GetSegment (Trail' Loop v n) -> Codomain (GetSegment (Trail' Loop v n)) (N (GetSegment (Trail' Loop v n))) # atEnd :: GetSegment (Trail' Loop v n) -> Codomain (GetSegment (Trail' Loop v n)) (N (GetSegment (Trail' Loop v n))) #
(Metric v, OrderedField n, Real n) => EndValues (GetSegment (Trail v n))
Instance details Defined in Diagrams.Trail Methods atStart :: GetSegment (Trail v n) -> Codomain (GetSegment (Trail v n)) (N (GetSegment (Trail v n))) # atEnd :: GetSegment (Trail v n) -> Codomain (GetSegment (Trail v n)) (N (GetSegment (Trail v n))) #
type V (GetSegment t)
Instance details Defined in Diagrams.Trail type V (GetSegment t) = V t
type N (GetSegment t)
Instance details Defined in Diagrams.Trail type N (GetSegment t) = N t
type Codomain (GetSegment t)
Instance details Defined in Diagrams.Trail type Codomain (GetSegment t) = GetSegmentCodomain (V t)

newtype GetSegmentCodomain (v :: Type -> Type) n #

Constructors

GetSegmentCodomain (Maybe (v n, Segment Closed v n, AnIso' n n))

data Trail (v :: Type -> Type) n where #

Trail is a wrapper around Trail', hiding whether the underlying Trail' is a line or loop (though which it is can be recovered; see e.g. withTrail).

Constructors

Trail :: forall (v :: Type -> Type) n l. Trail' l v n -> Trail v n

Instances

ToPath (Located (Trail v n))
Instance details Defined in Diagrams.Path Methods toPath :: Located (Trail v n) -> Path (V (Located (Trail v n))) (N (Located (Trail v n))) #
(Metric v, OrderedField n, Real n) => Parametric (GetSegment (Trail v n))
Instance details Defined in Diagrams.Trail Methods atParam :: GetSegment (Trail v n) -> N (GetSegment (Trail v n)) -> Codomain (GetSegment (Trail v n)) (N (GetSegment (Trail v n))) #
(Metric v, OrderedField n, Real n) => Parametric (Tangent (Trail v n))
Instance details Defined in Diagrams.Trail Methods atParam :: Tangent (Trail v n) -> N (Tangent (Trail v n)) -> Codomain (Tangent (Trail v n)) (N (Tangent (Trail v n))) #
(Metric v, OrderedField n, Real n) => EndValues (GetSegment (Trail v n))
Instance details Defined in Diagrams.Trail Methods atStart :: GetSegment (Trail v n) -> Codomain (GetSegment (Trail v n)) (N (GetSegment (Trail v n))) # atEnd :: GetSegment (Trail v n) -> Codomain (GetSegment (Trail v n)) (N (GetSegment (Trail v n))) #
(Metric v, OrderedField n, Real n) => EndValues (Tangent (Trail v n))
Instance details Defined in Diagrams.Trail Methods atStart :: Tangent (Trail v n) -> Codomain (Tangent (Trail v n)) (N (Tangent (Trail v n))) # atEnd :: Tangent (Trail v n) -> Codomain (Tangent (Trail v n)) (N (Tangent (Trail v n))) #
(Metric v, OrderedField n) => Reversing (Located (Trail v n))	Same as `reverseLocTrail`.
Instance details Defined in Diagrams.Trail Methods reversing :: Located (Trail v n) -> Located (Trail v n) #
(Metric v, Metric u, OrderedField n, r ~ Located (Trail u n)) => Deformable (Located (Trail v n)) r
Instance details Defined in Diagrams.Deform Methods deform' :: N (Located (Trail v n)) -> Deformation (V (Located (Trail v n))) (V r) (N (Located (Trail v n))) -> Located (Trail v n) -> r # deform :: Deformation (V (Located (Trail v n))) (V r) (N (Located (Trail v n))) -> Located (Trail v n) -> r #
Eq (v n) => Eq (Trail v n)
Instance details Defined in Diagrams.Trail Methods (==) :: Trail v n -> Trail v n -> Bool # (/=) :: Trail v n -> Trail v n -> Bool #
Ord (v n) => Ord (Trail v n)
Instance details Defined in Diagrams.Trail Methods compare :: Trail v n -> Trail v n -> Ordering # (<) :: Trail v n -> Trail v n -> Bool # (<=) :: Trail v n -> Trail v n -> Bool # (>) :: Trail v n -> Trail v n -> Bool # (>=) :: Trail v n -> Trail v n -> Bool # max :: Trail v n -> Trail v n -> Trail v n # min :: Trail v n -> Trail v n -> Trail v n #
Show (v n) => Show (Trail v n)
Instance details Defined in Diagrams.Trail Methods showsPrec :: Int -> Trail v n -> ShowS # show :: Trail v n -> String # showList :: [Trail v n] -> ShowS #
(OrderedField n, Metric v) => Semigroup (Trail v n)	Two `Trail`s are combined by first ensuring they are both lines (using `cutTrail` on loops) and then concatenating them. The result, in general, is a line. However, there is a special case for the empty line, which acts as the identity (so combining the empty line with a loop results in a loop).
Instance details Defined in Diagrams.Trail Methods (<>) :: Trail v n -> Trail v n -> Trail v n # sconcat :: NonEmpty (Trail v n) -> Trail v n # stimes :: Integral b => b -> Trail v n -> Trail v n #
(Metric v, OrderedField n) => Monoid (Trail v n)	`Trail`s are combined as described in the `Semigroup` instance; the empty line is the identity element, with special cases so that combining the empty line with a loop results in the unchanged loop (in all other cases loops will be cut). Note that this does, in fact, satisfy the monoid laws, though it is a bit strange. Mostly it is provided for convenience, so one can work directly with `Trail`s instead of working with `Trail' Line`s and then wrapping.
Instance details Defined in Diagrams.Trail Methods mempty :: Trail v n # mappend :: Trail v n -> Trail v n -> Trail v n # mconcat :: [Trail v n] -> Trail v n #
(Serialize (v n), OrderedField n, Metric v) => Serialize (Trail v n)
Instance details Defined in Diagrams.Trail Methods put :: Putter (Trail v n) # get :: Get (Trail v n) #
(Metric v, OrderedField n) => Enveloped (Trail v n)
Instance details Defined in Diagrams.Trail Methods getEnvelope :: Trail v n -> Envelope (V (Trail v n)) (N (Trail v n)) #
(HasLinearMap v, Metric v, OrderedField n) => Transformable (Trail v n)
Instance details Defined in Diagrams.Trail Methods transform :: Transformation (V (Trail v n)) (N (Trail v n)) -> Trail v n -> Trail v n #
ToPath (Trail v n)
Instance details Defined in Diagrams.Path Methods toPath :: Trail v n -> Path (V (Trail v n)) (N (Trail v n)) #
(Metric v, OrderedField n) => TrailLike (Trail v n)	`Trail`s are trail-like; the location is simply ignored.
Instance details Defined in Diagrams.TrailLike Methods trailLike :: Located (Trail (V (Trail v n)) (N (Trail v n))) -> Trail v n #
(Metric v, OrderedField n, Real n) => Parametric (Trail v n)
Instance details Defined in Diagrams.Trail Methods atParam :: Trail v n -> N (Trail v n) -> Codomain (Trail v n) (N (Trail v n)) #
Num n => DomainBounds (Trail v n)
Instance details Defined in Diagrams.Trail Methods domainLower :: Trail v n -> N (Trail v n) # domainUpper :: Trail v n -> N (Trail v n) #
(Metric v, OrderedField n, Real n) => EndValues (Trail v n)
Instance details Defined in Diagrams.Trail Methods atStart :: Trail v n -> Codomain (Trail v n) (N (Trail v n)) # atEnd :: Trail v n -> Codomain (Trail v n) (N (Trail v n)) #
(Metric v, OrderedField n, Real n) => Sectionable (Trail v n)	Note that there is no `Sectionable` instance for `Trail' Loop`, because it does not make sense (splitting a loop at a parameter results in a single line, not two loops). However, it's convenient to have a `Sectionable` instance for `Trail`; if the `Trail` contains a loop the loop will first be cut and then `splitAtParam` called on the resulting line. This is semantically a bit silly, so please don't rely on it. (E.g. if this is really the behavior you want, consider first calling `cutLoop` yourself.)
Instance details Defined in Diagrams.Trail Methods splitAtParam :: Trail v n -> N (Trail v n) -> (Trail v n, Trail v n) # section :: Trail v n -> N (Trail v n) -> N (Trail v n) -> Trail v n # reverseDomain :: Trail v n -> Trail v n #
(Metric v, OrderedField n, Real n) => HasArcLength (Trail v n)
Instance details Defined in Diagrams.Trail Methods arcLengthBounded :: N (Trail v n) -> Trail v n -> Interval (N (Trail v n)) # arcLength :: N (Trail v n) -> Trail v n -> N (Trail v n) # stdArcLength :: Trail v n -> N (Trail v n) # arcLengthToParam :: N (Trail v n) -> Trail v n -> N (Trail v n) -> N (Trail v n) # stdArcLengthToParam :: Trail v n -> N (Trail v n) -> N (Trail v n) #
(Metric v, OrderedField n) => Reversing (Trail v n)	Same as `reverseTrail`.
Instance details Defined in Diagrams.Trail Methods reversing :: Trail v n -> Trail v n #
(Metric v, OrderedField n) => AsEmpty (Trail v n)
Instance details Defined in Diagrams.Trail Methods _Empty :: Prism' (Trail v n) () #
Wrapped (Trail v n)
Instance details Defined in Diagrams.Trail Associated Types type Unwrapped (Trail v n) :: Type # Methods _Wrapped' :: Iso' (Trail v n) (Unwrapped (Trail v n)) #
Rewrapped (Trail v n) (Trail v' n')
Instance details Defined in Diagrams.Trail
Snoc (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))
Instance details Defined in Diagrams.Path Methods _Snoc :: Prism (Path v n) (Path v' n') (Path v n, Located (Trail v n)) (Path v' n', Located (Trail v' n')) #
Cons (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))
Instance details Defined in Diagrams.Path Methods _Cons :: Prism (Path v n) (Path v' n') (Located (Trail v n), Path v n) (Located (Trail v' n'), Path v' n') #
Each (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))
Instance details Defined in Diagrams.Path Methods each :: Traversal (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n')) #
type V (Trail v n)
Instance details Defined in Diagrams.Trail type V (Trail v n) = v
type N (Trail v n)
Instance details Defined in Diagrams.Trail type N (Trail v n) = n
type Codomain (Trail v n)
Instance details Defined in Diagrams.Trail type Codomain (Trail v n) = v
type Unwrapped (Trail v n)
Instance details Defined in Diagrams.Trail type Unwrapped (Trail v n) = Either (Trail' Line v n) (Trail' Loop v n)

normalAtEnd :: (InSpace V2 n t, EndValues (Tangent t), Floating n) => t -> V2 n #

Compute the normal vector at the end of a segment or trail.

normalAtStart :: (InSpace V2 n t, EndValues (Tangent t), Floating n) => t -> V2 n #

Compute the normal vector at the start of a segment or trail.

normalAtParam :: (InSpace V2 n t, Parametric (Tangent t), Floating n) => t -> n -> V2 n #

Compute the (unit) normal vector to a segment or trail at a particular parameter.

Examples of more specific types this function can have include

Segment Closed V2 Double -> Double -> V2 Double

Trail' Line V2 Double -> Double -> V2 Double

Located (Trail V2 Double) -> Double -> V2 Double

See the instances listed for the Tangent newtype for more.

tangentAtEnd :: EndValues (Tangent t) => t -> Vn t #

Compute the tangent vector at the end of a segment or trail.

tangentAtStart :: EndValues (Tangent t) => t -> Vn t #

Compute the tangent vector at the start of a segment or trail.

tangentAtParam :: Parametric (Tangent t) => t -> N t -> Vn t #

Compute the tangent vector to a segment or trail at a particular parameter.

Examples of more specific types this function can have include

Segment Closed V2 -> Double -> V2 Double

```
Trail' Line V2 -> Double -> V2 Double
```

Located (Trail V2) -> Double -> V2 Double

See the instances listed for the Tangent newtype for more.

newtype Tangent t #

A newtype wrapper used to give different instances of Parametric and EndValues that compute tangent vectors.

Constructors

Tangent t

Instances

(Parametric (GetSegment (Trail' c v n)), Additive v, Num n) => Parametric (Tangent (Trail' c v n))
Instance details Defined in Diagrams.Trail Methods atParam :: Tangent (Trail' c v n) -> N (Tangent (Trail' c v n)) -> Codomain (Tangent (Trail' c v n)) (N (Tangent (Trail' c v n))) #
(Metric v, OrderedField n, Real n) => Parametric (Tangent (Trail v n))
Instance details Defined in Diagrams.Trail Methods atParam :: Tangent (Trail v n) -> N (Tangent (Trail v n)) -> Codomain (Tangent (Trail v n)) (N (Tangent (Trail v n))) #
(Additive v, Num n) => Parametric (Tangent (Segment Closed v n))
Instance details Defined in Diagrams.Tangent Methods atParam :: Tangent (Segment Closed v n) -> N (Tangent (Segment Closed v n)) -> Codomain (Tangent (Segment Closed v n)) (N (Tangent (Segment Closed v n))) #
(Additive v, Num n) => Parametric (Tangent (FixedSegment v n))
Instance details Defined in Diagrams.Tangent Methods atParam :: Tangent (FixedSegment v n) -> N (Tangent (FixedSegment v n)) -> Codomain (Tangent (FixedSegment v n)) (N (Tangent (FixedSegment v n))) #
Parametric (Tangent t) => Parametric (Tangent (Located t))
Instance details Defined in Diagrams.Tangent Methods atParam :: Tangent (Located t) -> N (Tangent (Located t)) -> Codomain (Tangent (Located t)) (N (Tangent (Located t))) #
DomainBounds t => DomainBounds (Tangent t)
Instance details Defined in Diagrams.Tangent Methods domainLower :: Tangent t -> N (Tangent t) # domainUpper :: Tangent t -> N (Tangent t) #
(Parametric (GetSegment (Trail' c v n)), EndValues (GetSegment (Trail' c v n)), Additive v, Num n) => EndValues (Tangent (Trail' c v n))
Instance details Defined in Diagrams.Trail Methods atStart :: Tangent (Trail' c v n) -> Codomain (Tangent (Trail' c v n)) (N (Tangent (Trail' c v n))) # atEnd :: Tangent (Trail' c v n) -> Codomain (Tangent (Trail' c v n)) (N (Tangent (Trail' c v n))) #
(Metric v, OrderedField n, Real n) => EndValues (Tangent (Trail v n))
Instance details Defined in Diagrams.Trail Methods atStart :: Tangent (Trail v n) -> Codomain (Tangent (Trail v n)) (N (Tangent (Trail v n))) # atEnd :: Tangent (Trail v n) -> Codomain (Tangent (Trail v n)) (N (Tangent (Trail v n))) #
(Additive v, Num n) => EndValues (Tangent (Segment Closed v n))
Instance details Defined in Diagrams.Tangent Methods atStart :: Tangent (Segment Closed v n) -> Codomain (Tangent (Segment Closed v n)) (N (Tangent (Segment Closed v n))) # atEnd :: Tangent (Segment Closed v n) -> Codomain (Tangent (Segment Closed v n)) (N (Tangent (Segment Closed v n))) #
(Additive v, Num n) => EndValues (Tangent (FixedSegment v n))
Instance details Defined in Diagrams.Tangent Methods atStart :: Tangent (FixedSegment v n) -> Codomain (Tangent (FixedSegment v n)) (N (Tangent (FixedSegment v n))) # atEnd :: Tangent (FixedSegment v n) -> Codomain (Tangent (FixedSegment v n)) (N (Tangent (FixedSegment v n))) #
(DomainBounds t, EndValues (Tangent t)) => EndValues (Tangent (Located t))
Instance details Defined in Diagrams.Tangent Methods atStart :: Tangent (Located t) -> Codomain (Tangent (Located t)) (N (Tangent (Located t))) # atEnd :: Tangent (Located t) -> Codomain (Tangent (Located t)) (N (Tangent (Located t))) #
type V (Tangent t)
Instance details Defined in Diagrams.Tangent type V (Tangent t) = V t
type N (Tangent t)
Instance details Defined in Diagrams.Tangent type N (Tangent t) = N t
type Codomain (Tangent t)
Instance details Defined in Diagrams.Tangent type Codomain (Tangent t) = V t

oeOffset :: Lens' (OffsetEnvelope v n) (TotalOffset v n) #

oeEnvelope :: Lens' (OffsetEnvelope v n) (Envelope v n) #

type SegMeasure (v :: Type -> Type) n = SegCount ::: (ArcLength n ::: (OffsetEnvelope v n ::: ())) #

SegMeasure collects up all the measurements over a chain of segments.

getArcLengthBounded :: (Num n, Ord n) => n -> ArcLength n -> Interval n #

Given a specified tolerance, project out the cached arc length if it is accurate enough; otherwise call the generic arc length function with the given tolerance.

getArcLengthFun :: ArcLength n -> n -> Interval n #

Project out the generic arc length function taking the tolerance as an argument.

getArcLengthCached :: ArcLength n -> Interval n #

Project out the cached arc length, stored together with error bounds.

fixedSegIso :: (Num n, Additive v) => Iso' (FixedSegment v n) (Located (Segment Closed v n)) #

Use a FixedSegment to make an Iso between an a fixed segment and a located segment.

fromFixedSeg :: (Num n, Additive v) => FixedSegment v n -> Located (Segment Closed v n) #

Convert a FixedSegment back into a located Segment.

mkFixedSeg :: (Num n, Additive v) => Located (Segment Closed v n) -> FixedSegment v n #

Create a FixedSegment from a located Segment.

reverseSegment :: (Num n, Additive v) => Segment Closed v n -> Segment Closed v n #

Reverse the direction of a segment.

openCubic :: v n -> v n -> Segment Open v n #

An open cubic segment. This means the trail makes a cubic bézier with control vectors v1 and v2 to form a loop.

openLinear :: Segment Open v n #

An open linear segment. This means the trail makes a straight line from the last segment the beginning to form a loop.

segOffset :: Segment Closed v n -> v n #

Compute the offset from the start of a segment to the end. Note that in the case of a Bézier segment this is not the same as the length of the curve itself; for that, see arcLength.

bézier3 :: v n -> v n -> v n -> Segment Closed v n #

bézier3 is the same as bezier3, but with more snobbery.

bezier3 :: v n -> v n -> v n -> Segment Closed v n #

bezier3 c1 c2 x constructs a translationally invariant cubic Bézier curve where the offsets from the first endpoint to the first and second control point and endpoint are respectively given by c1, c2, and x.

straight :: v n -> Segment Closed v n #

straight v constructs a translationally invariant linear segment with direction and length given by the vector v.

mapSegmentVectors :: (v n -> v' n') -> Segment c v n -> Segment c v' n' #

Map over the vectors of each segment.

data Open #

Type tag for open segments.

Instances

Serialize (v n) => Serialize (Segment Open v n)
Instance details Defined in Diagrams.Segment Methods put :: Putter (Segment Open v n) # get :: Get (Segment Open v n) #

data Closed #

Type tag for closed segments.

Instances

ToPath (Located [Segment Closed v n])
Instance details Defined in Diagrams.Path Methods toPath :: Located [Segment Closed v n] -> Path (V (Located [Segment Closed v n])) (N (Located [Segment Closed v n])) #
ToPath (Located (Segment Closed v n))
Instance details Defined in Diagrams.Path Methods toPath :: Located (Segment Closed v n) -> Path (V (Located (Segment Closed v n))) (N (Located (Segment Closed v n))) #
(Additive v, Num n) => Parametric (Tangent (Segment Closed v n))
Instance details Defined in Diagrams.Tangent Methods atParam :: Tangent (Segment Closed v n) -> N (Tangent (Segment Closed v n)) -> Codomain (Tangent (Segment Closed v n)) (N (Tangent (Segment Closed v n))) #
(Additive v, Num n) => EndValues (Tangent (Segment Closed v n))
Instance details Defined in Diagrams.Tangent Methods atStart :: Tangent (Segment Closed v n) -> Codomain (Tangent (Segment Closed v n)) (N (Tangent (Segment Closed v n))) # atEnd :: Tangent (Segment Closed v n) -> Codomain (Tangent (Segment Closed v n)) (N (Tangent (Segment Closed v n))) #
(Metric v, OrderedField n, Metric u, OrderedField n') => Snoc (SegTree v n) (SegTree u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Snoc :: Prism (SegTree v n) (SegTree u n') (SegTree v n, Segment Closed v n) (SegTree u n', Segment Closed u n') #
(Metric v, OrderedField n, Metric u, OrderedField n') => Cons (SegTree v n) (SegTree u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Cons :: Prism (SegTree v n) (SegTree u n') (Segment Closed v n, SegTree v n) (Segment Closed u n', SegTree u n') #
(OrderedField n, Metric v) => Measured (SegMeasure v n) (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods measure :: Segment Closed v n -> SegMeasure v n #
Serialize (v n) => Serialize (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods put :: Putter (Segment Closed v n) # get :: Get (Segment Closed v n) #
(Metric v, OrderedField n) => Enveloped (Segment Closed v n)	The envelope for a segment is based at the segment's start.
Instance details Defined in Diagrams.Segment Methods getEnvelope :: Segment Closed v n -> Envelope (V (Segment Closed v n)) (N (Segment Closed v n)) #
(Additive v, Num n) => Parametric (Segment Closed v n)	`atParam` yields a parametrized view of segments as continuous functions `[0,1] -> v`, which give the offset from the start of the segment for each value of the parameter between `0` and `1`. It is designed to be used infix, like seg `atParam` 0.5.
Instance details Defined in Diagrams.Segment Methods atParam :: Segment Closed v n -> N (Segment Closed v n) -> Codomain (Segment Closed v n) (N (Segment Closed v n)) #
Num n => DomainBounds (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods domainLower :: Segment Closed v n -> N (Segment Closed v n) # domainUpper :: Segment Closed v n -> N (Segment Closed v n) #
(Additive v, Num n) => EndValues (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods atStart :: Segment Closed v n -> Codomain (Segment Closed v n) (N (Segment Closed v n)) # atEnd :: Segment Closed v n -> Codomain (Segment Closed v n) (N (Segment Closed v n)) #
(Additive v, Fractional n) => Sectionable (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods splitAtParam :: Segment Closed v n -> N (Segment Closed v n) -> (Segment Closed v n, Segment Closed v n) # section :: Segment Closed v n -> N (Segment Closed v n) -> N (Segment Closed v n) -> Segment Closed v n # reverseDomain :: Segment Closed v n -> Segment Closed v n #
(Metric v, OrderedField n) => HasArcLength (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods arcLengthBounded :: N (Segment Closed v n) -> Segment Closed v n -> Interval (N (Segment Closed v n)) # arcLength :: N (Segment Closed v n) -> Segment Closed v n -> N (Segment Closed v n) # stdArcLength :: Segment Closed v n -> N (Segment Closed v n) # arcLengthToParam :: N (Segment Closed v n) -> Segment Closed v n -> N (Segment Closed v n) -> N (Segment Closed v n) # stdArcLengthToParam :: Segment Closed v n -> N (Segment Closed v n) -> N (Segment Closed v n) #
(Additive v, Num n) => Reversing (Segment Closed v n)	Reverse the direction of a segment.
Instance details Defined in Diagrams.Segment Methods reversing :: Segment Closed v n -> Segment Closed v n #
(Metric v, OrderedField n, Metric u, OrderedField n') => Snoc (Trail' Line v n) (Trail' Line u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Snoc :: Prism (Trail' Line v n) (Trail' Line u n') (Trail' Line v n, Segment Closed v n) (Trail' Line u n', Segment Closed u n') #
(Metric v, OrderedField n, Metric u, OrderedField n') => Cons (Trail' Line v n) (Trail' Line u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Cons :: Prism (Trail' Line v n) (Trail' Line u n') (Segment Closed v n, Trail' Line v n) (Segment Closed u n', Trail' Line u n') #
type Codomain (Segment Closed v n)
Instance details Defined in Diagrams.Segment type Codomain (Segment Closed v n) = v

data Offset c (v :: Type -> Type) n where #

The offset of a segment is the vector from its starting point to its end. The offset for an open segment is determined by the context, i.e. its endpoint is not fixed. The offset for a closed segment is stored explicitly, i.e. its endpoint is at a fixed offset from its start.

Constructors

OffsetOpen :: forall c (v :: Type -> Type) n. Offset Open v n
OffsetClosed :: forall c (v :: Type -> Type) n. v n -> Offset Closed v n

Instances

Functor v => Functor (Offset c v)
Instance details Defined in Diagrams.Segment Methods fmap :: (a -> b) -> Offset c v a -> Offset c v b # (<$) :: a -> Offset c v b -> Offset c v a #
Eq (v n) => Eq (Offset c v n)
Instance details Defined in Diagrams.Segment Methods (==) :: Offset c v n -> Offset c v n -> Bool # (/=) :: Offset c v n -> Offset c v n -> Bool #
Ord (v n) => Ord (Offset c v n)
Instance details Defined in Diagrams.Segment Methods compare :: Offset c v n -> Offset c v n -> Ordering # (<) :: Offset c v n -> Offset c v n -> Bool # (<=) :: Offset c v n -> Offset c v n -> Bool # (>) :: Offset c v n -> Offset c v n -> Bool # (>=) :: Offset c v n -> Offset c v n -> Bool # max :: Offset c v n -> Offset c v n -> Offset c v n # min :: Offset c v n -> Offset c v n -> Offset c v n #
Show (v n) => Show (Offset c v n)
Instance details Defined in Diagrams.Segment Methods showsPrec :: Int -> Offset c v n -> ShowS # show :: Offset c v n -> String # showList :: [Offset c v n] -> ShowS #
Transformable (Offset c v n)
Instance details Defined in Diagrams.Segment Methods transform :: Transformation (V (Offset c v n)) (N (Offset c v n)) -> Offset c v n -> Offset c v n #
(Additive v, Num n) => Reversing (Offset c v n)	Reverses the direction of closed offsets.
Instance details Defined in Diagrams.Segment Methods reversing :: Offset c v n -> Offset c v n #
Each (Offset c v n) (Offset c v' n') (v n) (v' n')
Instance details Defined in Diagrams.Segment Methods each :: Traversal (Offset c v n) (Offset c v' n') (v n) (v' n') #
type V (Offset c v n)
Instance details Defined in Diagrams.Segment type V (Offset c v n) = v
type N (Offset c v n)
Instance details Defined in Diagrams.Segment type N (Offset c v n) = n

data Segment c (v :: Type -> Type) n #

The atomic constituents of the concrete representation currently used for trails are segments, currently limited to single straight lines or cubic Bézier curves. Segments are translationally invariant, that is, they have no particular "location" and are unaffected by translations. They are, however, affected by other transformations such as rotations and scales.

Constructors

Linear !(Offset c v n)	A linear segment with given offset.
Cubic !(v n) !(v n) !(Offset c v n)	A cubic Bézier segment specified by three offsets from the starting point to the first control point, second control point, and ending point, respectively.

Instances

ToPath (Located [Segment Closed v n])
Instance details Defined in Diagrams.Path Methods toPath :: Located [Segment Closed v n] -> Path (V (Located [Segment Closed v n])) (N (Located [Segment Closed v n])) #
ToPath (Located (Segment Closed v n))
Instance details Defined in Diagrams.Path Methods toPath :: Located (Segment Closed v n) -> Path (V (Located (Segment Closed v n))) (N (Located (Segment Closed v n))) #
(Additive v, Num n) => Parametric (Tangent (Segment Closed v n))
Instance details Defined in Diagrams.Tangent Methods atParam :: Tangent (Segment Closed v n) -> N (Tangent (Segment Closed v n)) -> Codomain (Tangent (Segment Closed v n)) (N (Tangent (Segment Closed v n))) #
(Additive v, Num n) => EndValues (Tangent (Segment Closed v n))
Instance details Defined in Diagrams.Tangent Methods atStart :: Tangent (Segment Closed v n) -> Codomain (Tangent (Segment Closed v n)) (N (Tangent (Segment Closed v n))) # atEnd :: Tangent (Segment Closed v n) -> Codomain (Tangent (Segment Closed v n)) (N (Tangent (Segment Closed v n))) #
Functor v => Functor (Segment c v)
Instance details Defined in Diagrams.Segment Methods fmap :: (a -> b) -> Segment c v a -> Segment c v b # (<$) :: a -> Segment c v b -> Segment c v a #
(Metric v, OrderedField n, Metric u, OrderedField n') => Snoc (SegTree v n) (SegTree u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Snoc :: Prism (SegTree v n) (SegTree u n') (SegTree v n, Segment Closed v n) (SegTree u n', Segment Closed u n') #
(Metric v, OrderedField n, Metric u, OrderedField n') => Cons (SegTree v n) (SegTree u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Cons :: Prism (SegTree v n) (SegTree u n') (Segment Closed v n, SegTree v n) (Segment Closed u n', SegTree u n') #
(OrderedField n, Metric v) => Measured (SegMeasure v n) (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods measure :: Segment Closed v n -> SegMeasure v n #
Eq (v n) => Eq (Segment c v n)
Instance details Defined in Diagrams.Segment Methods (==) :: Segment c v n -> Segment c v n -> Bool # (/=) :: Segment c v n -> Segment c v n -> Bool #
Ord (v n) => Ord (Segment c v n)
Instance details Defined in Diagrams.Segment Methods compare :: Segment c v n -> Segment c v n -> Ordering # (<) :: Segment c v n -> Segment c v n -> Bool # (<=) :: Segment c v n -> Segment c v n -> Bool # (>) :: Segment c v n -> Segment c v n -> Bool # (>=) :: Segment c v n -> Segment c v n -> Bool # max :: Segment c v n -> Segment c v n -> Segment c v n # min :: Segment c v n -> Segment c v n -> Segment c v n #
Show (v n) => Show (Segment c v n)
Instance details Defined in Diagrams.Segment Methods showsPrec :: Int -> Segment c v n -> ShowS # show :: Segment c v n -> String # showList :: [Segment c v n] -> ShowS #
Serialize (v n) => Serialize (Segment Open v n)
Instance details Defined in Diagrams.Segment Methods put :: Putter (Segment Open v n) # get :: Get (Segment Open v n) #
Serialize (v n) => Serialize (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods put :: Putter (Segment Closed v n) # get :: Get (Segment Closed v n) #
(Metric v, OrderedField n) => Enveloped (Segment Closed v n)	The envelope for a segment is based at the segment's start.
Instance details Defined in Diagrams.Segment Methods getEnvelope :: Segment Closed v n -> Envelope (V (Segment Closed v n)) (N (Segment Closed v n)) #
Transformable (Segment c v n)
Instance details Defined in Diagrams.Segment Methods transform :: Transformation (V (Segment c v n)) (N (Segment c v n)) -> Segment c v n -> Segment c v n #
(Additive v, Num n) => Parametric (Segment Closed v n)	`atParam` yields a parametrized view of segments as continuous functions `[0,1] -> v`, which give the offset from the start of the segment for each value of the parameter between `0` and `1`. It is designed to be used infix, like seg `atParam` 0.5.
Instance details Defined in Diagrams.Segment Methods atParam :: Segment Closed v n -> N (Segment Closed v n) -> Codomain (Segment Closed v n) (N (Segment Closed v n)) #
Num n => DomainBounds (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods domainLower :: Segment Closed v n -> N (Segment Closed v n) # domainUpper :: Segment Closed v n -> N (Segment Closed v n) #
(Additive v, Num n) => EndValues (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods atStart :: Segment Closed v n -> Codomain (Segment Closed v n) (N (Segment Closed v n)) # atEnd :: Segment Closed v n -> Codomain (Segment Closed v n) (N (Segment Closed v n)) #
(Additive v, Fractional n) => Sectionable (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods splitAtParam :: Segment Closed v n -> N (Segment Closed v n) -> (Segment Closed v n, Segment Closed v n) # section :: Segment Closed v n -> N (Segment Closed v n) -> N (Segment Closed v n) -> Segment Closed v n # reverseDomain :: Segment Closed v n -> Segment Closed v n #
(Metric v, OrderedField n) => HasArcLength (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods arcLengthBounded :: N (Segment Closed v n) -> Segment Closed v n -> Interval (N (Segment Closed v n)) # arcLength :: N (Segment Closed v n) -> Segment Closed v n -> N (Segment Closed v n) # stdArcLength :: Segment Closed v n -> N (Segment Closed v n) # arcLengthToParam :: N (Segment Closed v n) -> Segment Closed v n -> N (Segment Closed v n) -> N (Segment Closed v n) # stdArcLengthToParam :: Segment Closed v n -> N (Segment Closed v n) -> N (Segment Closed v n) #
(Additive v, Num n) => Reversing (Segment Closed v n)	Reverse the direction of a segment.
Instance details Defined in Diagrams.Segment Methods reversing :: Segment Closed v n -> Segment Closed v n #
Renderable (Segment c v n) NullBackend
Instance details Defined in Diagrams.Segment Methods render :: NullBackend -> Segment c v n -> Render NullBackend (V (Segment c v n)) (N (Segment c v n)) #
Each (Segment c v n) (Segment c v' n') (v n) (v' n')
Instance details Defined in Diagrams.Segment Methods each :: Traversal (Segment c v n) (Segment c v' n') (v n) (v' n') #
(Metric v, OrderedField n, Metric u, OrderedField n') => Snoc (Trail' Line v n) (Trail' Line u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Snoc :: Prism (Trail' Line v n) (Trail' Line u n') (Trail' Line v n, Segment Closed v n) (Trail' Line u n', Segment Closed u n') #
(Metric v, OrderedField n, Metric u, OrderedField n') => Cons (Trail' Line v n) (Trail' Line u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Cons :: Prism (Trail' Line v n) (Trail' Line u n') (Segment Closed v n, Trail' Line v n) (Segment Closed u n', Trail' Line u n') #
type V (Segment c v n)
Instance details Defined in Diagrams.Segment type V (Segment c v n) = v
type N (Segment c v n)
Instance details Defined in Diagrams.Segment type N (Segment c v n) = n
type Codomain (Segment Closed v n)
Instance details Defined in Diagrams.Segment type Codomain (Segment Closed v n) = v

data FixedSegment (v :: Type -> Type) n #

FixedSegments are like Segments except that they have absolute locations. FixedSegment v is isomorphic to Located (Segment Closed v), as witnessed by mkFixedSeg and fromFixedSeg, but FixedSegment is convenient when one needs the absolute locations of the vertices and control points.

Constructors

FLinear (Point v n) (Point v n)
FCubic (Point v n) (Point v n) (Point v n) (Point v n)

Instances

(Additive v, Num n) => Parametric (Tangent (FixedSegment v n))
Instance details Defined in Diagrams.Tangent Methods atParam :: Tangent (FixedSegment v n) -> N (Tangent (FixedSegment v n)) -> Codomain (Tangent (FixedSegment v n)) (N (Tangent (FixedSegment v n))) #
(Additive v, Num n) => EndValues (Tangent (FixedSegment v n))
Instance details Defined in Diagrams.Tangent Methods atStart :: Tangent (FixedSegment v n) -> Codomain (Tangent (FixedSegment v n)) (N (Tangent (FixedSegment v n))) # atEnd :: Tangent (FixedSegment v n) -> Codomain (Tangent (FixedSegment v n)) (N (Tangent (FixedSegment v n))) #
Show (v n) => Show (FixedSegment v n)
Instance details Defined in Diagrams.Segment Methods showsPrec :: Int -> FixedSegment v n -> ShowS # show :: FixedSegment v n -> String # showList :: [FixedSegment v n] -> ShowS #
(Metric v, OrderedField n) => Enveloped (FixedSegment v n)
Instance details Defined in Diagrams.Segment Methods getEnvelope :: FixedSegment v n -> Envelope (V (FixedSegment v n)) (N (FixedSegment v n)) #
(Additive v, Num n) => Transformable (FixedSegment v n)
Instance details Defined in Diagrams.Segment Methods transform :: Transformation (V (FixedSegment v n)) (N (FixedSegment v n)) -> FixedSegment v n -> FixedSegment v n #
(Additive v, Num n) => HasOrigin (FixedSegment v n)
Instance details Defined in Diagrams.Segment Methods moveOriginTo :: Point (V (FixedSegment v n)) (N (FixedSegment v n)) -> FixedSegment v n -> FixedSegment v n #
ToPath (FixedSegment v n)
Instance details Defined in Diagrams.Path Methods toPath :: FixedSegment v n -> Path (V (FixedSegment v n)) (N (FixedSegment v n)) #
(Additive v, Num n) => Parametric (FixedSegment v n)
Instance details Defined in Diagrams.Segment Methods atParam :: FixedSegment v n -> N (FixedSegment v n) -> Codomain (FixedSegment v n) (N (FixedSegment v n)) #
Num n => DomainBounds (FixedSegment v n)
Instance details Defined in Diagrams.Segment Methods domainLower :: FixedSegment v n -> N (FixedSegment v n) # domainUpper :: FixedSegment v n -> N (FixedSegment v n) #
(Additive v, Num n) => EndValues (FixedSegment v n)
Instance details Defined in Diagrams.Segment Methods atStart :: FixedSegment v n -> Codomain (FixedSegment v n) (N (FixedSegment v n)) # atEnd :: FixedSegment v n -> Codomain (FixedSegment v n) (N (FixedSegment v n)) #
(Additive v, Fractional n) => Sectionable (FixedSegment v n)
Instance details Defined in Diagrams.Segment Methods splitAtParam :: FixedSegment v n -> N (FixedSegment v n) -> (FixedSegment v n, FixedSegment v n) # section :: FixedSegment v n -> N (FixedSegment v n) -> N (FixedSegment v n) -> FixedSegment v n # reverseDomain :: FixedSegment v n -> FixedSegment v n #
(Metric v, OrderedField n) => HasArcLength (FixedSegment v n)
Instance details Defined in Diagrams.Segment Methods arcLengthBounded :: N (FixedSegment v n) -> FixedSegment v n -> Interval (N (FixedSegment v n)) # arcLength :: N (FixedSegment v n) -> FixedSegment v n -> N (FixedSegment v n) # stdArcLength :: FixedSegment v n -> N (FixedSegment v n) # arcLengthToParam :: N (FixedSegment v n) -> FixedSegment v n -> N (FixedSegment v n) -> N (FixedSegment v n) # stdArcLengthToParam :: FixedSegment v n -> N (FixedSegment v n) -> N (FixedSegment v n) #
Reversing (FixedSegment v n)	Reverses the control points.
Instance details Defined in Diagrams.Segment Methods reversing :: FixedSegment v n -> FixedSegment v n #
Each (FixedSegment v n) (FixedSegment v' n') (Point v n) (Point v' n')
Instance details Defined in Diagrams.Segment Methods each :: Traversal (FixedSegment v n) (FixedSegment v' n') (Point v n) (Point v' n') #
type V (FixedSegment v n)
Instance details Defined in Diagrams.Segment type V (FixedSegment v n) = v
type N (FixedSegment v n)
Instance details Defined in Diagrams.Segment type N (FixedSegment v n) = n
type Codomain (FixedSegment v n)
Instance details Defined in Diagrams.Segment type Codomain (FixedSegment v n) = Point v

newtype SegCount #

A type to track the count of segments in a Trail.

Constructors

SegCount (Sum Int)

Instances

Semigroup SegCount
Instance details Defined in Diagrams.Segment Methods (<>) :: SegCount -> SegCount -> SegCount # sconcat :: NonEmpty SegCount -> SegCount # stimes :: Integral b => b -> SegCount -> SegCount #
Monoid SegCount
Instance details Defined in Diagrams.Segment Methods mempty :: SegCount # mappend :: SegCount -> SegCount -> SegCount # mconcat :: [SegCount] -> SegCount #
Wrapped SegCount
Instance details Defined in Diagrams.Segment Associated Types type Unwrapped SegCount :: Type # Methods _Wrapped' :: Iso' SegCount (Unwrapped SegCount) #
Rewrapped SegCount SegCount
Instance details Defined in Diagrams.Segment
(Metric v, OrderedField n) => Measured (SegMeasure v n) (SegMeasure v n)
Instance details Defined in Diagrams.Segment Methods measure :: SegMeasure v n -> SegMeasure v n #
(Floating n, Ord n, Metric v) => Measured (SegMeasure v n) (SegTree v n)
Instance details Defined in Diagrams.Trail Methods measure :: SegTree v n -> SegMeasure v n #
(OrderedField n, Metric v) => Measured (SegMeasure v n) (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods measure :: Segment Closed v n -> SegMeasure v n #
type Unwrapped SegCount
Instance details Defined in Diagrams.Segment type Unwrapped SegCount = Sum Int

newtype ArcLength n #

A type to represent the total arc length of a chain of segments. The first component is a "standard" arc length, computed to within a tolerance of 10e-6. The second component is a generic arc length function taking the tolerance as an argument.

Constructors

ArcLength (Sum (Interval n), n -> Sum (Interval n))

Instances

(Num n, Ord n) => Semigroup (ArcLength n)
Instance details Defined in Diagrams.Segment Methods (<>) :: ArcLength n -> ArcLength n -> ArcLength n # sconcat :: NonEmpty (ArcLength n) -> ArcLength n # stimes :: Integral b => b -> ArcLength n -> ArcLength n #
(Num n, Ord n) => Monoid (ArcLength n)
Instance details Defined in Diagrams.Segment Methods mempty :: ArcLength n # mappend :: ArcLength n -> ArcLength n -> ArcLength n # mconcat :: [ArcLength n] -> ArcLength n #
Wrapped (ArcLength n)
Instance details Defined in Diagrams.Segment Associated Types type Unwrapped (ArcLength n) :: Type # Methods _Wrapped' :: Iso' (ArcLength n) (Unwrapped (ArcLength n)) #
Rewrapped (ArcLength n) (ArcLength n')
Instance details Defined in Diagrams.Segment
(Metric v, OrderedField n) => Measured (SegMeasure v n) (SegMeasure v n)
Instance details Defined in Diagrams.Segment Methods measure :: SegMeasure v n -> SegMeasure v n #
(Floating n, Ord n, Metric v) => Measured (SegMeasure v n) (SegTree v n)
Instance details Defined in Diagrams.Trail Methods measure :: SegTree v n -> SegMeasure v n #
(OrderedField n, Metric v) => Measured (SegMeasure v n) (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods measure :: Segment Closed v n -> SegMeasure v n #
type Unwrapped (ArcLength n)
Instance details Defined in Diagrams.Segment type Unwrapped (ArcLength n) = (Sum (Interval n), n -> Sum (Interval n))

newtype TotalOffset (v :: Type -> Type) n #

A type to represent the total cumulative offset of a chain of segments.

Constructors

TotalOffset (v n)

Instances

(Num n, Additive v) => Semigroup (TotalOffset v n)
Instance details Defined in Diagrams.Segment Methods (<>) :: TotalOffset v n -> TotalOffset v n -> TotalOffset v n # sconcat :: NonEmpty (TotalOffset v n) -> TotalOffset v n # stimes :: Integral b => b -> TotalOffset v n -> TotalOffset v n #
(Num n, Additive v) => Monoid (TotalOffset v n)
Instance details Defined in Diagrams.Segment Methods mempty :: TotalOffset v n # mappend :: TotalOffset v n -> TotalOffset v n -> TotalOffset v n # mconcat :: [TotalOffset v n] -> TotalOffset v n #
Wrapped (TotalOffset v n)
Instance details Defined in Diagrams.Segment Associated Types type Unwrapped (TotalOffset v n) :: Type # Methods _Wrapped' :: Iso' (TotalOffset v n) (Unwrapped (TotalOffset v n)) #
Rewrapped (TotalOffset v n) (TotalOffset v' n')
Instance details Defined in Diagrams.Segment
type Unwrapped (TotalOffset v n)
Instance details Defined in Diagrams.Segment type Unwrapped (TotalOffset v n) = v n

data OffsetEnvelope (v :: Type -> Type) n #

A type to represent the offset and envelope of a chain of segments. They have to be paired into one data structure, since combining the envelopes of two consecutive chains needs to take the offset of the first into account.

Constructors

OffsetEnvelope
Fields _oeOffset :: !(TotalOffset v n) _oeEnvelope :: Envelope v n

Instances

(Metric v, OrderedField n) => Semigroup (OffsetEnvelope v n)
Instance details Defined in Diagrams.Segment Methods (<>) :: OffsetEnvelope v n -> OffsetEnvelope v n -> OffsetEnvelope v n # sconcat :: NonEmpty (OffsetEnvelope v n) -> OffsetEnvelope v n # stimes :: Integral b => b -> OffsetEnvelope v n -> OffsetEnvelope v n #
(Metric v, OrderedField n) => Measured (SegMeasure v n) (SegMeasure v n)
Instance details Defined in Diagrams.Segment Methods measure :: SegMeasure v n -> SegMeasure v n #
(Floating n, Ord n, Metric v) => Measured (SegMeasure v n) (SegTree v n)
Instance details Defined in Diagrams.Trail Methods measure :: SegTree v n -> SegMeasure v n #
(OrderedField n, Metric v) => Measured (SegMeasure v n) (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods measure :: Segment Closed v n -> SegMeasure v n #

_loc :: Lens' (Located a) (Point (V a) (N a)) #

Lens onto the location of something Located.

located :: SameSpace a b => Lens (Located a) (Located b) a b #

A lens giving access to the object within a Located wrapper.

mapLoc :: SameSpace a b => (a -> b) -> Located a -> Located b #

Located is not a Functor, since changing the type could change the type of the associated vector space, in which case the associated location would no longer have the right type. mapLoc has an extra constraint specifying that the vector space must stay the same.

(Technically, one can say that for every vector space v, Located is a little-f (endo)functor on the category of types with associated vector space v; but that is not covered by the standard Functor class.)

viewLoc :: Located a -> (Point (V a) (N a), a) #

Deconstruct a Located a into a location and a value of type a. viewLoc can be especially useful in conjunction with the ViewPatterns extension.

at :: a -> Point (V a) (N a) -> Located a infix 5 #

Construct a Located a from a value of type a and a location. at is intended to be used infix, like x `at` origin.

data Located a #

"Located" things, i.e. things with a concrete location: intuitively, Located a ~ (Point, a). Wrapping a translationally invariant thing (e.g. a Segment or Trail) in Located pins it down to a particular location and makes it no longer translationally invariant.

Located is intentionally abstract. To construct Located values, use at. To destruct, use viewLoc, unLoc, or loc. To map, use mapLoc.

Much of the utility of having a concrete type for the Located concept lies in the type class instances we can give it. The HasOrigin, Transformable, Enveloped, Traced, and TrailLike instances are particularly useful; see the documented instances below for more information.

Constructors

Loc
Fields loc :: Point (V a) (N a) Project out the location of a `Located` value. unLoc :: a Project the value of type `a` out of a `Located a`, discarding the location.

Instances

(Eq (V a (N a)), Eq a) => Eq (Located a)
Instance details Defined in Diagrams.Located Methods (==) :: Located a -> Located a -> Bool # (/=) :: Located a -> Located a -> Bool #
(Ord (V a (N a)), Ord a) => Ord (Located a)
Instance details Defined in Diagrams.Located Methods compare :: Located a -> Located a -> Ordering # (<) :: Located a -> Located a -> Bool # (<=) :: Located a -> Located a -> Bool # (>) :: Located a -> Located a -> Bool # (>=) :: Located a -> Located a -> Bool # max :: Located a -> Located a -> Located a # min :: Located a -> Located a -> Located a #
(Read (V a (N a)), Read a) => Read (Located a)
Instance details Defined in Diagrams.Located Methods readsPrec :: Int -> ReadS (Located a) # readList :: ReadS [Located a] # readPrec :: ReadPrec (Located a) # readListPrec :: ReadPrec [Located a] #
(Show (V a (N a)), Show a) => Show (Located a)
Instance details Defined in Diagrams.Located Methods showsPrec :: Int -> Located a -> ShowS # show :: Located a -> String # showList :: [Located a] -> ShowS #
Generic (Located a)
Instance details Defined in Diagrams.Located Associated Types type Rep (Located a) :: Type -> Type # Methods from :: Located a -> Rep (Located a) x # to :: Rep (Located a) x -> Located a #
(Serialize a, Serialize (V a (N a))) => Serialize (Located a)
Instance details Defined in Diagrams.Located Methods put :: Putter (Located a) # get :: Get (Located a) #
Enveloped a => Juxtaposable (Located a)
Instance details Defined in Diagrams.Located Methods juxtapose :: Vn (Located a) -> Located a -> Located a -> Located a #
Enveloped a => Enveloped (Located a)	The envelope of a `Located a` is the envelope of the `a`, translated to the location.
Instance details Defined in Diagrams.Located Methods getEnvelope :: Located a -> Envelope (V (Located a)) (N (Located a)) #
(Traced a, Num (N a)) => Traced (Located a)	The trace of a `Located a` is the trace of the `a`, translated to the location.
Instance details Defined in Diagrams.Located Methods getTrace :: Located a -> Trace (V (Located a)) (N (Located a)) #
Qualifiable a => Qualifiable (Located a)
Instance details Defined in Diagrams.Located Methods (.>>) :: IsName a0 => a0 -> Located a -> Located a #
(Additive (V a), Num (N a), Transformable a) => Transformable (Located a)	Applying a transformation `t` to a `Located a` results in the transformation being applied to the location, and the linear portion of `t` being applied to the value of type `a` (i.e. it is not translated).
Instance details Defined in Diagrams.Located Methods transform :: Transformation (V (Located a)) (N (Located a)) -> Located a -> Located a #
(Num (N a), Additive (V a)) => HasOrigin (Located a)	`Located a` is an instance of `HasOrigin` whether `a` is or not. In particular, translating a `Located a` simply translates the associated point (and does not affect the value of type `a`).
Instance details Defined in Diagrams.Located Methods moveOriginTo :: Point (V (Located a)) (N (Located a)) -> Located a -> Located a #
ToPath (Located [Segment Closed v n])
Instance details Defined in Diagrams.Path Methods toPath :: Located [Segment Closed v n] -> Path (V (Located [Segment Closed v n])) (N (Located [Segment Closed v n])) #
ToPath (Located (Trail' l v n))
Instance details Defined in Diagrams.Path Methods toPath :: Located (Trail' l v n) -> Path (V (Located (Trail' l v n))) (N (Located (Trail' l v n))) #
ToPath (Located (Trail v n))
Instance details Defined in Diagrams.Path Methods toPath :: Located (Trail v n) -> Path (V (Located (Trail v n))) (N (Located (Trail v n))) #
ToPath (Located (Segment Closed v n))
Instance details Defined in Diagrams.Path Methods toPath :: Located (Segment Closed v n) -> Path (V (Located (Segment Closed v n))) (N (Located (Segment Closed v n))) #
TrailLike t => TrailLike (Located t)	`Located` things are trail-like as long as the underlying type is. The location is taken to be the location of the input located trail.
Instance details Defined in Diagrams.TrailLike Methods trailLike :: Located (Trail (V (Located t)) (N (Located t))) -> Located t #
Alignable a => Alignable (Located a)
Instance details Defined in Diagrams.Located Methods alignBy' :: (InSpace v n (Located a), Fractional n, HasOrigin (Located a)) => (v n -> Located a -> Point v n) -> v n -> n -> Located a -> Located a # defaultBoundary :: (V (Located a) ~ v, N (Located a) ~ n) => v n -> Located a -> Point v n # alignBy :: (InSpace v n (Located a), Fractional n, HasOrigin (Located a)) => v n -> n -> Located a -> Located a #
Parametric (Tangent t) => Parametric (Tangent (Located t))
Instance details Defined in Diagrams.Tangent Methods atParam :: Tangent (Located t) -> N (Tangent (Located t)) -> Codomain (Tangent (Located t)) (N (Tangent (Located t))) #
(InSpace v n a, Parametric a, Codomain a ~ v) => Parametric (Located a)
Instance details Defined in Diagrams.Located Methods atParam :: Located a -> N (Located a) -> Codomain (Located a) (N (Located a)) #
DomainBounds a => DomainBounds (Located a)
Instance details Defined in Diagrams.Located Methods domainLower :: Located a -> N (Located a) # domainUpper :: Located a -> N (Located a) #
(DomainBounds t, EndValues (Tangent t)) => EndValues (Tangent (Located t))
Instance details Defined in Diagrams.Tangent Methods atStart :: Tangent (Located t) -> Codomain (Tangent (Located t)) (N (Tangent (Located t))) # atEnd :: Tangent (Located t) -> Codomain (Tangent (Located t)) (N (Tangent (Located t))) #
(InSpace v n a, EndValues a, Codomain a ~ v) => EndValues (Located a)
Instance details Defined in Diagrams.Located Methods atStart :: Located a -> Codomain (Located a) (N (Located a)) # atEnd :: Located a -> Codomain (Located a) (N (Located a)) #
(InSpace v n a, Fractional n, Parametric a, Sectionable a, Codomain a ~ v) => Sectionable (Located a)
Instance details Defined in Diagrams.Located Methods splitAtParam :: Located a -> N (Located a) -> (Located a, Located a) # section :: Located a -> N (Located a) -> N (Located a) -> Located a # reverseDomain :: Located a -> Located a #
(InSpace v n a, Fractional n, HasArcLength a, Codomain a ~ v) => HasArcLength (Located a)
Instance details Defined in Diagrams.Located Methods arcLengthBounded :: N (Located a) -> Located a -> Interval (N (Located a)) # arcLength :: N (Located a) -> Located a -> N (Located a) # stdArcLength :: Located a -> N (Located a) # arcLengthToParam :: N (Located a) -> Located a -> N (Located a) -> N (Located a) # stdArcLengthToParam :: Located a -> N (Located a) -> N (Located a) #
(Metric v, OrderedField n) => Reversing (Located (Trail' l v n))	Same as `reverseLocLine` or `reverseLocLoop`.
Instance details Defined in Diagrams.Trail Methods reversing :: Located (Trail' l v n) -> Located (Trail' l v n) #
(Metric v, OrderedField n) => Reversing (Located (Trail v n))	Same as `reverseLocTrail`.
Instance details Defined in Diagrams.Trail Methods reversing :: Located (Trail v n) -> Located (Trail v n) #
(Metric v, Metric u, OrderedField n, r ~ Located (Trail u n)) => Deformable (Located (Trail v n)) r
Instance details Defined in Diagrams.Deform Methods deform' :: N (Located (Trail v n)) -> Deformation (V (Located (Trail v n))) (V r) (N (Located (Trail v n))) -> Located (Trail v n) -> r # deform :: Deformation (V (Located (Trail v n))) (V r) (N (Located (Trail v n))) -> Located (Trail v n) -> r #
Snoc (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))
Instance details Defined in Diagrams.Path Methods _Snoc :: Prism (Path v n) (Path v' n') (Path v n, Located (Trail v n)) (Path v' n', Located (Trail v' n')) #
Cons (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))
Instance details Defined in Diagrams.Path Methods _Cons :: Prism (Path v n) (Path v' n') (Located (Trail v n), Path v n) (Located (Trail v' n'), Path v' n') #
Each (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))
Instance details Defined in Diagrams.Path Methods each :: Traversal (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n')) #
type Rep (Located a)
Instance details Defined in Diagrams.Located type Rep (Located a) = D1 (MetaData "Located" "Diagrams.Located" "diagrams-lib-1.4.2.3-4IkVVBmK9qBElHMtgqeLQ1" False) (C1 (MetaCons "Loc" PrefixI True) (S1 (MetaSel (Just "loc") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Point (V a) (N a))) :*: S1 (MetaSel (Just "unLoc") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type V (Located a)
Instance details Defined in Diagrams.Located type V (Located a) = V a
type N (Located a)
Instance details Defined in Diagrams.Located type N (Located a) = N a
type Codomain (Located a)
Instance details Defined in Diagrams.Located type Codomain (Located a) = Point (Codomain a)

snugCenterXYZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a #

centerXYZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a #

Center an object in three dimensions.

snugCenterYZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a #

centerYZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a #

Center along both the Y- and Z-axes.

snugCenterXZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a #

centerXZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a #

Center along both the X- and Z-axes.

snugCenterZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a #

centerZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a #

Center the local origin along the Z-axis.

snugZ :: (V a ~ v, N a ~ n, Alignable a, Traced a, HasOrigin a, R3 v, Fractional n) => n -> a -> a #

See the documentation for alignZ.

alignZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => n -> a -> a #

Like alignX, but moving the local origin in the Z direction, with an argument of 1 corresponding to the top edge and (-1) corresponding to the bottom edge.

snugZMax :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a #

alignZMax :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a #

Translate the diagram along unitZ so that all points have negative z-values.

snugZMin :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a #

alignZMin :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a #

Translate the diagram along unitZ so that all points have positive z-values.

snugYMax :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a #

alignYMax :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a) => a -> a #

Translate the diagram along unitY so that all points have negative y-values.

snugYMin :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a #

alignYMin :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a) => a -> a #

Translate the diagram along unitY so that all points have positive y-values.

snugXMax :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a #

alignXMax :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a) => a -> a #

Translate the diagram along unitX so that all points have negative x-values.

snugXMin :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a #

alignXMin :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a) => a -> a #

Translate the diagram along unitX so that all points have positive x-values.

snugCenterXY :: (InSpace v n a, R2 v, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a #

centerXY :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a) => a -> a #

Center along both the X- and Y-axes.

snugCenterY :: (InSpace v n a, R2 v, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a #

centerY :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a) => a -> a #

Center the local origin along the Y-axis.

snugCenterX :: (InSpace v n a, R1 v, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a #

centerX :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a) => a -> a #

Center the local origin along the X-axis.

snugY :: (InSpace v n a, R2 v, Fractional n, Alignable a, Traced a, HasOrigin a) => n -> a -> a #

See the documentation for alignY.

alignY :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a) => n -> a -> a #

Like alignX, but moving the local origin vertically, with an argument of 1 corresponding to the top edge and (-1) corresponding to the bottom edge.

snugX :: (InSpace v n a, R1 v, Fractional n, Alignable a, Traced a, HasOrigin a) => n -> a -> a #

See the documentation for alignX.

alignX :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a) => n -> a -> a #

alignX and snugX move the local origin horizontally as follows:

alignX (-1) moves the local origin to the left edge of the boundary;
align 1 moves the local origin to the right edge;
any other argument interpolates linearly between these. For example, alignX 0 centers, alignX 2 moves the origin one "radius" to the right of the right edge, and so on.
snugX works the same way.

alignBR :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a #

alignBL :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a #

alignTR :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a #

alignTL :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a #

snugB :: (InSpace V2 n a, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a #

alignB :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a #

Align along the bottom edge.

snugT :: (InSpace V2 n a, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a #

alignT :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a #

Align along the top edge.

snugR :: (InSpace V2 n a, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a #

alignR :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a #

Align along the right edge.

snugL :: (InSpace V2 n a, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a #

alignL :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a #

Align along the left edge, i.e. translate the diagram in a horizontal direction so that the local origin is on the left edge of the envelope.

snugCenter :: (InSpace v n a, Traversable v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a #

Like center using trace.

snugCenterV :: (InSpace v n a, Fractional n, Alignable a, Traced a, HasOrigin a) => v n -> a -> a #

Like centerV using trace.

center :: (InSpace v n a, Fractional n, Traversable v, Alignable a, HasOrigin a) => a -> a #

center centers an enveloped object along all of its basis vectors.

centerV :: (InSpace v n a, Fractional n, Alignable a, HasOrigin a) => v n -> a -> a #

centerV v centers an enveloped object along the direction of v.

snug :: (InSpace v n a, Fractional n, Alignable a, Traced a, HasOrigin a) => v n -> a -> a #

Like align but uses trace.

snugBy :: (InSpace v n a, Fractional n, Alignable a, Traced a, HasOrigin a) => v n -> n -> a -> a #

Version of alignBy specialized to use traceBoundary

align :: (InSpace v n a, Fractional n, Alignable a, HasOrigin a) => v n -> a -> a #

align v aligns an enveloped object along the edge in the direction of v. That is, it moves the local origin in the direction of v until it is on the edge of the envelope. (Note that if the local origin is outside the envelope to begin with, it may have to move "backwards".)

traceBoundary :: (V a ~ v, N a ~ n, Num n, Traced a) => v n -> a -> Point v n #

envelopeBoundary :: (V a ~ v, N a ~ n, Enveloped a) => v n -> a -> Point v n #

Some standard functions which can be used as the boundary argument to alignBy'.

alignBy'Default :: (InSpace v n a, Fractional n, HasOrigin a) => (v n -> a -> Point v n) -> v n -> n -> a -> a #

Default implementation of alignBy for types with HasOrigin and AdditiveGroup instances.

class Alignable a where #

Class of things which can be aligned.

Minimal complete definition

defaultBoundary

Methods

alignBy' :: (InSpace v n a, Fractional n, HasOrigin a) => (v n -> a -> Point v n) -> v n -> n -> a -> a #

alignBy v d a moves the origin of a along the vector v. If d = 1, the origin is moved to the edge of the boundary in the direction of v; if d = -1, it moves to the edge of the boundary in the direction of the negation of v. Other values of d interpolate linearly (so for example, d = 0 centers the origin along the direction of v).

defaultBoundary :: (V a ~ v, N a ~ n) => v n -> a -> Point v n #

alignBy :: (InSpace v n a, Fractional n, HasOrigin a) => v n -> n -> a -> a #

Instances

(V b ~ v, N b ~ n, Metric v, OrderedField n, Alignable b) => Alignable [b]
Instance details Defined in Diagrams.Align Methods alignBy' :: (InSpace v n [b], Fractional n, HasOrigin [b]) => (v n -> [b] -> Point v n) -> v n -> n -> [b] -> [b] # defaultBoundary :: (V [b] ~ v, N [b] ~ n) => v n -> [b] -> Point v n # alignBy :: (InSpace v n [b], Fractional n, HasOrigin [b]) => v n -> n -> [b] -> [b] #
(V b ~ v, N b ~ n, Metric v, OrderedField n, Alignable b) => Alignable (Set b)
Instance details Defined in Diagrams.Align Methods alignBy' :: (InSpace v n (Set b), Fractional n, HasOrigin (Set b)) => (v n -> Set b -> Point v n) -> v n -> n -> Set b -> Set b # defaultBoundary :: (V (Set b) ~ v, N (Set b) ~ n) => v n -> Set b -> Point v n # alignBy :: (InSpace v n (Set b), Fractional n, HasOrigin (Set b)) => v n -> n -> Set b -> Set b #
Alignable a => Alignable (Located a)
Instance details Defined in Diagrams.Located Methods alignBy' :: (InSpace v n (Located a), Fractional n, HasOrigin (Located a)) => (v n -> Located a -> Point v n) -> v n -> n -> Located a -> Located a # defaultBoundary :: (V (Located a) ~ v, N (Located a) ~ n) => v n -> Located a -> Point v n # alignBy :: (InSpace v n (Located a), Fractional n, HasOrigin (Located a)) => v n -> n -> Located a -> Located a #
(InSpace v n a, HasOrigin a, Alignable a) => Alignable (b -> a)	Although the `alignBy` method for the `(b -> a)` instance is sensible, there is no good implementation for `defaultBoundary`. Instead, we provide a total method, but one that is not sensible. This should not present a serious problem as long as your use of `Alignable` happens through `alignBy`.
Instance details Defined in Diagrams.Align Methods alignBy' :: (InSpace v n (b -> a), Fractional n, HasOrigin (b -> a)) => (v n -> (b -> a) -> Point v n) -> v n -> n -> (b -> a) -> b -> a # defaultBoundary :: (V (b -> a) ~ v, N (b -> a) ~ n) => v n -> (b -> a) -> Point v n # alignBy :: (InSpace v n (b -> a), Fractional n, HasOrigin (b -> a)) => v n -> n -> (b -> a) -> b -> a #
(V b ~ v, N b ~ n, Metric v, OrderedField n, Alignable b) => Alignable (Map k b)
Instance details Defined in Diagrams.Align Methods alignBy' :: (InSpace v n (Map k b), Fractional n, HasOrigin (Map k b)) => (v n -> Map k b -> Point v n) -> v n -> n -> Map k b -> Map k b # defaultBoundary :: (V (Map k b) ~ v, N (Map k b) ~ n) => v n -> Map k b -> Point v n # alignBy :: (InSpace v n (Map k b), Fractional n, HasOrigin (Map k b)) => v n -> n -> Map k b -> Map k b #
(Metric v, OrderedField n) => Alignable (Envelope v n)
Instance details Defined in Diagrams.Align Methods alignBy' :: (InSpace v0 n0 (Envelope v n), Fractional n0, HasOrigin (Envelope v n)) => (v0 n0 -> Envelope v n -> Point v0 n0) -> v0 n0 -> n0 -> Envelope v n -> Envelope v n # defaultBoundary :: (V (Envelope v n) ~ v0, N (Envelope v n) ~ n0) => v0 n0 -> Envelope v n -> Point v0 n0 # alignBy :: (InSpace v0 n0 (Envelope v n), Fractional n0, HasOrigin (Envelope v n)) => v0 n0 -> n0 -> Envelope v n -> Envelope v n #
(Metric v, OrderedField n) => Alignable (Trace v n)
Instance details Defined in Diagrams.Align Methods alignBy' :: (InSpace v0 n0 (Trace v n), Fractional n0, HasOrigin (Trace v n)) => (v0 n0 -> Trace v n -> Point v0 n0) -> v0 n0 -> n0 -> Trace v n -> Trace v n # defaultBoundary :: (V (Trace v n) ~ v0, N (Trace v n) ~ n0) => v0 n0 -> Trace v n -> Point v0 n0 # alignBy :: (InSpace v0 n0 (Trace v n), Fractional n0, HasOrigin (Trace v n)) => v0 n0 -> n0 -> Trace v n -> Trace v n #
(Metric v, Traversable v, OrderedField n) => Alignable (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox Methods alignBy' :: (InSpace v0 n0 (BoundingBox v n), Fractional n0, HasOrigin (BoundingBox v n)) => (v0 n0 -> BoundingBox v n -> Point v0 n0) -> v0 n0 -> n0 -> BoundingBox v n -> BoundingBox v n # defaultBoundary :: (V (BoundingBox v n) ~ v0, N (BoundingBox v n) ~ n0) => v0 n0 -> BoundingBox v n -> Point v0 n0 # alignBy :: (InSpace v0 n0 (BoundingBox v n), Fractional n0, HasOrigin (BoundingBox v n)) => v0 n0 -> n0 -> BoundingBox v n -> BoundingBox v n #
(Metric v, OrderedField n) => Alignable (Path v n)
Instance details Defined in Diagrams.Path Methods alignBy' :: (InSpace v0 n0 (Path v n), Fractional n0, HasOrigin (Path v n)) => (v0 n0 -> Path v n -> Point v0 n0) -> v0 n0 -> n0 -> Path v n -> Path v n # defaultBoundary :: (V (Path v n) ~ v0, N (Path v n) ~ n0) => v0 n0 -> Path v n -> Point v0 n0 # alignBy :: (InSpace v0 n0 (Path v n), Fractional n0, HasOrigin (Path v n)) => v0 n0 -> n0 -> Path v n -> Path v n #
(Metric v, OrderedField n, Monoid' m) => Alignable (QDiagram b v n m)
Instance details Defined in Diagrams.Align Methods alignBy' :: (InSpace v0 n0 (QDiagram b v n m), Fractional n0, HasOrigin (QDiagram b v n m)) => (v0 n0 -> QDiagram b v n m -> Point v0 n0) -> v0 n0 -> n0 -> QDiagram b v n m -> QDiagram b v n m # defaultBoundary :: (V (QDiagram b v n m) ~ v0, N (QDiagram b v n m) ~ n0) => v0 n0 -> QDiagram b v n m -> Point v0 n0 # alignBy :: (InSpace v0 n0 (QDiagram b v n m), Fractional n0, HasOrigin (QDiagram b v n m)) => v0 n0 -> n0 -> QDiagram b v n m -> QDiagram b v n m #

globalPackage :: IO FilePath #

Find ghc's global package database. Throws an error if it isn't found.

findSandbox :: [FilePath] -> IO (Maybe FilePath) #

Search for a sandbox in the following order:

Test given FilePaths if they point directly to a database or contain a cabal config file (or any parent directory containing a config file).
Same test for DIAGRAMS_SANDBOX environment value
Environment values of GHC_PACKAGE_PATH, HSENV and PACKAGE_DB_FOR_GHC that point to a database.
Test for config file (cabal.sandbox.config) in the current directory and its parents.

findHsFile :: FilePath -> IO (Maybe FilePath) #

Given some file (no extension or otherwise) try to find a haskell source file.

foldB :: (a -> a -> a) -> a -> [a] -> a #

Given an associative binary operation and a default value to use in the case of an empty list, perform a balanced fold over a list. For example,

  foldB (+) z [a,b,c,d,e,f] == ((a+b) + (c+d)) + (e+f)

tau :: Floating a => a #

The circle constant, the ratio of a circle's circumference to its radius. Note that pi = tau/2.

For more information and a well-reasoned argument why we should all be using tau instead of pi, see The Tau Manifesto, http://tauday.com/.

To hear what it sounds like (and to easily memorize the first 30 digits or so), try http://youtu.be/3174T-3-59Q.

iterateN :: Int -> (a -> a) -> a -> [a] #

iterateN n f x returns the list of the first n iterates of f starting at x, that is, the list [x, f x, f (f x), ...] of length n. (Note that the last element of the list will be f applied to x (n-1) times.)

(##) :: AReview t b -> b -> t infixr 8 #

A replacement for lenses' # operator.

(#) :: a -> (a -> b) -> b infixl 8 #

Postfix function application, for conveniently applying attributes. Unlike ($), (#) has a high precedence (8), so d # foo # bar can be combined with other things using operators like (|||) or (<>) without needing parentheses.

applyAll :: [a -> a] -> a -> a #

applyAll takes a list of functions and applies them all to a value, in sequence from the last function in the list to the first. For example, applyAll [f1, f2, f3] a == f1 . f2 . f3 $ a.

with :: Default d => d #

Several functions exported by the diagrams library take a number of arguments giving the user control to "tweak" various aspects of their behavior. Rather than give such functions a long list of arguments, and to make it possible for the user to selectively override only certain arguments and use default values for others, such sets of arguments are collected into a record with named fields (see PolygonOpts in Diagrams.TwoD.Shapes for an example). Such record types are made instances of the Default class, which provides a single record structure (def) collecting the "default" arguments to the function. with is a synonym for def, which provides nice-looking syntax for simulating optional, named arguments in Haskell. For example,

  polygon with {sides = 7, edgeSkip = 2}

calls the polygon function with a single argument (note that record update binds more tightly than function application!), namely, with (the record of default arguments) where the sides and edgeSkip fields have been updated.

camAspect :: (Floating n, CameraLens l) => Camera l n -> n #

camLens :: Camera l n -> l n #

camRight :: Fractional n => Camera l n -> Direction V3 n #

camUp :: Camera l n -> Direction V3 n #

camForward :: Camera l n -> Direction V3 n #

mm50Narrow :: Floating n => PerspectiveLens n #

mm50Narrow has the same vertical field of view as mm50, but an aspect ratio of 4:3, for VGA and similar computer resolutions.

mm50Wide :: Floating n => PerspectiveLens n #

mm50blWide has the same vertical field of view as mm50, but an aspect ratio of 1.6, suitable for wide screen computer monitors.

mm50 :: Floating n => PerspectiveLens n #

mm50 has the field of view of a 50mm lens on standard 35mm film, hence an aspect ratio of 3:2.

facing_ZCamera :: (Floating n, Ord n, Typeable n, CameraLens l, Renderable (Camera l n) b) => l n -> QDiagram b V3 n Any #

'facing_ZCamera l' is a camera at the origin facing along the negative Z axis, with its up-axis coincident with the positive Y axis, with the projection defined by l.

mm50Camera :: (Typeable n, Floating n, Ord n, Renderable (Camera PerspectiveLens n) b) => QDiagram b V3 n Any #

A camera at the origin facing along the negative Z axis, with its up-axis coincident with the positive Y axis. The field of view is chosen to match a 50mm camera on 35mm film. Note that Cameras take up no space in the Diagram.

orthoWidth :: Lens' (OrthoLens n) n #

orthoHeight :: Lens' (OrthoLens n) n #

verticalFieldOfView :: Lens' (PerspectiveLens n) (Angle n) #

horizontalFieldOfView :: Lens' (PerspectiveLens n) (Angle n) #

data OrthoLens n #

An orthographic projection

Constructors

OrthoLens
Fields _orthoWidth :: n Width _orthoHeight :: n Height

Instances

CameraLens OrthoLens
Instance details Defined in Diagrams.ThreeD.Camera Methods aspect :: Floating n => OrthoLens n -> n #
type V (OrthoLens n)
Instance details Defined in Diagrams.ThreeD.Camera type V (OrthoLens n) = V3
type N (OrthoLens n)
Instance details Defined in Diagrams.ThreeD.Camera type N (OrthoLens n) = n

data Camera (l :: Type -> Type) n #

Instances

Num n => Transformable (Camera l n)
Instance details Defined in Diagrams.ThreeD.Camera Methods transform :: Transformation (V (Camera l n)) (N (Camera l n)) -> Camera l n -> Camera l n #
Num n => Renderable (Camera l n) NullBackend
Instance details Defined in Diagrams.ThreeD.Camera Methods render :: NullBackend -> Camera l n -> Render NullBackend (V (Camera l n)) (N (Camera l n)) #
type V (Camera l n)
Instance details Defined in Diagrams.ThreeD.Camera type V (Camera l n) = V3
type N (Camera l n)
Instance details Defined in Diagrams.ThreeD.Camera type N (Camera l n) = n

data PerspectiveLens n #

A perspective projection

Constructors

PerspectiveLens
Fields _horizontalFieldOfView :: Angle n Horizontal field of view. _verticalFieldOfView :: Angle n Vertical field of view.

Instances

CameraLens PerspectiveLens
Instance details Defined in Diagrams.ThreeD.Camera Methods aspect :: Floating n => PerspectiveLens n -> n #
type V (PerspectiveLens n)
Instance details Defined in Diagrams.ThreeD.Camera type V (PerspectiveLens n) = V3
type N (PerspectiveLens n)
Instance details Defined in Diagrams.ThreeD.Camera type N (PerspectiveLens n) = n

difference :: (CsgPrim a, CsgPrim b) => a n -> b n -> CSG n #

intersection :: (CsgPrim a, CsgPrim b) => a n -> b n -> CSG n #

union :: (CsgPrim a, CsgPrim b) => a n -> b n -> CSG n #

cylinder :: Num n => Frustum n #

A circular cylinder of radius 1 with one end cap centered on the origin, and extending to Z=1.

cone :: Num n => Frustum n #

A cone with its base centered on the origin, with radius 1 at the base, height 1, and it's apex on the positive Z axis.

frustum :: Num n => n -> n -> Frustum n #

A frustum of a right circular cone. It has height 1 oriented along the positive z axis, and radii r0 and r1 at Z=0 and Z=1. cone and cylinder are special cases.

cube :: Num n => Box n #

A cube with side length 1, in the positive octant, with one vertex at the origin.

sphere :: Num n => Ellipsoid n #

A sphere of radius 1 with its center at the origin.

data Ellipsoid n #

Constructors

Ellipsoid (Transformation V3 n)

Instances

CsgPrim Ellipsoid
Instance details Defined in Diagrams.ThreeD.Shapes Methods toCsg :: Ellipsoid n -> CSG n
OrderedField n => Enveloped (Ellipsoid n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods getEnvelope :: Ellipsoid n -> Envelope (V (Ellipsoid n)) (N (Ellipsoid n)) #
OrderedField n => Traced (Ellipsoid n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods getTrace :: Ellipsoid n -> Trace (V (Ellipsoid n)) (N (Ellipsoid n)) #
Fractional n => Transformable (Ellipsoid n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods transform :: Transformation (V (Ellipsoid n)) (N (Ellipsoid n)) -> Ellipsoid n -> Ellipsoid n #
OrderedField n => Skinned (Ellipsoid n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods skin :: (Renderable (Ellipsoid n) b, N (Ellipsoid n) ~ n0, TypeableFloat n0) => Ellipsoid n -> QDiagram b V3 n0 Any #
Fractional n => Renderable (Ellipsoid n) NullBackend
Instance details Defined in Diagrams.ThreeD.Shapes Methods render :: NullBackend -> Ellipsoid n -> Render NullBackend (V (Ellipsoid n)) (N (Ellipsoid n)) #
(Num n, Ord n) => HasQuery (Ellipsoid n) Any
Instance details Defined in Diagrams.ThreeD.Shapes Methods getQuery :: Ellipsoid n -> Query (V (Ellipsoid n)) (N (Ellipsoid n)) Any #
type V (Ellipsoid n)
Instance details Defined in Diagrams.ThreeD.Shapes type V (Ellipsoid n) = V3
type N (Ellipsoid n)
Instance details Defined in Diagrams.ThreeD.Shapes type N (Ellipsoid n) = n

data Box n #

Constructors

Box (Transformation V3 n)

Instances

CsgPrim Box
Instance details Defined in Diagrams.ThreeD.Shapes Methods toCsg :: Box n -> CSG n
OrderedField n => Enveloped (Box n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods getEnvelope :: Box n -> Envelope (V (Box n)) (N (Box n)) #
(Fractional n, Ord n) => Traced (Box n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods getTrace :: Box n -> Trace (V (Box n)) (N (Box n)) #
Fractional n => Transformable (Box n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods transform :: Transformation (V (Box n)) (N (Box n)) -> Box n -> Box n #
OrderedField n => Skinned (Box n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods skin :: (Renderable (Box n) b, N (Box n) ~ n0, TypeableFloat n0) => Box n -> QDiagram b V3 n0 Any #
Fractional n => Renderable (Box n) NullBackend
Instance details Defined in Diagrams.ThreeD.Shapes Methods render :: NullBackend -> Box n -> Render NullBackend (V (Box n)) (N (Box n)) #
(Num n, Ord n) => HasQuery (Box n) Any
Instance details Defined in Diagrams.ThreeD.Shapes Methods getQuery :: Box n -> Query (V (Box n)) (N (Box n)) Any #
type V (Box n)
Instance details Defined in Diagrams.ThreeD.Shapes type V (Box n) = V3
type N (Box n)
Instance details Defined in Diagrams.ThreeD.Shapes type N (Box n) = n

data Frustum n #

Constructors

Frustum n n (Transformation V3 n)

Instances

CsgPrim Frustum
Instance details Defined in Diagrams.ThreeD.Shapes Methods toCsg :: Frustum n -> CSG n
(OrderedField n, RealFloat n) => Enveloped (Frustum n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods getEnvelope :: Frustum n -> Envelope (V (Frustum n)) (N (Frustum n)) #
(RealFloat n, Ord n) => Traced (Frustum n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods getTrace :: Frustum n -> Trace (V (Frustum n)) (N (Frustum n)) #
Fractional n => Transformable (Frustum n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods transform :: Transformation (V (Frustum n)) (N (Frustum n)) -> Frustum n -> Frustum n #
Skinned (Frustum n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods skin :: (Renderable (Frustum n) b, N (Frustum n) ~ n0, TypeableFloat n0) => Frustum n -> QDiagram b V3 n0 Any #
Fractional n => Renderable (Frustum n) NullBackend
Instance details Defined in Diagrams.ThreeD.Shapes Methods render :: NullBackend -> Frustum n -> Render NullBackend (V (Frustum n)) (N (Frustum n)) #
OrderedField n => HasQuery (Frustum n) Any
Instance details Defined in Diagrams.ThreeD.Shapes Methods getQuery :: Frustum n -> Query (V (Frustum n)) (N (Frustum n)) Any #
type V (Frustum n)
Instance details Defined in Diagrams.ThreeD.Shapes type V (Frustum n) = V3
type N (Frustum n)
Instance details Defined in Diagrams.ThreeD.Shapes type N (Frustum n) = n

class Skinned t where #

Types which can be rendered as 3D Diagrams.

Methods

skin :: (Renderable t b, N t ~ n, TypeableFloat n) => t -> QDiagram b V3 n Any #

Instances

OrderedField n => Skinned (Ellipsoid n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods skin :: (Renderable (Ellipsoid n) b, N (Ellipsoid n) ~ n0, TypeableFloat n0) => Ellipsoid n -> QDiagram b V3 n0 Any #
OrderedField n => Skinned (Box n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods skin :: (Renderable (Box n) b, N (Box n) ~ n0, TypeableFloat n0) => Box n -> QDiagram b V3 n0 Any #
Skinned (Frustum n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods skin :: (Renderable (Frustum n) b, N (Frustum n) ~ n0, TypeableFloat n0) => Frustum n -> QDiagram b V3 n0 Any #
(RealFloat n, Ord n) => Skinned (CSG n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods skin :: (Renderable (CSG n) b, N (CSG n) ~ n0, TypeableFloat n0) => CSG n -> QDiagram b V3 n0 Any #

data CSG n #

A tree of Constructive Solid Geometry operations and the primitives that can be used in them.

Constructors

CsgEllipsoid (Ellipsoid n)
CsgBox (Box n)
CsgFrustum (Frustum n)
CsgUnion [CSG n]
CsgIntersection [CSG n]
CsgDifference (CSG n) (CSG n)

Instances

CsgPrim CSG
Instance details Defined in Diagrams.ThreeD.Shapes Methods toCsg :: CSG n -> CSG n
RealFloat n => Enveloped (CSG n)	The Envelope for an Intersection or Difference is simply the Envelope of the Union. This is wrong but easy to implement.
Instance details Defined in Diagrams.ThreeD.Shapes Methods getEnvelope :: CSG n -> Envelope (V (CSG n)) (N (CSG n)) #
(RealFloat n, Ord n) => Traced (CSG n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods getTrace :: CSG n -> Trace (V (CSG n)) (N (CSG n)) #
Fractional n => Transformable (CSG n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods transform :: Transformation (V (CSG n)) (N (CSG n)) -> CSG n -> CSG n #
(RealFloat n, Ord n) => Skinned (CSG n)
Instance details Defined in Diagrams.ThreeD.Shapes Methods skin :: (Renderable (CSG n) b, N (CSG n) ~ n0, TypeableFloat n0) => CSG n -> QDiagram b V3 n0 Any #
(Floating n, Ord n) => HasQuery (CSG n) Any
Instance details Defined in Diagrams.ThreeD.Shapes Methods getQuery :: CSG n -> Query (V (CSG n)) (N (CSG n)) Any #
type V (CSG n)
Instance details Defined in Diagrams.ThreeD.Shapes type V (CSG n) = V3
type N (CSG n)
Instance details Defined in Diagrams.ThreeD.Shapes type N (CSG n) = n

zDir :: (R3 v, Additive v, Num n) => Direction v n #

A Direction pointing in the Z direction.

unit_Z :: (R3 v, Additive v, Num n) => v n #

The unit vector in the negative X direction.

unitZ :: (R3 v, Additive v, Num n) => v n #

The unit vector in the positive Y direction.

reflectAcross :: (InSpace v n t, Metric v, Fractional n, Transformable t) => Point v n -> v n -> t -> t #

reflectAcross p v reflects a diagram across the plane though the point p and the vector v. This also works as a 2D transform where v is the normal to the line passing through point p.

reflectionAcross :: (Metric v, Fractional n) => Point v n -> v n -> Transformation v n #

reflectionAcross p v is a reflection across the plane through the point p and normal to vector v. This also works as a 2D transform where v is the normal to the line passing through point p.

reflectZ :: (InSpace v n t, R3 v, Transformable t) => t -> t #

Flip a diagram across z=0, i.e. send the point (x,y,z) to (x,y,-z).

reflectionZ :: (Additive v, R3 v, Num n) => Transformation v n #

Construct a transformation which flips a diagram across z=0, i.e. sends the point (x,y,z) to (x,y,-z).

translateZ :: (InSpace v n t, R3 v, Transformable t) => n -> t -> t #

Translate a diagram by the given distance in the y direction.

translationZ :: (Additive v, R3 v, Num n) => n -> Transformation v n #

Construct a transformation which translates by the given distance in the z direction.

scaleZ :: (InSpace v n t, R3 v, Fractional n, Transformable t) => n -> t -> t #

Scale a diagram by the given factor in the z direction. To scale uniformly, use scale.

scalingZ :: (Additive v, R3 v, Fractional n) => n -> Transformation v n #

Construct a transformation which scales by the given factor in the z direction.

pointAt' :: (Floating n, Ord n) => V3 n -> V3 n -> V3 n -> Transformation V3 n #

pointAt' has the same behavior as pointAt, but takes vectors instead of directions.

pointAt :: (Floating n, Ord n) => Direction V3 n -> Direction V3 n -> Direction V3 n -> Transformation V3 n #

pointAt about initial final produces a rotation which brings the direction initial to point in the direction final by first panning around about, then tilting about the axis perpendicular to about and final. In particular, if this can be accomplished without tilting, it will be, otherwise if only tilting is necessary, no panning will occur. The tilt will always be between ± 1/4 turn.

rotateAbout #

Arguments

:: (InSpace V3 n t, Floating n, Transformable t)
=> Point V3 n	origin of rotation
-> Direction V3 n	direction of rotation axis
-> Angle n	angle of rotation
-> t
-> t

rotationAbout p d a is a rotation about a line parallel to d passing through p.

rotationAbout #

Arguments

:: Floating n
=> Point V3 n	origin of rotation
-> Direction V3 n	direction of rotation axis
-> Angle n	angle of rotation
-> Transformation V3 n

rotationAbout p d a is a rotation about a line parallel to d passing through p.

aboutY :: Floating n => Angle n -> Transformation V3 n #

Like aboutZ, but rotates about the Y axis, bringing postive x-values towards the negative z-axis.

aboutX :: Floating n => Angle n -> Transformation V3 n #

Like aboutZ, but rotates about the X axis, bringing positive y-values towards the positive z-axis.

aboutZ :: Floating n => Angle n -> Transformation V3 n #

Create a transformation which rotates by the given angle about a line parallel the Z axis passing through the local origin. A positive angle brings positive x-values towards the positive-y axis.

The angle can be expressed using any type which is an instance of Angle. For example, aboutZ (1/4 @@ turn), aboutZ (tau/4 @@ rad), and aboutZ (90 @@ deg) all represent the same transformation, namely, a counterclockwise rotation by a right angle. For more general rotations, see rotationAbout.

Note that writing aboutZ (1/4), with no type annotation, will yield an error since GHC cannot figure out which sort of angle you want to use.

shearY :: (InSpace V2 n t, Transformable t) => n -> t -> t #

shearY d performs a shear in the y-direction which sends (1,0) to (1,d).

shearingY :: Num n => n -> T2 n #

shearingY d is the linear transformation which is the identity on x coordinates and sends (1,0) to (1,d).

shearX :: (InSpace V2 n t, Transformable t) => n -> t -> t #

shearX d performs a shear in the x-direction which sends (0,1) to (d,1).

shearingX :: Num n => n -> T2 n #

shearingX d is the linear transformation which is the identity on y coordinates and sends (0,1) to (d,1).

reflectAbout :: (InSpace V2 n t, OrderedField n, Transformable t) => P2 n -> Direction V2 n -> t -> t #

reflectAbout p d reflects a diagram in the line determined by the point p and direction d.

reflectionAbout :: OrderedField n => P2 n -> Direction V2 n -> T2 n #

reflectionAbout p d is a reflection in the line determined by the point p and direction d.

reflectXY :: (InSpace v n t, R2 v, Transformable t) => t -> t #

Flips the diagram about x=y, i.e. send the point (x,y) to (y,x).

reflectionXY :: (Additive v, R2 v, Num n) => Transformation v n #

Construct a transformation which flips the diagram about x=y, i.e. sends the point (x,y) to (y,x).

reflectY :: (InSpace v n t, R2 v, Transformable t) => t -> t #

Flip a diagram from top to bottom, i.e. send the point (x,y) to (x,-y).

reflectionY :: (Additive v, R2 v, Num n) => Transformation v n #

Construct a transformation which flips a diagram from top to bottom, i.e. sends the point (x,y) to (x,-y).

reflectX :: (InSpace v n t, R1 v, Transformable t) => t -> t #

Flip a diagram from left to right, i.e. send the point (x,y) to (-x,y).

reflectionX :: (Additive v, R1 v, Num n) => Transformation v n #

Construct a transformation which flips a diagram from left to right, i.e. sends the point (x,y) to (-x,y).

scaleRotateTo :: (InSpace V2 n t, Transformable t, Floating n) => V2 n -> t -> t #

Rotate and uniformly scale around the local origin such that the x-axis aligns with the given vector. This satisfies the equation

scaleRotateTo v = rotateTo (dir v) . scale (norm v)

up to floating point rounding errors, but is more accurate and performant since it avoids cancellable uses of trigonometric functions.

scalingRotationTo :: Floating n => V2 n -> T2 n #

The angle-preserving linear map that aligns the x-axis unit vector with the given vector. See also scaleRotateTo.

translateY :: (InSpace v n t, R2 v, Transformable t) => n -> t -> t #

Translate a diagram by the given distance in the y (vertical) direction.

translationY :: (Additive v, R2 v, Num n) => n -> Transformation v n #

Construct a transformation which translates by the given distance in the y (vertical) direction.

translateX :: (InSpace v n t, R1 v, Transformable t) => n -> t -> t #

Translate a diagram by the given distance in the x (horizontal) direction.

translationX :: (Additive v, R1 v, Num n) => n -> Transformation v n #

Construct a transformation which translates by the given distance in the x (horizontal) direction.

scaleUToY :: (InSpace v n t, R2 v, Enveloped t, Transformable t) => n -> t -> t #

scaleUToY h scales a diagram uniformly by whatever factor required to make its height h. scaleUToY should not be applied to diagrams with a height of 0, such as hrule.

scaleUToX :: (InSpace v n t, R1 v, Enveloped t, Transformable t) => n -> t -> t #

scaleUToX w scales a diagram uniformly by whatever factor required to make its width w. scaleUToX should not be applied to diagrams with a width of 0, such as vrule.

scaleToY :: (InSpace v n t, R2 v, Enveloped t, Transformable t) => n -> t -> t #

scaleToY h scales a diagram in the y (vertical) direction by whatever factor required to make its height h. scaleToY should not be applied to diagrams with a height of 0, such as hrule.

scaleToX :: (InSpace v n t, R2 v, Enveloped t, Transformable t) => n -> t -> t #

scaleToX w scales a diagram in the x (horizontal) direction by whatever factor required to make its width w. scaleToX should not be applied to diagrams with a width of 0, such as vrule.

scaleY :: (InSpace v n t, R2 v, Fractional n, Transformable t) => n -> t -> t #

Scale a diagram by the given factor in the y (vertical) direction. To scale uniformly, use scale.

scalingY :: (Additive v, R2 v, Fractional n) => n -> Transformation v n #

Construct a transformation which scales by the given factor in the y (vertical) direction.

scaleX :: (InSpace v n t, R2 v, Fractional n, Transformable t) => n -> t -> t #

Scale a diagram by the given factor in the x (horizontal) direction. To scale uniformly, use scale.

scalingX :: (Additive v, R1 v, Fractional n) => n -> Transformation v n #

Construct a transformation which scales by the given factor in the x (horizontal) direction.

rotateTo :: (InSpace V2 n t, OrderedField n, Transformable t) => Direction V2 n -> t -> t #

Rotate around the local origin such that the x axis aligns with the given direction.

rotationTo :: OrderedField n => Direction V2 n -> T2 n #

The rotation that aligns the x-axis with the given direction.

rotateAround :: (InSpace V2 n t, Transformable t, Floating n) => P2 n -> Angle n -> t -> t #

rotateAbout p is like rotate, except it rotates around the point p instead of around the local origin.

rotationAround :: Floating n => P2 n -> Angle n -> T2 n #

rotationAbout p is a rotation about the point p (instead of around the local origin).

rotated :: (InSpace V2 n a, Floating n, SameSpace a b, Transformable a, Transformable b) => Angle n -> Iso a b a b #

Use an Angle to make an Iso between an object rotated and unrotated. This us useful for performing actions under a rotation:

under (rotated t) f = rotate (negated t) . f . rotate t
rotated t ## a      = rotate t a
a ^. rotated t      = rotate (-t) a
over (rotated t) f  = rotate t . f . rotate (negated t)

rotateBy :: (InSpace V2 n t, Transformable t, Floating n) => n -> t -> t #

A synonym for rotate, interpreting its argument in units of turns; it can be more convenient to write rotateBy (1/4) than rotate (1/4 @@ turn).

signedAngleBetweenDirs :: RealFloat n => Direction V2 n -> Direction V2 n -> Angle n #

Same as signedAngleBetween but for Directionss.

signedAngleBetween :: RealFloat n => V2 n -> V2 n -> Angle n #

Signed angle between two vectors. Currently defined as

signedAngleBetween u v = (u ^. _theta) ^-^ (v ^. _theta)

leftTurn :: (Num n, Ord n) => V2 n -> V2 n -> Bool #

leftTurn v1 v2 tests whether the direction of v2 is a left turn from v1 (that is, if the direction of v2 can be obtained from that of v1 by adding an angle 0 <= theta <= tau/2).

angleV :: Floating n => Angle n -> V2 n #

A unit vector at a specified angle counter-clockwise from the positive x-axis

angleDir :: Floating n => Angle n -> Direction V2 n #

A direction at a specified angle counter-clockwise from the xDir.

yDir :: (R2 v, Additive v, Num n) => Direction v n #

A Direction pointing in the Y direction.

xDir :: (R1 v, Additive v, Num n) => Direction v n #

A Direction pointing in the X direction.

unit_Y :: (R2 v, Additive v, Num n) => v n #

The unit vector in the negative Y direction.

unitY :: (R2 v, Additive v, Num n) => v n #

The unit vector in the positive Y direction.

unit_X :: (R1 v, Additive v, Num n) => v n #

The unit vector in the negative X direction.

unitX :: (R1 v, Additive v, Num n) => v n #

The unit vector in the positive X direction.

parallelLight #

Arguments

:: (Typeable n, OrderedField n, Renderable (ParallelLight n) b)
=> Direction V3 n	The direction in which the light travels.
-> Colour Double	The color of the light.
-> QDiagram b V3 n Any

Construct a Diagram with a single ParallelLight, which takes up no space.

pointLight #

Arguments

:: (Typeable n, Num n, Ord n, Renderable (PointLight n) b)
=> Colour Double	The color of the light
-> QDiagram b V3 n Any

Construct a Diagram with a single PointLight at the origin, which takes up no space.

data PointLight n #

A PointLight radiates uniformly in all directions from a given point.

Constructors

PointLight (Point V3 n) (Colour Double)

Instances

Fractional n => Transformable (PointLight n)
Instance details Defined in Diagrams.ThreeD.Light Methods transform :: Transformation (V (PointLight n)) (N (PointLight n)) -> PointLight n -> PointLight n #
type V (PointLight n)
Instance details Defined in Diagrams.ThreeD.Light type V (PointLight n) = V3
type N (PointLight n)
Instance details Defined in Diagrams.ThreeD.Light type N (PointLight n) = n

data ParallelLight n #

A ParallelLight casts parallel rays in the specified direction, from some distant location outside the scene.

Constructors

ParallelLight (V3 n) (Colour Double)

Instances

Transformable (ParallelLight n)
Instance details Defined in Diagrams.ThreeD.Light Methods transform :: Transformation (V (ParallelLight n)) (N (ParallelLight n)) -> ParallelLight n -> ParallelLight n #
type V (ParallelLight n)
Instance details Defined in Diagrams.ThreeD.Light type V (ParallelLight n) = V3
type N (ParallelLight n)
Instance details Defined in Diagrams.ThreeD.Light type N (ParallelLight n) = n

r3CylindricalIso :: RealFloat n => Iso' (V3 n) (n, Angle n, n) #

r3SphericalIso :: RealFloat n => Iso' (V3 n) (n, Angle n, Angle n) #

mkP3 :: n -> n -> n -> P3 n #

Curried version of r3.

p3Iso :: Iso' (P3 n) (n, n, n) #

unp3 :: P3 n -> (n, n, n) #

Convert a 3D point back into a triple of coordinates.

p3 :: (n, n, n) -> P3 n #

Construct a 3D point from a triple of coordinates.

unr3 :: V3 n -> (n, n, n) #

Convert a 3D vector back into a triple of components.

mkR3 :: n -> n -> n -> V3 n #

Curried version of r3.

r3 :: (n, n, n) -> V3 n #

Construct a 3D vector from a triple of components.

r3Iso :: Iso' (V3 n) (n, n, n) #

type P3 = Point V3 #

type T3 = Transformation V3 #

r2PolarIso :: RealFloat n => Iso' (V2 n) (n, Angle n) #

mkP2 :: n -> n -> P2 n #

Curried form of p2.

unp2 :: P2 n -> (n, n) #

Convert a 2D point back into a pair of coordinates. See also coords.

p2 :: (n, n) -> P2 n #

Construct a 2D point from a pair of coordinates. See also ^&.

mkR2 :: n -> n -> V2 n #

Curried form of r2.

unr2 :: V2 n -> (n, n) #

Convert a 2D vector back into a pair of components. See also coords.

r2 :: (n, n) -> V2 n #

Construct a 2D vector from a pair of components. See also &.

type P2 = Point V2 #

type T2 = Transformation V2 #

class HasR (t :: Type -> Type) where #

A space which has magnitude _r that can be calculated numerically.

Methods

_r :: RealFloat n => Lens' (t n) n #

Instances

HasR V2
Instance details Defined in Diagrams.TwoD.Types Methods _r :: RealFloat n => Lens' (V2 n) n #
HasR v => HasR (Point v)
Instance details Defined in Diagrams.TwoD.Types Methods _r :: RealFloat n => Lens' (Point v n) n #

translated :: (InSpace v n a, SameSpace a b, Transformable a, Transformable b) => v n -> Iso a b a b #

Use a vector to make an Iso between an object translated and untranslated.

under (translated v) f == translate (-v) . f . translate v
translated v ## a      == translate v a
a ^. translated v      == translate (-v) a
over (translated v) f  == translate v . f . translate (-v)

movedFrom :: (InSpace v n a, SameSpace a b, HasOrigin a, HasOrigin b) => Point v n -> Iso a b a b #

Use a Transformation to make an Iso between an object transformed and untransformed. We have

under (movedFrom p) f == moveTo p . f . moveTo (-p)
movedFrom p           == from (movedTo p)
movedFrom p ## a      == moveOriginTo p a
a ^. movedFrom p      == moveTo p a
over (movedFrom p) f  == moveTo (-p) . f . moveTo p

movedTo :: (InSpace v n a, SameSpace a b, HasOrigin a, HasOrigin b) => Point v n -> Iso a b a b #

Use a Point to make an Iso between an object moved to and from that point:

under (movedTo p) f == moveTo (-p) . f . moveTo p
over (movedTo p) f  == moveTo p . f . moveTo (-p)
movedTo p           == from (movedFrom p)
movedTo p ## a      == moveTo p a
a ^. movedTo p      == moveOriginTo p a

transformed :: (InSpace v n a, SameSpace a b, Transformable a, Transformable b) => Transformation v n -> Iso a b a b #

Use a Transformation to make an Iso between an object transformed and untransformed. This is useful for carrying out functions under another transform:

under (transformed t) f               == transform (inv t) . f . transform t
under (transformed t1) (transform t2) == transform (conjugate t1 t2)
transformed t ## a                    == transform t a
a ^. transformed t                    == transform (inv t) a

underT :: (InSpace v n a, SameSpace a b, Transformable a, Transformable b) => (a -> b) -> Transformation v n -> a -> b #

Carry out some transformation "under" another one: f `underT` t first applies t, then f, then the inverse of t. For example, scaleX 2 `underT` rotation (-1/8 @@ Turn) is the transformation which scales by a factor of 2 along the diagonal line y = x.

Note that

(transform t2) underT t1 == transform (conjugate t1 t2)

for all transformations t1 and t2.

See also the isomorphisms like transformed, movedTo, movedFrom, and translated.

conjugate :: (Additive v, Num n) => Transformation v n -> Transformation v n -> Transformation v n #

Conjugate one transformation by another. conjugate t1 t2 is the transformation which performs first t1, then t2, then the inverse of t1.

highlightSize :: Traversal' (Style v n) Double #

Traversal over the highlight size in a style. If the style has no Specular, setting this will do nothing.

highlightIntensity :: Traversal' (Style v n) Double #

Traversal over the highlight intensity of a style. If the style has no Specular, setting this will do nothing.

_highlight :: Lens' (Style v n) (Maybe Specular) #

Lens onto the possible specular highlight in a style

highlight :: HasStyle d => Specular -> d -> d #

Set the specular highlight.

_Highlight :: Iso' Highlight Specular #

specularSize :: Lens' Specular Double #

specularIntensity :: Lens' Specular Double #

newtype Highlight #

Constructors

Highlight (Last Specular)

Instances

Show Highlight
Instance details Defined in Diagrams.ThreeD.Attributes Methods showsPrec :: Int -> Highlight -> ShowS # show :: Highlight -> String # showList :: [Highlight] -> ShowS #
Semigroup Highlight
Instance details Defined in Diagrams.ThreeD.Attributes Methods (<>) :: Highlight -> Highlight -> Highlight # sconcat :: NonEmpty Highlight -> Highlight # stimes :: Integral b => b -> Highlight -> Highlight #
AttributeClass Highlight
Instance details Defined in Diagrams.ThreeD.Attributes

_ambient :: Lens' (Style v n) (Maybe Double) #

Lens onto the possible ambience in a style.

ambient :: HasStyle d => Double -> d -> d #

Set the emittance due to ambient light.

_Ambient :: Iso' Ambient Double #

_diffuse :: Lens' (Style v n) (Maybe Double) #

Lens onto the possible diffuse reflectance in a style.

diffuse :: HasStyle d => Double -> d -> d #

Set the diffuse reflectance.

_Diffuse :: Iso' Diffuse Double #

Isomorphism between Diffuse and Double

_sc :: Lens' (Style v n) (Maybe (Colour Double)) #

Lens onto the surface colour of a style.

sc :: HasStyle d => Colour Double -> d -> d #

Set the surface color.

_SurfaceColor :: Iso' SurfaceColor (Colour Double) #

newtype SurfaceColor #

SurfaceColor is the inherent pigment of an object, assumed to be opaque.

Constructors

SurfaceColor (Last (Colour Double))

Instances

Show SurfaceColor
Instance details Defined in Diagrams.ThreeD.Attributes Methods showsPrec :: Int -> SurfaceColor -> ShowS # show :: SurfaceColor -> String # showList :: [SurfaceColor] -> ShowS #
Semigroup SurfaceColor
Instance details Defined in Diagrams.ThreeD.Attributes Methods (<>) :: SurfaceColor -> SurfaceColor -> SurfaceColor # sconcat :: NonEmpty SurfaceColor -> SurfaceColor # stimes :: Integral b => b -> SurfaceColor -> SurfaceColor #
AttributeClass SurfaceColor
Instance details Defined in Diagrams.ThreeD.Attributes

newtype Diffuse #

Diffuse is the fraction of incident light reflected diffusely, that is, in all directions. The actual light reflected is the product of this value, the incident light, and the SurfaceColor Attribute. For physical reasonableness, Diffuse should have a value between 0 and 1; this is not checked.

Constructors

Diffuse (Last Double)

Instances

Show Diffuse
Instance details Defined in Diagrams.ThreeD.Attributes Methods showsPrec :: Int -> Diffuse -> ShowS # show :: Diffuse -> String # showList :: [Diffuse] -> ShowS #
Semigroup Diffuse
Instance details Defined in Diagrams.ThreeD.Attributes Methods (<>) :: Diffuse -> Diffuse -> Diffuse # sconcat :: NonEmpty Diffuse -> Diffuse # stimes :: Integral b => b -> Diffuse -> Diffuse #
AttributeClass Diffuse
Instance details Defined in Diagrams.ThreeD.Attributes

newtype Ambient #

Ambient is an ad-hoc representation of indirect lighting. The product of Ambient and SurfaceColor is added to the light leaving an object due to diffuse and specular terms. Ambient can be set per-object, and can be loosely thought of as the product of indirect lighting incident on that object and the diffuse reflectance.

Constructors

Ambient (Last Double)

Instances

Show Ambient
Instance details Defined in Diagrams.ThreeD.Attributes Methods showsPrec :: Int -> Ambient -> ShowS # show :: Ambient -> String # showList :: [Ambient] -> ShowS #
Semigroup Ambient
Instance details Defined in Diagrams.ThreeD.Attributes Methods (<>) :: Ambient -> Ambient -> Ambient # sconcat :: NonEmpty Ambient -> Ambient # stimes :: Integral b => b -> Ambient -> Ambient #
AttributeClass Ambient
Instance details Defined in Diagrams.ThreeD.Attributes

data Specular #

A specular highlight has two terms, the intensity, between 0 and 1, and the size. The highlight size is assumed to be the exponent in a Phong shading model (though Backends are free to use a different shading model). In this model, reasonable values are between 1 and 50 or so, with higher values for shinier objects. Physically, the intensity and the value of Diffuse must add up to less than 1; this is not enforced.

Constructors

Specular
Fields _specularIntensity :: Double _specularSize :: Double

Instances

Show Specular
Instance details Defined in Diagrams.ThreeD.Attributes Methods showsPrec :: Int -> Specular -> ShowS # show :: Specular -> String # showList :: [Specular] -> ShowS #

clearValue :: QDiagram b v n m -> QDiagram b v n Any #

Set all the query values of a diagram to False.

resetValue :: (Eq m, Monoid m) => QDiagram b v n m -> QDiagram b v n Any #

Reset the query values of a diagram to True/False: any values equal to mempty are set to False; any other values are set to True.

value :: Monoid m => m -> QDiagram b v n Any -> QDiagram b v n m #

Set the query value for True points in a diagram (i.e. points "inquire" the diagram); False points will be set to mempty.

sample :: HasQuery t m => t -> Point (V t) (N t) -> m #

Sample a diagram's query function at a given point.

sample :: QDiagram b v n m -> Point v n -> m
sample :: Query v n m      -> Point v n -> m
sample :: BoundingBox v n  -> Point v n -> Any
sample :: Path V2 Double   -> Point v n -> Crossings

inquire :: HasQuery t Any => t -> Point (V t) (N t) -> Bool #

Test if a point is not equal to mempty.

inquire :: QDiagram b v n Any -> Point v n -> Bool
inquire :: Query v n Any      -> Point v n -> Bool
inquire :: BoundingBox v n  -> Point v n -> Bool

class HasQuery t m | t -> m where #

Types which can answer a Query about points inside the geometric object.

If t and m are both a Semigroups, getQuery should satisfy

getQuery (t1 <> t2) = getQuery t1 <> getQuery t2

Methods

getQuery :: t -> Query (V t) (N t) m #

Extract the query of an object.

Instances

RealFloat n => HasQuery (Clip n) All	A point inside a clip if the point is in `All` invididual clipping paths.
Instance details Defined in Diagrams.TwoD.Path Methods getQuery :: Clip n -> Query (V (Clip n)) (N (Clip n)) All #
(Num n, Ord n) => HasQuery (Ellipsoid n) Any
Instance details Defined in Diagrams.ThreeD.Shapes Methods getQuery :: Ellipsoid n -> Query (V (Ellipsoid n)) (N (Ellipsoid n)) Any #
(Num n, Ord n) => HasQuery (Box n) Any
Instance details Defined in Diagrams.ThreeD.Shapes Methods getQuery :: Box n -> Query (V (Box n)) (N (Box n)) Any #
OrderedField n => HasQuery (Frustum n) Any
Instance details Defined in Diagrams.ThreeD.Shapes Methods getQuery :: Frustum n -> Query (V (Frustum n)) (N (Frustum n)) Any #
(Floating n, Ord n) => HasQuery (CSG n) Any
Instance details Defined in Diagrams.ThreeD.Shapes Methods getQuery :: CSG n -> Query (V (CSG n)) (N (CSG n)) Any #
(Additive v, Foldable v, Ord n) => HasQuery (BoundingBox v n) Any
Instance details Defined in Diagrams.BoundingBox Methods getQuery :: BoundingBox v n -> Query (V (BoundingBox v n)) (N (BoundingBox v n)) Any #
RealFloat n => HasQuery (DImage n a) Any
Instance details Defined in Diagrams.TwoD.Image Methods getQuery :: DImage n a -> Query (V (DImage n a)) (N (DImage n a)) Any #
HasQuery (Query v n m) m
Instance details Defined in Diagrams.Query Methods getQuery :: Query v n m -> Query (V (Query v n m)) (N (Query v n m)) m #
Monoid m => HasQuery (QDiagram b v n m) m
Instance details Defined in Diagrams.Query Methods getQuery :: QDiagram b v n m -> Query (V (QDiagram b v n m)) (N (QDiagram b v n m)) m #

dirBetween :: (Additive v, Num n) => Point v n -> Point v n -> Direction v n #

dirBetween p q returns the direction from p to q.

angleBetweenDirs :: (Metric v, Floating n, Ord n) => Direction v n -> Direction v n -> Angle n #

compute the positive angle between the two directions in their common plane

fromDir :: (Metric v, Floating n) => Direction v n -> v n #

Synonym for fromDirection.

fromDirection :: (Metric v, Floating n) => Direction v n -> v n #

fromDirection d is the unit vector in the direction d.

direction :: v n -> Direction v n #

direction v is the direction in which v points. Returns an unspecified value when given the zero vector as input.

_Dir :: Iso' (Direction v n) (v n) #

_Dir is provided to allow efficient implementations of functions in particular vector-spaces, but should be used with care as it exposes too much information.

data Direction (v :: Type -> Type) n #

A vector is described by a Direction and a magnitude. So we can think of a Direction as a vector that has forgotten its magnitude. Directions can be used with fromDirection and the lenses provided by its instances.

Instances

Functor v => Functor (Direction v)
Instance details Defined in Diagrams.Direction Methods fmap :: (a -> b) -> Direction v a -> Direction v b # (<$) :: a -> Direction v b -> Direction v a #
HasTheta v => HasTheta (Direction v)
Instance details Defined in Diagrams.Direction Methods _theta :: RealFloat n => Lens' (Direction v n) (Angle n) #
HasPhi v => HasPhi (Direction v)
Instance details Defined in Diagrams.Direction Methods _phi :: RealFloat n => Lens' (Direction v n) (Angle n) #
Eq (v n) => Eq (Direction v n)
Instance details Defined in Diagrams.Direction Methods (==) :: Direction v n -> Direction v n -> Bool # (/=) :: Direction v n -> Direction v n -> Bool #
Ord (v n) => Ord (Direction v n)
Instance details Defined in Diagrams.Direction Methods compare :: Direction v n -> Direction v n -> Ordering # (<) :: Direction v n -> Direction v n -> Bool # (<=) :: Direction v n -> Direction v n -> Bool # (>) :: Direction v n -> Direction v n -> Bool # (>=) :: Direction v n -> Direction v n -> Bool # max :: Direction v n -> Direction v n -> Direction v n # min :: Direction v n -> Direction v n -> Direction v n #
Read (v n) => Read (Direction v n)
Instance details Defined in Diagrams.Direction Methods readsPrec :: Int -> ReadS (Direction v n) # readList :: ReadS [Direction v n] # readPrec :: ReadPrec (Direction v n) # readListPrec :: ReadPrec [Direction v n] #
Show (v n) => Show (Direction v n)
Instance details Defined in Diagrams.Direction Methods showsPrec :: Int -> Direction v n -> ShowS # show :: Direction v n -> String # showList :: [Direction v n] -> ShowS #
(V (v n) ~ v, N (v n) ~ n, Transformable (v n)) => Transformable (Direction v n)
Instance details Defined in Diagrams.Direction Methods transform :: Transformation (V (Direction v n)) (N (Direction v n)) -> Direction v n -> Direction v n #
type V (Direction v n)
Instance details Defined in Diagrams.Direction type V (Direction v n) = v
type N (Direction v n)
Instance details Defined in Diagrams.Direction type N (Direction v n) = n

rotate :: (InSpace V2 n t, Transformable t, Floating n) => Angle n -> t -> t #

Rotate about the local origin by the given angle. Positive angles correspond to counterclockwise rotation, negative to clockwise. The angle can be expressed using any of the Isos on Angle. For example, rotate (1/4 @@ turn), rotate (tau/4 @@ rad), and rotate (90 @@ deg) all represent the same transformation, namely, a counterclockwise rotation by a right angle. To rotate about some point other than the local origin, see rotateAbout.

Note that writing rotate (1/4), with no Angle constructor, will yield an error since GHC cannot figure out which sort of angle you want to use. In this common situation you can use rotateBy, which interprets its argument as a number of turns.

rotation :: Floating n => Angle n -> Transformation V2 n #

Create a transformation which performs a rotation about the local origin by the given angle. See also rotate.

normalizeAngle :: (Floating n, Real n) => Angle n -> Angle n #

Normalize an angle so that it lies in the [0,tau) range.

angleBetween :: (Metric v, Floating n, Ord n) => v n -> v n -> Angle n #

Compute the positive angle between the two vectors in their common plane in the [0,pi] range. For a signed angle see signedAngleBetween.

Returns NaN if either of the vectors are zero.

(@@) :: b -> AReview a b -> a infixl 5 #

30 @@ deg is an Angle of the given measure and units.

>>> pi @@ rad
3.141592653589793 @@ rad

>>> 1 @@ turn
6.283185307179586 @@ rad

>>> 30 @@ deg
0.5235987755982988 @@ rad

For Iso's, (@@) reverses the Iso' on its right, and applies the Iso' to the value on the left. Angles are the motivating example where this order improves readability.

This is the same as a flipped review.

(@@) :: a -> Iso'      s a -> s
(@@) :: a -> Prism'    s a -> s
(@@) :: a -> Review    s a -> s
(@@) :: a -> Equality' s a -> s

atan2A' :: OrderedField n => n -> n -> Angle n #

Similar to atan2A but without the RealFloat constraint. This means it doesn't handle negative zero cases. However, for most geometric purposes, the outcome will be the same.

atan2A :: RealFloat n => n -> n -> Angle n #

atan2A y x is the angle between the positive x-axis and the vector given by the coordinates (x, y). The Angle returned is in the [-pi,pi] range.

atanA :: Floating n => n -> Angle n #

The Angle with the given tangent.

acosA :: Floating n => n -> Angle n #

The Angle with the given cosine.

asinA :: Floating n => n -> Angle n #

The Angle with the given sine.

tanA :: Floating n => Angle n -> n #

The tangent function of the given Angle.

cosA :: Floating n => Angle n -> n #

The cosine of the given Angle.

sinA :: Floating n => Angle n -> n #

The sine of the given Angle.

angleRatio :: Floating n => Angle n -> Angle n -> n #

Calculate ratio between two angles.

quarterTurn :: Floating v => Angle v #

An angle representing a quarter turn.

halfTurn :: Floating v => Angle v #

An angle representing a half turn.

fullTurn :: Floating v => Angle v #

An angle representing one full turn.

deg :: Floating n => Iso' (Angle n) n #

The degree measure of an Angle a can be accessed as a ^. deg. A new Angle can be defined in degrees as 180 @@ deg.

turn :: Floating n => Iso' (Angle n) n #

The measure of an Angle a in full circles can be accessed as a ^. turn. A new Angle of one-half circle can be defined in as 1/2 @@ turn.

rad :: Iso' (Angle n) n #

The radian measure of an Angle a can be accessed as a ^. rad. A new Angle can be defined in radians as pi @@ rad.

data Angle n #

Angles can be expressed in a variety of units. Internally, they are represented in radians.

Instances

Functor Angle
Instance details Defined in Diagrams.Angle Methods fmap :: (a -> b) -> Angle a -> Angle b # (<$) :: a -> Angle b -> Angle a #
Applicative Angle
Instance details Defined in Diagrams.Angle Methods pure :: a -> Angle a # (<>) :: Angle (a -> b) -> Angle a -> Angle b # liftA2 :: (a -> b -> c) -> Angle a -> Angle b -> Angle c # (>) :: Angle a -> Angle b -> Angle b # (<*) :: Angle a -> Angle b -> Angle a #
Additive Angle
Instance details Defined in Diagrams.Angle Methods zero :: Num a => Angle a # (^+^) :: Num a => Angle a -> Angle a -> Angle a # (^-^) :: Num a => Angle a -> Angle a -> Angle a # lerp :: Num a => a -> Angle a -> Angle a -> Angle a # liftU2 :: (a -> a -> a) -> Angle a -> Angle a -> Angle a # liftI2 :: (a -> b -> c) -> Angle a -> Angle b -> Angle c #
Enum n => Enum (Angle n)
Instance details Defined in Diagrams.Angle Methods succ :: Angle n -> Angle n # pred :: Angle n -> Angle n # toEnum :: Int -> Angle n # fromEnum :: Angle n -> Int # enumFrom :: Angle n -> [Angle n] # enumFromThen :: Angle n -> Angle n -> [Angle n] # enumFromTo :: Angle n -> Angle n -> [Angle n] # enumFromThenTo :: Angle n -> Angle n -> Angle n -> [Angle n] #
Eq n => Eq (Angle n)
Instance details Defined in Diagrams.Angle Methods (==) :: Angle n -> Angle n -> Bool # (/=) :: Angle n -> Angle n -> Bool #
Ord n => Ord (Angle n)
Instance details Defined in Diagrams.Angle Methods compare :: Angle n -> Angle n -> Ordering # (<) :: Angle n -> Angle n -> Bool # (<=) :: Angle n -> Angle n -> Bool # (>) :: Angle n -> Angle n -> Bool # (>=) :: Angle n -> Angle n -> Bool # max :: Angle n -> Angle n -> Angle n # min :: Angle n -> Angle n -> Angle n #
Read n => Read (Angle n)
Instance details Defined in Diagrams.Angle Methods readsPrec :: Int -> ReadS (Angle n) # readList :: ReadS [Angle n] # readPrec :: ReadPrec (Angle n) # readListPrec :: ReadPrec [Angle n] #
Show n => Show (Angle n)
Instance details Defined in Diagrams.Angle Methods showsPrec :: Int -> Angle n -> ShowS # show :: Angle n -> String # showList :: [Angle n] -> ShowS #
Num n => Semigroup (Angle n)
Instance details Defined in Diagrams.Angle Methods (<>) :: Angle n -> Angle n -> Angle n # sconcat :: NonEmpty (Angle n) -> Angle n # stimes :: Integral b => b -> Angle n -> Angle n #
Num n => Monoid (Angle n)
Instance details Defined in Diagrams.Angle Methods mempty :: Angle n # mappend :: Angle n -> Angle n -> Angle n # mconcat :: [Angle n] -> Angle n #
(V t ~ V2, N t ~ n, Transformable t, Floating n) => Action (Angle n) t	Angles act on other things by rotation.
Instance details Defined in Diagrams.Angle Methods act :: Angle n -> t -> t #
type N (Angle n)
Instance details Defined in Diagrams.Angle type N (Angle n) = n

class HasTheta (t :: Type -> Type) where #

The class of types with at least one angle coordinate, called _theta.

Methods

_theta :: RealFloat n => Lens' (t n) (Angle n) #

Instances

HasTheta v => HasTheta (Point v)
Instance details Defined in Diagrams.Angle Methods _theta :: RealFloat n => Lens' (Point v n) (Angle n) #
HasTheta v => HasTheta (Direction v)
Instance details Defined in Diagrams.Direction Methods _theta :: RealFloat n => Lens' (Direction v n) (Angle n) #

class HasTheta t => HasPhi (t :: Type -> Type) where #

The class of types with at least two angle coordinates, the second called _phi. _phi is the positive angle measured from the z axis.

Methods

_phi :: RealFloat n => Lens' (t n) (Angle n) #

Instances

HasPhi v => HasPhi (Point v)
Instance details Defined in Diagrams.Angle Methods _phi :: RealFloat n => Lens' (Point v n) (Angle n) #
HasPhi v => HasPhi (Direction v)
Instance details Defined in Diagrams.Direction Methods _phi :: RealFloat n => Lens' (Direction v n) (Angle n) #

class Coordinates c where #

Types which are instances of the Coordinates class can be constructed using ^& (for example, a three-dimensional vector could be constructed by 1 ^& 6 ^& 3), and deconstructed using coords. A common pattern is to use coords in conjunction with the ViewPatterns extension, like so:

foo :: Vector3 -> ...
foo (coords -> x :& y :& z) = ...

Minimal complete definition

(^&), coords

Associated Types

type FinalCoord c :: Type #

The type of the final coordinate.

type PrevDim c :: Type #

The type of everything other than the final coordinate.

type Decomposition c :: Type #

Decomposition of c into applications of :&.

Methods

(^&) :: PrevDim c -> FinalCoord c -> c infixl 7 #

Construct a value of type c by providing something of one less dimension (which is perhaps itself recursively constructed using (^&)) and a final coordinate. For example,

2 ^& 3 :: P2
3 ^& 5 ^& 6 :: V3

Note that ^& is left-associative.

pr :: PrevDim c -> FinalCoord c -> c #

Prefix synonym for ^&. pr stands for pair of PrevDim, FinalCoord

coords :: c -> Decomposition c #

Decompose a value of type c into its constituent coordinates, stored in a nested (:&) structure.

Instances

Coordinates (V2 n)
Instance details Defined in Diagrams.Coordinates Associated Types type FinalCoord (V2 n) :: Type # type PrevDim (V2 n) :: Type # type Decomposition (V2 n) :: Type # Methods (^&) :: PrevDim (V2 n) -> FinalCoord (V2 n) -> V2 n # pr :: PrevDim (V2 n) -> FinalCoord (V2 n) -> V2 n # coords :: V2 n -> Decomposition (V2 n) #
Coordinates (V3 n)
Instance details Defined in Diagrams.Coordinates Associated Types type FinalCoord (V3 n) :: Type # type PrevDim (V3 n) :: Type # type Decomposition (V3 n) :: Type # Methods (^&) :: PrevDim (V3 n) -> FinalCoord (V3 n) -> V3 n # pr :: PrevDim (V3 n) -> FinalCoord (V3 n) -> V3 n # coords :: V3 n -> Decomposition (V3 n) #
Coordinates (V4 n)
Instance details Defined in Diagrams.Coordinates Associated Types type FinalCoord (V4 n) :: Type # type PrevDim (V4 n) :: Type # type Decomposition (V4 n) :: Type # Methods (^&) :: PrevDim (V4 n) -> FinalCoord (V4 n) -> V4 n # pr :: PrevDim (V4 n) -> FinalCoord (V4 n) -> V4 n # coords :: V4 n -> Decomposition (V4 n) #
Coordinates (a, b)
Instance details Defined in Diagrams.Coordinates Associated Types type FinalCoord (a, b) :: Type # type PrevDim (a, b) :: Type # type Decomposition (a, b) :: Type # Methods (^&) :: PrevDim (a, b) -> FinalCoord (a, b) -> (a, b) # pr :: PrevDim (a, b) -> FinalCoord (a, b) -> (a, b) # coords :: (a, b) -> Decomposition (a, b) #
Coordinates (v n) => Coordinates (Point v n)
Instance details Defined in Diagrams.Coordinates Associated Types type FinalCoord (Point v n) :: Type # type PrevDim (Point v n) :: Type # type Decomposition (Point v n) :: Type # Methods (^&) :: PrevDim (Point v n) -> FinalCoord (Point v n) -> Point v n # pr :: PrevDim (Point v n) -> FinalCoord (Point v n) -> Point v n # coords :: Point v n -> Decomposition (Point v n) #
Coordinates (a :& b)
Instance details Defined in Diagrams.Coordinates Associated Types type FinalCoord (a :& b) :: Type # type PrevDim (a :& b) :: Type # type Decomposition (a :& b) :: Type # Methods (^&) :: PrevDim (a :& b) -> FinalCoord (a :& b) -> a :& b # pr :: PrevDim (a :& b) -> FinalCoord (a :& b) -> a :& b # coords :: (a :& b) -> Decomposition (a :& b) #
Coordinates (a, b, c)
Instance details Defined in Diagrams.Coordinates Associated Types type FinalCoord (a, b, c) :: Type # type PrevDim (a, b, c) :: Type # type Decomposition (a, b, c) :: Type # Methods (^&) :: PrevDim (a, b, c) -> FinalCoord (a, b, c) -> (a, b, c) # pr :: PrevDim (a, b, c) -> FinalCoord (a, b, c) -> (a, b, c) # coords :: (a, b, c) -> Decomposition (a, b, c) #
Coordinates (a, b, c, d)
Instance details Defined in Diagrams.Coordinates Associated Types type FinalCoord (a, b, c, d) :: Type # type PrevDim (a, b, c, d) :: Type # type Decomposition (a, b, c, d) :: Type # Methods (^&) :: PrevDim (a, b, c, d) -> FinalCoord (a, b, c, d) -> (a, b, c, d) # pr :: PrevDim (a, b, c, d) -> FinalCoord (a, b, c, d) -> (a, b, c, d) # coords :: (a, b, c, d) -> Decomposition (a, b, c, d) #

data a :& b infixl 7 #

A pair of values, with a convenient infix (left-associative) data constructor.

Constructors

a :& b infixl 7

Instances

(Eq a, Eq b) => Eq (a :& b)
Instance details Defined in Diagrams.Coordinates Methods (==) :: (a :& b) -> (a :& b) -> Bool # (/=) :: (a :& b) -> (a :& b) -> Bool #
(Ord a, Ord b) => Ord (a :& b)
Instance details Defined in Diagrams.Coordinates Methods compare :: (a :& b) -> (a :& b) -> Ordering # (<) :: (a :& b) -> (a :& b) -> Bool # (<=) :: (a :& b) -> (a :& b) -> Bool # (>) :: (a :& b) -> (a :& b) -> Bool # (>=) :: (a :& b) -> (a :& b) -> Bool # max :: (a :& b) -> (a :& b) -> a :& b # min :: (a :& b) -> (a :& b) -> a :& b #
(Show a, Show b) => Show (a :& b)
Instance details Defined in Diagrams.Coordinates Methods showsPrec :: Int -> (a :& b) -> ShowS # show :: (a :& b) -> String # showList :: [a :& b] -> ShowS #
Coordinates (a :& b)
Instance details Defined in Diagrams.Coordinates Associated Types type FinalCoord (a :& b) :: Type # type PrevDim (a :& b) :: Type # type Decomposition (a :& b) :: Type # Methods (^&) :: PrevDim (a :& b) -> FinalCoord (a :& b) -> a :& b # pr :: PrevDim (a :& b) -> FinalCoord (a :& b) -> a :& b # coords :: (a :& b) -> Decomposition (a :& b) #
type Decomposition (a :& b)
Instance details Defined in Diagrams.Coordinates type Decomposition (a :& b) = a :& b
type PrevDim (a :& b)
Instance details Defined in Diagrams.Coordinates type PrevDim (a :& b) = a
type FinalCoord (a :& b)
Instance details Defined in Diagrams.Coordinates type FinalCoord (a :& b) = b

centroid :: (Additive v, Fractional n) => [Point v n] -> Point v n #

The centroid of a set of n points is their sum divided by n. Returns the origin for an empty list of points.

adjust :: (N t ~ n, Sectionable t, HasArcLength t, Fractional n) => t -> AdjustOpts n -> t #

Adjust the length of a parametric object such as a segment or trail. The second parameter is an option record which controls how the adjustment should be performed; see AdjustOpts.

adjSide :: Lens' (AdjustOpts n) AdjustSide #

Which end(s) of the object should be adjusted?

adjMethod :: Lens' (AdjustOpts n) (AdjustMethod n) #

Which method should be used for adjusting?

adjEps :: Lens' (AdjustOpts n) n #

Tolerance to use when doing adjustment.

data AdjustMethod n #

What method should be used for adjusting a segment, trail, or path?

Constructors

ByParam n	Extend by the given parameter value (use a negative parameter to shrink)
ByAbsolute n	Extend by the given arc length (use a negative length to shrink)
ToAbsolute n	Extend or shrink to the given arc length

Instances

Fractional n => Default (AdjustMethod n)
Instance details Defined in Diagrams.Parametric.Adjust Methods def :: AdjustMethod n #

data AdjustSide #

Which side of a segment, trail, or path should be adjusted?

Constructors

Start	Adjust only the beginning
End	Adjust only the end
Both	Adjust both sides equally

Instances

Bounded AdjustSide
Instance details Defined in Diagrams.Parametric.Adjust Methods minBound :: AdjustSide # maxBound :: AdjustSide #
Enum AdjustSide
Instance details Defined in Diagrams.Parametric.Adjust Methods succ :: AdjustSide -> AdjustSide # pred :: AdjustSide -> AdjustSide # toEnum :: Int -> AdjustSide # fromEnum :: AdjustSide -> Int # enumFrom :: AdjustSide -> [AdjustSide] # enumFromThen :: AdjustSide -> AdjustSide -> [AdjustSide] # enumFromTo :: AdjustSide -> AdjustSide -> [AdjustSide] # enumFromThenTo :: AdjustSide -> AdjustSide -> AdjustSide -> [AdjustSide] #
Eq AdjustSide
Instance details Defined in Diagrams.Parametric.Adjust Methods (==) :: AdjustSide -> AdjustSide -> Bool # (/=) :: AdjustSide -> AdjustSide -> Bool #
Ord AdjustSide
Instance details Defined in Diagrams.Parametric.Adjust Methods compare :: AdjustSide -> AdjustSide -> Ordering # (<) :: AdjustSide -> AdjustSide -> Bool # (<=) :: AdjustSide -> AdjustSide -> Bool # (>) :: AdjustSide -> AdjustSide -> Bool # (>=) :: AdjustSide -> AdjustSide -> Bool # max :: AdjustSide -> AdjustSide -> AdjustSide # min :: AdjustSide -> AdjustSide -> AdjustSide #
Read AdjustSide
Instance details Defined in Diagrams.Parametric.Adjust Methods readsPrec :: Int -> ReadS AdjustSide # readList :: ReadS [AdjustSide] # readPrec :: ReadPrec AdjustSide # readListPrec :: ReadPrec [AdjustSide] #
Show AdjustSide
Instance details Defined in Diagrams.Parametric.Adjust Methods showsPrec :: Int -> AdjustSide -> ShowS # show :: AdjustSide -> String # showList :: [AdjustSide] -> ShowS #
Default AdjustSide
Instance details Defined in Diagrams.Parametric.Adjust Methods def :: AdjustSide #

data AdjustOpts n #

How should a segment, trail, or path be adjusted?

Instances

Fractional n => Default (AdjustOpts n)
Instance details Defined in Diagrams.Parametric.Adjust Methods def :: AdjustOpts n #

stdTolerance :: Fractional a => a #

The standard tolerance used by std... functions (like stdArcLength and stdArcLengthToParam, currently set at 1e-6.

domainBounds :: DomainBounds p => p -> (N p, N p) #

Return the lower and upper bounds of a parametric domain together as a pair.

type family Codomain p :: Type -> Type #

Codomain of parametric classes. This is usually either (V p), for relative vector results, or (Point (V p)), for functions with absolute coordinates.

Instances

type Codomain (GetSegment t)
Instance details Defined in Diagrams.Trail type Codomain (GetSegment t) = GetSegmentCodomain (V t)
type Codomain (Tangent t)
Instance details Defined in Diagrams.Tangent type Codomain (Tangent t) = V t
type Codomain (Located a)
Instance details Defined in Diagrams.Located type Codomain (Located a) = Point (Codomain a)
type Codomain (BernsteinPoly n)
Instance details Defined in Diagrams.TwoD.Segment.Bernstein type Codomain (BernsteinPoly n) = V1
type Codomain (SegTree v n)
Instance details Defined in Diagrams.Trail type Codomain (SegTree v n) = v
type Codomain (Trail v n)
Instance details Defined in Diagrams.Trail type Codomain (Trail v n) = v
type Codomain (FixedSegment v n)
Instance details Defined in Diagrams.Segment type Codomain (FixedSegment v n) = Point v
type Codomain (Trail' l v n)
Instance details Defined in Diagrams.Trail type Codomain (Trail' l v n) = v
type Codomain (Segment Closed v n)
Instance details Defined in Diagrams.Segment type Codomain (Segment Closed v n) = v

class Parametric p where #

Type class for parametric functions.

Methods

atParam :: p -> N p -> Codomain p (N p) #

atParam yields a parameterized view of an object as a continuous function. It is designed to be used infix, like path `atParam` 0.5.

Instances

(Metric v, OrderedField n) => Parametric (GetSegment (Trail' Line v n))	Parameters less than 0 yield the first segment; parameters greater than 1 yield the last. A parameter exactly at the junction of two segments yields the second segment (i.e. the one with higher parameter values).
Instance details Defined in Diagrams.Trail Methods atParam :: GetSegment (Trail' Line v n) -> N (GetSegment (Trail' Line v n)) -> Codomain (GetSegment (Trail' Line v n)) (N (GetSegment (Trail' Line v n))) #
(Metric v, OrderedField n, Real n) => Parametric (GetSegment (Trail' Loop v n))	The parameterization for loops wraps around, i.e. parameters are first reduced "mod 1".
Instance details Defined in Diagrams.Trail Methods atParam :: GetSegment (Trail' Loop v n) -> N (GetSegment (Trail' Loop v n)) -> Codomain (GetSegment (Trail' Loop v n)) (N (GetSegment (Trail' Loop v n))) #
(Metric v, OrderedField n, Real n) => Parametric (GetSegment (Trail v n))
Instance details Defined in Diagrams.Trail Methods atParam :: GetSegment (Trail v n) -> N (GetSegment (Trail v n)) -> Codomain (GetSegment (Trail v n)) (N (GetSegment (Trail v n))) #
(Parametric (GetSegment (Trail' c v n)), Additive v, Num n) => Parametric (Tangent (Trail' c v n))
Instance details Defined in Diagrams.Trail Methods atParam :: Tangent (Trail' c v n) -> N (Tangent (Trail' c v n)) -> Codomain (Tangent (Trail' c v n)) (N (Tangent (Trail' c v n))) #
(Metric v, OrderedField n, Real n) => Parametric (Tangent (Trail v n))
Instance details Defined in Diagrams.Trail Methods atParam :: Tangent (Trail v n) -> N (Tangent (Trail v n)) -> Codomain (Tangent (Trail v n)) (N (Tangent (Trail v n))) #
(Additive v, Num n) => Parametric (Tangent (Segment Closed v n))
Instance details Defined in Diagrams.Tangent Methods atParam :: Tangent (Segment Closed v n) -> N (Tangent (Segment Closed v n)) -> Codomain (Tangent (Segment Closed v n)) (N (Tangent (Segment Closed v n))) #
(Additive v, Num n) => Parametric (Tangent (FixedSegment v n))
Instance details Defined in Diagrams.Tangent Methods atParam :: Tangent (FixedSegment v n) -> N (Tangent (FixedSegment v n)) -> Codomain (Tangent (FixedSegment v n)) (N (Tangent (FixedSegment v n))) #
Parametric (Tangent t) => Parametric (Tangent (Located t))
Instance details Defined in Diagrams.Tangent Methods atParam :: Tangent (Located t) -> N (Tangent (Located t)) -> Codomain (Tangent (Located t)) (N (Tangent (Located t))) #
(InSpace v n a, Parametric a, Codomain a ~ v) => Parametric (Located a)
Instance details Defined in Diagrams.Located Methods atParam :: Located a -> N (Located a) -> Codomain (Located a) (N (Located a)) #
Fractional n => Parametric (BernsteinPoly n)
Instance details Defined in Diagrams.TwoD.Segment.Bernstein Methods atParam :: BernsteinPoly n -> N (BernsteinPoly n) -> Codomain (BernsteinPoly n) (N (BernsteinPoly n)) #
(Metric v, OrderedField n, Real n) => Parametric (SegTree v n)
Instance details Defined in Diagrams.Trail Methods atParam :: SegTree v n -> N (SegTree v n) -> Codomain (SegTree v n) (N (SegTree v n)) #
(Metric v, OrderedField n, Real n) => Parametric (Trail v n)
Instance details Defined in Diagrams.Trail Methods atParam :: Trail v n -> N (Trail v n) -> Codomain (Trail v n) (N (Trail v n)) #
(Additive v, Num n) => Parametric (FixedSegment v n)
Instance details Defined in Diagrams.Segment Methods atParam :: FixedSegment v n -> N (FixedSegment v n) -> Codomain (FixedSegment v n) (N (FixedSegment v n)) #
(Metric v, OrderedField n, Real n) => Parametric (Trail' l v n)
Instance details Defined in Diagrams.Trail Methods atParam :: Trail' l v n -> N (Trail' l v n) -> Codomain (Trail' l v n) (N (Trail' l v n)) #
(Additive v, Num n) => Parametric (Segment Closed v n)	`atParam` yields a parametrized view of segments as continuous functions `[0,1] -> v`, which give the offset from the start of the segment for each value of the parameter between `0` and `1`. It is designed to be used infix, like seg `atParam` 0.5.
Instance details Defined in Diagrams.Segment Methods atParam :: Segment Closed v n -> N (Segment Closed v n) -> Codomain (Segment Closed v n) (N (Segment Closed v n)) #

class DomainBounds p where #

Type class for parametric functions with a bounded domain. The default bounds are [0,1].

Note that this domain indicates the main "interesting" portion of the function. It must be defined within this range, but for some instances may still have sensible values outside.

Minimal complete definition

Nothing

Methods

domainLower :: p -> N p #

domainLower defaults to being constantly 0 (for vector spaces with numeric scalars).

domainUpper :: p -> N p #

domainUpper defaults to being constantly 1 (for vector spaces with numeric scalars).

Instances

DomainBounds t => DomainBounds (GetSegment t)
Instance details Defined in Diagrams.Trail Methods domainLower :: GetSegment t -> N (GetSegment t) # domainUpper :: GetSegment t -> N (GetSegment t) #
DomainBounds t => DomainBounds (Tangent t)
Instance details Defined in Diagrams.Tangent Methods domainLower :: Tangent t -> N (Tangent t) # domainUpper :: Tangent t -> N (Tangent t) #
DomainBounds a => DomainBounds (Located a)
Instance details Defined in Diagrams.Located Methods domainLower :: Located a -> N (Located a) # domainUpper :: Located a -> N (Located a) #
Num n => DomainBounds (BernsteinPoly n)
Instance details Defined in Diagrams.TwoD.Segment.Bernstein Methods domainLower :: BernsteinPoly n -> N (BernsteinPoly n) # domainUpper :: BernsteinPoly n -> N (BernsteinPoly n) #
Num n => DomainBounds (SegTree v n)
Instance details Defined in Diagrams.Trail Methods domainLower :: SegTree v n -> N (SegTree v n) # domainUpper :: SegTree v n -> N (SegTree v n) #
Num n => DomainBounds (Trail v n)
Instance details Defined in Diagrams.Trail Methods domainLower :: Trail v n -> N (Trail v n) # domainUpper :: Trail v n -> N (Trail v n) #
Num n => DomainBounds (FixedSegment v n)
Instance details Defined in Diagrams.Segment Methods domainLower :: FixedSegment v n -> N (FixedSegment v n) # domainUpper :: FixedSegment v n -> N (FixedSegment v n) #
Num n => DomainBounds (Trail' l v n)
Instance details Defined in Diagrams.Trail Methods domainLower :: Trail' l v n -> N (Trail' l v n) # domainUpper :: Trail' l v n -> N (Trail' l v n) #
Num n => DomainBounds (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods domainLower :: Segment Closed v n -> N (Segment Closed v n) # domainUpper :: Segment Closed v n -> N (Segment Closed v n) #

class (Parametric p, DomainBounds p) => EndValues p where #

Type class for querying the values of a parametric object at the ends of its domain.

Minimal complete definition

Nothing

Methods

atStart :: p -> Codomain p (N p) #

atStart is the value at the start of the domain. That is,

atStart x = x `atParam` domainLower x

This is the default implementation, but some representations will have a more efficient and/or precise implementation.

atEnd :: p -> Codomain p (N p) #

atEnd is the value at the end of the domain. That is,

atEnd x = x `atParam` domainUpper x

This is the default implementation, but some representations will have a more efficient and/or precise implementation.

Instances

(Metric v, OrderedField n) => EndValues (GetSegment (Trail' Line v n))
Instance details Defined in Diagrams.Trail Methods atStart :: GetSegment (Trail' Line v n) -> Codomain (GetSegment (Trail' Line v n)) (N (GetSegment (Trail' Line v n))) # atEnd :: GetSegment (Trail' Line v n) -> Codomain (GetSegment (Trail' Line v n)) (N (GetSegment (Trail' Line v n))) #
(Metric v, OrderedField n, Real n) => EndValues (GetSegment (Trail' Loop v n))
Instance details Defined in Diagrams.Trail Methods atStart :: GetSegment (Trail' Loop v n) -> Codomain (GetSegment (Trail' Loop v n)) (N (GetSegment (Trail' Loop v n))) # atEnd :: GetSegment (Trail' Loop v n) -> Codomain (GetSegment (Trail' Loop v n)) (N (GetSegment (Trail' Loop v n))) #
(Metric v, OrderedField n, Real n) => EndValues (GetSegment (Trail v n))
Instance details Defined in Diagrams.Trail Methods atStart :: GetSegment (Trail v n) -> Codomain (GetSegment (Trail v n)) (N (GetSegment (Trail v n))) # atEnd :: GetSegment (Trail v n) -> Codomain (GetSegment (Trail v n)) (N (GetSegment (Trail v n))) #
(Parametric (GetSegment (Trail' c v n)), EndValues (GetSegment (Trail' c v n)), Additive v, Num n) => EndValues (Tangent (Trail' c v n))
Instance details Defined in Diagrams.Trail Methods atStart :: Tangent (Trail' c v n) -> Codomain (Tangent (Trail' c v n)) (N (Tangent (Trail' c v n))) # atEnd :: Tangent (Trail' c v n) -> Codomain (Tangent (Trail' c v n)) (N (Tangent (Trail' c v n))) #
(Metric v, OrderedField n, Real n) => EndValues (Tangent (Trail v n))
Instance details Defined in Diagrams.Trail Methods atStart :: Tangent (Trail v n) -> Codomain (Tangent (Trail v n)) (N (Tangent (Trail v n))) # atEnd :: Tangent (Trail v n) -> Codomain (Tangent (Trail v n)) (N (Tangent (Trail v n))) #
(Additive v, Num n) => EndValues (Tangent (Segment Closed v n))
Instance details Defined in Diagrams.Tangent Methods atStart :: Tangent (Segment Closed v n) -> Codomain (Tangent (Segment Closed v n)) (N (Tangent (Segment Closed v n))) # atEnd :: Tangent (Segment Closed v n) -> Codomain (Tangent (Segment Closed v n)) (N (Tangent (Segment Closed v n))) #
(Additive v, Num n) => EndValues (Tangent (FixedSegment v n))
Instance details Defined in Diagrams.Tangent Methods atStart :: Tangent (FixedSegment v n) -> Codomain (Tangent (FixedSegment v n)) (N (Tangent (FixedSegment v n))) # atEnd :: Tangent (FixedSegment v n) -> Codomain (Tangent (FixedSegment v n)) (N (Tangent (FixedSegment v n))) #
(DomainBounds t, EndValues (Tangent t)) => EndValues (Tangent (Located t))
Instance details Defined in Diagrams.Tangent Methods atStart :: Tangent (Located t) -> Codomain (Tangent (Located t)) (N (Tangent (Located t))) # atEnd :: Tangent (Located t) -> Codomain (Tangent (Located t)) (N (Tangent (Located t))) #
(InSpace v n a, EndValues a, Codomain a ~ v) => EndValues (Located a)
Instance details Defined in Diagrams.Located Methods atStart :: Located a -> Codomain (Located a) (N (Located a)) # atEnd :: Located a -> Codomain (Located a) (N (Located a)) #
Fractional n => EndValues (BernsteinPoly n)
Instance details Defined in Diagrams.TwoD.Segment.Bernstein Methods atStart :: BernsteinPoly n -> Codomain (BernsteinPoly n) (N (BernsteinPoly n)) # atEnd :: BernsteinPoly n -> Codomain (BernsteinPoly n) (N (BernsteinPoly n)) #
(Metric v, OrderedField n, Real n) => EndValues (SegTree v n)
Instance details Defined in Diagrams.Trail Methods atStart :: SegTree v n -> Codomain (SegTree v n) (N (SegTree v n)) # atEnd :: SegTree v n -> Codomain (SegTree v n) (N (SegTree v n)) #
(Metric v, OrderedField n, Real n) => EndValues (Trail v n)
Instance details Defined in Diagrams.Trail Methods atStart :: Trail v n -> Codomain (Trail v n) (N (Trail v n)) # atEnd :: Trail v n -> Codomain (Trail v n) (N (Trail v n)) #
(Additive v, Num n) => EndValues (FixedSegment v n)
Instance details Defined in Diagrams.Segment Methods atStart :: FixedSegment v n -> Codomain (FixedSegment v n) (N (FixedSegment v n)) # atEnd :: FixedSegment v n -> Codomain (FixedSegment v n) (N (FixedSegment v n)) #
(Metric v, OrderedField n, Real n) => EndValues (Trail' l v n)
Instance details Defined in Diagrams.Trail Methods atStart :: Trail' l v n -> Codomain (Trail' l v n) (N (Trail' l v n)) # atEnd :: Trail' l v n -> Codomain (Trail' l v n) (N (Trail' l v n)) #
(Additive v, Num n) => EndValues (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods atStart :: Segment Closed v n -> Codomain (Segment Closed v n) (N (Segment Closed v n)) # atEnd :: Segment Closed v n -> Codomain (Segment Closed v n) (N (Segment Closed v n)) #

class DomainBounds p => Sectionable p where #

Type class for parametric objects which can be split into subobjects.

Minimal definition: Either splitAtParam or section, plus reverseDomain.

Minimal complete definition

reverseDomain

Methods

splitAtParam :: p -> N p -> (p, p) #

splitAtParam splits an object p into two new objects (l,r) at the parameter t, where l corresponds to the portion of p for parameter values from 0 to t and r for to that from t to 1. The following property should hold:

  prop_splitAtParam f t u =
    | u < t     = atParam f u == atParam l (u / t)
    | otherwise = atParam f u == atParam f t ??? atParam l ((u - t) / (domainUpper f - t))
    where (l,r) = splitAtParam f t

where (???) = (^+^) if the codomain is a vector type, or const flip if the codomain is a point type. Stated more intuitively, all this is to say that the parameterization scales linearly with splitting.

splitAtParam can also be used with parameters outside the range of the domain. For example, using the parameter 2 with a path (where the domain is the default [0,1]) gives two result paths where the first is the original path extended to the parameter 2, and the second result path travels backwards from the end of the first to the end of the original path.

section :: p -> N p -> N p -> p #

Extract a particular section of the domain, linearly reparameterized to the same domain as the original. Should satisfy the property:

prop_section x l u t =
  let s = section x l u
  in     domainBounds x == domainBounds x
      && (x `atParam` lerp l u t) == (s `atParam` t)

That is, the section should have the same domain as the original, and the reparameterization should be linear.

reverseDomain :: p -> p #

Flip the parameterization on the domain.

Instances

(InSpace v n a, Fractional n, Parametric a, Sectionable a, Codomain a ~ v) => Sectionable (Located a)
Instance details Defined in Diagrams.Located Methods splitAtParam :: Located a -> N (Located a) -> (Located a, Located a) # section :: Located a -> N (Located a) -> N (Located a) -> Located a # reverseDomain :: Located a -> Located a #
Fractional n => Sectionable (BernsteinPoly n)
Instance details Defined in Diagrams.TwoD.Segment.Bernstein Methods splitAtParam :: BernsteinPoly n -> N (BernsteinPoly n) -> (BernsteinPoly n, BernsteinPoly n) # section :: BernsteinPoly n -> N (BernsteinPoly n) -> N (BernsteinPoly n) -> BernsteinPoly n # reverseDomain :: BernsteinPoly n -> BernsteinPoly n #
(Metric v, OrderedField n, Real n) => Sectionable (SegTree v n)
Instance details Defined in Diagrams.Trail Methods splitAtParam :: SegTree v n -> N (SegTree v n) -> (SegTree v n, SegTree v n) # section :: SegTree v n -> N (SegTree v n) -> N (SegTree v n) -> SegTree v n # reverseDomain :: SegTree v n -> SegTree v n #
(Metric v, OrderedField n, Real n) => Sectionable (Trail v n)	Note that there is no `Sectionable` instance for `Trail' Loop`, because it does not make sense (splitting a loop at a parameter results in a single line, not two loops). However, it's convenient to have a `Sectionable` instance for `Trail`; if the `Trail` contains a loop the loop will first be cut and then `splitAtParam` called on the resulting line. This is semantically a bit silly, so please don't rely on it. (E.g. if this is really the behavior you want, consider first calling `cutLoop` yourself.)
Instance details Defined in Diagrams.Trail Methods splitAtParam :: Trail v n -> N (Trail v n) -> (Trail v n, Trail v n) # section :: Trail v n -> N (Trail v n) -> N (Trail v n) -> Trail v n # reverseDomain :: Trail v n -> Trail v n #
(Additive v, Fractional n) => Sectionable (FixedSegment v n)
Instance details Defined in Diagrams.Segment Methods splitAtParam :: FixedSegment v n -> N (FixedSegment v n) -> (FixedSegment v n, FixedSegment v n) # section :: FixedSegment v n -> N (FixedSegment v n) -> N (FixedSegment v n) -> FixedSegment v n # reverseDomain :: FixedSegment v n -> FixedSegment v n #
(Metric v, OrderedField n, Real n) => Sectionable (Trail' Line v n)
Instance details Defined in Diagrams.Trail Methods splitAtParam :: Trail' Line v n -> N (Trail' Line v n) -> (Trail' Line v n, Trail' Line v n) # section :: Trail' Line v n -> N (Trail' Line v n) -> N (Trail' Line v n) -> Trail' Line v n # reverseDomain :: Trail' Line v n -> Trail' Line v n #
(Additive v, Fractional n) => Sectionable (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods splitAtParam :: Segment Closed v n -> N (Segment Closed v n) -> (Segment Closed v n, Segment Closed v n) # section :: Segment Closed v n -> N (Segment Closed v n) -> N (Segment Closed v n) -> Segment Closed v n # reverseDomain :: Segment Closed v n -> Segment Closed v n #

class Parametric p => HasArcLength p where #

Type class for parametric things with a notion of arc length.

Minimal complete definition

arcLengthBounded, arcLengthToParam

Methods

arcLengthBounded :: N p -> p -> Interval (N p) #

arcLengthBounded eps x approximates the arc length of x. The true arc length is guaranteed to lie within the interval returned, which will have a size of at most eps.

arcLength :: N p -> p -> N p #

arcLength eps s approximates the arc length of x up to the accuracy eps (plus or minus).

stdArcLength :: p -> N p #

Approximate the arc length up to a standard accuracy of stdTolerance (1e-6).

arcLengthToParam :: N p -> p -> N p -> N p #

arcLengthToParam eps s l converts the absolute arc length l, measured from the start of the domain, to a parameter on the object s. The true arc length at the parameter returned is guaranteed to be within eps of the requested arc length.

This should work for any arc length, and may return any parameter value (not just parameters in the domain).

stdArcLengthToParam :: p -> N p -> N p #

A simple interface to convert arc length to a parameter, guaranteed to be accurate within stdTolerance, or 1e-6.

Instances

(InSpace v n a, Fractional n, HasArcLength a, Codomain a ~ v) => HasArcLength (Located a)
Instance details Defined in Diagrams.Located Methods arcLengthBounded :: N (Located a) -> Located a -> Interval (N (Located a)) # arcLength :: N (Located a) -> Located a -> N (Located a) # stdArcLength :: Located a -> N (Located a) # arcLengthToParam :: N (Located a) -> Located a -> N (Located a) -> N (Located a) # stdArcLengthToParam :: Located a -> N (Located a) -> N (Located a) #
(Metric v, OrderedField n, Real n) => HasArcLength (SegTree v n)
Instance details Defined in Diagrams.Trail Methods arcLengthBounded :: N (SegTree v n) -> SegTree v n -> Interval (N (SegTree v n)) # arcLength :: N (SegTree v n) -> SegTree v n -> N (SegTree v n) # stdArcLength :: SegTree v n -> N (SegTree v n) # arcLengthToParam :: N (SegTree v n) -> SegTree v n -> N (SegTree v n) -> N (SegTree v n) # stdArcLengthToParam :: SegTree v n -> N (SegTree v n) -> N (SegTree v n) #
(Metric v, OrderedField n, Real n) => HasArcLength (Trail v n)
Instance details Defined in Diagrams.Trail Methods arcLengthBounded :: N (Trail v n) -> Trail v n -> Interval (N (Trail v n)) # arcLength :: N (Trail v n) -> Trail v n -> N (Trail v n) # stdArcLength :: Trail v n -> N (Trail v n) # arcLengthToParam :: N (Trail v n) -> Trail v n -> N (Trail v n) -> N (Trail v n) # stdArcLengthToParam :: Trail v n -> N (Trail v n) -> N (Trail v n) #
(Metric v, OrderedField n) => HasArcLength (FixedSegment v n)
Instance details Defined in Diagrams.Segment Methods arcLengthBounded :: N (FixedSegment v n) -> FixedSegment v n -> Interval (N (FixedSegment v n)) # arcLength :: N (FixedSegment v n) -> FixedSegment v n -> N (FixedSegment v n) # stdArcLength :: FixedSegment v n -> N (FixedSegment v n) # arcLengthToParam :: N (FixedSegment v n) -> FixedSegment v n -> N (FixedSegment v n) -> N (FixedSegment v n) # stdArcLengthToParam :: FixedSegment v n -> N (FixedSegment v n) -> N (FixedSegment v n) #
(Metric v, OrderedField n, Real n) => HasArcLength (Trail' l v n)
Instance details Defined in Diagrams.Trail Methods arcLengthBounded :: N (Trail' l v n) -> Trail' l v n -> Interval (N (Trail' l v n)) # arcLength :: N (Trail' l v n) -> Trail' l v n -> N (Trail' l v n) # stdArcLength :: Trail' l v n -> N (Trail' l v n) # arcLengthToParam :: N (Trail' l v n) -> Trail' l v n -> N (Trail' l v n) -> N (Trail' l v n) # stdArcLengthToParam :: Trail' l v n -> N (Trail' l v n) -> N (Trail' l v n) #
(Metric v, OrderedField n) => HasArcLength (Segment Closed v n)
Instance details Defined in Diagrams.Segment Methods arcLengthBounded :: N (Segment Closed v n) -> Segment Closed v n -> Interval (N (Segment Closed v n)) # arcLength :: N (Segment Closed v n) -> Segment Closed v n -> N (Segment Closed v n) # stdArcLength :: Segment Closed v n -> N (Segment Closed v n) # arcLengthToParam :: N (Segment Closed v n) -> Segment Closed v n -> N (Segment Closed v n) -> N (Segment Closed v n) # stdArcLengthToParam :: Segment Closed v n -> N (Segment Closed v n) -> N (Segment Closed v n) #

namePoint :: (IsName nm, Metric v, OrderedField n, Semigroup m) => (QDiagram b v n m -> Point v n) -> nm -> QDiagram b v n m -> QDiagram b v n m #

Attach an atomic name to a certain point (which may be computed from the given diagram), treated as a subdiagram with no content and a point envelope.

named :: (IsName nm, Metric v, OrderedField n, Semigroup m) => nm -> QDiagram b v n m -> QDiagram b v n m #

Attach an atomic name to a diagram.

committed :: Iso (Recommend a) (Recommend b) a b #

Commit a value for any Recommend. This is *not* a valid Iso because the resulting Recommend b is always a Commit. This is useful because it means any Recommend styles set with a lens will not be accidentally overridden. If you want a valid lens onto a recommend value use _recommend.

Other lenses that use this are labeled with a warning.

isCommitted :: Lens' (Recommend a) Bool #

Lens onto whether something is committed or not.

_recommend :: Lens (Recommend a) (Recommend b) a b #

Lens onto the value inside either a Recommend or Commit. Unlike committed, this is a valid lens.

_Commit :: Prism' (Recommend a) a #

Prism onto a Commit.

_Recommend :: Prism' (Recommend a) a #

Prism onto a Recommend.

_lineMiterLimit :: Lens' (Style v n) Double #

Lens onto the line miter limit in a style.

lineMiterLimitA :: HasStyle a => LineMiterLimit -> a -> a #

Apply a LineMiterLimit attribute.

lineMiterLimit :: HasStyle a => Double -> a -> a #

Set the miter limit for joins with LineJoinMiter.

getLineMiterLimit :: LineMiterLimit -> Double #

_LineMiterLimit :: Iso' LineMiterLimit Double #

_lineJoin :: Lens' (Style v n) LineJoin #

Lens onto the line join type in a style.

lineJoin :: HasStyle a => LineJoin -> a -> a #

Set the segment join style.

getLineJoin :: LineJoin -> LineJoin #

_lineCap :: Lens' (Style v n) LineCap #

Lens onto the line cap in a style.

lineCap :: HasStyle a => LineCap -> a -> a #

Set the line end cap attribute.

getLineCap :: LineCap -> LineCap #

_strokeOpacity :: Lens' (Style v n) Double #

Lens onto the stroke opacity in a style.

strokeOpacity :: HasStyle a => Double -> a -> a #

Multiply the stroke opacity (see StrokeOpacity) by the given value. For example, strokeOpacity 0.8 means "decrease this diagram's stroke opacity to 80% of its previous value".

getStrokeOpacity :: StrokeOpacity -> Double #

_StrokeOpacity :: Iso' StrokeOpacity Double #

_fillOpacity :: Lens' (Style v n) Double #

Lens onto the fill opacity in a style.

fillOpacity :: HasStyle a => Double -> a -> a #

Multiply the fill opacity (see FillOpacity) by the given value. For example, fillOpacity 0.8 means "decrease this diagram's fill opacity to 80% of its previous value".

getFillOpacity :: FillOpacity -> Double #

_FillOpacity :: Iso' FillOpacity Double #

_opacity :: Lens' (Style v n) Double #

Lens onto the opacity in a style.

opacity :: HasStyle a => Double -> a -> a #

Multiply the opacity (see Opacity) by the given value. For example, opacity 0.8 means "decrease this diagram's opacity to 80% of its previous opacity".

getOpacity :: Opacity -> Double #

_Opacity :: Iso' Opacity Double #

colorToRGBA :: Color c => c -> (Double, Double, Double, Double) #

Convert to sRGBA.

colorToSRGBA :: Color c => c -> (Double, Double, Double, Double) #

Convert to sRGBA.

someToAlpha :: SomeColor -> AlphaColour Double #

_SomeColor :: Iso' SomeColor (AlphaColour Double) #

Isomorphism between SomeColor and AlphaColour Double.

_dashingU :: Typeable n => Lens' (Style v n) (Maybe (Dashing n)) #

Lens onto the unmeasured Dashing attribute. This is useful for backends to use on styles once they have been unmeasured. Using on a diagram style could lead to unexpected results.

_dashing :: Typeable n => Lens' (Style v n) (Maybe (Measured n (Dashing n))) #

Lens onto a measured dashing attribute in a style.

dashingL :: (N a ~ n, HasStyle a, Typeable n, Num n) => [n] -> n -> a -> a #

A convenient sysnonym for 'dashing (local w)'.

dashingO :: (N a ~ n, HasStyle a, Typeable n) => [n] -> n -> a -> a #

A convenient synonym for 'dashing (output w)'.

dashingN :: (N a ~ n, HasStyle a, Typeable n, Num n) => [n] -> n -> a -> a #

A convenient synonym for 'dashing (normalized w)'.

dashingG :: (N a ~ n, HasStyle a, Typeable n, Num n) => [n] -> n -> a -> a #

A convenient synonym for 'dashing (global w)'.

dashing #

Arguments

:: (N a ~ n, HasStyle a, Typeable n)
=> [Measure n]	A list specifying alternate lengths of on and off portions of the stroke. The empty list indicates no dashing.
-> Measure n	An offset into the dash pattern at which the stroke should start.
-> a
-> a

Set the line dashing style.

getDashing :: Dashing n -> Dashing n #

_lineWidthU :: Typeable n => Lens' (Style v n) (Maybe n) #

Lens onto the unmeasured linewith attribute. This is useful for backends to use on styles once they have been unmeasured. Using on a diagram style could lead to unexpected results.

_lw :: (Typeable n, OrderedField n) => Lens' (Style v n) (Measure n) #

Lens onto a measured line width in a style.

_lineWidth :: (Typeable n, OrderedField n) => Lens' (Style v n) (Measure n) #

Lens onto a measured line width in a style.

lwL :: (N a ~ n, HasStyle a, Typeable n, Num n) => n -> a -> a #

A convenient sysnonym for 'lineWidth (local w)'.

lwO :: (N a ~ n, HasStyle a, Typeable n) => n -> a -> a #

A convenient synonym for 'lineWidth (output w)'.

lwN :: (N a ~ n, HasStyle a, Typeable n, Num n) => n -> a -> a #

A convenient synonym for 'lineWidth (normalized w)'.

lwG :: (N a ~ n, HasStyle a, Typeable n, Num n) => n -> a -> a #

A convenient synonym for 'lineWidth (global w)'.

lw :: (N a ~ n, HasStyle a, Typeable n) => Measure n -> a -> a #

Default for lineWidth.

lineWidthM :: (N a ~ n, HasStyle a, Typeable n) => LineWidthM n -> a -> a #

Apply a LineWidth attribute.

lineWidth :: (N a ~ n, HasStyle a, Typeable n) => Measure n -> a -> a #

Set the line (stroke) width.

getLineWidth :: LineWidth n -> n #

_LineWidthM :: Iso' (LineWidthM n) (Measure n) #

_LineWidth :: Iso' (LineWidth n) n #

huge :: OrderedField n => Measure n #

veryLarge :: OrderedField n => Measure n #

large :: OrderedField n => Measure n #

normal :: OrderedField n => Measure n #

small :: OrderedField n => Measure n #

verySmall :: OrderedField n => Measure n #

tiny :: OrderedField n => Measure n #

ultraThick :: OrderedField n => Measure n #

veryThick :: OrderedField n => Measure n #

thick :: OrderedField n => Measure n #

medium :: OrderedField n => Measure n #

thin :: OrderedField n => Measure n #

veryThin :: OrderedField n => Measure n #

ultraThin :: OrderedField n => Measure n #

none :: OrderedField n => Measure n #

data LineWidth n #

Line widths specified on child nodes always override line widths specified at parent nodes.

Instances

Semigroup (LineWidth n)
Instance details Defined in Diagrams.Attributes Methods (<>) :: LineWidth n -> LineWidth n -> LineWidth n # sconcat :: NonEmpty (LineWidth n) -> LineWidth n # stimes :: Integral b => b -> LineWidth n -> LineWidth n #
OrderedField n => Default (LineWidthM n)
Instance details Defined in Diagrams.Attributes Methods def :: LineWidthM n #
Typeable n => AttributeClass (LineWidth n)
Instance details Defined in Diagrams.Attributes

data Dashing n #

Create lines that are dashing... er, dashed.

Constructors

Dashing [n] n

Instances

Functor Dashing
Instance details Defined in Diagrams.Attributes Methods fmap :: (a -> b) -> Dashing a -> Dashing b # (<$) :: a -> Dashing b -> Dashing a #
Eq n => Eq (Dashing n)
Instance details Defined in Diagrams.Attributes Methods (==) :: Dashing n -> Dashing n -> Bool # (/=) :: Dashing n -> Dashing n -> Bool #
Semigroup (Dashing n)
Instance details Defined in Diagrams.Attributes Methods (<>) :: Dashing n -> Dashing n -> Dashing n # sconcat :: NonEmpty (Dashing n) -> Dashing n # stimes :: Integral b => b -> Dashing n -> Dashing n #
Typeable n => AttributeClass (Dashing n)
Instance details Defined in Diagrams.Attributes

class Color c where #

The Color type class encompasses color representations which can be used by the Diagrams library. Instances are provided for both the Colour and AlphaColour types from the Data.Colour library.

Methods

toAlphaColour :: c -> AlphaColour Double #

Convert a color to its standard representation, AlphaColour.

fromAlphaColour :: AlphaColour Double -> c #

Convert from an AlphaColour Double. Note that this direction may lose some information. For example, the instance for Colour drops the alpha channel.

Instances

Color SomeColor
Instance details Defined in Diagrams.Attributes Methods toAlphaColour :: SomeColor -> AlphaColour Double # fromAlphaColour :: AlphaColour Double -> SomeColor #
a ~ Double => Color (Colour a)
Instance details Defined in Diagrams.Attributes Methods toAlphaColour :: Colour a -> AlphaColour Double # fromAlphaColour :: AlphaColour Double -> Colour a #
a ~ Double => Color (AlphaColour a)
Instance details Defined in Diagrams.Attributes Methods toAlphaColour :: AlphaColour a -> AlphaColour Double # fromAlphaColour :: AlphaColour Double -> AlphaColour a #

data SomeColor where #

An existential wrapper for instances of the Color class.

Constructors

SomeColor :: forall c. Color c => c -> SomeColor

Instances

Show SomeColor
Instance details Defined in Diagrams.Attributes Methods showsPrec :: Int -> SomeColor -> ShowS # show :: SomeColor -> String # showList :: [SomeColor] -> ShowS #
Color SomeColor
Instance details Defined in Diagrams.Attributes Methods toAlphaColour :: SomeColor -> AlphaColour Double # fromAlphaColour :: AlphaColour Double -> SomeColor #

data Opacity #

Although the individual colors in a diagram can have transparency, the opacity/transparency of a diagram as a whole can be specified with the Opacity attribute. The opacity is a value between 1 (completely opaque, the default) and 0 (completely transparent). Opacity is multiplicative, that is, opacity o1 . opacity o2 === opacity (o1 * o2). In other words, for example, opacity 0.8 means "decrease this diagram's opacity to 80% of its previous opacity".

Instances

Semigroup Opacity
Instance details Defined in Diagrams.Attributes Methods (<>) :: Opacity -> Opacity -> Opacity # sconcat :: NonEmpty Opacity -> Opacity # stimes :: Integral b => b -> Opacity -> Opacity #
AttributeClass Opacity
Instance details Defined in Diagrams.Attributes

data FillOpacity #

Like Opacity, but set the opacity only for fills (as opposed to strokes). As with Opacity, the fill opacity is a value between 1 (completely opaque, the default) and 0 (completely transparent), and is multiplicative.

Instances

Semigroup FillOpacity
Instance details Defined in Diagrams.Attributes Methods (<>) :: FillOpacity -> FillOpacity -> FillOpacity # sconcat :: NonEmpty FillOpacity -> FillOpacity # stimes :: Integral b => b -> FillOpacity -> FillOpacity #
AttributeClass FillOpacity
Instance details Defined in Diagrams.Attributes

data StrokeOpacity #

Like Opacity, but set the opacity only for strokes (as opposed to fills). As with Opacity, the fill opacity is a value between 1 (completely opaque, the default) and 0 (completely transparent), and is multiplicative.

Instances

Semigroup StrokeOpacity
Instance details Defined in Diagrams.Attributes Methods (<>) :: StrokeOpacity -> StrokeOpacity -> StrokeOpacity # sconcat :: NonEmpty StrokeOpacity -> StrokeOpacity # stimes :: Integral b => b -> StrokeOpacity -> StrokeOpacity #
AttributeClass StrokeOpacity
Instance details Defined in Diagrams.Attributes

data LineCap #

What sort of shape should be placed at the endpoints of lines?

Constructors

LineCapButt	Lines end precisely at their endpoints.
LineCapRound	Lines are capped with semicircles centered on endpoints.
LineCapSquare	Lines are capped with a squares centered on endpoints.

Instances

Eq LineCap
Instance details Defined in Diagrams.Attributes Methods (==) :: LineCap -> LineCap -> Bool # (/=) :: LineCap -> LineCap -> Bool #
Ord LineCap
Instance details Defined in Diagrams.Attributes Methods compare :: LineCap -> LineCap -> Ordering # (<) :: LineCap -> LineCap -> Bool # (<=) :: LineCap -> LineCap -> Bool # (>) :: LineCap -> LineCap -> Bool # (>=) :: LineCap -> LineCap -> Bool # max :: LineCap -> LineCap -> LineCap # min :: LineCap -> LineCap -> LineCap #
Show LineCap
Instance details Defined in Diagrams.Attributes Methods showsPrec :: Int -> LineCap -> ShowS # show :: LineCap -> String # showList :: [LineCap] -> ShowS #
Semigroup LineCap	Last semigroup structure.
Instance details Defined in Diagrams.Attributes Methods (<>) :: LineCap -> LineCap -> LineCap # sconcat :: NonEmpty LineCap -> LineCap # stimes :: Integral b => b -> LineCap -> LineCap #
Default LineCap
Instance details Defined in Diagrams.Attributes Methods def :: LineCap #
AttributeClass LineCap
Instance details Defined in Diagrams.Attributes

data LineJoin #

How should the join points between line segments be drawn?

Constructors

LineJoinMiter	Use a "miter" shape (whatever that is).
LineJoinRound	Use rounded join points.
LineJoinBevel	Use a "bevel" shape (whatever that is). Are these... carpentry terms?

Instances

Eq LineJoin
Instance details Defined in Diagrams.Attributes Methods (==) :: LineJoin -> LineJoin -> Bool # (/=) :: LineJoin -> LineJoin -> Bool #
Ord LineJoin
Instance details Defined in Diagrams.Attributes Methods compare :: LineJoin -> LineJoin -> Ordering # (<) :: LineJoin -> LineJoin -> Bool # (<=) :: LineJoin -> LineJoin -> Bool # (>) :: LineJoin -> LineJoin -> Bool # (>=) :: LineJoin -> LineJoin -> Bool # max :: LineJoin -> LineJoin -> LineJoin # min :: LineJoin -> LineJoin -> LineJoin #
Show LineJoin
Instance details Defined in Diagrams.Attributes Methods showsPrec :: Int -> LineJoin -> ShowS # show :: LineJoin -> String # showList :: [LineJoin] -> ShowS #
Semigroup LineJoin	Last semigroup structure.
Instance details Defined in Diagrams.Attributes Methods (<>) :: LineJoin -> LineJoin -> LineJoin # sconcat :: NonEmpty LineJoin -> LineJoin # stimes :: Integral b => b -> LineJoin -> LineJoin #
Default LineJoin
Instance details Defined in Diagrams.Attributes Methods def :: LineJoin #
AttributeClass LineJoin
Instance details Defined in Diagrams.Attributes

newtype LineMiterLimit #

Miter limit attribute affecting the LineJoinMiter joins. For some backends this value may have additional effects.

Constructors

LineMiterLimit (Last Double)

Instances

Eq LineMiterLimit
Instance details Defined in Diagrams.Attributes Methods (==) :: LineMiterLimit -> LineMiterLimit -> Bool # (/=) :: LineMiterLimit -> LineMiterLimit -> Bool #
Ord LineMiterLimit
Instance details Defined in Diagrams.Attributes Methods compare :: LineMiterLimit -> LineMiterLimit -> Ordering # (<) :: LineMiterLimit -> LineMiterLimit -> Bool # (<=) :: LineMiterLimit -> LineMiterLimit -> Bool # (>) :: LineMiterLimit -> LineMiterLimit -> Bool # (>=) :: LineMiterLimit -> LineMiterLimit -> Bool # max :: LineMiterLimit -> LineMiterLimit -> LineMiterLimit # min :: LineMiterLimit -> LineMiterLimit -> LineMiterLimit #
Semigroup LineMiterLimit
Instance details Defined in Diagrams.Attributes Methods (<>) :: LineMiterLimit -> LineMiterLimit -> LineMiterLimit # sconcat :: NonEmpty LineMiterLimit -> LineMiterLimit # stimes :: Integral b => b -> LineMiterLimit -> LineMiterLimit #
Default LineMiterLimit
Instance details Defined in Diagrams.Attributes Methods def :: LineMiterLimit #
AttributeClass LineMiterLimit
Instance details Defined in Diagrams.Attributes

project :: (Metric v, Fractional a) => v a -> v a -> v a #

project u v computes the projection of v onto u.

class R1 (t :: Type -> Type) where #

A space that has at least 1 basis vector _x.

Methods

_x :: Lens' (t a) a #

>>> V1 2 ^._x
2

>>> V1 2 & _x .~ 3
V1 3

Instances

R1 Identity
Instance details Defined in Linear.V1 Methods _x :: Lens' (Identity a) a #
R1 V2
Instance details Defined in Linear.V2 Methods _x :: Lens' (V2 a) a #
R1 V3
Instance details Defined in Linear.V3 Methods _x :: Lens' (V3 a) a #
R1 V4
Instance details Defined in Linear.V4 Methods _x :: Lens' (V4 a) a #
R1 V1
Instance details Defined in Linear.V1 Methods _x :: Lens' (V1 a) a #
R1 f => R1 (Point f)
Instance details Defined in Linear.Affine Methods _x :: Lens' (Point f a) a #

class R1 t => R2 (t :: Type -> Type) where #

A space that distinguishes 2 orthogonal basis vectors _x and _y, but may have more.

Minimal complete definition

_xy

Methods

_y :: Lens' (t a) a #

>>> V2 1 2 ^._y
2

>>> V2 1 2 & _y .~ 3
V2 1 3

_xy :: Lens' (t a) (V2 a) #

Instances

R2 V2
Instance details Defined in Linear.V2 Methods _y :: Lens' (V2 a) a # _xy :: Lens' (V2 a) (V2 a) #
R2 V3
Instance details Defined in Linear.V3 Methods _y :: Lens' (V3 a) a # _xy :: Lens' (V3 a) (V2 a) #
R2 V4
Instance details Defined in Linear.V4 Methods _y :: Lens' (V4 a) a # _xy :: Lens' (V4 a) (V2 a) #
R2 f => R2 (Point f)
Instance details Defined in Linear.Affine Methods _y :: Lens' (Point f a) a # _xy :: Lens' (Point f a) (V2 a) #

data V2 a #

A 2-dimensional vector

>>> pure 1 :: V2 Int
V2 1 1

>>> V2 1 2 + V2 3 4
V2 4 6

>>> V2 1 2 * V2 3 4
V2 3 8

>>> sum (V2 1 2)
3

Constructors

V2 !a !a

Instances

Monad V2
Instance details Defined in Linear.V2 Methods (>>=) :: V2 a -> (a -> V2 b) -> V2 b # (>>) :: V2 a -> V2 b -> V2 b # return :: a -> V2 a # fail :: String -> V2 a #
Functor V2
Instance details Defined in Linear.V2 Methods fmap :: (a -> b) -> V2 a -> V2 b # (<$) :: a -> V2 b -> V2 a #
MonadFix V2
Instance details Defined in Linear.V2 Methods mfix :: (a -> V2 a) -> V2 a #
Applicative V2
Instance details Defined in Linear.V2 Methods pure :: a -> V2 a # (<>) :: V2 (a -> b) -> V2 a -> V2 b # liftA2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c # (>) :: V2 a -> V2 b -> V2 b # (<*) :: V2 a -> V2 b -> V2 a #
Foldable V2
Instance details Defined in Linear.V2 Methods fold :: Monoid m => V2 m -> m # foldMap :: Monoid m => (a -> m) -> V2 a -> m # foldr :: (a -> b -> b) -> b -> V2 a -> b # foldr' :: (a -> b -> b) -> b -> V2 a -> b # foldl :: (b -> a -> b) -> b -> V2 a -> b # foldl' :: (b -> a -> b) -> b -> V2 a -> b # foldr1 :: (a -> a -> a) -> V2 a -> a # foldl1 :: (a -> a -> a) -> V2 a -> a # toList :: V2 a -> [a] # null :: V2 a -> Bool # length :: V2 a -> Int # elem :: Eq a => a -> V2 a -> Bool # maximum :: Ord a => V2 a -> a # minimum :: Ord a => V2 a -> a # sum :: Num a => V2 a -> a # product :: Num a => V2 a -> a #
Traversable V2
Instance details Defined in Linear.V2 Methods traverse :: Applicative f => (a -> f b) -> V2 a -> f (V2 b) # sequenceA :: Applicative f => V2 (f a) -> f (V2 a) # mapM :: Monad m => (a -> m b) -> V2 a -> m (V2 b) # sequence :: Monad m => V2 (m a) -> m (V2 a) #
Apply V2
Instance details Defined in Linear.V2 Methods (<.>) :: V2 (a -> b) -> V2 a -> V2 b # (.>) :: V2 a -> V2 b -> V2 b # (<.) :: V2 a -> V2 b -> V2 a # liftF2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c #
Distributive V2
Instance details Defined in Linear.V2 Methods distribute :: Functor f => f (V2 a) -> V2 (f a) # collect :: Functor f => (a -> V2 b) -> f a -> V2 (f b) # distributeM :: Monad m => m (V2 a) -> V2 (m a) # collectM :: Monad m => (a -> V2 b) -> m a -> V2 (m b) #
Representable V2
Instance details Defined in Linear.V2 Associated Types type Rep V2 :: Type # Methods tabulate :: (Rep V2 -> a) -> V2 a # index :: V2 a -> Rep V2 -> a #
Eq1 V2
Instance details Defined in Linear.V2 Methods liftEq :: (a -> b -> Bool) -> V2 a -> V2 b -> Bool #
Ord1 V2
Instance details Defined in Linear.V2 Methods liftCompare :: (a -> b -> Ordering) -> V2 a -> V2 b -> Ordering #
Read1 V2
Instance details Defined in Linear.V2 Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V2 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V2 a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V2 a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V2 a] #
Show1 V2
Instance details Defined in Linear.V2 Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V2 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V2 a] -> ShowS #
MonadZip V2
Instance details Defined in Linear.V2 Methods mzip :: V2 a -> V2 b -> V2 (a, b) # mzipWith :: (a -> b -> c) -> V2 a -> V2 b -> V2 c # munzip :: V2 (a, b) -> (V2 a, V2 b) #
Serial1 V2
Instance details Defined in Linear.V2 Methods serializeWith :: MonadPut m => (a -> m ()) -> V2 a -> m () # deserializeWith :: MonadGet m => m a -> m (V2 a) #
Additive V2
Instance details Defined in Linear.V2 Methods zero :: Num a => V2 a # (^+^) :: Num a => V2 a -> V2 a -> V2 a # (^-^) :: Num a => V2 a -> V2 a -> V2 a # lerp :: Num a => a -> V2 a -> V2 a -> V2 a # liftU2 :: (a -> a -> a) -> V2 a -> V2 a -> V2 a # liftI2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c #
Metric V2
Instance details Defined in Linear.V2 Methods dot :: Num a => V2 a -> V2 a -> a # quadrance :: Num a => V2 a -> a # qd :: Num a => V2 a -> V2 a -> a # distance :: Floating a => V2 a -> V2 a -> a # norm :: Floating a => V2 a -> a # signorm :: Floating a => V2 a -> V2 a #
Affine V2
Instance details Defined in Linear.Affine Associated Types type Diff V2 :: Type -> Type # Methods (.-.) :: Num a => V2 a -> V2 a -> Diff V2 a # (.+^) :: Num a => V2 a -> Diff V2 a -> V2 a # (.-^) :: Num a => V2 a -> Diff V2 a -> V2 a #
HasR V2
Instance details Defined in Diagrams.TwoD.Types Methods _r :: RealFloat n => Lens' (V2 n) n #
R1 V2
Instance details Defined in Linear.V2 Methods _x :: Lens' (V2 a) a #
R2 V2
Instance details Defined in Linear.V2 Methods _y :: Lens' (V2 a) a # _xy :: Lens' (V2 a) (V2 a) #
Traversable1 V2
Instance details Defined in Linear.V2 Methods traverse1 :: Apply f => (a -> f b) -> V2 a -> f (V2 b) # sequence1 :: Apply f => V2 (f b) -> f (V2 b) #
Hashable1 V2
Instance details Defined in Linear.V2 Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> V2 a -> Int #
Finite V2
Instance details Defined in Linear.V2 Associated Types type Size V2 :: Nat # Methods toV :: V2 a -> V (Size V2) a # fromV :: V (Size V2) a -> V2 a #
Foldable1 V2
Instance details Defined in Linear.V2 Methods fold1 :: Semigroup m => V2 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V2 a -> m # toNonEmpty :: V2 a -> NonEmpty a #
Bind V2
Instance details Defined in Linear.V2 Methods (>>-) :: V2 a -> (a -> V2 b) -> V2 b # join :: V2 (V2 a) -> V2 a #
SVGFloat n => Backend SVG V2 n
Instance details Defined in Diagrams.Backend.SVG Associated Types data Render SVG V2 n :: Type # type Result SVG V2 n :: Type # data Options SVG V2 n :: Type # Methods adjustDia :: (Additive V2, Monoid' m, Num n) => SVG -> Options SVG V2 n -> QDiagram SVG V2 n m -> (Options SVG V2 n, Transformation V2 n, QDiagram SVG V2 n m) # renderRTree :: SVG -> Options SVG V2 n -> RTree SVG V2 n Annotation -> Result SVG V2 n #
Unbox a => Vector Vector (V2 a)
Instance details Defined in Linear.V2 Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V2 a) -> m (Vector (V2 a)) # basicUnsafeThaw :: PrimMonad m => Vector (V2 a) -> m (Mutable Vector (PrimState m) (V2 a)) # basicLength :: Vector (V2 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V2 a) -> Vector (V2 a) # basicUnsafeIndexM :: Monad m => Vector (V2 a) -> Int -> m (V2 a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V2 a) -> Vector (V2 a) -> m () # elemseq :: Vector (V2 a) -> V2 a -> b -> b #
Unbox a => MVector MVector (V2 a)
Instance details Defined in Linear.V2 Methods basicLength :: MVector s (V2 a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (V2 a) -> MVector s (V2 a) # basicOverlaps :: MVector s (V2 a) -> MVector s (V2 a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V2 a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (V2 a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V2 a -> m (MVector (PrimState m) (V2 a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> m (V2 a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> V2 a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (V2 a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (V2 a) -> V2 a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V2 a) -> MVector (PrimState m) (V2 a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V2 a) -> MVector (PrimState m) (V2 a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> m (MVector (PrimState m) (V2 a)) #
Bounded a => Bounded (V2 a)
Instance details Defined in Linear.V2 Methods minBound :: V2 a # maxBound :: V2 a #
Eq a => Eq (V2 a)
Instance details Defined in Linear.V2 Methods (==) :: V2 a -> V2 a -> Bool # (/=) :: V2 a -> V2 a -> Bool #
Floating a => Floating (V2 a)
Instance details Defined in Linear.V2 Methods pi :: V2 a # exp :: V2 a -> V2 a # log :: V2 a -> V2 a # sqrt :: V2 a -> V2 a # (**) :: V2 a -> V2 a -> V2 a # logBase :: V2 a -> V2 a -> V2 a # sin :: V2 a -> V2 a # cos :: V2 a -> V2 a # tan :: V2 a -> V2 a # asin :: V2 a -> V2 a # acos :: V2 a -> V2 a # atan :: V2 a -> V2 a # sinh :: V2 a -> V2 a # cosh :: V2 a -> V2 a # tanh :: V2 a -> V2 a # asinh :: V2 a -> V2 a # acosh :: V2 a -> V2 a # atanh :: V2 a -> V2 a # log1p :: V2 a -> V2 a # expm1 :: V2 a -> V2 a # log1pexp :: V2 a -> V2 a # log1mexp :: V2 a -> V2 a #
Fractional a => Fractional (V2 a)
Instance details Defined in Linear.V2 Methods (/) :: V2 a -> V2 a -> V2 a # recip :: V2 a -> V2 a # fromRational :: Rational -> V2 a #
Data a => Data (V2 a)
Instance details Defined in Linear.V2 Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V2 a -> c (V2 a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V2 a) # toConstr :: V2 a -> Constr # dataTypeOf :: V2 a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (V2 a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V2 a)) # gmapT :: (forall b. Data b => b -> b) -> V2 a -> V2 a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V2 a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V2 a -> r # gmapQ :: (forall d. Data d => d -> u) -> V2 a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> V2 a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> V2 a -> m (V2 a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V2 a -> m (V2 a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V2 a -> m (V2 a) #
Num a => Num (V2 a)
Instance details Defined in Linear.V2 Methods (+) :: V2 a -> V2 a -> V2 a # (-) :: V2 a -> V2 a -> V2 a # (*) :: V2 a -> V2 a -> V2 a # negate :: V2 a -> V2 a # abs :: V2 a -> V2 a # signum :: V2 a -> V2 a # fromInteger :: Integer -> V2 a #
Ord a => Ord (V2 a)
Instance details Defined in Linear.V2 Methods compare :: V2 a -> V2 a -> Ordering # (<) :: V2 a -> V2 a -> Bool # (<=) :: V2 a -> V2 a -> Bool # (>) :: V2 a -> V2 a -> Bool # (>=) :: V2 a -> V2 a -> Bool # max :: V2 a -> V2 a -> V2 a # min :: V2 a -> V2 a -> V2 a #
Read a => Read (V2 a)
Instance details Defined in Linear.V2 Methods readsPrec :: Int -> ReadS (V2 a) # readList :: ReadS [V2 a] # readPrec :: ReadPrec (V2 a) # readListPrec :: ReadPrec [V2 a] #
Show a => Show (V2 a)
Instance details Defined in Linear.V2 Methods showsPrec :: Int -> V2 a -> ShowS # show :: V2 a -> String # showList :: [V2 a] -> ShowS #
Ix a => Ix (V2 a)
Instance details Defined in Linear.V2 Methods range :: (V2 a, V2 a) -> [V2 a] # index :: (V2 a, V2 a) -> V2 a -> Int # unsafeIndex :: (V2 a, V2 a) -> V2 a -> Int inRange :: (V2 a, V2 a) -> V2 a -> Bool # rangeSize :: (V2 a, V2 a) -> Int # unsafeRangeSize :: (V2 a, V2 a) -> Int
Generic (V2 a)
Instance details Defined in Linear.V2 Associated Types type Rep (V2 a) :: Type -> Type # Methods from :: V2 a -> Rep (V2 a) x # to :: Rep (V2 a) x -> V2 a #
Lift a => Lift (V2 a)
Instance details Defined in Linear.V2 Methods lift :: V2 a -> Q Exp #
Hashable a => Hashable (V2 a)
Instance details Defined in Linear.V2 Methods hashWithSalt :: Int -> V2 a -> Int # hash :: V2 a -> Int #
Storable a => Storable (V2 a)
Instance details Defined in Linear.V2 Methods sizeOf :: V2 a -> Int # alignment :: V2 a -> Int # peekElemOff :: Ptr (V2 a) -> Int -> IO (V2 a) # pokeElemOff :: Ptr (V2 a) -> Int -> V2 a -> IO () # peekByteOff :: Ptr b -> Int -> IO (V2 a) # pokeByteOff :: Ptr b -> Int -> V2 a -> IO () # peek :: Ptr (V2 a) -> IO (V2 a) # poke :: Ptr (V2 a) -> V2 a -> IO () #
Binary a => Binary (V2 a)
Instance details Defined in Linear.V2 Methods put :: V2 a -> Put # get :: Get (V2 a) # putList :: [V2 a] -> Put #
Serial a => Serial (V2 a)
Instance details Defined in Linear.V2 Methods serialize :: MonadPut m => V2 a -> m () # deserialize :: MonadGet m => m (V2 a) #
Serialize a => Serialize (V2 a)
Instance details Defined in Linear.V2 Methods put :: Putter (V2 a) # get :: Get (V2 a) #
NFData a => NFData (V2 a)
Instance details Defined in Linear.V2 Methods rnf :: V2 a -> () #
Coordinates (V2 n)
Instance details Defined in Diagrams.Coordinates Associated Types type FinalCoord (V2 n) :: Type # type PrevDim (V2 n) :: Type # type Decomposition (V2 n) :: Type # Methods (^&) :: PrevDim (V2 n) -> FinalCoord (V2 n) -> V2 n # pr :: PrevDim (V2 n) -> FinalCoord (V2 n) -> V2 n # coords :: V2 n -> Decomposition (V2 n) #
Ixed (V2 a)
Instance details Defined in Linear.V2 Methods ix :: Index (V2 a) -> Traversal' (V2 a) (IxValue (V2 a)) #
Unbox a => Unbox (V2 a)
Instance details Defined in Linear.V2
Epsilon a => Epsilon (V2 a)
Instance details Defined in Linear.V2 Methods nearZero :: V2 a -> Bool #
Generic1 V2
Instance details Defined in Linear.V2 Associated Types type Rep1 V2 :: k -> Type # Methods from1 :: V2 a -> Rep1 V2 a # to1 :: Rep1 V2 a -> V2 a #
TraversableWithIndex (E V2) V2
Instance details Defined in Linear.V2 Methods itraverse :: Applicative f => (E V2 -> a -> f b) -> V2 a -> f (V2 b) # itraversed :: IndexedTraversal (E V2) (V2 a) (V2 b) a b #
FoldableWithIndex (E V2) V2
Instance details Defined in Linear.V2 Methods ifoldMap :: Monoid m => (E V2 -> a -> m) -> V2 a -> m # ifolded :: IndexedFold (E V2) (V2 a) a # ifoldr :: (E V2 -> a -> b -> b) -> b -> V2 a -> b # ifoldl :: (E V2 -> b -> a -> b) -> b -> V2 a -> b # ifoldr' :: (E V2 -> a -> b -> b) -> b -> V2 a -> b # ifoldl' :: (E V2 -> b -> a -> b) -> b -> V2 a -> b #
FunctorWithIndex (E V2) V2
Instance details Defined in Linear.V2 Methods imap :: (E V2 -> a -> b) -> V2 a -> V2 b # imapped :: IndexedSetter (E V2) (V2 a) (V2 b) a b #
Field2 (V2 a) (V2 a) a a
Instance details Defined in Linear.V2 Methods _2 :: Lens (V2 a) (V2 a) a a #
Field1 (V2 a) (V2 a) a a
Instance details Defined in Linear.V2 Methods _1 :: Lens (V2 a) (V2 a) a a #
Each (V2 a) (V2 b) a b
Instance details Defined in Linear.V2 Methods each :: Traversal (V2 a) (V2 b) a b #
RealFloat n => Traced (BoundingBox V2 n)
Instance details Defined in Diagrams.BoundingBox Methods getTrace :: BoundingBox V2 n -> Trace (V (BoundingBox V2 n)) (N (BoundingBox V2 n)) #
SVGFloat n => Renderable (Path V2 n) SVG
Instance details Defined in Diagrams.Backend.SVG Methods render :: SVG -> Path V2 n -> Render SVG (V (Path V2 n)) (N (Path V2 n)) #
Semigroup (Render SVG V2 n)
Instance details Defined in Diagrams.Backend.SVG Methods (<>) :: Render SVG V2 n -> Render SVG V2 n -> Render SVG V2 n # sconcat :: NonEmpty (Render SVG V2 n) -> Render SVG V2 n # stimes :: Integral b => b -> Render SVG V2 n -> Render SVG V2 n #
Monoid (Render SVG V2 n)
Instance details Defined in Diagrams.Backend.SVG Methods mempty :: Render SVG V2 n # mappend :: Render SVG V2 n -> Render SVG V2 n -> Render SVG V2 n # mconcat :: [Render SVG V2 n] -> Render SVG V2 n #
Hashable n => Hashable (Options SVG V2 n)
Instance details Defined in Diagrams.Backend.SVG Methods hashWithSalt :: Int -> Options SVG V2 n -> Int # hash :: Options SVG V2 n -> Int #
type Rep V2
Instance details Defined in Linear.V2 type Rep V2 = E V2
type Diff V2
Instance details Defined in Linear.Affine type Diff V2 = V2
type Size V2
Instance details Defined in Linear.V2 type Size V2 = 2
data Options SVG V2 n
Instance details Defined in Diagrams.Backend.SVG data Options SVG V2 n = SVGOptions { _size :: SizeSpec V2 n _svgDefinitions :: Maybe Element _idPrefix :: Text _svgAttributes :: [Attribute] _generateDoctype :: Bool }
newtype Render SVG V2 n
Instance details Defined in Diagrams.Backend.SVG newtype Render SVG V2 n = R (SvgRenderM n)
type Result SVG V2 n
Instance details Defined in Diagrams.Backend.SVG type Result SVG V2 n = Element
data MVector s (V2 a)
Instance details Defined in Linear.V2 data MVector s (V2 a) = MV_V2 !Int !(MVector s a)
type Rep (V2 a)
Instance details Defined in Linear.V2 type Rep (V2 a) = D1 (MetaData "V2" "Linear.V2" "linear-1.20.9-27UQiD0kWRO59L1Ww4Df0c" False) (C1 (MetaCons "V2" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)))
type V (V2 n)
Instance details Defined in Diagrams.TwoD.Types type V (V2 n) = V2
type N (V2 n)
Instance details Defined in Diagrams.TwoD.Types type N (V2 n) = n
data Vector (V2 a)
Instance details Defined in Linear.V2 data Vector (V2 a) = V_V2 !Int !(Vector a)
type Decomposition (V2 n)
Instance details Defined in Diagrams.Coordinates type Decomposition (V2 n) = n :& n
type PrevDim (V2 n)
Instance details Defined in Diagrams.Coordinates type PrevDim (V2 n) = n
type FinalCoord (V2 n)
Instance details Defined in Diagrams.Coordinates type FinalCoord (V2 n) = n
type IxValue (V2 a)
Instance details Defined in Linear.V2 type IxValue (V2 a) = a
type Index (V2 a)
Instance details Defined in Linear.V2 type Index (V2 a) = E V2
type Rep1 V2
Instance details Defined in Linear.V2 type Rep1 V2 = D1 (MetaData "V2" "Linear.V2" "linear-1.20.9-27UQiD0kWRO59L1Ww4Df0c" False) (C1 (MetaCons "V2" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1 :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1))

perp :: Num a => V2 a -> V2 a #

the counter-clockwise perpendicular vector

>>> perp $ V2 10 20
V2 (-20) 10

class R2 t => R3 (t :: Type -> Type) where #

A space that distinguishes 3 orthogonal basis vectors: _x, _y, and _z. (It may have more)

Methods

_z :: Lens' (t a) a #

>>> V3 1 2 3 ^. _z
3

_xyz :: Lens' (t a) (V3 a) #

Instances

R3 V3
Instance details Defined in Linear.V3 Methods _z :: Lens' (V3 a) a # _xyz :: Lens' (V3 a) (V3 a) #
R3 V4
Instance details Defined in Linear.V4 Methods _z :: Lens' (V4 a) a # _xyz :: Lens' (V4 a) (V3 a) #
R3 f => R3 (Point f)
Instance details Defined in Linear.Affine Methods _z :: Lens' (Point f a) a # _xyz :: Lens' (Point f a) (V3 a) #

data V3 a #

A 3-dimensional vector

Constructors

V3 !a !a !a

Instances

Monad V3
Instance details Defined in Linear.V3 Methods (>>=) :: V3 a -> (a -> V3 b) -> V3 b # (>>) :: V3 a -> V3 b -> V3 b # return :: a -> V3 a # fail :: String -> V3 a #
Functor V3
Instance details Defined in Linear.V3 Methods fmap :: (a -> b) -> V3 a -> V3 b # (<$) :: a -> V3 b -> V3 a #
MonadFix V3
Instance details Defined in Linear.V3 Methods mfix :: (a -> V3 a) -> V3 a #
Applicative V3
Instance details Defined in Linear.V3 Methods pure :: a -> V3 a # (<>) :: V3 (a -> b) -> V3 a -> V3 b # liftA2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c # (>) :: V3 a -> V3 b -> V3 b # (<*) :: V3 a -> V3 b -> V3 a #
Foldable V3
Instance details Defined in Linear.V3 Methods fold :: Monoid m => V3 m -> m # foldMap :: Monoid m => (a -> m) -> V3 a -> m # foldr :: (a -> b -> b) -> b -> V3 a -> b # foldr' :: (a -> b -> b) -> b -> V3 a -> b # foldl :: (b -> a -> b) -> b -> V3 a -> b # foldl' :: (b -> a -> b) -> b -> V3 a -> b # foldr1 :: (a -> a -> a) -> V3 a -> a # foldl1 :: (a -> a -> a) -> V3 a -> a # toList :: V3 a -> [a] # null :: V3 a -> Bool # length :: V3 a -> Int # elem :: Eq a => a -> V3 a -> Bool # maximum :: Ord a => V3 a -> a # minimum :: Ord a => V3 a -> a # sum :: Num a => V3 a -> a # product :: Num a => V3 a -> a #
Traversable V3
Instance details Defined in Linear.V3 Methods traverse :: Applicative f => (a -> f b) -> V3 a -> f (V3 b) # sequenceA :: Applicative f => V3 (f a) -> f (V3 a) # mapM :: Monad m => (a -> m b) -> V3 a -> m (V3 b) # sequence :: Monad m => V3 (m a) -> m (V3 a) #
Apply V3
Instance details Defined in Linear.V3 Methods (<.>) :: V3 (a -> b) -> V3 a -> V3 b # (.>) :: V3 a -> V3 b -> V3 b # (<.) :: V3 a -> V3 b -> V3 a # liftF2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c #
Distributive V3
Instance details Defined in Linear.V3 Methods distribute :: Functor f => f (V3 a) -> V3 (f a) # collect :: Functor f => (a -> V3 b) -> f a -> V3 (f b) # distributeM :: Monad m => m (V3 a) -> V3 (m a) # collectM :: Monad m => (a -> V3 b) -> m a -> V3 (m b) #
Representable V3
Instance details Defined in Linear.V3 Associated Types type Rep V3 :: Type # Methods tabulate :: (Rep V3 -> a) -> V3 a # index :: V3 a -> Rep V3 -> a #
Eq1 V3
Instance details Defined in Linear.V3 Methods liftEq :: (a -> b -> Bool) -> V3 a -> V3 b -> Bool #
Ord1 V3
Instance details Defined in Linear.V3 Methods liftCompare :: (a -> b -> Ordering) -> V3 a -> V3 b -> Ordering #
Read1 V3
Instance details Defined in Linear.V3 Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V3 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V3 a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V3 a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V3 a] #
Show1 V3
Instance details Defined in Linear.V3 Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V3 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V3 a] -> ShowS #
MonadZip V3
Instance details Defined in Linear.V3 Methods mzip :: V3 a -> V3 b -> V3 (a, b) # mzipWith :: (a -> b -> c) -> V3 a -> V3 b -> V3 c # munzip :: V3 (a, b) -> (V3 a, V3 b) #
Serial1 V3
Instance details Defined in Linear.V3 Methods serializeWith :: MonadPut m => (a -> m ()) -> V3 a -> m () # deserializeWith :: MonadGet m => m a -> m (V3 a) #
Additive V3
Instance details Defined in Linear.V3 Methods zero :: Num a => V3 a # (^+^) :: Num a => V3 a -> V3 a -> V3 a # (^-^) :: Num a => V3 a -> V3 a -> V3 a # lerp :: Num a => a -> V3 a -> V3 a -> V3 a # liftU2 :: (a -> a -> a) -> V3 a -> V3 a -> V3 a # liftI2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c #
Metric V3
Instance details Defined in Linear.V3 Methods dot :: Num a => V3 a -> V3 a -> a # quadrance :: Num a => V3 a -> a # qd :: Num a => V3 a -> V3 a -> a # distance :: Floating a => V3 a -> V3 a -> a # norm :: Floating a => V3 a -> a # signorm :: Floating a => V3 a -> V3 a #
Affine V3
Instance details Defined in Linear.Affine Associated Types type Diff V3 :: Type -> Type # Methods (.-.) :: Num a => V3 a -> V3 a -> Diff V3 a # (.+^) :: Num a => V3 a -> Diff V3 a -> V3 a # (.-^) :: Num a => V3 a -> Diff V3 a -> V3 a #
R1 V3
Instance details Defined in Linear.V3 Methods _x :: Lens' (V3 a) a #
R2 V3
Instance details Defined in Linear.V3 Methods _y :: Lens' (V3 a) a # _xy :: Lens' (V3 a) (V2 a) #
R3 V3
Instance details Defined in Linear.V3 Methods _z :: Lens' (V3 a) a # _xyz :: Lens' (V3 a) (V3 a) #
Traversable1 V3
Instance details Defined in Linear.V3 Methods traverse1 :: Apply f => (a -> f b) -> V3 a -> f (V3 b) # sequence1 :: Apply f => V3 (f b) -> f (V3 b) #
Hashable1 V3
Instance details Defined in Linear.V3 Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> V3 a -> Int #
Finite V3
Instance details Defined in Linear.V3 Associated Types type Size V3 :: Nat # Methods toV :: V3 a -> V (Size V3) a # fromV :: V (Size V3) a -> V3 a #
Foldable1 V3
Instance details Defined in Linear.V3 Methods fold1 :: Semigroup m => V3 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V3 a -> m # toNonEmpty :: V3 a -> NonEmpty a #
Bind V3
Instance details Defined in Linear.V3 Methods (>>-) :: V3 a -> (a -> V3 b) -> V3 b # join :: V3 (V3 a) -> V3 a #
Unbox a => Vector Vector (V3 a)
Instance details Defined in Linear.V3 Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> m (Vector (V3 a)) # basicUnsafeThaw :: PrimMonad m => Vector (V3 a) -> m (Mutable Vector (PrimState m) (V3 a)) # basicLength :: Vector (V3 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V3 a) -> Vector (V3 a) # basicUnsafeIndexM :: Monad m => Vector (V3 a) -> Int -> m (V3 a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> Vector (V3 a) -> m () # elemseq :: Vector (V3 a) -> V3 a -> b -> b #
Unbox a => MVector MVector (V3 a)
Instance details Defined in Linear.V3 Methods basicLength :: MVector s (V3 a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (V3 a) -> MVector s (V3 a) # basicOverlaps :: MVector s (V3 a) -> MVector s (V3 a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V3 a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (V3 a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V3 a -> m (MVector (PrimState m) (V3 a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (V3 a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> V3 a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (V3 a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (V3 a) -> V3 a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (MVector (PrimState m) (V3 a)) #
Bounded a => Bounded (V3 a)
Instance details Defined in Linear.V3 Methods minBound :: V3 a # maxBound :: V3 a #
Eq a => Eq (V3 a)
Instance details Defined in Linear.V3 Methods (==) :: V3 a -> V3 a -> Bool # (/=) :: V3 a -> V3 a -> Bool #
Floating a => Floating (V3 a)
Instance details Defined in Linear.V3 Methods pi :: V3 a # exp :: V3 a -> V3 a # log :: V3 a -> V3 a # sqrt :: V3 a -> V3 a # (**) :: V3 a -> V3 a -> V3 a # logBase :: V3 a -> V3 a -> V3 a # sin :: V3 a -> V3 a # cos :: V3 a -> V3 a # tan :: V3 a -> V3 a # asin :: V3 a -> V3 a # acos :: V3 a -> V3 a # atan :: V3 a -> V3 a # sinh :: V3 a -> V3 a # cosh :: V3 a -> V3 a # tanh :: V3 a -> V3 a # asinh :: V3 a -> V3 a # acosh :: V3 a -> V3 a # atanh :: V3 a -> V3 a # log1p :: V3 a -> V3 a # expm1 :: V3 a -> V3 a # log1pexp :: V3 a -> V3 a # log1mexp :: V3 a -> V3 a #
Fractional a => Fractional (V3 a)
Instance details Defined in Linear.V3 Methods (/) :: V3 a -> V3 a -> V3 a # recip :: V3 a -> V3 a # fromRational :: Rational -> V3 a #
Data a => Data (V3 a)
Instance details Defined in Linear.V3 Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V3 a -> c (V3 a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V3 a) # toConstr :: V3 a -> Constr # dataTypeOf :: V3 a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (V3 a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V3 a)) # gmapT :: (forall b. Data b => b -> b) -> V3 a -> V3 a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r # gmapQ :: (forall d. Data d => d -> u) -> V3 a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> V3 a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a) #
Num a => Num (V3 a)
Instance details Defined in Linear.V3 Methods (+) :: V3 a -> V3 a -> V3 a # (-) :: V3 a -> V3 a -> V3 a # (*) :: V3 a -> V3 a -> V3 a # negate :: V3 a -> V3 a # abs :: V3 a -> V3 a # signum :: V3 a -> V3 a # fromInteger :: Integer -> V3 a #
Ord a => Ord (V3 a)
Instance details Defined in Linear.V3 Methods compare :: V3 a -> V3 a -> Ordering # (<) :: V3 a -> V3 a -> Bool # (<=) :: V3 a -> V3 a -> Bool # (>) :: V3 a -> V3 a -> Bool # (>=) :: V3 a -> V3 a -> Bool # max :: V3 a -> V3 a -> V3 a # min :: V3 a -> V3 a -> V3 a #
Read a => Read (V3 a)
Instance details Defined in Linear.V3 Methods readsPrec :: Int -> ReadS (V3 a) # readList :: ReadS [V3 a] # readPrec :: ReadPrec (V3 a) # readListPrec :: ReadPrec [V3 a] #
Show a => Show (V3 a)
Instance details Defined in Linear.V3 Methods showsPrec :: Int -> V3 a -> ShowS # show :: V3 a -> String # showList :: [V3 a] -> ShowS #
Ix a => Ix (V3 a)
Instance details Defined in Linear.V3 Methods range :: (V3 a, V3 a) -> [V3 a] # index :: (V3 a, V3 a) -> V3 a -> Int # unsafeIndex :: (V3 a, V3 a) -> V3 a -> Int inRange :: (V3 a, V3 a) -> V3 a -> Bool # rangeSize :: (V3 a, V3 a) -> Int # unsafeRangeSize :: (V3 a, V3 a) -> Int
Generic (V3 a)
Instance details Defined in Linear.V3 Associated Types type Rep (V3 a) :: Type -> Type # Methods from :: V3 a -> Rep (V3 a) x # to :: Rep (V3 a) x -> V3 a #
Lift a => Lift (V3 a)
Instance details Defined in Linear.V3 Methods lift :: V3 a -> Q Exp #
Hashable a => Hashable (V3 a)
Instance details Defined in Linear.V3 Methods hashWithSalt :: Int -> V3 a -> Int # hash :: V3 a -> Int #
Storable a => Storable (V3 a)
Instance details Defined in Linear.V3 Methods sizeOf :: V3 a -> Int # alignment :: V3 a -> Int # peekElemOff :: Ptr (V3 a) -> Int -> IO (V3 a) # pokeElemOff :: Ptr (V3 a) -> Int -> V3 a -> IO () # peekByteOff :: Ptr b -> Int -> IO (V3 a) # pokeByteOff :: Ptr b -> Int -> V3 a -> IO () # peek :: Ptr (V3 a) -> IO (V3 a) # poke :: Ptr (V3 a) -> V3 a -> IO () #
Binary a => Binary (V3 a)
Instance details Defined in Linear.V3 Methods put :: V3 a -> Put # get :: Get (V3 a) # putList :: [V3 a] -> Put #
Serial a => Serial (V3 a)
Instance details Defined in Linear.V3 Methods serialize :: MonadPut m => V3 a -> m () # deserialize :: MonadGet m => m (V3 a) #
Serialize a => Serialize (V3 a)
Instance details Defined in Linear.V3 Methods put :: Putter (V3 a) # get :: Get (V3 a) #
NFData a => NFData (V3 a)
Instance details Defined in Linear.V3 Methods rnf :: V3 a -> () #
Coordinates (V3 n)
Instance details Defined in Diagrams.Coordinates Associated Types type FinalCoord (V3 n) :: Type # type PrevDim (V3 n) :: Type # type Decomposition (V3 n) :: Type # Methods (^&) :: PrevDim (V3 n) -> FinalCoord (V3 n) -> V3 n # pr :: PrevDim (V3 n) -> FinalCoord (V3 n) -> V3 n # coords :: V3 n -> Decomposition (V3 n) #
Ixed (V3 a)
Instance details Defined in Linear.V3 Methods ix :: Index (V3 a) -> Traversal' (V3 a) (IxValue (V3 a)) #
Unbox a => Unbox (V3 a)
Instance details Defined in Linear.V3
Epsilon a => Epsilon (V3 a)
Instance details Defined in Linear.V3 Methods nearZero :: V3 a -> Bool #
Generic1 V3
Instance details Defined in Linear.V3 Associated Types type Rep1 V3 :: k -> Type # Methods from1 :: V3 a -> Rep1 V3 a # to1 :: Rep1 V3 a -> V3 a #
TraversableWithIndex (E V3) V3
Instance details Defined in Linear.V3 Methods itraverse :: Applicative f => (E V3 -> a -> f b) -> V3 a -> f (V3 b) # itraversed :: IndexedTraversal (E V3) (V3 a) (V3 b) a b #
FoldableWithIndex (E V3) V3
Instance details Defined in Linear.V3 Methods ifoldMap :: Monoid m => (E V3 -> a -> m) -> V3 a -> m # ifolded :: IndexedFold (E V3) (V3 a) a # ifoldr :: (E V3 -> a -> b -> b) -> b -> V3 a -> b # ifoldl :: (E V3 -> b -> a -> b) -> b -> V3 a -> b # ifoldr' :: (E V3 -> a -> b -> b) -> b -> V3 a -> b # ifoldl' :: (E V3 -> b -> a -> b) -> b -> V3 a -> b #
FunctorWithIndex (E V3) V3
Instance details Defined in Linear.V3 Methods imap :: (E V3 -> a -> b) -> V3 a -> V3 b # imapped :: IndexedSetter (E V3) (V3 a) (V3 b) a b #
Field3 (V3 a) (V3 a) a a
Instance details Defined in Linear.V3 Methods _3 :: Lens (V3 a) (V3 a) a a #
Field2 (V3 a) (V3 a) a a
Instance details Defined in Linear.V3 Methods _2 :: Lens (V3 a) (V3 a) a a #
Field1 (V3 a) (V3 a) a a
Instance details Defined in Linear.V3 Methods _1 :: Lens (V3 a) (V3 a) a a #
Each (V3 a) (V3 b) a b
Instance details Defined in Linear.V3 Methods each :: Traversal (V3 a) (V3 b) a b #
TypeableFloat n => Traced (BoundingBox V3 n)
Instance details Defined in Diagrams.BoundingBox Methods getTrace :: BoundingBox V3 n -> Trace (V (BoundingBox V3 n)) (N (BoundingBox V3 n)) #
type Rep V3
Instance details Defined in Linear.V3 type Rep V3 = E V3
type Diff V3
Instance details Defined in Linear.Affine type Diff V3 = V3
type Size V3
Instance details Defined in Linear.V3 type Size V3 = 3
data MVector s (V3 a)
Instance details Defined in Linear.V3 data MVector s (V3 a) = MV_V3 !Int !(MVector s a)
type Rep (V3 a)
Instance details Defined in Linear.V3 type Rep (V3 a) = D1 (MetaData "V3" "Linear.V3" "linear-1.20.9-27UQiD0kWRO59L1Ww4Df0c" False) (C1 (MetaCons "V3" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a) :: (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a) :: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a))))
type V (V3 n)
Instance details Defined in Diagrams.ThreeD.Types type V (V3 n) = V3
type N (V3 n)
Instance details Defined in Diagrams.ThreeD.Types type N (V3 n) = n
data Vector (V3 a)
Instance details Defined in Linear.V3 data Vector (V3 a) = V_V3 !Int !(Vector a)
type Decomposition (V3 n)
Instance details Defined in Diagrams.Coordinates type Decomposition (V3 n) = (n :& n) :& n
type PrevDim (V3 n)
Instance details Defined in Diagrams.Coordinates type PrevDim (V3 n) = V2 n
type FinalCoord (V3 n)
Instance details Defined in Diagrams.Coordinates type FinalCoord (V3 n) = n
type IxValue (V3 a)
Instance details Defined in Linear.V3 type IxValue (V3 a) = a
type Index (V3 a)
Instance details Defined in Linear.V3 type Index (V3 a) = E V3
type Rep1 V3
Instance details Defined in Linear.V3 type Rep1 V3 = D1 (MetaData "V3" "Linear.V3" "linear-1.20.9-27UQiD0kWRO59L1Ww4Df0c" False) (C1 (MetaCons "V3" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1 :: (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1 :: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1)))

lensP :: Lens' (Point g a) (g a) #

class Profunctor p => Choice (p :: Type -> Type -> Type) where #

The generalization of Costar of Functor that is strong with respect to Either.

Note: This is also a notion of strength, except with regards to another monoidal structure that we can choose to equip Hask with: the cocartesian coproduct.

Minimal complete definition

left' | right'

Methods

left' :: p a b -> p (Either a c) (Either b c) #

Laws:

left' ≡ dimap swapE swapE . right' where
  swapE :: Either a b -> Either b a
  swapE = either Right Left
rmap Left ≡ lmap Left . left'
lmap (right f) . left' ≡ rmap (right f) . left'
left' . left' ≡ dimap assocE unassocE . left' where
  assocE :: Either (Either a b) c -> Either a (Either b c)
  assocE (Left (Left a)) = Left a
  assocE (Left (Right b)) = Right (Left b)
  assocE (Right c) = Right (Right c)
  unassocE :: Either a (Either b c) -> Either (Either a b) c
  unassocE (Left a) = Left (Left a)
  unassocE (Right (Left b) = Left (Right b)
  unassocE (Right (Right c)) = Right c)

right' :: p a b -> p (Either c a) (Either c b) #

Laws:

right' ≡ dimap swapE swapE . left' where
  swapE :: Either a b -> Either b a
  swapE = either Right Left
rmap Right ≡ lmap Right . right'
lmap (left f) . right' ≡ rmap (left f) . right'
right' . right' ≡ dimap unassocE assocE . right' where
  assocE :: Either (Either a b) c -> Either a (Either b c)
  assocE (Left (Left a)) = Left a
  assocE (Left (Right b)) = Right (Left b)
  assocE (Right c) = Right (Right c)
  unassocE :: Either a (Either b c) -> Either (Either a b) c
  unassocE (Left a) = Left (Left a)
  unassocE (Right (Left b) = Left (Right b)
  unassocE (Right (Right c)) = Right c)

Instances

Choice ReifiedFold
Instance details Defined in Control.Lens.Reified Methods left' :: ReifiedFold a b -> ReifiedFold (Either a c) (Either b c) # right' :: ReifiedFold a b -> ReifiedFold (Either c a) (Either c b) #
Choice ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods left' :: ReifiedGetter a b -> ReifiedGetter (Either a c) (Either b c) # right' :: ReifiedGetter a b -> ReifiedGetter (Either c a) (Either c b) #
Monad m => Choice (Kleisli m)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Kleisli m a b -> Kleisli m (Either a c) (Either b c) # right' :: Kleisli m a b -> Kleisli m (Either c a) (Either c b) #
Choice (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods left' :: Indexed i a b -> Indexed i (Either a c) (Either b c) # right' :: Indexed i a b -> Indexed i (Either c a) (Either c b) #
Profunctor p => Choice (TambaraSum p)
Instance details Defined in Data.Profunctor.Choice Methods left' :: TambaraSum p a b -> TambaraSum p (Either a c) (Either b c) # right' :: TambaraSum p a b -> TambaraSum p (Either c a) (Either c b) #
Choice (PastroSum p)
Instance details Defined in Data.Profunctor.Choice Methods left' :: PastroSum p a b -> PastroSum p (Either a c) (Either b c) # right' :: PastroSum p a b -> PastroSum p (Either c a) (Either c b) #
Choice p => Choice (Tambara p)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Tambara p a b -> Tambara p (Either a c) (Either b c) # right' :: Tambara p a b -> Tambara p (Either c a) (Either c b) #
Applicative f => Choice (Star f)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Star f a b -> Star f (Either a c) (Either b c) # right' :: Star f a b -> Star f (Either c a) (Either c b) #
Traversable w => Choice (Costar w)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Costar w a b -> Costar w (Either a c) (Either b c) # right' :: Costar w a b -> Costar w (Either c a) (Either c b) #
ArrowChoice p => Choice (WrappedArrow p)
Instance details Defined in Data.Profunctor.Choice Methods left' :: WrappedArrow p a b -> WrappedArrow p (Either a c) (Either b c) # right' :: WrappedArrow p a b -> WrappedArrow p (Either c a) (Either c b) #
Monoid r => Choice (Forget r)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Forget r a b -> Forget r (Either a c) (Either b c) # right' :: Forget r a b -> Forget r (Either c a) (Either c b) #
Choice (Tagged :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Tagged a b -> Tagged (Either a c) (Either b c) # right' :: Tagged a b -> Tagged (Either c a) (Either c b) #
Choice ((->) :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Choice Methods left' :: (a -> b) -> Either a c -> Either b c # right' :: (a -> b) -> Either c a -> Either c b #
Comonad w => Choice (Cokleisli w)	`extract` approximates `costrength`
Instance details Defined in Data.Profunctor.Choice Methods left' :: Cokleisli w a b -> Cokleisli w (Either a c) (Either b c) # right' :: Cokleisli w a b -> Cokleisli w (Either c a) (Either c b) #
(Choice p, Choice q) => Choice (Procompose p q)
Instance details Defined in Data.Profunctor.Composition Methods left' :: Procompose p q a b -> Procompose p q (Either a c) (Either b c) # right' :: Procompose p q a b -> Procompose p q (Either c a) (Either c b) #
Functor f => Choice (Joker f :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Joker f a b -> Joker f (Either a c) (Either b c) # right' :: Joker f a b -> Joker f (Either c a) (Either c b) #
(Choice p, Choice q) => Choice (Product p q)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Product p q a b -> Product p q (Either a c) (Either b c) # right' :: Product p q a b -> Product p q (Either c a) (Either c b) #
(Functor f, Choice p) => Choice (Tannen f p)
Instance details Defined in Data.Profunctor.Choice Methods left' :: Tannen f p a b -> Tannen f p (Either a c) (Either b c) # right' :: Tannen f p a b -> Tannen f p (Either c a) (Either c b) #

sequenceBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> t (f a) -> f (t a) #

Sequence a container using its Traversable instance using explicitly provided Applicative operations. This is like sequence where the Applicative instance can be manually specified.

traverseBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> t a -> f (t b) #

Traverse a container using its Traversable instance using explicitly provided Applicative operations. This is like traverse where the Applicative instance can be manually specified.

foldMapBy :: Foldable t => (r -> r -> r) -> r -> (a -> r) -> t a -> r #

Fold a value using its Foldable instance using explicitly provided Monoid operations. This is like foldMap where the Monoid instance can be manually specified.

foldMapBy mappend mempty ≡ foldMap

>>> foldMapBy (+) 0 length ["hello","world"]
10

foldBy :: Foldable t => (a -> a -> a) -> a -> t a -> a #

Fold a value using its Foldable instance using explicitly provided Monoid operations. This is like fold where the Monoid instance can be manually specified.

foldBy mappend mempty ≡ fold

>>> foldBy (++) [] ["hello","world"]
"helloworld"

class (Foldable1 t, Traversable t) => Traversable1 (t :: Type -> Type) where #

Minimal complete definition

traverse1 | sequence1

Methods

traverse1 :: Apply f => (a -> f b) -> t a -> f (t b) #

Instances

Traversable1 Par1
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Par1 a -> f (Par1 b) # sequence1 :: Apply f => Par1 (f b) -> f (Par1 b) #
Traversable1 Identity
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Identity a -> f (Identity b) # sequence1 :: Apply f => Identity (f b) -> f (Identity b) #
Traversable1 Complex
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Complex a -> f (Complex b) # sequence1 :: Apply f => Complex (f b) -> f (Complex b) #
Traversable1 Min
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Min a -> f (Min b) # sequence1 :: Apply f => Min (f b) -> f (Min b) #
Traversable1 Max
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Max a -> f (Max b) # sequence1 :: Apply f => Max (f b) -> f (Max b) #
Traversable1 First
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> First a -> f (First b) # sequence1 :: Apply f => First (f b) -> f (First b) #
Traversable1 Last
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Last a -> f (Last b) # sequence1 :: Apply f => Last (f b) -> f (Last b) #
Traversable1 Dual
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Dual a -> f (Dual b) # sequence1 :: Apply f => Dual (f b) -> f (Dual b) #
Traversable1 Sum
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Sum a -> f (Sum b) # sequence1 :: Apply f => Sum (f b) -> f (Sum b) #
Traversable1 Product
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Product a -> f (Product b) # sequence1 :: Apply f => Product (f b) -> f (Product b) #
Traversable1 NonEmpty
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) # sequence1 :: Apply f => NonEmpty (f b) -> f (NonEmpty b) #
Traversable1 Tree
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Tree a -> f (Tree b) # sequence1 :: Apply f => Tree (f b) -> f (Tree b) #
Traversable1 V2
Instance details Defined in Linear.V2 Methods traverse1 :: Apply f => (a -> f b) -> V2 a -> f (V2 b) # sequence1 :: Apply f => V2 (f b) -> f (V2 b) #
Traversable1 V3
Instance details Defined in Linear.V3 Methods traverse1 :: Apply f => (a -> f b) -> V3 a -> f (V3 b) # sequence1 :: Apply f => V3 (f b) -> f (V3 b) #
Traversable1 Plucker
Instance details Defined in Linear.Plucker Methods traverse1 :: Apply f => (a -> f b) -> Plucker a -> f (Plucker b) # sequence1 :: Apply f => Plucker (f b) -> f (Plucker b) #
Traversable1 V4
Instance details Defined in Linear.V4 Methods traverse1 :: Apply f => (a -> f b) -> V4 a -> f (V4 b) # sequence1 :: Apply f => V4 (f b) -> f (V4 b) #
Traversable1 V1
Instance details Defined in Linear.V1 Methods traverse1 :: Apply f => (a -> f b) -> V1 a -> f (V1 b) # sequence1 :: Apply f => V1 (f b) -> f (V1 b) #
Traversable1 (V1 :: Type -> Type)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> V1 a -> f (V1 b) # sequence1 :: Apply f => V1 (f b) -> f (V1 b) #
Traversable1 ((,) a)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a0 -> f b) -> (a, a0) -> f (a, b) # sequence1 :: Apply f => (a, f b) -> f (a, b) #
Traversable1 f => Traversable1 (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods traverse1 :: Apply f0 => (a -> f0 b) -> Cofree f a -> f0 (Cofree f b) # sequence1 :: Apply f0 => Cofree f (f0 b) -> f0 (Cofree f b) #
Traversable1 f => Traversable1 (Free f)
Instance details Defined in Control.Monad.Free Methods traverse1 :: Apply f0 => (a -> f0 b) -> Free f a -> f0 (Free f b) # sequence1 :: Apply f0 => Free f (f0 b) -> f0 (Free f b) #
Traversable1 f => Traversable1 (Yoneda f)
Instance details Defined in Data.Functor.Yoneda Methods traverse1 :: Apply f0 => (a -> f0 b) -> Yoneda f a -> f0 (Yoneda f b) # sequence1 :: Apply f0 => Yoneda f (f0 b) -> f0 (Yoneda f b) #
Traversable1 f => Traversable1 (Lift f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Lift f a -> f0 (Lift f b) # sequence1 :: Apply f0 => Lift f (f0 b) -> f0 (Lift f b) #
Traversable1 f => Traversable1 (Rec1 f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) # sequence1 :: Apply f0 => Rec1 f (f0 b) -> f0 (Rec1 f b) #
Traversable1 f => Traversable1 (IdentityT f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> IdentityT f a -> f0 (IdentityT f b) # sequence1 :: Apply f0 => IdentityT f (f0 b) -> f0 (IdentityT f b) #
Traversable1 f => Traversable1 (Alt f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) # sequence1 :: Apply f0 => Alt f (f0 b) -> f0 (Alt f b) #
Bitraversable1 p => Traversable1 (Join p)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Join p a -> f (Join p b) # sequence1 :: Apply f => Join p (f b) -> f (Join p b) #
Traversable1 f => Traversable1 (Backwards f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Backwards f a -> f0 (Backwards f b) # sequence1 :: Apply f0 => Backwards f (f0 b) -> f0 (Backwards f b) #
Traversable1 f => Traversable1 (AlongsideLeft f b)
Instance details Defined in Control.Lens.Internal.Getter Methods traverse1 :: Apply f0 => (a -> f0 b0) -> AlongsideLeft f b a -> f0 (AlongsideLeft f b b0) # sequence1 :: Apply f0 => AlongsideLeft f b (f0 b0) -> f0 (AlongsideLeft f b b0) #
Traversable1 f => Traversable1 (AlongsideRight f a)
Instance details Defined in Control.Lens.Internal.Getter Methods traverse1 :: Apply f0 => (a0 -> f0 b) -> AlongsideRight f a a0 -> f0 (AlongsideRight f a b) # sequence1 :: Apply f0 => AlongsideRight f a (f0 b) -> f0 (AlongsideRight f a b) #
Traversable1 (Tagged a)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a0 -> f b) -> Tagged a a0 -> f (Tagged a b) # sequence1 :: Apply f => Tagged a (f b) -> f (Tagged a b) #
Traversable1 f => Traversable1 (Reverse f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Reverse f a -> f0 (Reverse f b) # sequence1 :: Apply f0 => Reverse f (f0 b) -> f0 (Reverse f b) #
(Traversable1 f, Traversable1 g) => Traversable1 (f :+: g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) # sequence1 :: Apply f0 => (f :+: g) (f0 b) -> f0 ((f :+: g) b) #
(Traversable1 f, Traversable1 g) => Traversable1 (f :*: g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) # sequence1 :: Apply f0 => (f :: g) (f0 b) -> f0 ((f :: g) b) #
(Traversable1 f, Traversable1 g) => Traversable1 (Product f g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b) # sequence1 :: Apply f0 => Product f g (f0 b) -> f0 (Product f g b) #
(Traversable1 f, Traversable1 g) => Traversable1 (Sum f g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Sum f g a -> f0 (Sum f g b) # sequence1 :: Apply f0 => Sum f g (f0 b) -> f0 (Sum f g b) #
Traversable1 f => Traversable1 (M1 i c f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> M1 i c f a -> f0 (M1 i c f b) # sequence1 :: Apply f0 => M1 i c f (f0 b) -> f0 (M1 i c f b) #
(Traversable1 f, Traversable1 g) => Traversable1 (f :.: g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) # sequence1 :: Apply f0 => (f :.: g) (f0 b) -> f0 ((f :.: g) b) #
(Traversable1 f, Traversable1 g) => Traversable1 (Compose f g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Compose f g a -> f0 (Compose f g b) # sequence1 :: Apply f0 => Compose f g (f0 b) -> f0 (Compose f g b) #
Traversable1 g => Traversable1 (Joker g a)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a0 -> f b) -> Joker g a a0 -> f (Joker g a b) # sequence1 :: Apply f => Joker g a (f b) -> f (Joker g a b) #

data Rightmost a #

Used for lastOf.

Instances

Semigroup (Rightmost a)
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Rightmost a -> Rightmost a -> Rightmost a # sconcat :: NonEmpty (Rightmost a) -> Rightmost a # stimes :: Integral b => b -> Rightmost a -> Rightmost a #
Monoid (Rightmost a)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Rightmost a # mappend :: Rightmost a -> Rightmost a -> Rightmost a # mconcat :: [Rightmost a] -> Rightmost a #

data Leftmost a #

Used for firstOf.

Instances

Semigroup (Leftmost a)
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Leftmost a -> Leftmost a -> Leftmost a # sconcat :: NonEmpty (Leftmost a) -> Leftmost a # stimes :: Integral b => b -> Leftmost a -> Leftmost a #
Monoid (Leftmost a)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Leftmost a # mappend :: Leftmost a -> Leftmost a -> Leftmost a # mconcat :: [Leftmost a] -> Leftmost a #

data Sequenced a (m :: Type -> Type) #

Used internally by mapM_ and the like.

The argument a of the result should not be used!

See 4.16 Changelog entry for the explanation of "why not Apply f =>"?

Instances

Monad m => Semigroup (Sequenced a m)
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Sequenced a m -> Sequenced a m -> Sequenced a m # sconcat :: NonEmpty (Sequenced a m) -> Sequenced a m # stimes :: Integral b => b -> Sequenced a m -> Sequenced a m #
Monad m => Monoid (Sequenced a m)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Sequenced a m # mappend :: Sequenced a m -> Sequenced a m -> Sequenced a m # mconcat :: [Sequenced a m] -> Sequenced a m #

data Traversed a (f :: Type -> Type) #

Used internally by traverseOf_ and the like.

The argument a of the result should not be used!

Instances

Applicative f => Semigroup (Traversed a f)
Instance details Defined in Control.Lens.Internal.Fold Methods (<>) :: Traversed a f -> Traversed a f -> Traversed a f # sconcat :: NonEmpty (Traversed a f) -> Traversed a f # stimes :: Integral b => b -> Traversed a f -> Traversed a f #
Applicative f => Monoid (Traversed a f)
Instance details Defined in Control.Lens.Internal.Fold Methods mempty :: Traversed a f # mappend :: Traversed a f -> Traversed a f -> Traversed a f # mconcat :: [Traversed a f] -> Traversed a f #

newtype Indexed i a b #

A function with access to a index. This constructor may be useful when you need to store an Indexable in a container to avoid ImpredicativeTypes.

index :: Indexed i a b -> i -> a -> b

Constructors

Indexed
Fields runIndexed :: i -> a -> b

Instances

i ~ j => Indexable i (Indexed j)
Instance details Defined in Control.Lens.Internal.Indexed Methods indexed :: Indexed j a b -> i -> a -> b #
Arrow (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods arr :: (b -> c) -> Indexed i b c # first :: Indexed i b c -> Indexed i (b, d) (c, d) # second :: Indexed i b c -> Indexed i (d, b) (d, c) # (***) :: Indexed i b c -> Indexed i b' c' -> Indexed i (b, b') (c, c') # (&&&) :: Indexed i b c -> Indexed i b c' -> Indexed i b (c, c') #
ArrowChoice (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods left :: Indexed i b c -> Indexed i (Either b d) (Either c d) # right :: Indexed i b c -> Indexed i (Either d b) (Either d c) # (+++) :: Indexed i b c -> Indexed i b' c' -> Indexed i (Either b b') (Either c c') # (\|\|\|) :: Indexed i b d -> Indexed i c d -> Indexed i (Either b c) d #
ArrowApply (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods app :: Indexed i (Indexed i b c, b) c #
ArrowLoop (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods loop :: Indexed i (b, d) (c, d) -> Indexed i b c #
Choice (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods left' :: Indexed i a b -> Indexed i (Either a c) (Either b c) # right' :: Indexed i a b -> Indexed i (Either c a) (Either c b) #
Conjoined (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods distrib :: Functor f => Indexed i a b -> Indexed i (f a) (f b) # conjoined :: ((Indexed i ~ (->)) -> q (a -> b) r) -> q (Indexed i a b) r -> q (Indexed i a b) r #
Profunctor (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods dimap :: (a -> b) -> (c -> d) -> Indexed i b c -> Indexed i a d # lmap :: (a -> b) -> Indexed i b c -> Indexed i a c # rmap :: (b -> c) -> Indexed i a b -> Indexed i a c # (#.) :: Coercible c b => q b c -> Indexed i a b -> Indexed i a c # (.#) :: Coercible b a => Indexed i b c -> q a b -> Indexed i a c #
Representable (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Associated Types type Rep (Indexed i) :: Type -> Type # Methods tabulate :: (d -> Rep (Indexed i) c) -> Indexed i d c #
Corepresentable (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Associated Types type Corep (Indexed i) :: Type -> Type # Methods cotabulate :: (Corep (Indexed i) d -> c) -> Indexed i d c #
Closed (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods closed :: Indexed i a b -> Indexed i (x -> a) (x -> b) #
Strong (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods first' :: Indexed i a b -> Indexed i (a, c) (b, c) # second' :: Indexed i a b -> Indexed i (c, a) (c, b) #
Costrong (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods unfirst :: Indexed i (a, d) (b, d) -> Indexed i a b # unsecond :: Indexed i (d, a) (d, b) -> Indexed i a b #
Bizarre (Indexed Int) Mafic
Instance details Defined in Control.Lens.Internal.Magma Methods bazaar :: Applicative f => Indexed Int a (f b) -> Mafic a b t -> f t #
Category (Indexed i :: Type -> Type -> Type)
Instance details Defined in Control.Lens.Internal.Indexed Methods id :: Indexed i a a # (.) :: Indexed i b c -> Indexed i a b -> Indexed i a c #
Bizarre (Indexed i) (Molten i)
Instance details Defined in Control.Lens.Internal.Magma Methods bazaar :: Applicative f => Indexed i a (f b) -> Molten i a b t -> f t #
Sellable (Indexed i) (Molten i)
Instance details Defined in Control.Lens.Internal.Magma Methods sell :: Indexed i a (Molten i a b b) #
Cosieve (Indexed i) ((,) i)
Instance details Defined in Control.Lens.Internal.Indexed Methods cosieve :: Indexed i a b -> (i, a) -> b #
Sieve (Indexed i) ((->) i :: Type -> Type)
Instance details Defined in Control.Lens.Internal.Indexed Methods sieve :: Indexed i a b -> a -> i -> b #
Monad (Indexed i a)
Instance details Defined in Control.Lens.Internal.Indexed Methods (>>=) :: Indexed i a a0 -> (a0 -> Indexed i a b) -> Indexed i a b # (>>) :: Indexed i a a0 -> Indexed i a b -> Indexed i a b # return :: a0 -> Indexed i a a0 # fail :: String -> Indexed i a a0 #
Functor (Indexed i a)
Instance details Defined in Control.Lens.Internal.Indexed Methods fmap :: (a0 -> b) -> Indexed i a a0 -> Indexed i a b # (<$) :: a0 -> Indexed i a b -> Indexed i a a0 #
MonadFix (Indexed i a)
Instance details Defined in Control.Lens.Internal.Indexed Methods mfix :: (a0 -> Indexed i a a0) -> Indexed i a a0 #
Applicative (Indexed i a)
Instance details Defined in Control.Lens.Internal.Indexed Methods pure :: a0 -> Indexed i a a0 # (<>) :: Indexed i a (a0 -> b) -> Indexed i a a0 -> Indexed i a b # liftA2 :: (a0 -> b -> c) -> Indexed i a a0 -> Indexed i a b -> Indexed i a c # (>) :: Indexed i a a0 -> Indexed i a b -> Indexed i a b # (<*) :: Indexed i a a0 -> Indexed i a b -> Indexed i a a0 #
Apply (Indexed i a)
Instance details Defined in Control.Lens.Internal.Indexed Methods (<.>) :: Indexed i a (a0 -> b) -> Indexed i a a0 -> Indexed i a b # (.>) :: Indexed i a a0 -> Indexed i a b -> Indexed i a b # (<.) :: Indexed i a a0 -> Indexed i a b -> Indexed i a a0 # liftF2 :: (a0 -> b -> c) -> Indexed i a a0 -> Indexed i a b -> Indexed i a c #
Bind (Indexed i a)
Instance details Defined in Control.Lens.Internal.Indexed Methods (>>-) :: Indexed i a a0 -> (a0 -> Indexed i a b) -> Indexed i a b # join :: Indexed i a (Indexed i a a0) -> Indexed i a a0 #
type Rep (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed type Rep (Indexed i) = ((->) i :: Type -> Type)
type Corep (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed type Corep (Indexed i) = (,) i

class Conjoined p => Indexable i (p :: Type -> Type -> Type) #

This class permits overloading of function application for things that also admit a notion of a key or index.

Minimal complete definition

indexed

Instances

i ~ j => Indexable i (Indexed j)
Instance details Defined in Control.Lens.Internal.Indexed Methods indexed :: Indexed j a b -> i -> a -> b #
Indexable i ((->) :: Type -> Type -> Type)
Instance details Defined in Control.Lens.Internal.Indexed Methods indexed :: (a -> b) -> i -> a -> b #

class (Choice p, Corepresentable p, Comonad (Corep p), Traversable (Corep p), Strong p, Representable p, Monad (Rep p), MonadFix (Rep p), Distributive (Rep p), Costrong p, ArrowLoop p, ArrowApply p, ArrowChoice p, Closed p) => Conjoined (p :: Type -> Type -> Type) where #

This is a Profunctor that is both Corepresentable by f and Representable by g such that f is left adjoint to g. From this you can derive a lot of structure due to the preservation of limits and colimits.

Minimal complete definition

Nothing

Methods

distrib :: Functor f => p a b -> p (f a) (f b) #

Conjoined is strong enough to let us distribute every Conjoined Profunctor over every Haskell Functor. This is effectively a generalization of fmap.

conjoined :: ((p ~ ((->) :: Type -> Type -> Type)) -> q (a -> b) r) -> q (p a b) r -> q (p a b) r #

This permits us to make a decision at an outermost point about whether or not we use an index.

Ideally any use of this function should be done in such a way so that you compute the same answer, but this cannot be enforced at the type level.

Instances

Conjoined ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods distrib :: Functor f => ReifiedGetter a b -> ReifiedGetter (f a) (f b) # conjoined :: ((ReifiedGetter ~ (->)) -> q (a -> b) r) -> q (ReifiedGetter a b) r -> q (ReifiedGetter a b) r #
Conjoined (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods distrib :: Functor f => Indexed i a b -> Indexed i (f a) (f b) # conjoined :: ((Indexed i ~ (->)) -> q (a -> b) r) -> q (Indexed i a b) r -> q (Indexed i a b) r #
Conjoined ((->) :: Type -> Type -> Type)
Instance details Defined in Control.Lens.Internal.Indexed Methods distrib :: Functor f => (a -> b) -> f a -> f b # conjoined :: (((->) ~ (->)) -> q (a -> b) r) -> q (a -> b) r -> q (a -> b) r #

indexing :: Indexable Int p => ((a -> Indexing f b) -> s -> Indexing f t) -> p a (f b) -> s -> f t #

Transform a Traversal into an IndexedTraversal or a Fold into an IndexedFold, etc.

indexing :: Traversal s t a b -> IndexedTraversal Int s t a b
indexing :: Prism s t a b     -> IndexedTraversal Int s t a b
indexing :: Lens s t a b      -> IndexedLens Int  s t a b
indexing :: Iso s t a b       -> IndexedLens Int s t a b
indexing :: Fold s a          -> IndexedFold Int s a
indexing :: Getter s a        -> IndexedGetter Int s a

indexing :: Indexable Int p => LensLike (Indexing f) s t a b -> Over p f s t a b

indexing64 :: Indexable Int64 p => ((a -> Indexing64 f b) -> s -> Indexing64 f t) -> p a (f b) -> s -> f t #

Transform a Traversal into an IndexedTraversal or a Fold into an IndexedFold, etc.

This combinator is like indexing except that it handles large traversals and folds gracefully.

indexing64 :: Traversal s t a b -> IndexedTraversal Int64 s t a b
indexing64 :: Prism s t a b     -> IndexedTraversal Int64 s t a b
indexing64 :: Lens s t a b      -> IndexedLens Int64 s t a b
indexing64 :: Iso s t a b       -> IndexedLens Int64 s t a b
indexing64 :: Fold s a          -> IndexedFold Int64 s a
indexing64 :: Getter s a        -> IndexedGetter Int64 s a

indexing64 :: Indexable Int64 p => LensLike (Indexing64 f) s t a b -> Over p f s t a b

withIndex :: (Indexable i p, Functor f) => p (i, s) (f (j, t)) -> Indexed i s (f t) #

Fold a container with indices returning both the indices and the values.

The result is only valid to compose in a Traversal, if you don't edit the index as edits to the index have no effect.

>>> [10, 20, 30] ^.. ifolded . withIndex
[(0,10),(1,20),(2,30)]

>>> [10, 20, 30] ^.. ifolded . withIndex . alongside negated (re _Show)
[(0,"10"),(-1,"20"),(-2,"30")]

asIndex :: (Indexable i p, Contravariant f, Functor f) => p i (f i) -> Indexed i s (f s) #

When composed with an IndexedFold or IndexedTraversal this yields an (Indexed) Fold of the indices.

type Context' a = Context a a #

type Context' a s = Context a a s

data Context a b t #

The indexed store can be used to characterize a Lens and is used by cloneLens.

Context a b t is isomorphic to newtype Context a b t = Context { runContext :: forall f. Functor f => (a -> f b) -> f t }, and to exists s. (s, Lens s t a b).

A Context is like a Lens that has already been applied to a some structure.

Constructors

Context (b -> t) a

Instances

IndexedFunctor Context
Instance details Defined in Control.Lens.Internal.Context Methods ifmap :: (s -> t) -> Context a b s -> Context a b t #
IndexedComonad Context
Instance details Defined in Control.Lens.Internal.Context Methods iextract :: Context a a t -> t # iduplicate :: Context a c t -> Context a b (Context b c t) # iextend :: (Context b c t -> r) -> Context a c t -> Context a b r #
IndexedComonadStore Context
Instance details Defined in Control.Lens.Internal.Context Methods ipos :: Context a c t -> a # ipeek :: c -> Context a c t -> t # ipeeks :: (a -> c) -> Context a c t -> t # iseek :: b -> Context a c t -> Context b c t # iseeks :: (a -> b) -> Context a c t -> Context b c t # iexperiment :: Functor f => (b -> f c) -> Context b c t -> f t # context :: Context a b t -> Context a b t #
a ~ b => ComonadStore a (Context a b)
Instance details Defined in Control.Lens.Internal.Context Methods pos :: Context a b a0 -> a # peek :: a -> Context a b a0 -> a0 # peeks :: (a -> a) -> Context a b a0 -> a0 # seek :: a -> Context a b a0 -> Context a b a0 # seeks :: (a -> a) -> Context a b a0 -> Context a b a0 # experiment :: Functor f => (a -> f a) -> Context a b a0 -> f a0 #
Functor (Context a b)
Instance details Defined in Control.Lens.Internal.Context Methods fmap :: (a0 -> b0) -> Context a b a0 -> Context a b b0 # (<$) :: a0 -> Context a b b0 -> Context a b a0 #
a ~ b => Comonad (Context a b)
Instance details Defined in Control.Lens.Internal.Context Methods extract :: Context a b a0 -> a0 # duplicate :: Context a b a0 -> Context a b (Context a b a0) # extend :: (Context a b a0 -> b0) -> Context a b a0 -> Context a b b0 #
Sellable ((->) :: Type -> Type -> Type) Context
Instance details Defined in Control.Lens.Internal.Context Methods sell :: a -> Context a b b #

type Bazaar1' (p :: Type -> Type -> Type) a = Bazaar1 p a a #

This alias is helpful when it comes to reducing repetition in type signatures.

type Bazaar1' p a t = Bazaar1 p a a t

newtype Bazaar1 (p :: Type -> Type -> Type) a b t #

This is used to characterize a Traversal.

a.k.a. indexed Cartesian store comonad, indexed Kleene store comonad, or an indexed FunList.

http://twanvl.nl/blog/haskell/non-regular1

A Bazaar1 is like a Traversal that has already been applied to some structure.

Where a Context a b t holds an a and a function from b to t, a Bazaar1 a b t holds N as and a function from N bs to t, (where N might be infinite).

Mnemonically, a Bazaar1 holds many stores and you can easily add more.

This is a final encoding of Bazaar1.

Constructors

Bazaar1
Fields runBazaar1 :: forall (f :: Type -> Type). Apply f => p a (f b) -> f t

Instances

Profunctor p => Bizarre1 p (Bazaar1 p)
Instance details Defined in Control.Lens.Internal.Bazaar Methods bazaar1 :: Apply f => p a (f b) -> Bazaar1 p a b t -> f t #
Corepresentable p => Sellable p (Bazaar1 p)
Instance details Defined in Control.Lens.Internal.Bazaar Methods sell :: p a (Bazaar1 p a b b) #
IndexedFunctor (Bazaar1 p)
Instance details Defined in Control.Lens.Internal.Bazaar Methods ifmap :: (s -> t) -> Bazaar1 p a b s -> Bazaar1 p a b t #
Conjoined p => IndexedComonad (Bazaar1 p)
Instance details Defined in Control.Lens.Internal.Bazaar Methods iextract :: Bazaar1 p a a t -> t # iduplicate :: Bazaar1 p a c t -> Bazaar1 p a b (Bazaar1 p b c t) # iextend :: (Bazaar1 p b c t -> r) -> Bazaar1 p a c t -> Bazaar1 p a b r #
Functor (Bazaar1 p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods fmap :: (a0 -> b0) -> Bazaar1 p a b a0 -> Bazaar1 p a b b0 # (<$) :: a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b a0 #
Apply (Bazaar1 p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods (<.>) :: Bazaar1 p a b (a0 -> b0) -> Bazaar1 p a b a0 -> Bazaar1 p a b b0 # (.>) :: Bazaar1 p a b a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b b0 # (<.) :: Bazaar1 p a b a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b a0 # liftF2 :: (a0 -> b0 -> c) -> Bazaar1 p a b a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b c #
(a ~ b, Conjoined p) => Comonad (Bazaar1 p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods extract :: Bazaar1 p a b a0 -> a0 # duplicate :: Bazaar1 p a b a0 -> Bazaar1 p a b (Bazaar1 p a b a0) # extend :: (Bazaar1 p a b a0 -> b0) -> Bazaar1 p a b a0 -> Bazaar1 p a b b0 #
(a ~ b, Conjoined p) => ComonadApply (Bazaar1 p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods (<@>) :: Bazaar1 p a b (a0 -> b0) -> Bazaar1 p a b a0 -> Bazaar1 p a b b0 # (@>) :: Bazaar1 p a b a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b b0 # (<@) :: Bazaar1 p a b a0 -> Bazaar1 p a b b0 -> Bazaar1 p a b a0 #

type Bazaar' (p :: Type -> Type -> Type) a = Bazaar p a a #

This alias is helpful when it comes to reducing repetition in type signatures.

type Bazaar' p a t = Bazaar p a a t

newtype Bazaar (p :: Type -> Type -> Type) a b t #

This is used to characterize a Traversal.

a.k.a. indexed Cartesian store comonad, indexed Kleene store comonad, or an indexed FunList.

http://twanvl.nl/blog/haskell/non-regular1

A Bazaar is like a Traversal that has already been applied to some structure.

Where a Context a b t holds an a and a function from b to t, a Bazaar a b t holds N as and a function from N bs to t, (where N might be infinite).

Mnemonically, a Bazaar holds many stores and you can easily add more.

This is a final encoding of Bazaar.

Constructors

Bazaar
Fields runBazaar :: forall (f :: Type -> Type). Applicative f => p a (f b) -> f t

Instances

Profunctor p => Bizarre p (Bazaar p)
Instance details Defined in Control.Lens.Internal.Bazaar Methods bazaar :: Applicative f => p a (f b) -> Bazaar p a b t -> f t #
Corepresentable p => Sellable p (Bazaar p)
Instance details Defined in Control.Lens.Internal.Bazaar Methods sell :: p a (Bazaar p a b b) #
IndexedFunctor (Bazaar p)
Instance details Defined in Control.Lens.Internal.Bazaar Methods ifmap :: (s -> t) -> Bazaar p a b s -> Bazaar p a b t #
Conjoined p => IndexedComonad (Bazaar p)
Instance details Defined in Control.Lens.Internal.Bazaar Methods iextract :: Bazaar p a a t -> t # iduplicate :: Bazaar p a c t -> Bazaar p a b (Bazaar p b c t) # iextend :: (Bazaar p b c t -> r) -> Bazaar p a c t -> Bazaar p a b r #
Functor (Bazaar p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods fmap :: (a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 # (<$) :: a0 -> Bazaar p a b b0 -> Bazaar p a b a0 #
Applicative (Bazaar p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods pure :: a0 -> Bazaar p a b a0 # (<>) :: Bazaar p a b (a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 # liftA2 :: (a0 -> b0 -> c) -> Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b c # (>) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b b0 # (<*) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b a0 #
Apply (Bazaar p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods (<.>) :: Bazaar p a b (a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 # (.>) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b b0 # (<.) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b a0 # liftF2 :: (a0 -> b0 -> c) -> Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b c #
(a ~ b, Conjoined p) => Comonad (Bazaar p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods extract :: Bazaar p a b a0 -> a0 # duplicate :: Bazaar p a b a0 -> Bazaar p a b (Bazaar p a b a0) # extend :: (Bazaar p a b a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 #
(a ~ b, Conjoined p) => ComonadApply (Bazaar p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods (<@>) :: Bazaar p a b (a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 # (@>) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b b0 # (<@) :: Bazaar p a b a0 -> Bazaar p a b b0 -> Bazaar p a b a0 #

class Reversing t where #

This class provides a generalized notion of list reversal extended to other containers.

Methods

reversing :: t -> t #

Instances

Reversing ByteString
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: ByteString -> ByteString #
Reversing ByteString
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: ByteString -> ByteString #
Reversing Text
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Text -> Text #
Reversing Text
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Text -> Text #
Reversing [a]
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: [a] -> [a] #
Storable a => Reversing (Vector a)
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Vector a -> Vector a #
Reversing (NonEmpty a)
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: NonEmpty a -> NonEmpty a #
Reversing (Vector a)
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Vector a -> Vector a #
Reversing (Seq a)
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Seq a -> Seq a #
Unbox a => Reversing (Vector a)
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Vector a -> Vector a #
(Metric v, OrderedField n) => Reversing (Located (Trail' l v n))	Same as `reverseLocLine` or `reverseLocLoop`.
Instance details Defined in Diagrams.Trail Methods reversing :: Located (Trail' l v n) -> Located (Trail' l v n) #
(Metric v, OrderedField n) => Reversing (Located (Trail v n))	Same as `reverseLocTrail`.
Instance details Defined in Diagrams.Trail Methods reversing :: Located (Trail v n) -> Located (Trail v n) #
Prim a => Reversing (Vector a)
Instance details Defined in Control.Lens.Internal.Iso Methods reversing :: Vector a -> Vector a #
(Metric v, OrderedField n) => Reversing (Path v n)	Same as `reversePath`.
Instance details Defined in Diagrams.Path Methods reversing :: Path v n -> Path v n #
(Metric v, OrderedField n) => Reversing (Trail v n)	Same as `reverseTrail`.
Instance details Defined in Diagrams.Trail Methods reversing :: Trail v n -> Trail v n #
Reversing (FixedSegment v n)	Reverses the control points.
Instance details Defined in Diagrams.Segment Methods reversing :: FixedSegment v n -> FixedSegment v n #
(Metric v, OrderedField n) => Reversing (Trail' l v n)	Same as `reverseLine` or `reverseLoop`.
Instance details Defined in Diagrams.Trail Methods reversing :: Trail' l v n -> Trail' l v n #
(Additive v, Num n) => Reversing (Offset c v n)	Reverses the direction of closed offsets.
Instance details Defined in Diagrams.Segment Methods reversing :: Offset c v n -> Offset c v n #
(Additive v, Num n) => Reversing (Segment Closed v n)	Reverse the direction of a segment.
Instance details Defined in Diagrams.Segment Methods reversing :: Segment Closed v n -> Segment Closed v n #

data Level i a #

This data type represents a path-compressed copy of one level of a source data structure. We can safely use path-compression because we know the depth of the tree.

Path compression is performed by viewing a Level as a PATRICIA trie of the paths into the structure to leaves at a given depth, similar in many ways to a IntMap, but unlike a regular PATRICIA trie we do not need to store the mask bits merely the depth of the fork.

One invariant of this structure is that underneath a Two node you will not find any Zero nodes, so Zero can only occur at the root.

Instances

TraversableWithIndex i (Level i)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (i -> a -> f b) -> Level i a -> f (Level i b) # itraversed :: IndexedTraversal i (Level i a) (Level i b) a b #
FoldableWithIndex i (Level i)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (i -> a -> m) -> Level i a -> m # ifolded :: IndexedFold i (Level i a) a # ifoldr :: (i -> a -> b -> b) -> b -> Level i a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Level i a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Level i a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Level i a -> b #
FunctorWithIndex i (Level i)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b) -> Level i a -> Level i b # imapped :: IndexedSetter i (Level i a) (Level i b) a b #
Functor (Level i)
Instance details Defined in Control.Lens.Internal.Level Methods fmap :: (a -> b) -> Level i a -> Level i b # (<$) :: a -> Level i b -> Level i a #
Foldable (Level i)
Instance details Defined in Control.Lens.Internal.Level Methods fold :: Monoid m => Level i m -> m # foldMap :: Monoid m => (a -> m) -> Level i a -> m # foldr :: (a -> b -> b) -> b -> Level i a -> b # foldr' :: (a -> b -> b) -> b -> Level i a -> b # foldl :: (b -> a -> b) -> b -> Level i a -> b # foldl' :: (b -> a -> b) -> b -> Level i a -> b # foldr1 :: (a -> a -> a) -> Level i a -> a # foldl1 :: (a -> a -> a) -> Level i a -> a # toList :: Level i a -> [a] # null :: Level i a -> Bool # length :: Level i a -> Int # elem :: Eq a => a -> Level i a -> Bool # maximum :: Ord a => Level i a -> a # minimum :: Ord a => Level i a -> a # sum :: Num a => Level i a -> a # product :: Num a => Level i a -> a #
Traversable (Level i)
Instance details Defined in Control.Lens.Internal.Level Methods traverse :: Applicative f => (a -> f b) -> Level i a -> f (Level i b) # sequenceA :: Applicative f => Level i (f a) -> f (Level i a) # mapM :: Monad m => (a -> m b) -> Level i a -> m (Level i b) # sequence :: Monad m => Level i (m a) -> m (Level i a) #
(Eq i, Eq a) => Eq (Level i a)
Instance details Defined in Control.Lens.Internal.Level Methods (==) :: Level i a -> Level i a -> Bool # (/=) :: Level i a -> Level i a -> Bool #
(Ord i, Ord a) => Ord (Level i a)
Instance details Defined in Control.Lens.Internal.Level Methods compare :: Level i a -> Level i a -> Ordering # (<) :: Level i a -> Level i a -> Bool # (<=) :: Level i a -> Level i a -> Bool # (>) :: Level i a -> Level i a -> Bool # (>=) :: Level i a -> Level i a -> Bool # max :: Level i a -> Level i a -> Level i a # min :: Level i a -> Level i a -> Level i a #
(Read i, Read a) => Read (Level i a)
Instance details Defined in Control.Lens.Internal.Level Methods readsPrec :: Int -> ReadS (Level i a) # readList :: ReadS [Level i a] # readPrec :: ReadPrec (Level i a) # readListPrec :: ReadPrec [Level i a] #
(Show i, Show a) => Show (Level i a)
Instance details Defined in Control.Lens.Internal.Level Methods showsPrec :: Int -> Level i a -> ShowS # show :: Level i a -> String # showList :: [Level i a] -> ShowS #

data Magma i t b a #

This provides a way to peek at the internal structure of a Traversal or IndexedTraversal

Instances

TraversableWithIndex i (Magma i t b)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (i -> a -> f b0) -> Magma i t b a -> f (Magma i t b b0) # itraversed :: IndexedTraversal i (Magma i t b a) (Magma i t b b0) a b0 #
FoldableWithIndex i (Magma i t b)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (i -> a -> m) -> Magma i t b a -> m # ifolded :: IndexedFold i (Magma i t b a) a # ifoldr :: (i -> a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # ifoldl :: (i -> b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 # ifoldr' :: (i -> a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # ifoldl' :: (i -> b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 #
FunctorWithIndex i (Magma i t b)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b0) -> Magma i t b a -> Magma i t b b0 # imapped :: IndexedSetter i (Magma i t b a) (Magma i t b b0) a b0 #
Functor (Magma i t b)
Instance details Defined in Control.Lens.Internal.Magma Methods fmap :: (a -> b0) -> Magma i t b a -> Magma i t b b0 # (<$) :: a -> Magma i t b b0 -> Magma i t b a #
Foldable (Magma i t b)
Instance details Defined in Control.Lens.Internal.Magma Methods fold :: Monoid m => Magma i t b m -> m # foldMap :: Monoid m => (a -> m) -> Magma i t b a -> m # foldr :: (a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # foldr' :: (a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # foldl :: (b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 # foldl' :: (b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 # foldr1 :: (a -> a -> a) -> Magma i t b a -> a # foldl1 :: (a -> a -> a) -> Magma i t b a -> a # toList :: Magma i t b a -> [a] # null :: Magma i t b a -> Bool # length :: Magma i t b a -> Int # elem :: Eq a => a -> Magma i t b a -> Bool # maximum :: Ord a => Magma i t b a -> a # minimum :: Ord a => Magma i t b a -> a # sum :: Num a => Magma i t b a -> a # product :: Num a => Magma i t b a -> a #
Traversable (Magma i t b)
Instance details Defined in Control.Lens.Internal.Magma Methods traverse :: Applicative f => (a -> f b0) -> Magma i t b a -> f (Magma i t b b0) # sequenceA :: Applicative f => Magma i t b (f a) -> f (Magma i t b a) # mapM :: Monad m => (a -> m b0) -> Magma i t b a -> m (Magma i t b b0) # sequence :: Monad m => Magma i t b (m a) -> m (Magma i t b a) #
(Show i, Show a) => Show (Magma i t b a)
Instance details Defined in Control.Lens.Internal.Magma Methods showsPrec :: Int -> Magma i t b a -> ShowS # show :: Magma i t b a -> String # showList :: [Magma i t b a] -> ShowS #

class (Profunctor p, Bifunctor p) => Reviewable (p :: Type -> Type -> Type) #

This class is provided mostly for backwards compatibility with lens 3.8, but it can also shorten type signatures.

Instances

(Profunctor p, Bifunctor p) => Reviewable p
Instance details Defined in Control.Lens.Internal.Review

retagged :: (Profunctor p, Bifunctor p) => p a b -> p s b #

This is a profunctor used internally to implement Review

It plays a role similar to that of Accessor or Const do for Control.Lens.Getter

class (Applicative f, Distributive f, Traversable f) => Settable (f :: Type -> Type) #

Anything Settable must be isomorphic to the Identity Functor.

Minimal complete definition

untainted

Instances

Settable Identity	So you can pass our `Setter` into combinators from other lens libraries.
Instance details Defined in Control.Lens.Internal.Setter Methods untainted :: Identity a -> a # untaintedDot :: Profunctor p => p a (Identity b) -> p a b # taintedDot :: Profunctor p => p a b -> p a (Identity b) #
Settable f => Settable (Backwards f)	`backwards`
Instance details Defined in Control.Lens.Internal.Setter Methods untainted :: Backwards f a -> a # untaintedDot :: Profunctor p => p a (Backwards f b) -> p a b # taintedDot :: Profunctor p => p a b -> p a (Backwards f b) #
(Settable f, Settable g) => Settable (Compose f g)
Instance details Defined in Control.Lens.Internal.Setter Methods untainted :: Compose f g a -> a # untaintedDot :: Profunctor p => p a (Compose f g b) -> p a b # taintedDot :: Profunctor p => p a b -> p a (Compose f g b) #

type Over' (p :: Type -> Type -> Type) (f :: Type -> Type) s a = Over p f s s a a #

This is a convenient alias for use when you need to consume either indexed or non-indexed lens-likes based on context.

type Over' p f = Simple (Over p f)

type Over (p :: k -> Type -> Type) (f :: k1 -> Type) s (t :: k1) (a :: k) (b :: k1) = p a (f b) -> s -> f t #

This is a convenient alias for use when you need to consume either indexed or non-indexed lens-likes based on context.

type IndexedLensLike' i (f :: Type -> Type) s a = IndexedLensLike i f s s a a #

Convenient alias for constructing simple indexed lenses and their ilk.

type IndexedLensLike i (f :: k -> Type) s (t :: k) a (b :: k) = forall (p :: Type -> Type -> Type). Indexable i p => p a (f b) -> s -> f t #

Convenient alias for constructing indexed lenses and their ilk.

type LensLike' (f :: Type -> Type) s a = LensLike f s s a a #

type LensLike' f = Simple (LensLike f)

type LensLike (f :: k -> Type) s (t :: k) a (b :: k) = (a -> f b) -> s -> f t #

Many combinators that accept a Lens can also accept a Traversal in limited situations.

They do so by specializing the type of Functor that they require of the caller.

If a function accepts a LensLike f s t a b for some Functor f, then they may be passed a Lens.

Further, if f is an Applicative, they may also be passed a Traversal.

type Optical' (p :: k1 -> k -> Type) (q :: k1 -> k -> Type) (f :: k1 -> k) (s :: k1) (a :: k1) = Optical p q f s s a a #

type Optical' p q f s a = Simple (Optical p q f) s a

type Optical (p :: k2 -> k -> Type) (q :: k1 -> k -> Type) (f :: k3 -> k) (s :: k1) (t :: k3) (a :: k2) (b :: k3) = p a (f b) -> q s (f t) #

type LensLike f s t a b = Optical (->) (->) f s t a b

type Over p f s t a b = Optical p (->) f s t a b

type Optic p f s t a b = Optical p p f s t a b

type Optic' (p :: k1 -> k -> Type) (f :: k1 -> k) (s :: k1) (a :: k1) = Optic p f s s a a #

type Optic' p f s a = Simple (Optic p f) s a

type Optic (p :: k1 -> k -> Type) (f :: k2 -> k) (s :: k1) (t :: k2) (a :: k1) (b :: k2) = p a (f b) -> p s (f t) #

A valid Optic l should satisfy the laws:

l pure ≡ pure
l (Procompose f g) = Procompose (l f) (l g)

This gives rise to the laws for Equality, Iso, Prism, Lens, Traversal, Traversal1, Setter, Fold, Fold1, and Getter as well along with their index-preserving variants.

type LensLike f s t a b = Optic (->) f s t a b

type Simple (f :: k -> k -> k1 -> k1 -> k2) (s :: k) (a :: k1) = f s s a a #

A Simple Lens, Simple Traversal, ... can be used instead of a Lens,Traversal, ... whenever the type variables don't change upon setting a value.

_imagPart :: Simple Lens (Complex a) a
traversed :: Simple (IndexedTraversal Int) [a] a

Note: To use this alias in your own code with LensLike f or Setter, you may have to turn on LiberalTypeSynonyms.

This is commonly abbreviated as a "prime" marker, e.g. Lens' = Simple Lens.

type IndexPreservingFold1 s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Contravariant f, Apply f) => p a (f a) -> p s (f s) #

type IndexedFold1 i s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Contravariant f, Apply f) => p a (f a) -> s -> f s #

type Fold1 s a = forall (f :: Type -> Type). (Contravariant f, Apply f) => (a -> f a) -> s -> f s #

A relevant Fold (aka Fold1) has one or more targets.

type IndexPreservingFold s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Contravariant f, Applicative f) => p a (f a) -> p s (f s) #

An IndexPreservingFold can be used as a Fold, but when composed with an IndexedTraversal, IndexedFold, or IndexedLens yields an IndexedFold respectively.

type IndexedFold i s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Contravariant f, Applicative f) => p a (f a) -> s -> f s #

Every IndexedFold is a valid Fold and can be used for Getting.

type Fold s a = forall (f :: Type -> Type). (Contravariant f, Applicative f) => (a -> f a) -> s -> f s #

A Fold describes how to retrieve multiple values in a way that can be composed with other LensLike constructions.

A Fold s a provides a structure with operations very similar to those of the Foldable typeclass, see foldMapOf and the other Fold combinators.

By convention, if there exists a foo method that expects a Foldable (f a), then there should be a fooOf method that takes a Fold s a and a value of type s.

A Getter is a legal Fold that just ignores the supplied Monoid.

Unlike a Traversal a Fold is read-only. Since a Fold cannot be used to write back there are no Lens laws that apply.

type IndexPreservingGetter s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Contravariant f, Functor f) => p a (f a) -> p s (f s) #

An IndexPreservingGetter can be used as a Getter, but when composed with an IndexedTraversal, IndexedFold, or IndexedLens yields an IndexedFold, IndexedFold or IndexedGetter respectively.

type IndexedGetter i s a = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Contravariant f, Functor f) => p a (f a) -> s -> f s #

Every IndexedGetter is a valid IndexedFold and can be used for Getting like a Getter.

type Getter s a = forall (f :: Type -> Type). (Contravariant f, Functor f) => (a -> f a) -> s -> f s #

A Getter describes how to retrieve a single value in a way that can be composed with other LensLike constructions.

Unlike a Lens a Getter is read-only. Since a Getter cannot be used to write back there are no Lens laws that can be applied to it. In fact, it is isomorphic to an arbitrary function from (s -> a).

Moreover, a Getter can be used directly as a Fold, since it just ignores the Applicative.

type As (a :: k2) = Equality' a a #

Composable asTypeOf. Useful for constraining excess polymorphism, foo . (id :: As Int) . bar.

type Equality' (s :: k2) (a :: k2) = Equality s s a a #

A Simple Equality.

type Equality (s :: k1) (t :: k2) (a :: k1) (b :: k2) = forall k3 (p :: k1 -> k3 -> Type) (f :: k2 -> k3). p a (f b) -> p s (f t) #

A witness that (a ~ s, b ~ t).

Note: Composition with an Equality is index-preserving.

type Prism' s a = Prism s s a a #

A Simple Prism.

type Prism s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Choice p, Applicative f) => p a (f b) -> p s (f t) #

A Prism l is a Traversal that can also be turned around with re to obtain a Getter in the opposite direction.

There are three laws that a Prism should satisfy:

First, if I re or review a value with a Prism and then preview or use (^?), I will get it back:

preview l (review l b) ≡ Just b

Second, if you can extract a value a using a Prism l from a value s, then the value s is completely described by l and a:

preview l s ≡ Just a ⟹ review l a ≡ s

Third, if you get non-match t, you can convert it result back to s:

matching l s ≡ Left t ⟹ matching l t ≡ Left s

The first two laws imply that the Traversal laws hold for every Prism and that we traverse at most 1 element:

lengthOf l x <= 1

It may help to think of this as a Iso that can be partial in one direction.

Every Prism is a valid Traversal.

Every Iso is a valid Prism.

For example, you might have a Prism' Integer Natural allows you to always go from a Natural to an Integer, and provide you with tools to check if an Integer is a Natural and/or to edit one if it is.

nat :: Prism' Integer Natural
nat = prism toInteger $ \ i ->
   if i < 0
   then Left i
   else Right (fromInteger i)

Now we can ask if an Integer is a Natural.

>>> 5^?nat
Just 5

>>> (-5)^?nat
Nothing

We can update the ones that are:

>>> (-3,4) & both.nat *~ 2
(-3,8)

And we can then convert from a Natural to an Integer.

>>> 5 ^. re nat -- :: Natural
5

Similarly we can use a Prism to traverse the Left half of an Either:

>>> Left "hello" & _Left %~ length
Left 5

or to construct an Either:

>>> 5^.re _Left
Left 5

such that if you query it with the Prism, you will get your original input back.

>>> 5^.re _Left ^? _Left
Just 5

Another interesting way to think of a Prism is as the categorical dual of a Lens -- a co-Lens, so to speak. This is what permits the construction of outside.

Note: Composition with a Prism is index-preserving.

type AReview t b = Optic' (Tagged :: Type -> Type -> Type) Identity t b #

If you see this in a signature for a function, the function is expecting a Review (in practice, this usually means a Prism).

type Review t b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Choice p, Bifunctor p, Settable f) => Optic' p f t b #

This is a limited form of a Prism that can only be used for re operations.

Like with a Getter, there are no laws to state for a Review.

You can generate a Review by using unto. You can also use any Prism or Iso directly as a Review.

type Iso' s a = Iso s s a a #

type Iso' = Simple Iso

type Iso s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Profunctor p, Functor f) => p a (f b) -> p s (f t) #

Isomorphism families can be composed with another Lens using (.) and id.

Since every Iso is both a valid Lens and a valid Prism, the laws for those types imply the following laws for an Iso f:

f . from f ≡ id
from f . f ≡ id

Note: Composition with an Iso is index- and measure- preserving.

type IndexPreservingSetter' s a = IndexPreservingSetter s s a a #

type IndexedPreservingSetter' i = Simple IndexedPreservingSetter

type IndexPreservingSetter s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Settable f) => p a (f b) -> p s (f t) #

An IndexPreservingSetter can be composed with a IndexedSetter, IndexedTraversal or IndexedLens and leaves the index intact, yielding an IndexedSetter.

type IndexedSetter' i s a = IndexedSetter i s s a a #

type IndexedSetter' i = Simple (IndexedSetter i)

type IndexedSetter i s t a b = forall (f :: Type -> Type) (p :: Type -> Type -> Type). (Indexable i p, Settable f) => p a (f b) -> s -> f t #

Every IndexedSetter is a valid Setter.

The Setter laws are still required to hold.

type Setter' s a = Setter s s a a #

A Setter' is just a Setter that doesn't change the types.

These are particularly common when talking about monomorphic containers. e.g.

sets Data.Text.map :: Setter' Text Char

type Setter' = Simple Setter

type Setter s t a b = forall (f :: Type -> Type). Settable f => (a -> f b) -> s -> f t #

The only LensLike law that can apply to a Setter l is that

set l y (set l x a) ≡ set l y a

You can't view a Setter in general, so the other two laws are irrelevant.

However, two Functor laws apply to a Setter:

over l id ≡ id
over l f . over l g ≡ over l (f . g)

These can be stated more directly:

l pure ≡ pure
l f . untainted . l g ≡ l (f . untainted . g)

You can compose a Setter with a Lens or a Traversal using (.) from the Prelude and the result is always only a Setter and nothing more.

>>> over traverse f [a,b,c,d]
[f a,f b,f c,f d]

>>> over _1 f (a,b)
(f a,b)

>>> over (traverse._1) f [(a,b),(c,d)]
[(f a,b),(f c,d)]

>>> over both f (a,b)
(f a,f b)

>>> over (traverse.both) f [(a,b),(c,d)]
[(f a,f b),(f c,f d)]

type IndexPreservingTraversal1' s a = IndexPreservingTraversal1 s s a a #

type IndexPreservingTraversal1 s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Apply f) => p a (f b) -> p s (f t) #

type IndexPreservingTraversal' s a = IndexPreservingTraversal s s a a #

type IndexPreservingTraversal' = Simple IndexPreservingTraversal

type IndexPreservingTraversal s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Applicative f) => p a (f b) -> p s (f t) #

An IndexPreservingLens leaves any index it is composed with alone.

type IndexedTraversal1' i s a = IndexedTraversal1 i s s a a #

type IndexedTraversal1 i s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Apply f) => p a (f b) -> s -> f t #

type IndexedTraversal' i s a = IndexedTraversal i s s a a #

type IndexedTraversal' i = Simple (IndexedTraversal i)

type IndexedTraversal i s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Indexable i p, Applicative f) => p a (f b) -> s -> f t #

Every IndexedTraversal is a valid Traversal or IndexedFold.

The Indexed constraint is used to allow an IndexedTraversal to be used directly as a Traversal.

The Traversal laws are still required to hold.

In addition, the index i should satisfy the requirement that it stays unchanged even when modifying the value a, otherwise traversals like indices break the Traversal laws.

type Traversal1' s a = Traversal1 s s a a #

type Traversal1 s t a b = forall (f :: Type -> Type). Apply f => (a -> f b) -> s -> f t #

type Traversal' s a = Traversal s s a a #

type Traversal' = Simple Traversal

type Traversal s t a b = forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t #

A Traversal can be used directly as a Setter or a Fold (but not as a Lens) and provides the ability to both read and update multiple fields, subject to some relatively weak Traversal laws.

These have also been known as multilenses, but they have the signature and spirit of

traverse :: Traversable f => Traversal (f a) (f b) a b

and the more evocative name suggests their application.

Most of the time the Traversal you will want to use is just traverse, but you can also pass any Lens or Iso as a Traversal, and composition of a Traversal (or Lens or Iso) with a Traversal (or Lens or Iso) using (.) forms a valid Traversal.

The laws for a Traversal t follow from the laws for Traversable as stated in "The Essence of the Iterator Pattern".

t pure ≡ pure
fmap (t f) . t g ≡ getCompose . t (Compose . fmap f . g)

One consequence of this requirement is that a Traversal needs to leave the same number of elements as a candidate for subsequent Traversal that it started with. Another testament to the strength of these laws is that the caveat expressed in section 5.5 of the "Essence of the Iterator Pattern" about exotic Traversable instances that traverse the same entry multiple times was actually already ruled out by the second law in that same paper!

type IndexPreservingLens' s a = IndexPreservingLens s s a a #

type IndexPreservingLens' = Simple IndexPreservingLens

type IndexPreservingLens s t a b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Conjoined p, Functor f) => p a (f b) -> p s (f t) #

An IndexPreservingLens leaves any index it is composed with alone.

type IndexedLens' i s a = IndexedLens i s s a a #

type IndexedLens' i = Simple (IndexedLens i)

type IndexedLens i s t a b = forall (f :: Type -> Type) (p :: Type -> Type -> Type). (Indexable i p, Functor f) => p a (f b) -> s -> f t #

Every IndexedLens is a valid Lens and a valid IndexedTraversal.

type Lens' s a = Lens s s a a #

type Lens' = Simple Lens

type Lens s t a b = forall (f :: Type -> Type). Functor f => (a -> f b) -> s -> f t #

A Lens is actually a lens family as described in http://comonad.com/reader/2012/mirrored-lenses/.

With great power comes great responsibility and a Lens is subject to the three common sense Lens laws:

1) You get back what you put in:

view l (set l v s)  ≡ v

2) Putting back what you got doesn't change anything:

set l (view l s) s  ≡ s

3) Setting twice is the same as setting once:

set l v' (set l v s) ≡ set l v' s

These laws are strong enough that the 4 type parameters of a Lens cannot vary fully independently. For more on how they interact, read the "Why is it a Lens Family?" section of http://comonad.com/reader/2012/mirrored-lenses/.

There are some emergent properties of these laws:

1) set l s must be injective for every s This is a consequence of law #1

2) set l must be surjective, because of law #2, which indicates that it is possible to obtain any v from some s such that set s v = s

3) Given just the first two laws you can prove a weaker form of law #3 where the values v that you are setting match:

set l v (set l v s) ≡ set l v s

Every Lens can be used directly as a Setter or Traversal.

You can also use a Lens for Getting as if it were a Fold or Getter.

Since every Lens is a valid Traversal, the Traversal laws are required of any Lens you create:

l pure ≡ pure
fmap (l f) . l g ≡ getCompose . l (Compose . fmap f . g)

type Lens s t a b = forall f. Functor f => LensLike f s t a b

type Setting' (p :: Type -> Type -> Type) s a = Setting p s s a a #

This is a convenient alias when defining highly polymorphic code that takes both ASetter' and AnIndexedSetter' as appropriate. If a function takes this it is expecting one of those two things based on context.

type Setting (p :: Type -> Type -> Type) s t a b = p a (Identity b) -> s -> Identity t #

This is a convenient alias when defining highly polymorphic code that takes both ASetter and AnIndexedSetter as appropriate. If a function takes this it is expecting one of those two things based on context.

type AnIndexedSetter' i s a = AnIndexedSetter i s s a a #

type AnIndexedSetter' i = Simple (AnIndexedSetter i)

type AnIndexedSetter i s t a b = Indexed i a (Identity b) -> s -> Identity t #

Running an IndexedSetter instantiates it to a concrete type.

When consuming a setter directly to perform a mapping, you can use this type, but most user code will not need to use this type.

type ASetter' s a = ASetter s s a a #

This is a useful alias for use when consuming a Setter'.

Most user code will never have to use this type.

type ASetter' = Simple ASetter

type ASetter s t a b = (a -> Identity b) -> s -> Identity t #

Running a Setter instantiates it to a concrete type.

When consuming a setter directly to perform a mapping, you can use this type, but most user code will not need to use this type.

mapped :: Functor f => Setter (f a) (f b) a b #

This Setter can be used to map over all of the values in a Functor.

fmap ≡ over mapped
fmapDefault ≡ over traverse
(<$) ≡ set mapped

>>> over mapped f [a,b,c]
[f a,f b,f c]

>>> over mapped (+1) [1,2,3]
[2,3,4]

>>> set mapped x [a,b,c]
[x,x,x]

>>> [[a,b],[c]] & mapped.mapped +~ x
[[a + x,b + x],[c + x]]

>>> over (mapped._2) length [("hello","world"),("leaders","!!!")]
[("hello",5),("leaders",3)]

mapped :: Functor f => Setter (f a) (f b) a b

If you want an IndexPreservingSetter use setting fmap.

lifted :: Monad m => Setter (m a) (m b) a b #

This setter can be used to modify all of the values in a Monad.

You sometimes have to use this rather than mapped -- due to temporary insanity Functor was not a superclass of Monad until GHC 7.10.

liftM ≡ over lifted

>>> over lifted f [a,b,c]
[f a,f b,f c]

>>> set lifted b (Just a)
Just b

If you want an IndexPreservingSetter use setting liftM.

contramapped :: Contravariant f => Setter (f b) (f a) a b #

This Setter can be used to map over all of the inputs to a Contravariant.

contramap ≡ over contramapped

>>> getPredicate (over contramapped (*2) (Predicate even)) 5
True

>>> getOp (over contramapped (*5) (Op show)) 100
"500"

>>> Prelude.map ($ 1) $ over (mapped . _Unwrapping' Op . contramapped) (*12) [(*2),(+1),(^3)]
[24,13,1728]

setting :: ((a -> b) -> s -> t) -> IndexPreservingSetter s t a b #

Build an index-preserving Setter from a map-like function.

Your supplied function f is required to satisfy:

f id ≡ id
f g . f h ≡ f (g . h)

Equational reasoning:

setting . over ≡ id
over . setting ≡ id

Another way to view sets is that it takes a "semantic editor combinator" and transforms it into a Setter.

setting :: ((a -> b) -> s -> t) -> Setter s t a b

sets :: (Profunctor p, Profunctor q, Settable f) => (p a b -> q s t) -> Optical p q f s t a b #

Build a Setter, IndexedSetter or IndexPreservingSetter depending on your choice of Profunctor.

sets :: ((a -> b) -> s -> t) -> Setter s t a b

cloneSetter :: ASetter s t a b -> Setter s t a b #

Restore ASetter to a full Setter.

cloneIndexPreservingSetter :: ASetter s t a b -> IndexPreservingSetter s t a b #

Build an IndexPreservingSetter from any Setter.

cloneIndexedSetter :: AnIndexedSetter i s t a b -> IndexedSetter i s t a b #

Clone an IndexedSetter.

over :: ASetter s t a b -> (a -> b) -> s -> t #

Modify the target of a Lens or all the targets of a Setter or Traversal with a function.

fmap ≡ over mapped
fmapDefault ≡ over traverse
sets . over ≡ id
over . sets ≡ id

Given any valid Setter l, you can also rely on the law:

over l f . over l g = over l (f . g)

e.g.

>>> over mapped f (over mapped g [a,b,c]) == over mapped (f . g) [a,b,c]
True

Another way to view over is to say that it transforms a Setter into a "semantic editor combinator".

>>> over mapped f (Just a)
Just (f a)

>>> over mapped (*10) [1,2,3]
[10,20,30]

>>> over _1 f (a,b)
(f a,b)

>>> over _1 show (10,20)
("10",20)

over :: Setter s t a b -> (a -> b) -> s -> t
over :: ASetter s t a b -> (a -> b) -> s -> t

set :: ASetter s t a b -> b -> s -> t #

Replace the target of a Lens or all of the targets of a Setter or Traversal with a constant value.

(<$) ≡ set mapped

>>> set _2 "hello" (1,())
(1,"hello")

>>> set mapped () [1,2,3,4]
[(),(),(),()]

Note: Attempting to set a Fold or Getter will fail at compile time with an relatively nice error message.

set :: Setter s t a b    -> b -> s -> t
set :: Iso s t a b       -> b -> s -> t
set :: Lens s t a b      -> b -> s -> t
set :: Traversal s t a b -> b -> s -> t

set' :: ASetter' s a -> a -> s -> s #

Replace the target of a Lens or all of the targets of a Setter' or Traversal with a constant value, without changing its type.

This is a type restricted version of set, which retains the type of the original.

>>> set' mapped x [a,b,c,d]
[x,x,x,x]

>>> set' _2 "hello" (1,"world")
(1,"hello")

>>> set' mapped 0 [1,2,3,4]
[0,0,0,0]

Note: Attempting to adjust set' a Fold or Getter will fail at compile time with an relatively nice error message.

set' :: Setter' s a    -> a -> s -> s
set' :: Iso' s a       -> a -> s -> s
set' :: Lens' s a      -> a -> s -> s
set' :: Traversal' s a -> a -> s -> s

(%~) :: ASetter s t a b -> (a -> b) -> s -> t infixr 4 #

Modifies the target of a Lens or all of the targets of a Setter or Traversal with a user supplied function.

This is an infix version of over.

fmap f ≡ mapped %~ f
fmapDefault f ≡ traverse %~ f

>>> (a,b,c) & _3 %~ f
(a,b,f c)

>>> (a,b) & both %~ f
(f a,f b)

>>> _2 %~ length $ (1,"hello")
(1,5)

>>> traverse %~ f $ [a,b,c]
[f a,f b,f c]

>>> traverse %~ even $ [1,2,3]
[False,True,False]

>>> traverse.traverse %~ length $ [["hello","world"],["!!!"]]
[[5,5],[3]]

(%~) :: Setter s t a b    -> (a -> b) -> s -> t
(%~) :: Iso s t a b       -> (a -> b) -> s -> t
(%~) :: Lens s t a b      -> (a -> b) -> s -> t
(%~) :: Traversal s t a b -> (a -> b) -> s -> t

(.~) :: ASetter s t a b -> b -> s -> t infixr 4 #

Replace the target of a Lens or all of the targets of a Setter or Traversal with a constant value.

This is an infix version of set, provided for consistency with (.=).

f <$ a ≡ mapped .~ f $ a

>>> (a,b,c,d) & _4 .~ e
(a,b,c,e)

>>> (42,"world") & _1 .~ "hello"
("hello","world")

>>> (a,b) & both .~ c
(c,c)

(.~) :: Setter s t a b    -> b -> s -> t
(.~) :: Iso s t a b       -> b -> s -> t
(.~) :: Lens s t a b      -> b -> s -> t
(.~) :: Traversal s t a b -> b -> s -> t

(?~) :: ASetter s t a (Maybe b) -> b -> s -> t infixr 4 #

Set the target of a Lens, Traversal or Setter to Just a value.

l ?~ t ≡ set l (Just t)

>>> Nothing & id ?~ a
Just a

>>> Map.empty & at 3 ?~ x
fromList [(3,x)]

?~ can be used type-changily:

>>> ('a', ('b', 'c')) & _2.both ?~ 'x'
('a',(Just 'x',Just 'x'))

(?~) :: Setter s t a (Maybe b)    -> b -> s -> t
(?~) :: Iso s t a (Maybe b)       -> b -> s -> t
(?~) :: Lens s t a (Maybe b)      -> b -> s -> t
(?~) :: Traversal s t a (Maybe b) -> b -> s -> t

(<.~) :: ASetter s t a b -> b -> s -> (b, t) infixr 4 #

Set with pass-through.

This is mostly present for consistency, but may be useful for chaining assignments.

If you do not need a copy of the intermediate result, then using l .~ t directly is a good idea.

>>> (a,b) & _1 <.~ c
(c,(c,b))

>>> ("good","morning","vietnam") & _3 <.~ "world"
("world",("good","morning","world"))

>>> (42,Map.fromList [("goodnight","gracie")]) & _2.at "hello" <.~ Just "world"
(Just "world",(42,fromList [("goodnight","gracie"),("hello","world")]))

(<.~) :: Setter s t a b    -> b -> s -> (b, t)
(<.~) :: Iso s t a b       -> b -> s -> (b, t)
(<.~) :: Lens s t a b      -> b -> s -> (b, t)
(<.~) :: Traversal s t a b -> b -> s -> (b, t)

(<?~) :: ASetter s t a (Maybe b) -> b -> s -> (b, t) infixr 4 #

Set to Just a value with pass-through.

This is mostly present for consistency, but may be useful for for chaining assignments.

If you do not need a copy of the intermediate result, then using l ?~ d directly is a good idea.

>>> import Data.Map as Map
>>> _2.at "hello" <?~ "world" $ (42,Map.fromList [("goodnight","gracie")])
("world",(42,fromList [("goodnight","gracie"),("hello","world")]))

(<?~) :: Setter s t a (Maybe b)    -> b -> s -> (b, t)
(<?~) :: Iso s t a (Maybe b)       -> b -> s -> (b, t)
(<?~) :: Lens s t a (Maybe b)      -> b -> s -> (b, t)
(<?~) :: Traversal s t a (Maybe b) -> b -> s -> (b, t)

(+~) :: Num a => ASetter s t a a -> a -> s -> t infixr 4 #

Increment the target(s) of a numerically valued Lens, Setter or Traversal.

>>> (a,b) & _1 +~ c
(a + c,b)

>>> (a,b) & both +~ c
(a + c,b + c)

>>> (1,2) & _2 +~ 1
(1,3)

>>> [(a,b),(c,d)] & traverse.both +~ e
[(a + e,b + e),(c + e,d + e)]

(+~) :: Num a => Setter' s a    -> a -> s -> s
(+~) :: Num a => Iso' s a       -> a -> s -> s
(+~) :: Num a => Lens' s a      -> a -> s -> s
(+~) :: Num a => Traversal' s a -> a -> s -> s

(*~) :: Num a => ASetter s t a a -> a -> s -> t infixr 4 #

Multiply the target(s) of a numerically valued Lens, Iso, Setter or Traversal.

>>> (a,b) & _1 *~ c
(a * c,b)

>>> (a,b) & both *~ c
(a * c,b * c)

>>> (1,2) & _2 *~ 4
(1,8)

>>> Just 24 & mapped *~ 2
Just 48

(*~) :: Num a => Setter' s a    -> a -> s -> s
(*~) :: Num a => Iso' s a       -> a -> s -> s
(*~) :: Num a => Lens' s a      -> a -> s -> s
(*~) :: Num a => Traversal' s a -> a -> s -> s

(-~) :: Num a => ASetter s t a a -> a -> s -> t infixr 4 #

Decrement the target(s) of a numerically valued Lens, Iso, Setter or Traversal.

>>> (a,b) & _1 -~ c
(a - c,b)

>>> (a,b) & both -~ c
(a - c,b - c)

>>> _1 -~ 2 $ (1,2)
(-1,2)

>>> mapped.mapped -~ 1 $ [[4,5],[6,7]]
[[3,4],[5,6]]

(-~) :: Num a => Setter' s a    -> a -> s -> s
(-~) :: Num a => Iso' s a       -> a -> s -> s
(-~) :: Num a => Lens' s a      -> a -> s -> s
(-~) :: Num a => Traversal' s a -> a -> s -> s

(//~) :: Fractional a => ASetter s t a a -> a -> s -> t infixr 4 #

Divide the target(s) of a numerically valued Lens, Iso, Setter or Traversal.

>>> (a,b) & _1 //~ c
(a / c,b)

>>> (a,b) & both //~ c
(a / c,b / c)

>>> ("Hawaii",10) & _2 //~ 2
("Hawaii",5.0)

(//~) :: Fractional a => Setter' s a    -> a -> s -> s
(//~) :: Fractional a => Iso' s a       -> a -> s -> s
(//~) :: Fractional a => Lens' s a      -> a -> s -> s
(//~) :: Fractional a => Traversal' s a -> a -> s -> s

(^~) :: (Num a, Integral e) => ASetter s t a a -> e -> s -> t infixr 4 #

Raise the target(s) of a numerically valued Lens, Setter or Traversal to a non-negative integral power.

>>> (1,3) & _2 ^~ 2
(1,9)

(^~) :: (Num a, Integral e) => Setter' s a    -> e -> s -> s
(^~) :: (Num a, Integral e) => Iso' s a       -> e -> s -> s
(^~) :: (Num a, Integral e) => Lens' s a      -> e -> s -> s
(^~) :: (Num a, Integral e) => Traversal' s a -> e -> s -> s

(^^~) :: (Fractional a, Integral e) => ASetter s t a a -> e -> s -> t infixr 4 #

Raise the target(s) of a fractionally valued Lens, Setter or Traversal to an integral power.

>>> (1,2) & _2 ^^~ (-1)
(1,0.5)

(^^~) :: (Fractional a, Integral e) => Setter' s a    -> e -> s -> s
(^^~) :: (Fractional a, Integral e) => Iso' s a       -> e -> s -> s
(^^~) :: (Fractional a, Integral e) => Lens' s a      -> e -> s -> s
(^^~) :: (Fractional a, Integral e) => Traversal' s a -> e -> s -> s

(**~) :: Floating a => ASetter s t a a -> a -> s -> t infixr 4 #

Raise the target(s) of a floating-point valued Lens, Setter or Traversal to an arbitrary power.

>>> (a,b) & _1 **~ c
(a**c,b)

>>> (a,b) & both **~ c
(a**c,b**c)

>>> _2 **~ 10 $ (3,2)
(3,1024.0)

(**~) :: Floating a => Setter' s a    -> a -> s -> s
(**~) :: Floating a => Iso' s a       -> a -> s -> s
(**~) :: Floating a => Lens' s a      -> a -> s -> s
(**~) :: Floating a => Traversal' s a -> a -> s -> s

(||~) :: ASetter s t Bool Bool -> Bool -> s -> t infixr 4 #

Logically || the target(s) of a Bool-valued Lens or Setter.

>>> both ||~ True $ (False,True)
(True,True)

>>> both ||~ False $ (False,True)
(False,True)

(||~) :: Setter' s Bool    -> Bool -> s -> s
(||~) :: Iso' s Bool       -> Bool -> s -> s
(||~) :: Lens' s Bool      -> Bool -> s -> s
(||~) :: Traversal' s Bool -> Bool -> s -> s

(&&~) :: ASetter s t Bool Bool -> Bool -> s -> t infixr 4 #

Logically && the target(s) of a Bool-valued Lens or Setter.

>>> both &&~ True $ (False, True)
(False,True)

>>> both &&~ False $ (False, True)
(False,False)

(&&~) :: Setter' s Bool    -> Bool -> s -> s
(&&~) :: Iso' s Bool       -> Bool -> s -> s
(&&~) :: Lens' s Bool      -> Bool -> s -> s
(&&~) :: Traversal' s Bool -> Bool -> s -> s

assign :: MonadState s m => ASetter s s a b -> b -> m () #

Replace the target of a Lens or all of the targets of a Setter or Traversal in our monadic state with a new value, irrespective of the old.

This is an alias for (.=).

>>> execState (do assign _1 c; assign _2 d) (a,b)
(c,d)

>>> execState (both .= c) (a,b)
(c,c)

assign :: MonadState s m => Iso' s a       -> a -> m ()
assign :: MonadState s m => Lens' s a      -> a -> m ()
assign :: MonadState s m => Traversal' s a -> a -> m ()
assign :: MonadState s m => Setter' s a    -> a -> m ()

(.=) :: MonadState s m => ASetter s s a b -> b -> m () infix 4 #

Replace the target of a Lens or all of the targets of a Setter or Traversal in our monadic state with a new value, irrespective of the old.

This is an infix version of assign.

>>> execState (do _1 .= c; _2 .= d) (a,b)
(c,d)

>>> execState (both .= c) (a,b)
(c,c)

(.=) :: MonadState s m => Iso' s a       -> a -> m ()
(.=) :: MonadState s m => Lens' s a      -> a -> m ()
(.=) :: MonadState s m => Traversal' s a -> a -> m ()
(.=) :: MonadState s m => Setter' s a    -> a -> m ()

It puts the state in the monad or it gets the hose again.

(%=) :: MonadState s m => ASetter s s a b -> (a -> b) -> m () infix 4 #

Map over the target of a Lens or all of the targets of a Setter or Traversal in our monadic state.

>>> execState (do _1 %= f;_2 %= g) (a,b)
(f a,g b)

>>> execState (do both %= f) (a,b)
(f a,f b)

(%=) :: MonadState s m => Iso' s a       -> (a -> a) -> m ()
(%=) :: MonadState s m => Lens' s a      -> (a -> a) -> m ()
(%=) :: MonadState s m => Traversal' s a -> (a -> a) -> m ()
(%=) :: MonadState s m => Setter' s a    -> (a -> a) -> m ()

(%=) :: MonadState s m => ASetter s s a b -> (a -> b) -> m ()

modifying :: MonadState s m => ASetter s s a b -> (a -> b) -> m () #

This is an alias for (%=).

(?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m () infix 4 #

Replace the target of a Lens or all of the targets of a Setter or Traversal in our monadic state with Just a new value, irrespective of the old.

>>> execState (do at 1 ?= a; at 2 ?= b) Map.empty
fromList [(1,a),(2,b)]

>>> execState (do _1 ?= b; _2 ?= c) (Just a, Nothing)
(Just b,Just c)

(?=) :: MonadState s m => Iso' s (Maybe a)       -> a -> m ()
(?=) :: MonadState s m => Lens' s (Maybe a)      -> a -> m ()
(?=) :: MonadState s m => Traversal' s (Maybe a) -> a -> m ()
(?=) :: MonadState s m => Setter' s (Maybe a)    -> a -> m ()

(+=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m () infix 4 #

Modify the target(s) of a Lens', Iso, Setter or Traversal by adding a value.

Example:

fresh :: MonadState Int m => m Int
fresh = do
  id += 1
  use id

>>> execState (do _1 += c; _2 += d) (a,b)
(a + c,b + d)

>>> execState (do _1.at 1.non 0 += 10) (Map.fromList [(2,100)],"hello")
(fromList [(1,10),(2,100)],"hello")

(+=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
(+=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
(+=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
(+=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()

(-=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m () infix 4 #

Modify the target(s) of a Lens', Iso, Setter or Traversal by subtracting a value.

>>> execState (do _1 -= c; _2 -= d) (a,b)
(a - c,b - d)

(-=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
(-=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
(-=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
(-=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()

(*=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m () infix 4 #

Modify the target(s) of a Lens', Iso, Setter or Traversal by multiplying by value.

>>> execState (do _1 *= c; _2 *= d) (a,b)
(a * c,b * d)

(*=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
(*=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
(*=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
(*=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()

(//=) :: (MonadState s m, Fractional a) => ASetter' s a -> a -> m () infix 4 #

Modify the target(s) of a Lens', Iso, Setter or Traversal by dividing by a value.

>>> execState (do _1 //= c; _2 //= d) (a,b)
(a / c,b / d)

(//=) :: (MonadState s m, Fractional a) => Setter' s a    -> a -> m ()
(//=) :: (MonadState s m, Fractional a) => Iso' s a       -> a -> m ()
(//=) :: (MonadState s m, Fractional a) => Lens' s a      -> a -> m ()
(//=) :: (MonadState s m, Fractional a) => Traversal' s a -> a -> m ()

(^=) :: (MonadState s m, Num a, Integral e) => ASetter' s a -> e -> m () infix 4 #

Raise the target(s) of a numerically valued Lens, Setter or Traversal to a non-negative integral power.

(^=) ::  (MonadState s m, Num a, Integral e) => Setter' s a    -> e -> m ()
(^=) ::  (MonadState s m, Num a, Integral e) => Iso' s a       -> e -> m ()
(^=) ::  (MonadState s m, Num a, Integral e) => Lens' s a      -> e -> m ()
(^=) ::  (MonadState s m, Num a, Integral e) => Traversal' s a -> e -> m ()

(^^=) :: (MonadState s m, Fractional a, Integral e) => ASetter' s a -> e -> m () infix 4 #

Raise the target(s) of a numerically valued Lens, Setter or Traversal to an integral power.

(^^=) ::  (MonadState s m, Fractional a, Integral e) => Setter' s a    -> e -> m ()
(^^=) ::  (MonadState s m, Fractional a, Integral e) => Iso' s a       -> e -> m ()
(^^=) ::  (MonadState s m, Fractional a, Integral e) => Lens' s a      -> e -> m ()
(^^=) ::  (MonadState s m, Fractional a, Integral e) => Traversal' s a -> e -> m ()

(**=) :: (MonadState s m, Floating a) => ASetter' s a -> a -> m () infix 4 #

Raise the target(s) of a numerically valued Lens, Setter or Traversal to an arbitrary power

>>> execState (do _1 **= c; _2 **= d) (a,b)
(a**c,b**d)

(**=) ::  (MonadState s m, Floating a) => Setter' s a    -> a -> m ()
(**=) ::  (MonadState s m, Floating a) => Iso' s a       -> a -> m ()
(**=) ::  (MonadState s m, Floating a) => Lens' s a      -> a -> m ()
(**=) ::  (MonadState s m, Floating a) => Traversal' s a -> a -> m ()

(&&=) :: MonadState s m => ASetter' s Bool -> Bool -> m () infix 4 #

Modify the target(s) of a Lens', Iso, Setter or Traversal by taking their logical && with a value.

>>> execState (do _1 &&= True; _2 &&= False; _3 &&= True; _4 &&= False) (True,True,False,False)
(True,False,False,False)

(&&=) :: MonadState s m => Setter' s Bool    -> Bool -> m ()
(&&=) :: MonadState s m => Iso' s Bool       -> Bool -> m ()
(&&=) :: MonadState s m => Lens' s Bool      -> Bool -> m ()
(&&=) :: MonadState s m => Traversal' s Bool -> Bool -> m ()

(||=) :: MonadState s m => ASetter' s Bool -> Bool -> m () infix 4 #

Modify the target(s) of a Lens', 'Iso, Setter or Traversal by taking their logical || with a value.

>>> execState (do _1 ||= True; _2 ||= False; _3 ||= True; _4 ||= False) (True,True,False,False)
(True,True,True,False)

(||=) :: MonadState s m => Setter' s Bool    -> Bool -> m ()
(||=) :: MonadState s m => Iso' s Bool       -> Bool -> m ()
(||=) :: MonadState s m => Lens' s Bool      -> Bool -> m ()
(||=) :: MonadState s m => Traversal' s Bool -> Bool -> m ()

(<~) :: MonadState s m => ASetter s s a b -> m b -> m () infixr 2 #

Run a monadic action, and set all of the targets of a Lens, Setter or Traversal to its result.

(<~) :: MonadState s m => Iso s s a b       -> m b -> m ()
(<~) :: MonadState s m => Lens s s a b      -> m b -> m ()
(<~) :: MonadState s m => Traversal s s a b -> m b -> m ()
(<~) :: MonadState s m => Setter s s a b    -> m b -> m ()

As a reasonable mnemonic, this lets you store the result of a monadic action in a Lens rather than in a local variable.

do foo <- bar
   ...

will store the result in a variable, while

do foo <~ bar
   ...

will store the result in a Lens, Setter, or Traversal.

(<.=) :: MonadState s m => ASetter s s a b -> b -> m b infix 4 #

Set with pass-through

This is useful for chaining assignment without round-tripping through your Monad stack.

do x <- _2 <.= ninety_nine_bottles_of_beer_on_the_wall

If you do not need a copy of the intermediate result, then using l .= d will avoid unused binding warnings.

(<.=) :: MonadState s m => Setter s s a b    -> b -> m b
(<.=) :: MonadState s m => Iso s s a b       -> b -> m b
(<.=) :: MonadState s m => Lens s s a b      -> b -> m b
(<.=) :: MonadState s m => Traversal s s a b -> b -> m b

(<?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m b infix 4 #

Set Just a value with pass-through

This is useful for chaining assignment without round-tripping through your Monad stack.

do x <- at "foo" <?= ninety_nine_bottles_of_beer_on_the_wall

If you do not need a copy of the intermediate result, then using l ?= d will avoid unused binding warnings.

(<?=) :: MonadState s m => Setter s s a (Maybe b)    -> b -> m b
(<?=) :: MonadState s m => Iso s s a (Maybe b)       -> b -> m b
(<?=) :: MonadState s m => Lens s s a (Maybe b)      -> b -> m b
(<?=) :: MonadState s m => Traversal s s a (Maybe b) -> b -> m b

(<>~) :: Monoid a => ASetter s t a a -> a -> s -> t infixr 4 #

Modify the target of a monoidally valued by mappending another value.

>>> (Sum a,b) & _1 <>~ Sum c
(Sum {getSum = a + c},b)

>>> (Sum a,Sum b) & both <>~ Sum c
(Sum {getSum = a + c},Sum {getSum = b + c})

>>> both <>~ "!!!" $ ("hello","world")
("hello!!!","world!!!")

(<>~) :: Monoid a => Setter s t a a    -> a -> s -> t
(<>~) :: Monoid a => Iso s t a a       -> a -> s -> t
(<>~) :: Monoid a => Lens s t a a      -> a -> s -> t
(<>~) :: Monoid a => Traversal s t a a -> a -> s -> t

(<>=) :: (MonadState s m, Monoid a) => ASetter' s a -> a -> m () infix 4 #

Modify the target(s) of a Lens', Iso, Setter or Traversal by mappending a value.

>>> execState (do _1 <>= Sum c; _2 <>= Product d) (Sum a,Product b)
(Sum {getSum = a + c},Product {getProduct = b * d})

>>> execState (both <>= "!!!") ("hello","world")
("hello!!!","world!!!")

(<>=) :: (MonadState s m, Monoid a) => Setter' s a -> a -> m ()
(<>=) :: (MonadState s m, Monoid a) => Iso' s a -> a -> m ()
(<>=) :: (MonadState s m, Monoid a) => Lens' s a -> a -> m ()
(<>=) :: (MonadState s m, Monoid a) => Traversal' s a -> a -> m ()

scribe :: (MonadWriter t m, Monoid s) => ASetter s t a b -> b -> m () #

Write to a fragment of a larger Writer format.

passing :: MonadWriter w m => Setter w w u v -> m (a, u -> v) -> m a #

This is a generalization of pass that allows you to modify just a portion of the resulting MonadWriter.

ipassing :: MonadWriter w m => IndexedSetter i w w u v -> m (a, i -> u -> v) -> m a #

This is a generalization of pass that allows you to modify just a portion of the resulting MonadWriter with access to the index of an IndexedSetter.

censoring :: MonadWriter w m => Setter w w u v -> (u -> v) -> m a -> m a #

This is a generalization of censor that allows you to censor just a portion of the resulting MonadWriter.

icensoring :: MonadWriter w m => IndexedSetter i w w u v -> (i -> u -> v) -> m a -> m a #

This is a generalization of censor that allows you to censor just a portion of the resulting MonadWriter, with access to the index of an IndexedSetter.

locally :: MonadReader s m => ASetter s s a b -> (a -> b) -> m r -> m r #

Modify the value of the Reader environment associated with the target of a Setter, Lens, or Traversal.

locally l id a ≡ a
locally l f . locally l g ≡ locally l (f . g)

>>> (1,1) & locally _1 (+1) (uncurry (+))
3

>>> "," & locally ($) ("Hello" <>) (<> " world!")
"Hello, world!"

locally :: MonadReader s m => Iso s s a b       -> (a -> b) -> m r -> m r
locally :: MonadReader s m => Lens s s a b      -> (a -> b) -> m r -> m r
locally :: MonadReader s m => Traversal s s a b -> (a -> b) -> m r -> m r
locally :: MonadReader s m => Setter s s a b    -> (a -> b) -> m r -> m r

ilocally :: MonadReader s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m r -> m r #

This is a generalization of locally that allows one to make indexed local changes to a Reader environment associated with the target of a Setter, Lens, or Traversal.

locally l f ≡ ilocally l f . const
ilocally l f ≡ locally l f . Indexed

ilocally :: MonadReader s m => IndexedLens s s a b      -> (i -> a -> b) -> m r -> m r
ilocally :: MonadReader s m => IndexedTraversal s s a b -> (i -> a -> b) -> m r -> m r
ilocally :: MonadReader s m => IndexedSetter s s a b    -> (i -> a -> b) -> m r -> m r

iover :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t #

Map with index. This is an alias for imapOf.

When you do not need access to the index, then over is more liberal in what it can accept.

over l ≡ iover l . const
iover l ≡ over l . Indexed

iover :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
iover :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
iover :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t

iset :: AnIndexedSetter i s t a b -> (i -> b) -> s -> t #

Set with index. Equivalent to iover with the current value ignored.

When you do not need access to the index, then set is more liberal in what it can accept.

set l ≡ iset l . const

iset :: IndexedSetter i s t a b    -> (i -> b) -> s -> t
iset :: IndexedLens i s t a b      -> (i -> b) -> s -> t
iset :: IndexedTraversal i s t a b -> (i -> b) -> s -> t

isets :: ((i -> a -> b) -> s -> t) -> IndexedSetter i s t a b #

Build an IndexedSetter from an imap-like function.

Your supplied function f is required to satisfy:

f id ≡ id
f g . f h ≡ f (g . h)

Equational reasoning:

isets . iover ≡ id
iover . isets ≡ id

Another way to view isets is that it takes a "semantic editor combinator" which has been modified to carry an index and transforms it into a IndexedSetter.

(%@~) :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t infixr 4 #

Adjust every target of an IndexedSetter, IndexedLens or IndexedTraversal with access to the index.

(%@~) ≡ iover

When you do not need access to the index then (%~) is more liberal in what it can accept.

l %~ f ≡ l %@~ const f

(%@~) :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
(%@~) :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
(%@~) :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t

(.@~) :: AnIndexedSetter i s t a b -> (i -> b) -> s -> t infixr 4 #

Replace every target of an IndexedSetter, IndexedLens or IndexedTraversal with access to the index.

(.@~) ≡ iset

When you do not need access to the index then (.~) is more liberal in what it can accept.

l .~ b ≡ l .@~ const b

(.@~) :: IndexedSetter i s t a b    -> (i -> b) -> s -> t
(.@~) :: IndexedLens i s t a b      -> (i -> b) -> s -> t
(.@~) :: IndexedTraversal i s t a b -> (i -> b) -> s -> t

(%@=) :: MonadState s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m () infix 4 #

Adjust every target in the current state of an IndexedSetter, IndexedLens or IndexedTraversal with access to the index.

When you do not need access to the index then (%=) is more liberal in what it can accept.

l %= f ≡ l %@= const f

(%@=) :: MonadState s m => IndexedSetter i s s a b    -> (i -> a -> b) -> m ()
(%@=) :: MonadState s m => IndexedLens i s s a b      -> (i -> a -> b) -> m ()
(%@=) :: MonadState s m => IndexedTraversal i s t a b -> (i -> a -> b) -> m ()

imodifying :: MonadState s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m () #

This is an alias for (%@=).

(.@=) :: MonadState s m => AnIndexedSetter i s s a b -> (i -> b) -> m () infix 4 #

Replace every target in the current state of an IndexedSetter, IndexedLens or IndexedTraversal with access to the index.

When you do not need access to the index then (.=) is more liberal in what it can accept.

l .= b ≡ l .@= const b

(.@=) :: MonadState s m => IndexedSetter i s s a b    -> (i -> b) -> m ()
(.@=) :: MonadState s m => IndexedLens i s s a b      -> (i -> b) -> m ()
(.@=) :: MonadState s m => IndexedTraversal i s t a b -> (i -> b) -> m ()

assignA :: Arrow p => ASetter s t a b -> p s b -> p s t #

Run an arrow command and use the output to set all the targets of a Lens, Setter or Traversal to the result.

assignA can be used very similarly to (<~), except that the type of the object being modified can change; for example:

runKleisli action ((), (), ()) where
  action =      assignA _1 (Kleisli (const getVal1))
           >>> assignA _2 (Kleisli (const getVal2))
           >>> assignA _3 (Kleisli (const getVal3))
  getVal1 :: Either String Int
  getVal1 = ...
  getVal2 :: Either String Bool
  getVal2 = ...
  getVal3 :: Either String Char
  getVal3 = ...

has the type Either String (Int, Bool, Char)

assignA :: Arrow p => Iso s t a b       -> p s b -> p s t
assignA :: Arrow p => Lens s t a b      -> p s b -> p s t
assignA :: Arrow p => Traversal s t a b -> p s b -> p s t
assignA :: Arrow p => Setter s t a b    -> p s b -> p s t

mapOf :: ASetter s t a b -> (a -> b) -> s -> t #

mapOf is a deprecated alias for over.

imapOf :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t #

Map with index. (Deprecated alias for iover).

When you do not need access to the index, then mapOf is more liberal in what it can accept.

mapOf l ≡ imapOf l . const

imapOf :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
imapOf :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
imapOf :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t

type AnIndexedLens' i s a = AnIndexedLens i s s a a #

type AnIndexedLens' = Simple (AnIndexedLens i)

type AnIndexedLens i s t a b = Optical (Indexed i) ((->) :: Type -> Type -> Type) (Pretext (Indexed i) a b) s t a b #

When you see this as an argument to a function, it expects an IndexedLens

type ALens' s a = ALens s s a a #

type ALens' = Simple ALens

type ALens s t a b = LensLike (Pretext ((->) :: Type -> Type -> Type) a b) s t a b #

When you see this as an argument to a function, it expects a Lens.

This type can also be used when you need to store a Lens in a container, since it is rank-1. You can turn them back into a Lens with cloneLens, or use it directly with combinators like storing and (^#).

lens :: (s -> a) -> (s -> b -> t) -> Lens s t a b #

Build a Lens from a getter and a setter.

lens :: Functor f => (s -> a) -> (s -> b -> t) -> (a -> f b) -> s -> f t

>>> s ^. lens getter setter
getter s

>>> s & lens getter setter .~ b
setter s b

>>> s & lens getter setter %~ f
setter s (f (getter s))

lens :: (s -> a) -> (s -> a -> s) -> Lens' s a

iplens :: (s -> a) -> (s -> b -> t) -> IndexPreservingLens s t a b #

Build an index-preserving Lens from a Getter and a Setter.

ilens :: (s -> (i, a)) -> (s -> b -> t) -> IndexedLens i s t a b #

Build an IndexedLens from a Getter and a Setter.

(&~) :: s -> State s a -> s infixl 1 #

This can be used to chain lens operations using op= syntax rather than op~ syntax for simple non-type-changing cases.

>>> (10,20) & _1 .~ 30 & _2 .~ 40
(30,40)

>>> (10,20) &~ do _1 .= 30; _2 .= 40
(30,40)

This does not support type-changing assignment, e.g.

>>> (10,20) & _1 .~ "hello"
("hello",20)

(%%~) :: LensLike f s t a b -> (a -> f b) -> s -> f t infixr 4 #

(%%~) can be used in one of two scenarios:

When applied to a Lens, it can edit the target of the Lens in a structure, extracting a functorial result.

When applied to a Traversal, it can edit the targets of the traversals, extracting an applicative summary of its actions.

>>> [66,97,116,109,97,110] & each %%~ \a -> ("na", chr a)
("nananananana","Batman")

For all that the definition of this combinator is just:

(%%~) ≡ id

It may be beneficial to think about it as if it had these even more restricted types, however:

(%%~) :: Functor f =>     Iso s t a b       -> (a -> f b) -> s -> f t
(%%~) :: Functor f =>     Lens s t a b      -> (a -> f b) -> s -> f t
(%%~) :: Applicative f => Traversal s t a b -> (a -> f b) -> s -> f t

When applied to a Traversal, it can edit the targets of the traversals, extracting a supplemental monoidal summary of its actions, by choosing f = ((,) m)

(%%~) ::             Iso s t a b       -> (a -> (r, b)) -> s -> (r, t)
(%%~) ::             Lens s t a b      -> (a -> (r, b)) -> s -> (r, t)
(%%~) :: Monoid m => Traversal s t a b -> (a -> (m, b)) -> s -> (m, t)

(%%=) :: MonadState s m => Over p ((,) r) s s a b -> p a (r, b) -> m r infix 4 #

Modify the target of a Lens in the current state returning some extra information of type r or modify all targets of a Traversal in the current state, extracting extra information of type r and return a monoidal summary of the changes.

>>> runState (_1 %%= \x -> (f x, g x)) (a,b)
(f a,(g a,b))

(%%=) ≡ (state .)

It may be useful to think of (%%=), instead, as having either of the following more restricted type signatures:

(%%=) :: MonadState s m             => Iso s s a b       -> (a -> (r, b)) -> m r
(%%=) :: MonadState s m             => Lens s s a b      -> (a -> (r, b)) -> m r
(%%=) :: (MonadState s m, Monoid r) => Traversal s s a b -> (a -> (r, b)) -> m r

(??) :: Functor f => f (a -> b) -> a -> f b infixl 1 #

This is convenient to flip argument order of composite functions defined as:

fab ?? a = fmap ($ a) fab

For the Functor instance f = ((->) r) you can reason about this function as if the definition was (??) ≡ flip:

>>> (h ?? x) a
h a x

>>> execState ?? [] $ modify (1:)
[1]

>>> over _2 ?? ("hello","world") $ length
("hello",5)

>>> over ?? length ?? ("hello","world") $ _2
("hello",5)

choosing :: Functor f => LensLike f s t a b -> LensLike f s' t' a b -> LensLike f (Either s s') (Either t t') a b #

Merge two lenses, getters, setters, folds or traversals.

chosen ≡ choosing id id

choosing :: Getter s a     -> Getter s' a     -> Getter (Either s s') a
choosing :: Fold s a       -> Fold s' a       -> Fold (Either s s') a
choosing :: Lens' s a      -> Lens' s' a      -> Lens' (Either s s') a
choosing :: Traversal' s a -> Traversal' s' a -> Traversal' (Either s s') a
choosing :: Setter' s a    -> Setter' s' a    -> Setter' (Either s s') a

chosen :: IndexPreservingLens (Either a a) (Either b b) a b #

This is a Lens that updates either side of an Either, where both sides have the same type.

chosen ≡ choosing id id

>>> Left a^.chosen
a

>>> Right a^.chosen
a

>>> Right "hello"^.chosen
"hello"

>>> Right a & chosen *~ b
Right (a * b)

chosen :: Lens (Either a a) (Either b b) a b
chosen f (Left a)  = Left <$> f a
chosen f (Right a) = Right <$> f a

alongside :: LensLike (AlongsideLeft f b') s t a b -> LensLike (AlongsideRight f t) s' t' a' b' -> LensLike f (s, s') (t, t') (a, a') (b, b') #

alongside makes a Lens from two other lenses or a Getter from two other getters by executing them on their respective halves of a product.

>>> (Left a, Right b)^.alongside chosen chosen
(a,b)

>>> (Left a, Right b) & alongside chosen chosen .~ (c,d)
(Left c,Right d)

alongside :: Lens   s t a b -> Lens   s' t' a' b' -> Lens   (s,s') (t,t') (a,a') (b,b')
alongside :: Getter s   a   -> Getter s'    a'    -> Getter (s,s')        (a,a')

locus :: IndexedComonadStore p => Lens (p a c s) (p b c s) a b #

This Lens lets you view the current pos of any indexed store comonad and seek to a new position. This reduces the API for working these instances to a single Lens.

ipos w ≡ w ^. locus
iseek s w ≡ w & locus .~ s
iseeks f w ≡ w & locus %~ f

locus :: Lens' (Context' a s) a
locus :: Conjoined p => Lens' (Pretext' p a s) a
locus :: Conjoined p => Lens' (PretextT' p g a s) a

cloneLens :: ALens s t a b -> Lens s t a b #

Cloning a Lens is one way to make sure you aren't given something weaker, such as a Traversal and can be used as a way to pass around lenses that have to be monomorphic in f.

Note: This only accepts a proper Lens.

>>> let example l x = set (cloneLens l) (x^.cloneLens l + 1) x in example _2 ("hello",1,"you")
("hello",2,"you")

cloneIndexPreservingLens :: ALens s t a b -> IndexPreservingLens s t a b #

Clone a Lens as an IndexedPreservingLens that just passes through whatever index is on any IndexedLens, IndexedFold, IndexedGetter or IndexedTraversal it is composed with.

cloneIndexedLens :: AnIndexedLens i s t a b -> IndexedLens i s t a b #

Clone an IndexedLens as an IndexedLens with the same index.

(<%~) :: LensLike ((,) b) s t a b -> (a -> b) -> s -> (b, t) infixr 4 #

Modify the target of a Lens and return the result.

When you do not need the result of the operation, (%~) is more flexible.

(<%~) ::             Lens s t a b      -> (a -> b) -> s -> (b, t)
(<%~) ::             Iso s t a b       -> (a -> b) -> s -> (b, t)
(<%~) :: Monoid b => Traversal s t a b -> (a -> b) -> s -> (b, t)

(<+~) :: Num a => LensLike ((,) a) s t a a -> a -> s -> (a, t) infixr 4 #

Increment the target of a numerically valued Lens and return the result.

When you do not need the result of the addition, (+~) is more flexible.

(<+~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<+~) :: Num a => Iso' s a  -> a -> s -> (a, s)

(<-~) :: Num a => LensLike ((,) a) s t a a -> a -> s -> (a, t) infixr 4 #

Decrement the target of a numerically valued Lens and return the result.

When you do not need the result of the subtraction, (-~) is more flexible.

(<-~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<-~) :: Num a => Iso' s a  -> a -> s -> (a, s)

(<*~) :: Num a => LensLike ((,) a) s t a a -> a -> s -> (a, t) infixr 4 #

Multiply the target of a numerically valued Lens and return the result.

When you do not need the result of the multiplication, (*~) is more flexible.

(<*~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<*~) :: Num a => Iso'  s a -> a -> s -> (a, s)

(<//~) :: Fractional a => LensLike ((,) a) s t a a -> a -> s -> (a, t) infixr 4 #

Divide the target of a fractionally valued Lens and return the result.

When you do not need the result of the division, (//~) is more flexible.

(<//~) :: Fractional a => Lens' s a -> a -> s -> (a, s)
(<//~) :: Fractional a => Iso'  s a -> a -> s -> (a, s)

(<^~) :: (Num a, Integral e) => LensLike ((,) a) s t a a -> e -> s -> (a, t) infixr 4 #

Raise the target of a numerically valued Lens to a non-negative Integral power and return the result.

When you do not need the result of the operation, (^~) is more flexible.

(<^~) :: (Num a, Integral e) => Lens' s a -> e -> s -> (a, s)
(<^~) :: (Num a, Integral e) => Iso' s a -> e -> s -> (a, s)

(<^^~) :: (Fractional a, Integral e) => LensLike ((,) a) s t a a -> e -> s -> (a, t) infixr 4 #

Raise the target of a fractionally valued Lens to an Integral power and return the result.

When you do not need the result of the operation, (^^~) is more flexible.

(<^^~) :: (Fractional a, Integral e) => Lens' s a -> e -> s -> (a, s)
(<^^~) :: (Fractional a, Integral e) => Iso' s a -> e -> s -> (a, s)

(<**~) :: Floating a => LensLike ((,) a) s t a a -> a -> s -> (a, t) infixr 4 #

Raise the target of a floating-point valued Lens to an arbitrary power and return the result.

When you do not need the result of the operation, (**~) is more flexible.

(<**~) :: Floating a => Lens' s a -> a -> s -> (a, s)
(<**~) :: Floating a => Iso' s a  -> a -> s -> (a, s)

(<||~) :: LensLike ((,) Bool) s t Bool Bool -> Bool -> s -> (Bool, t) infixr 4 #

Logically || a Boolean valued Lens and return the result.

When you do not need the result of the operation, (||~) is more flexible.

(<||~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
(<||~) :: Iso' s Bool  -> Bool -> s -> (Bool, s)

(<&&~) :: LensLike ((,) Bool) s t Bool Bool -> Bool -> s -> (Bool, t) infixr 4 #

Logically && a Boolean valued Lens and return the result.

When you do not need the result of the operation, (&&~) is more flexible.

(<&&~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
(<&&~) :: Iso' s Bool  -> Bool -> s -> (Bool, s)

(<<%~) :: LensLike ((,) a) s t a b -> (a -> b) -> s -> (a, t) infixr 4 #

Modify the target of a Lens, but return the old value.

When you do not need the old value, (%~) is more flexible.

(<<%~) ::             Lens s t a b      -> (a -> b) -> s -> (a, t)
(<<%~) ::             Iso s t a b       -> (a -> b) -> s -> (a, t)
(<<%~) :: Monoid a => Traversal s t a b -> (a -> b) -> s -> (a, t)

(<<.~) :: LensLike ((,) a) s t a b -> b -> s -> (a, t) infixr 4 #

Replace the target of a Lens, but return the old value.

When you do not need the old value, (.~) is more flexible.

(<<.~) ::             Lens s t a b      -> b -> s -> (a, t)
(<<.~) ::             Iso s t a b       -> b -> s -> (a, t)
(<<.~) :: Monoid a => Traversal s t a b -> b -> s -> (a, t)

(<<?~) :: LensLike ((,) a) s t a (Maybe b) -> b -> s -> (a, t) infixr 4 #

Replace the target of a Lens with a Just value, but return the old value.

If you do not need the old value (?~) is more flexible.

>>> import Data.Map as Map
>>> _2.at "hello" <<?~ "world" $ (42,Map.fromList [("goodnight","gracie")])
(Nothing,(42,fromList [("goodnight","gracie"),("hello","world")]))

(<<?~) :: Iso s t a (Maybe b)       -> b -> s -> (a, t)
(<<?~) :: Lens s t a (Maybe b)      -> b -> s -> (a, t)
(<<?~) :: Traversal s t a (Maybe b) -> b -> s -> (a, t)

(<<+~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s) infixr 4 #

Increment the target of a numerically valued Lens and return the old value.

When you do not need the old value, (+~) is more flexible.

>>> (a,b) & _1 <<+~ c
(a,(a + c,b))

>>> (a,b) & _2 <<+~ c
(b,(a,b + c))

(<<+~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<<+~) :: Num a => Iso' s a -> a -> s -> (a, s)

(<<-~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s) infixr 4 #

Decrement the target of a numerically valued Lens and return the old value.

When you do not need the old value, (-~) is more flexible.

>>> (a,b) & _1 <<-~ c
(a,(a - c,b))

>>> (a,b) & _2 <<-~ c
(b,(a,b - c))

(<<-~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<<-~) :: Num a => Iso' s a -> a -> s -> (a, s)

(<<*~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s) infixr 4 #

Multiply the target of a numerically valued Lens and return the old value.

When you do not need the old value, (-~) is more flexible.

>>> (a,b) & _1 <<*~ c
(a,(a * c,b))

>>> (a,b) & _2 <<*~ c
(b,(a,b * c))

(<<*~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<<*~) :: Num a => Iso' s a -> a -> s -> (a, s)

(<<//~) :: Fractional a => LensLike' ((,) a) s a -> a -> s -> (a, s) infixr 4 #

Divide the target of a numerically valued Lens and return the old value.

When you do not need the old value, (//~) is more flexible.

>>> (a,b) & _1 <<//~ c
(a,(a / c,b))

>>> ("Hawaii",10) & _2 <<//~ 2
(10.0,("Hawaii",5.0))

(<<//~) :: Fractional a => Lens' s a -> a -> s -> (a, s)
(<<//~) :: Fractional a => Iso' s a -> a -> s -> (a, s)

(<<^~) :: (Num a, Integral e) => LensLike' ((,) a) s a -> e -> s -> (a, s) infixr 4 #

Raise the target of a numerically valued Lens to a non-negative power and return the old value.

When you do not need the old value, (^~) is more flexible.

(<<^~) :: (Num a, Integral e) => Lens' s a -> e -> s -> (a, s)
(<<^~) :: (Num a, Integral e) => Iso' s a -> e -> s -> (a, s)

(<<^^~) :: (Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> s -> (a, s) infixr 4 #

Raise the target of a fractionally valued Lens to an integral power and return the old value.

When you do not need the old value, (^^~) is more flexible.

(<<^^~) :: (Fractional a, Integral e) => Lens' s a -> e -> s -> (a, s)
(<<^^~) :: (Fractional a, Integral e) => Iso' s a -> e -> S -> (a, s)

(<<**~) :: Floating a => LensLike' ((,) a) s a -> a -> s -> (a, s) infixr 4 #

Raise the target of a floating-point valued Lens to an arbitrary power and return the old value.

When you do not need the old value, (**~) is more flexible.

>>> (a,b) & _1 <<**~ c
(a,(a**c,b))

>>> (a,b) & _2 <<**~ c
(b,(a,b**c))

(<<**~) :: Floating a => Lens' s a -> a -> s -> (a, s)
(<<**~) :: Floating a => Iso' s a -> a -> s -> (a, s)

(<<||~) :: LensLike' ((,) Bool) s Bool -> Bool -> s -> (Bool, s) infixr 4 #

Logically || the target of a Bool-valued Lens and return the old value.

When you do not need the old value, (||~) is more flexible.

>>> (False,6) & _1 <<||~ True
(False,(True,6))

>>> ("hello",True) & _2 <<||~ False
(True,("hello",True))

(<<||~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
(<<||~) :: Iso' s Bool -> Bool -> s -> (Bool, s)

(<<&&~) :: LensLike' ((,) Bool) s Bool -> Bool -> s -> (Bool, s) infixr 4 #

Logically && the target of a Bool-valued Lens and return the old value.

When you do not need the old value, (&&~) is more flexible.

>>> (False,6) & _1 <<&&~ True
(False,(False,6))

>>> ("hello",True) & _2 <<&&~ False
(True,("hello",False))

(<<&&~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
(<<&&~) :: Iso' s Bool -> Bool -> s -> (Bool, s)

(<<<>~) :: Monoid r => LensLike' ((,) r) s r -> r -> s -> (r, s) infixr 4 #

Modify the target of a monoidally valued Lens by mappending a new value and return the old value.

When you do not need the old value, (<>~) is more flexible.

>>> (Sum a,b) & _1 <<<>~ Sum c
(Sum {getSum = a},(Sum {getSum = a + c},b))

>>> _2 <<<>~ ", 007" $ ("James", "Bond")
("Bond",("James","Bond, 007"))

(<<<>~) :: Monoid r => Lens' s r -> r -> s -> (r, s)
(<<<>~) :: Monoid r => Iso' s r -> r -> s -> (r, s)

(<%=) :: MonadState s m => LensLike ((,) b) s s a b -> (a -> b) -> m b infix 4 #

Modify the target of a Lens into your Monad's state by a user supplied function and return the result.

When applied to a Traversal, it this will return a monoidal summary of all of the intermediate results.

When you do not need the result of the operation, (%=) is more flexible.

(<%=) :: MonadState s m             => Lens' s a      -> (a -> a) -> m a
(<%=) :: MonadState s m             => Iso' s a       -> (a -> a) -> m a
(<%=) :: (MonadState s m, Monoid a) => Traversal' s a -> (a -> a) -> m a

(<+=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Add to the target of a numerically valued Lens into your Monad's state and return the result.

When you do not need the result of the addition, (+=) is more flexible.

(<+=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<+=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a

(<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Subtract from the target of a numerically valued Lens into your Monad's state and return the result.

When you do not need the result of the subtraction, (-=) is more flexible.

(<-=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<-=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a

(<*=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Multiply the target of a numerically valued Lens into your Monad's state and return the result.

When you do not need the result of the multiplication, (*=) is more flexible.

(<*=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<*=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a

(<//=) :: (MonadState s m, Fractional a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Divide the target of a fractionally valued Lens into your Monad's state and return the result.

When you do not need the result of the division, (//=) is more flexible.

(<//=) :: (MonadState s m, Fractional a) => Lens' s a -> a -> m a
(<//=) :: (MonadState s m, Fractional a) => Iso' s a -> a -> m a

(<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a infix 4 #

Raise the target of a numerically valued Lens into your Monad's state to a non-negative Integral power and return the result.

When you do not need the result of the operation, (^=) is more flexible.

(<^=) :: (MonadState s m, Num a, Integral e) => Lens' s a -> e -> m a
(<^=) :: (MonadState s m, Num a, Integral e) => Iso' s a -> e -> m a

(<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a infix 4 #

Raise the target of a fractionally valued Lens into your Monad's state to an Integral power and return the result.

When you do not need the result of the operation, (^^=) is more flexible.

(<^^=) :: (MonadState s m, Fractional b, Integral e) => Lens' s a -> e -> m a
(<^^=) :: (MonadState s m, Fractional b, Integral e) => Iso' s a  -> e -> m a

(<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Raise the target of a floating-point valued Lens into your Monad's state to an arbitrary power and return the result.

When you do not need the result of the operation, (**=) is more flexible.

(<**=) :: (MonadState s m, Floating a) => Lens' s a -> a -> m a
(<**=) :: (MonadState s m, Floating a) => Iso' s a -> a -> m a

(<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool infix 4 #

Logically || a Boolean valued Lens into your Monad's state and return the result.

When you do not need the result of the operation, (||=) is more flexible.

(<||=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
(<||=) :: MonadState s m => Iso' s Bool  -> Bool -> m Bool

(<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool infix 4 #

Logically && a Boolean valued Lens into your Monad's state and return the result.

When you do not need the result of the operation, (&&=) is more flexible.

(<&&=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
(<&&=) :: MonadState s m => Iso' s Bool  -> Bool -> m Bool

(<<%=) :: (Strong p, MonadState s m) => Over p ((,) a) s s a b -> p a b -> m a infix 4 #

Modify the target of a Lens into your Monad's state by a user supplied function and return the old value that was replaced.

When applied to a Traversal, this will return a monoidal summary of all of the old values present.

When you do not need the result of the operation, (%=) is more flexible.

(<<%=) :: MonadState s m             => Lens' s a      -> (a -> a) -> m a
(<<%=) :: MonadState s m             => Iso' s a       -> (a -> a) -> m a
(<<%=) :: (MonadState s m, Monoid a) => Traversal' s a -> (a -> a) -> m a

(<<%=) :: MonadState s m => LensLike ((,)a) s s a b -> (a -> b) -> m a

(<<.=) :: MonadState s m => LensLike ((,) a) s s a b -> b -> m a infix 4 #

Replace the target of a Lens into your Monad's state with a user supplied value and return the old value that was replaced.

When applied to a Traversal, this will return a monoidal summary of all of the old values present.

When you do not need the result of the operation, (.=) is more flexible.

(<<.=) :: MonadState s m             => Lens' s a      -> a -> m a
(<<.=) :: MonadState s m             => Iso' s a       -> a -> m a
(<<.=) :: (MonadState s m, Monoid a) => Traversal' s a -> a -> m a

(<<?=) :: MonadState s m => LensLike ((,) a) s s a (Maybe b) -> b -> m a infix 4 #

Replace the target of a Lens into your Monad's state with Just a user supplied value and return the old value that was replaced.

When applied to a Traversal, this will return a monoidal summary of all of the old values present.

When you do not need the result of the operation, (?=) is more flexible.

(<<?=) :: MonadState s m             => Lens s t a (Maybe b)      -> b -> m a
(<<?=) :: MonadState s m             => Iso s t a (Maybe b)       -> b -> m a
(<<?=) :: (MonadState s m, Monoid a) => Traversal s t a (Maybe b) -> b -> m a

(<<+=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Modify the target of a Lens into your Monad's state by adding a value and return the old value that was replaced.

When you do not need the result of the operation, (+=) is more flexible.

(<<+=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<<+=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a

(<<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Modify the target of a Lens into your Monad's state by subtracting a value and return the old value that was replaced.

When you do not need the result of the operation, (-=) is more flexible.

(<<-=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<<-=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a

(<<*=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Modify the target of a Lens into your Monad's state by multipling a value and return the old value that was replaced.

When you do not need the result of the operation, (*=) is more flexible.

(<<*=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<<*=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a

(<<//=) :: (MonadState s m, Fractional a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Modify the target of a Lens into your Monads state by dividing by a value and return the old value that was replaced.

When you do not need the result of the operation, (//=) is more flexible.

(<<//=) :: (MonadState s m, Fractional a) => Lens' s a -> a -> m a
(<<//=) :: (MonadState s m, Fractional a) => Iso' s a -> a -> m a

(<<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a infix 4 #

Modify the target of a Lens into your Monad's state by raising it by a non-negative power and return the old value that was replaced.

When you do not need the result of the operation, (^=) is more flexible.

(<<^=) :: (MonadState s m, Num a, Integral e) => Lens' s a -> e -> m a
(<<^=) :: (MonadState s m, Num a, Integral e) => Iso' s a -> a -> m a

(<<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a infix 4 #

Modify the target of a Lens into your Monad's state by raising it by an integral power and return the old value that was replaced.

When you do not need the result of the operation, (^^=) is more flexible.

(<<^^=) :: (MonadState s m, Fractional a, Integral e) => Lens' s a -> e -> m a
(<<^^=) :: (MonadState s m, Fractional a, Integral e) => Iso' s a -> e -> m a

(<<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m a infix 4 #

Modify the target of a Lens into your Monad's state by raising it by an arbitrary power and return the old value that was replaced.

When you do not need the result of the operation, (**=) is more flexible.

(<<**=) :: (MonadState s m, Floating a) => Lens' s a -> a -> m a
(<<**=) :: (MonadState s m, Floating a) => Iso' s a -> a -> m a

(<<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool infix 4 #

Modify the target of a Lens into your Monad's state by taking its logical || with a value and return the old value that was replaced.

When you do not need the result of the operation, (||=) is more flexible.

(<<||=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
(<<||=) :: MonadState s m => Iso' s Bool -> Bool -> m Bool

(<<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool infix 4 #

Modify the target of a Lens into your Monad's state by taking its logical && with a value and return the old value that was replaced.

When you do not need the result of the operation, (&&=) is more flexible.

(<<&&=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
(<<&&=) :: MonadState s m => Iso' s Bool -> Bool -> m Bool

(<<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r infix 4 #

Modify the target of a Lens into your Monad's state by mappending a value and return the old value that was replaced.

When you do not need the result of the operation, (<>=) is more flexible.

(<<<>=) :: (MonadState s m, Monoid r) => Lens' s r -> r -> m r
(<<<>=) :: (MonadState s m, Monoid r) => Iso' s r -> r -> m r

(<<~) :: MonadState s m => ALens s s a b -> m b -> m b infixr 2 #

Run a monadic action, and set the target of Lens to its result.

(<<~) :: MonadState s m => Iso s s a b   -> m b -> m b
(<<~) :: MonadState s m => Lens s s a b  -> m b -> m b

NB: This is limited to taking an actual Lens than admitting a Traversal because there are potential loss of state issues otherwise.

(<<>~) :: Monoid m => LensLike ((,) m) s t m m -> m -> s -> (m, t) infixr 4 #

mappend a monoidal value onto the end of the target of a Lens and return the result.

When you do not need the result of the operation, (<>~) is more flexible.

(<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r infix 4 #

mappend a monoidal value onto the end of the target of a Lens into your Monad's state and return the result.

When you do not need the result of the operation, (<>=) is more flexible.

overA :: Arrow ar => LensLike (Context a b) s t a b -> ar a b -> ar s t #

over for Arrows.

Unlike over, overA can't accept a simple Setter, but requires a full lens, or close enough.

>>> overA _1 ((+1) *** (+2)) ((1,2),6)
((2,4),6)

overA :: Arrow ar => Lens s t a b -> ar a b -> ar s t

(<%@~) :: Over (Indexed i) ((,) b) s t a b -> (i -> a -> b) -> s -> (b, t) infixr 4 #

Adjust the target of an IndexedLens returning the intermediate result, or adjust all of the targets of an IndexedTraversal and return a monoidal summary along with the answer.

l <%~ f ≡ l <%@~ const f

When you do not need access to the index then (<%~) is more liberal in what it can accept.

If you do not need the intermediate result, you can use (%@~) or even (%~).

(<%@~) ::             IndexedLens i s t a b      -> (i -> a -> b) -> s -> (b, t)
(<%@~) :: Monoid b => IndexedTraversal i s t a b -> (i -> a -> b) -> s -> (b, t)

(<<%@~) :: Over (Indexed i) ((,) a) s t a b -> (i -> a -> b) -> s -> (a, t) infixr 4 #

Adjust the target of an IndexedLens returning the old value, or adjust all of the targets of an IndexedTraversal and return a monoidal summary of the old values along with the answer.

(<<%@~) ::             IndexedLens i s t a b      -> (i -> a -> b) -> s -> (a, t)
(<<%@~) :: Monoid a => IndexedTraversal i s t a b -> (i -> a -> b) -> s -> (a, t)

(%%@~) :: Over (Indexed i) f s t a b -> (i -> a -> f b) -> s -> f t infixr 4 #

Adjust the target of an IndexedLens returning a supplementary result, or adjust all of the targets of an IndexedTraversal and return a monoidal summary of the supplementary results and the answer.

(%%@~) ≡ withIndex

(%%@~) :: Functor f => IndexedLens i s t a b      -> (i -> a -> f b) -> s -> f t
(%%@~) :: Applicative f => IndexedTraversal i s t a b -> (i -> a -> f b) -> s -> f t

In particular, it is often useful to think of this function as having one of these even more restricted type signatures:

(%%@~) ::             IndexedLens i s t a b      -> (i -> a -> (r, b)) -> s -> (r, t)
(%%@~) :: Monoid r => IndexedTraversal i s t a b -> (i -> a -> (r, b)) -> s -> (r, t)

(%%@=) :: MonadState s m => Over (Indexed i) ((,) r) s s a b -> (i -> a -> (r, b)) -> m r infix 4 #

Adjust the target of an IndexedLens returning a supplementary result, or adjust all of the targets of an IndexedTraversal within the current state, and return a monoidal summary of the supplementary results.

l %%@= f ≡ state (l %%@~ f)

(%%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> (r, b)) -> s -> m r
(%%@=) :: (MonadState s m, Monoid r) => IndexedTraversal i s s a b -> (i -> a -> (r, b)) -> s -> m r

(<%@=) :: MonadState s m => Over (Indexed i) ((,) b) s s a b -> (i -> a -> b) -> m b infix 4 #

Adjust the target of an IndexedLens returning the intermediate result, or adjust all of the targets of an IndexedTraversal within the current state, and return a monoidal summary of the intermediate results.

(<%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> b) -> m b
(<%@=) :: (MonadState s m, Monoid b) => IndexedTraversal i s s a b -> (i -> a -> b) -> m b

(<<%@=) :: MonadState s m => Over (Indexed i) ((,) a) s s a b -> (i -> a -> b) -> m a infix 4 #

Adjust the target of an IndexedLens returning the old value, or adjust all of the targets of an IndexedTraversal within the current state, and return a monoidal summary of the old values.

(<<%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> b) -> m a
(<<%@=) :: (MonadState s m, Monoid b) => IndexedTraversal i s s a b -> (i -> a -> b) -> m a

(^#) :: s -> ALens s t a b -> a infixl 8 #

A version of (^.) that works on ALens.

>>> ("hello","world")^#_2
"world"

storing :: ALens s t a b -> b -> s -> t #

A version of set that works on ALens.

>>> storing _2 "world" ("hello","there")
("hello","world")

(#~) :: ALens s t a b -> b -> s -> t infixr 4 #

A version of (.~) that works on ALens.

>>> ("hello","there") & _2 #~ "world"
("hello","world")

(#%~) :: ALens s t a b -> (a -> b) -> s -> t infixr 4 #

A version of (%~) that works on ALens.

>>> ("hello","world") & _2 #%~ length
("hello",5)

(#%%~) :: Functor f => ALens s t a b -> (a -> f b) -> s -> f t infixr 4 #

A version of (%%~) that works on ALens.

>>> ("hello","world") & _2 #%%~ \x -> (length x, x ++ "!")
(5,("hello","world!"))

(#=) :: MonadState s m => ALens s s a b -> b -> m () infix 4 #

A version of (.=) that works on ALens.

(#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m () infix 4 #

A version of (%=) that works on ALens.

(<#%~) :: ALens s t a b -> (a -> b) -> s -> (b, t) infixr 4 #

A version of (<%~) that works on ALens.

>>> ("hello","world") & _2 <#%~ length
(5,("hello",5))

(<#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m b infix 4 #

A version of (<%=) that works on ALens.

(#%%=) :: MonadState s m => ALens s s a b -> (a -> (r, b)) -> m r infix 4 #

A version of (%%=) that works on ALens.

(<#~) :: ALens s t a b -> b -> s -> (b, t) infixr 4 #

A version of (<.~) that works on ALens.

>>> ("hello","there") & _2 <#~ "world"
("world",("hello","world"))

(<#=) :: MonadState s m => ALens s s a b -> b -> m b infix 4 #

A version of (<.=) that works on ALens.

devoid :: Over p f Void Void a b #

There is a field for every type in the Void. Very zen.

>>> [] & mapped.devoid +~ 1
[]

>>> Nothing & mapped.devoid %~ abs
Nothing

devoid :: Lens' Void a

united :: Lens' a () #

We can always retrieve a () from any type.

>>> "hello"^.united
()

>>> "hello" & united .~ ()
"hello"

fusing :: Functor f => LensLike (Yoneda f) s t a b -> LensLike f s t a b #

Fuse a composition of lenses using Yoneda to provide fmap fusion.

In general, given a pair of lenses foo and bar

fusing (foo.bar) = foo.bar

however, foo and bar are either going to fmap internally or they are trivial.

fusing exploits the Yoneda lemma to merge these separate uses into a single fmap.

This is particularly effective when the choice of functor f is unknown at compile time or when the Lens foo.bar in the above description is recursive or complex enough to prevent inlining.

fusing :: Lens s t a b -> Lens s t a b

class Field19 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 19th field of a tuple.

Minimal complete definition

Nothing

Methods

_19 :: Lens s t a b #

Access the 19th field of a tuple.

Instances

19 <= n => Field19 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _19 :: Lens (V n a) (V n a) a a #
Field19 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s') s s'
Instance details Defined in Control.Lens.Tuple Methods _19 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s') s s' #

class Field18 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 18th field of a tuple.

Minimal complete definition

Nothing

Methods

_18 :: Lens s t a b #

Access the 18th field of a tuple.

Instances

18 <= n => Field18 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _18 :: Lens (V n a) (V n a) a a #
Field18 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r') r r'
Instance details Defined in Control.Lens.Tuple Methods _18 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r') r r' #
Field18 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r', s) r r'
Instance details Defined in Control.Lens.Tuple Methods _18 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r', s) r r' #

class Field17 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 17th field of a tuple.

Minimal complete definition

Nothing

Methods

_17 :: Lens s t a b #

Access the 17th field of a tuple.

Instances

17 <= n => Field17 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _17 :: Lens (V n a) (V n a) a a #
Field17 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q') q q'
Instance details Defined in Control.Lens.Tuple Methods _17 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q') q q' #
Field17 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q', r) q q'
Instance details Defined in Control.Lens.Tuple Methods _17 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q', r) q q' #
Field17 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q', r, s) q q'
Instance details Defined in Control.Lens.Tuple Methods _17 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q', r, s) q q' #

class Field16 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 16th field of a tuple.

Minimal complete definition

Nothing

Methods

_16 :: Lens s t a b #

Access the 16th field of a tuple.

Instances

16 <= n => Field16 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _16 :: Lens (V n a) (V n a) a a #
Field16 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p') p p'
Instance details Defined in Control.Lens.Tuple Methods _16 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p') p p' #
Field16 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q) p p'
Instance details Defined in Control.Lens.Tuple Methods _16 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q) p p' #
Field16 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q, r) p p'
Instance details Defined in Control.Lens.Tuple Methods _16 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q, r) p p' #
Field16 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q, r, s) p p'
Instance details Defined in Control.Lens.Tuple Methods _16 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p', q, r, s) p p' #

class Field15 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 15th field of a tuple.

Minimal complete definition

Nothing

Methods

_15 :: Lens s t a b #

Access the 15th field of a tuple.

Instances

15 <= n => Field15 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _15 :: Lens (V n a) (V n a) a a #
Field15 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o') o o'
Instance details Defined in Control.Lens.Tuple Methods _15 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o') o o' #
Field15 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p) o o'
Instance details Defined in Control.Lens.Tuple Methods _15 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p) o o' #
Field15 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q) o o'
Instance details Defined in Control.Lens.Tuple Methods _15 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q) o o' #
Field15 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q, r) o o'
Instance details Defined in Control.Lens.Tuple Methods _15 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q, r) o o' #
Field15 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q, r, s) o o'
Instance details Defined in Control.Lens.Tuple Methods _15 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o', p, q, r, s) o o' #

class Field14 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 14th field of a tuple.

Minimal complete definition

Nothing

Methods

_14 :: Lens s t a b #

Access the 14th field of a tuple.

Instances

14 <= n => Field14 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _14 :: Lens (V n a) (V n a) a a #
Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n') n n'
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n') n n' #
Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o) n n'
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o) n n' #
Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p) n n'
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p) n n' #
Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q) n n'
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q) n n' #
Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q, r) n n'
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q, r) n n' #
Field14 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q, r, s) n n'
Instance details Defined in Control.Lens.Tuple Methods _14 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m, n', o, p, q, r, s) n n' #

class Field13 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 13th field of a tuple.

Minimal complete definition

Nothing

Methods

_13 :: Lens s t a b #

Access the 13th field of a tuple.

Instances

13 <= n => Field13 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _13 :: Lens (V n a) (V n a) a a #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk, l, m') m m'
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk, l, m') m m' #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n) m m'
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n) m m' #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o) m m'
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o) m m' #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p) m m'
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p) m m' #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q) m m'
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q) m m' #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q, r) m m'
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q, r) m m' #
Field13 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q, r, s) m m'
Instance details Defined in Control.Lens.Tuple Methods _13 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l, m', n, o, p, q, r, s) m m' #

class Field12 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 12th field of a tuple.

Minimal complete definition

Nothing

Methods

_12 :: Lens s t a b #

Access the 12th field of a tuple.

Instances

12 <= n => Field12 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _12 :: Lens (V n a) (V n a) a a #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j, kk, l') l l'
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j, kk, l') l l' #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk, l', m) l l'
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk, l', m) l l' #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n) l l'
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n) l l' #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o) l l'
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o) l l' #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p) l l'
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p) l l' #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q) l l'
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q) l l' #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q, r) l l'
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q, r) l l' #
Field12 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q, r, s) l l'
Instance details Defined in Control.Lens.Tuple Methods _12 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk, l', m, n, o, p, q, r, s) l l' #

class Field11 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 11th field of a tuple.

Minimal complete definition

Nothing

Methods

_11 :: Lens s t a b #

Access the 11th field of a tuple.

Instances

11 <= n => Field11 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _11 :: Lens (V n a) (V n a) a a #
Field11 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i, j, kk') kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i, j, kk') kk kk' #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j, kk', l) kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j, kk', l) kk kk' #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk', l, m) kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j, kk', l, m) kk kk' #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n) kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n) kk kk' #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o) kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o) kk kk' #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p) kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p) kk kk' #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q) kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q) kk kk' #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q, r) kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q, r) kk kk' #
Field11 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q, r, s) kk kk'
Instance details Defined in Control.Lens.Tuple Methods _11 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j, kk', l, m, n, o, p, q, r, s) kk kk' #

class Field10 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 10th field of a tuple.

Minimal complete definition

Nothing

Methods

_10 :: Lens s t a b #

Access the 10th field of a tuple.

Instances

10 <= n => Field10 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _10 :: Lens (V n a) (V n a) a a #
Field10 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h, i, j') j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h, i, j') j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i, j', kk) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i, j', kk) j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j', kk, l) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i, j', kk, l) j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j', kk, l, m) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i, j', kk, l, m) j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n) j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o) j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p) j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q) j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q, r) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q, r) j j' #
Field10 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q, r, s) j j'
Instance details Defined in Control.Lens.Tuple Methods _10 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i, j', kk, l, m, n, o, p, q, r, s) j j' #

class Field9 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 9th field of a tuple.

Minimal complete definition

Nothing

Methods

_9 :: Lens s t a b #

Access the 9th field of a tuple.

Instances

9 <= n => Field9 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _9 :: Lens (V n a) (V n a) a a #
Field9 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g, h, i') i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g, h, i') i i' #
Field9 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h, i', j) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h, i', j) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i', j, kk) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h, i', j, kk) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i', j, kk, l) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h, i', j, kk, l) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i', j, kk, l, m) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h, i', j, kk, l, m) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q, r) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q, r) i i' #
Field9 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q, r, s) i i'
Instance details Defined in Control.Lens.Tuple Methods _9 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h, i', j, kk, l, m, n, o, p, q, r, s) i i' #

class Field8 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provide access to the 8th field of a tuple.

Minimal complete definition

Nothing

Methods

_8 :: Lens s t a b #

Access the 8th field of a tuple.

Instances

8 <= n => Field8 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _8 :: Lens (V n a) (V n a) a a #
Field8 (a, b, c, d, e, f, g, h) (a, b, c, d, e, f, g, h') h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h) (a, b, c, d, e, f, g, h') h h' #
Field8 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g, h', i) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g, h', i) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h', i, j) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h', i, j) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h', i, j, kk) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g, h', i, j, kk) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h', i, j, kk, l) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g, h', i, j, kk, l) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h', i, j, kk, l, m) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g, h', i, j, kk, l, m) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q, r) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q, r) h h' #
Field8 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q, r, s) h h'
Instance details Defined in Control.Lens.Tuple Methods _8 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g, h', i, j, kk, l, m, n, o, p, q, r, s) h h' #

class Field7 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provide access to the 7th field of a tuple.

Minimal complete definition

Nothing

Methods

_7 :: Lens s t a b #

Access the 7th field of a tuple.

Instances

7 <= n => Field7 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _7 :: Lens (V n a) (V n a) a a #
Field7 (a, b, c, d, e, f, g) (a, b, c, d, e, f, g') g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g) (a, b, c, d, e, f, g') g g' #
Field7 (a, b, c, d, e, f, g, h) (a, b, c, d, e, f, g', h) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h) (a, b, c, d, e, f, g', h) g g' #
Field7 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g', h, i) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g', h, i) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g', h, i, j) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g', h, i, j) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g', h, i, j, kk) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f, g', h, i, j, kk) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g', h, i, j, kk, l) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f, g', h, i, j, kk, l) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g', h, i, j, kk, l, m) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f, g', h, i, j, kk, l, m) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q, r) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q, r) g g' #
Field7 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q, r, s) g g'
Instance details Defined in Control.Lens.Tuple Methods _7 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f, g', h, i, j, kk, l, m, n, o, p, q, r, s) g g' #

class Field6 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 6th element of a tuple.

Minimal complete definition

Nothing

Methods

_6 :: Lens s t a b #

Access the 6th field of a tuple.

Instances

Field6 (Plucker a) (Plucker a) a a
Instance details Defined in Linear.Plucker Methods _6 :: Lens (Plucker a) (Plucker a) a a #
6 <= n => Field6 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _6 :: Lens (V n a) (V n a) a a #
Field6 (a, b, c, d, e, f) (a, b, c, d, e, f') f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f) (a, b, c, d, e, f') f f' #
Field6 (a, b, c, d, e, f, g) (a, b, c, d, e, f', g) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g) (a, b, c, d, e, f', g) f f' #
Field6 (a, b, c, d, e, f, g, h) (a, b, c, d, e, f', g, h) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h) (a, b, c, d, e, f', g, h) f f' #
Field6 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f', g, h, i) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f', g, h, i) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f', g, h, i, j) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f', g, h, i, j) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f', g, h, i, j, kk) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e, f', g, h, i, j, kk) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f', g, h, i, j, kk, l) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e, f', g, h, i, j, kk, l) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f', g, h, i, j, kk, l, m) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e, f', g, h, i, j, kk, l, m) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q, r) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q, r) f f' #
Field6 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q, r, s) f f'
Instance details Defined in Control.Lens.Tuple Methods _6 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e, f', g, h, i, j, kk, l, m, n, o, p, q, r, s) f f' #

class Field5 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 5th field of a tuple.

Minimal complete definition

Nothing

Methods

_5 :: Lens s t a b #

Access the 5th field of a tuple.

Instances

Field5 (Plucker a) (Plucker a) a a
Instance details Defined in Linear.Plucker Methods _5 :: Lens (Plucker a) (Plucker a) a a #
5 <= n => Field5 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _5 :: Lens (V n a) (V n a) a a #
Field5 (a, b, c, d, e) (a, b, c, d, e') e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e) (a, b, c, d, e') e e' #
Field5 (a, b, c, d, e, f) (a, b, c, d, e', f) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f) (a, b, c, d, e', f) e e' #
Field5 (a, b, c, d, e, f, g) (a, b, c, d, e', f, g) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g) (a, b, c, d, e', f, g) e e' #
Field5 (a, b, c, d, e, f, g, h) (a, b, c, d, e', f, g, h) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h) (a, b, c, d, e', f, g, h) e e' #
Field5 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e', f, g, h, i) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d, e', f, g, h, i) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e', f, g, h, i, j) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e', f, g, h, i, j) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e', f, g, h, i, j, kk) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d, e', f, g, h, i, j, kk) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e', f, g, h, i, j, kk, l) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d, e', f, g, h, i, j, kk, l) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e', f, g, h, i, j, kk, l, m) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d, e', f, g, h, i, j, kk, l, m) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q, r) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q, r) e e' #
Field5 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q, r, s) e e'
Instance details Defined in Control.Lens.Tuple Methods _5 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d, e', f, g, h, i, j, kk, l, m, n, o, p, q, r, s) e e' #

class Field4 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provide access to the 4th field of a tuple.

Minimal complete definition

Nothing

Methods

_4 :: Lens s t a b #

Access the 4th field of a tuple.

Instances

Field4 (Plucker a) (Plucker a) a a
Instance details Defined in Linear.Plucker Methods _4 :: Lens (Plucker a) (Plucker a) a a #
Field4 (Quaternion a) (Quaternion a) a a
Instance details Defined in Linear.Quaternion Methods _4 :: Lens (Quaternion a) (Quaternion a) a a #
Field4 (V4 a) (V4 a) a a
Instance details Defined in Linear.V4 Methods _4 :: Lens (V4 a) (V4 a) a a #
4 <= n => Field4 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _4 :: Lens (V n a) (V n a) a a #
Field4 (a, b, c, d) (a, b, c, d') d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d) (a, b, c, d') d d' #
Field4 (a, b, c, d, e) (a, b, c, d', e) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e) (a, b, c, d', e) d d' #
Field4 (a, b, c, d, e, f) (a, b, c, d', e, f) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f) (a, b, c, d', e, f) d d' #
Field4 (a, b, c, d, e, f, g) (a, b, c, d', e, f, g) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g) (a, b, c, d', e, f, g) d d' #
Field4 (a, b, c, d, e, f, g, h) (a, b, c, d', e, f, g, h) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h) (a, b, c, d', e, f, g, h) d d' #
Field4 (a, b, c, d, e, f, g, h, i) (a, b, c, d', e, f, g, h, i) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c, d', e, f, g, h, i) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d', e, f, g, h, i, j) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c, d', e, f, g, h, i, j) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d', e, f, g, h, i, j, kk) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c, d', e, f, g, h, i, j, kk) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d', e, f, g, h, i, j, kk, l) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c, d', e, f, g, h, i, j, kk, l) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d', e, f, g, h, i, j, kk, l, m) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c, d', e, f, g, h, i, j, kk, l, m) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q, r) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q, r) d d' #
Field4 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) d d'
Instance details Defined in Control.Lens.Tuple Methods _4 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c, d', e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) d d' #

class Field3 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 3rd field of a tuple.

Minimal complete definition

Nothing

Methods

_3 :: Lens s t a b #

Access the 3rd field of a tuple.

Instances

Field3 (V3 a) (V3 a) a a
Instance details Defined in Linear.V3 Methods _3 :: Lens (V3 a) (V3 a) a a #
Field3 (Plucker a) (Plucker a) a a
Instance details Defined in Linear.Plucker Methods _3 :: Lens (Plucker a) (Plucker a) a a #
Field3 (Quaternion a) (Quaternion a) a a
Instance details Defined in Linear.Quaternion Methods _3 :: Lens (Quaternion a) (Quaternion a) a a #
Field3 (V4 a) (V4 a) a a
Instance details Defined in Linear.V4 Methods _3 :: Lens (V4 a) (V4 a) a a #
Field3 (a, b, c) (a, b, c') c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c) (a, b, c') c c' #
3 <= n => Field3 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _3 :: Lens (V n a) (V n a) a a #
Field3 (a, b, c, d) (a, b, c', d) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d) (a, b, c', d) c c' #
Field3 (a, b, c, d, e) (a, b, c', d, e) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e) (a, b, c', d, e) c c' #
Field3 (a, b, c, d, e, f) (a, b, c', d, e, f) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f) (a, b, c', d, e, f) c c' #
Field3 (a, b, c, d, e, f, g) (a, b, c', d, e, f, g) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g) (a, b, c', d, e, f, g) c c' #
Field3 (a, b, c, d, e, f, g, h) (a, b, c', d, e, f, g, h) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h) (a, b, c', d, e, f, g, h) c c' #
Field3 (a, b, c, d, e, f, g, h, i) (a, b, c', d, e, f, g, h, i) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i) (a, b, c', d, e, f, g, h, i) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j) (a, b, c', d, e, f, g, h, i, j) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b, c', d, e, f, g, h, i, j) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c', d, e, f, g, h, i, j, kk) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b, c', d, e, f, g, h, i, j, kk) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c', d, e, f, g, h, i, j, kk, l) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b, c', d, e, f, g, h, i, j, kk, l) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c', d, e, f, g, h, i, j, kk, l, m) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b, c', d, e, f, g, h, i, j, kk, l, m) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) c c' #
Field3 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) c c'
Instance details Defined in Control.Lens.Tuple Methods _3 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b, c', d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) c c' #

class Field2 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to the 2nd field of a tuple.

Minimal complete definition

Nothing

Methods

_2 :: Lens s t a b #

Access the 2nd field of a tuple.

>>> _2 .~ "hello" $ (1,(),3,4)
(1,"hello",3,4)

>>> (1,2,3,4) & _2 *~ 3
(1,6,3,4)

>>> _2 print (1,2)
2
(1,())

anyOf _2 :: (s -> Bool) -> (a, s) -> Bool
traverse . _2 :: (Applicative f, Traversable t) => (a -> f b) -> t (s, a) -> f (t (s, b))
foldMapOf (traverse . _2) :: (Traversable t, Monoid m) => (s -> m) -> t (b, s) -> m

Instances

Field2 (V2 a) (V2 a) a a
Instance details Defined in Linear.V2 Methods _2 :: Lens (V2 a) (V2 a) a a #
Field2 (V3 a) (V3 a) a a
Instance details Defined in Linear.V3 Methods _2 :: Lens (V3 a) (V3 a) a a #
Field2 (Plucker a) (Plucker a) a a
Instance details Defined in Linear.Plucker Methods _2 :: Lens (Plucker a) (Plucker a) a a #
Field2 (Quaternion a) (Quaternion a) a a
Instance details Defined in Linear.Quaternion Methods _2 :: Lens (Quaternion a) (Quaternion a) a a #
Field2 (V4 a) (V4 a) a a
Instance details Defined in Linear.V4 Methods _2 :: Lens (V4 a) (V4 a) a a #
Field2 (a, b) (a, b') b b'	`_2` k ~(a,b) = (\b' -> (a,b')) `<$>` k b
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b) (a, b') b b' #
Field2 (a, b, c) (a, b', c) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c) (a, b', c) b b' #
2 <= n => Field2 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _2 :: Lens (V n a) (V n a) a a #
Field2 (a, b, c, d) (a, b', c, d) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d) (a, b', c, d) b b' #
Field2 ((f :: g) p) ((f :: g') p) (g p) (g' p)
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens ((f :: g) p) ((f :: g') p) (g p) (g' p) #
Field2 (Product f g a) (Product f g' a) (g a) (g' a)
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (Product f g a) (Product f g' a) (g a) (g' a) #
Field2 (a, b, c, d, e) (a, b', c, d, e) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e) (a, b', c, d, e) b b' #
Field2 (a, b, c, d, e, f) (a, b', c, d, e, f) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f) (a, b', c, d, e, f) b b' #
Field2 (a, b, c, d, e, f, g) (a, b', c, d, e, f, g) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g) (a, b', c, d, e, f, g) b b' #
Field2 (a, b, c, d, e, f, g, h) (a, b', c, d, e, f, g, h) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h) (a, b', c, d, e, f, g, h) b b' #
Field2 (a, b, c, d, e, f, g, h, i) (a, b', c, d, e, f, g, h, i) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i) (a, b', c, d, e, f, g, h, i) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j) (a, b', c, d, e, f, g, h, i, j) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j) (a, b', c, d, e, f, g, h, i, j) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk) (a, b', c, d, e, f, g, h, i, j, kk) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a, b', c, d, e, f, g, h, i, j, kk) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b', c, d, e, f, g, h, i, j, kk, l) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a, b', c, d, e, f, g, h, i, j, kk, l) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b', c, d, e, f, g, h, i, j, kk, l, m) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a, b', c, d, e, f, g, h, i, j, kk, l, m) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) b b' #
Field2 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) b b'
Instance details Defined in Control.Lens.Tuple Methods _2 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a, b', c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) b b' #

class Field1 s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Provides access to 1st field of a tuple.

Minimal complete definition

Nothing

Methods

_1 :: Lens s t a b #

Access the 1st field of a tuple (and possibly change its type).

>>> (1,2)^._1
1

>>> _1 .~ "hello" $ (1,2)
("hello",2)

>>> (1,2) & _1 .~ "hello"
("hello",2)

>>> _1 putStrLn ("hello","world")
hello
((),"world")

This can also be used on larger tuples as well:

>>> (1,2,3,4,5) & _1 +~ 41
(42,2,3,4,5)

_1 :: Lens (a,b) (a',b) a a'
_1 :: Lens (a,b,c) (a',b,c) a a'
_1 :: Lens (a,b,c,d) (a',b,c,d) a a'
...
_1 :: Lens (a,b,c,d,e,f,g,h,i) (a',b,c,d,e,f,g,h,i) a a'

Instances

Field1 (Identity a) (Identity b) a b
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (Identity a) (Identity b) a b #
Field1 (V2 a) (V2 a) a a
Instance details Defined in Linear.V2 Methods _1 :: Lens (V2 a) (V2 a) a a #
Field1 (V3 a) (V3 a) a a
Instance details Defined in Linear.V3 Methods _1 :: Lens (V3 a) (V3 a) a a #
Field1 (Plucker a) (Plucker a) a a
Instance details Defined in Linear.Plucker Methods _1 :: Lens (Plucker a) (Plucker a) a a #
Field1 (Quaternion a) (Quaternion a) a a
Instance details Defined in Linear.Quaternion Methods _1 :: Lens (Quaternion a) (Quaternion a) a a #
Field1 (V4 a) (V4 a) a a
Instance details Defined in Linear.V4 Methods _1 :: Lens (V4 a) (V4 a) a a #
Field1 (V1 a) (V1 b) a b
Instance details Defined in Linear.V1 Methods _1 :: Lens (V1 a) (V1 b) a b #
Field1 (a, b) (a', b) a a'	`_1` k ~(a,b) = (\a' -> (a',b)) `<$>` k a
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b) (a', b) a a' #
Field1 (a, b, c) (a', b, c) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c) (a', b, c) a a' #
1 <= n => Field1 (V n a) (V n a) a a
Instance details Defined in Linear.V Methods _1 :: Lens (V n a) (V n a) a a #
Field1 (a, b, c, d) (a', b, c, d) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d) (a', b, c, d) a a' #
Field1 ((f :: g) p) ((f' :: g) p) (f p) (f' p)
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens ((f :: g) p) ((f' :: g) p) (f p) (f' p) #
Field1 (Product f g a) (Product f' g a) (f a) (f' a)
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (Product f g a) (Product f' g a) (f a) (f' a) #
Field1 (a, b, c, d, e) (a', b, c, d, e) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e) (a', b, c, d, e) a a' #
Field1 (a, b, c, d, e, f) (a', b, c, d, e, f) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f) (a', b, c, d, e, f) a a' #
Field1 (a, b, c, d, e, f, g) (a', b, c, d, e, f, g) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g) (a', b, c, d, e, f, g) a a' #
Field1 (a, b, c, d, e, f, g, h) (a', b, c, d, e, f, g, h) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h) (a', b, c, d, e, f, g, h) a a' #
Field1 (a, b, c, d, e, f, g, h, i) (a', b, c, d, e, f, g, h, i) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i) (a', b, c, d, e, f, g, h, i) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j) (a', b, c, d, e, f, g, h, i, j) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j) (a', b, c, d, e, f, g, h, i, j) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk) (a', b, c, d, e, f, g, h, i, j, kk) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk) (a', b, c, d, e, f, g, h, i, j, kk) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l) (a', b, c, d, e, f, g, h, i, j, kk, l) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l) (a', b, c, d, e, f, g, h, i, j, kk, l) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a', b, c, d, e, f, g, h, i, j, kk, l, m) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m) (a', b, c, d, e, f, g, h, i, j, kk, l, m) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r) a a' #
Field1 (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) a a'
Instance details Defined in Control.Lens.Tuple Methods _1 :: Lens (a, b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) (a', b, c, d, e, f, g, h, i, j, kk, l, m, n, o, p, q, r, s) a a' #

_1' :: Field1 s t a b => Lens s t a b #

Strict version of _1

_2' :: Field2 s t a b => Lens s t a b #

Strict version of _2

_3' :: Field3 s t a b => Lens s t a b #

Strict version of _3

_4' :: Field4 s t a b => Lens s t a b #

Strict version of _4

_5' :: Field5 s t a b => Lens s t a b #

Strict version of _5

_6' :: Field6 s t a b => Lens s t a b #

Strict version of _6

_7' :: Field7 s t a b => Lens s t a b #

Strict version of _7

_8' :: Field8 s t a b => Lens s t a b #

Strict version of _8

_9' :: Field9 s t a b => Lens s t a b #

Strict version of _9

_10' :: Field10 s t a b => Lens s t a b #

Strict version of _10

_11' :: Field11 s t a b => Lens s t a b #

Strict version of _11

_12' :: Field12 s t a b => Lens s t a b #

Strict version of _12

_13' :: Field13 s t a b => Lens s t a b #

Strict version of _13

_14' :: Field14 s t a b => Lens s t a b #

Strict version of _14

_15' :: Field15 s t a b => Lens s t a b #

Strict version of _15

_16' :: Field16 s t a b => Lens s t a b #

Strict version of _16

_17' :: Field17 s t a b => Lens s t a b #

Strict version of _17

_18' :: Field18 s t a b => Lens s t a b #

Strict version of _18

_19' :: Field19 s t a b => Lens s t a b #

Strict version of _19

type Accessing (p :: Type -> Type -> Type) m s a = p a (Const m a) -> s -> Const m s #

This is a convenient alias used when consuming (indexed) getters and (indexed) folds in a highly general fashion.

type IndexedGetting i m s a = Indexed i a (Const m a) -> s -> Const m s #

Used to consume an IndexedFold.

type Getting r s a = (a -> Const r a) -> s -> Const r s #

When you see this in a type signature it indicates that you can pass the function a Lens, Getter, Traversal, Fold, Prism, Iso, or one of the indexed variants, and it will just "do the right thing".

Most Getter combinators are able to be used with both a Getter or a Fold in limited situations, to do so, they need to be monomorphic in what we are going to extract with Const. To be compatible with Lens, Traversal and Iso we also restricted choices of the irrelevant t and b parameters.

If a function accepts a Getting r s a, then when r is a Monoid, then you can pass a Fold (or Traversal), otherwise you can only pass this a Getter or Lens.

to :: (Profunctor p, Contravariant f) => (s -> a) -> Optic' p f s a #

Build an (index-preserving) Getter from an arbitrary Haskell function.

to f . to g ≡ to (g . f)

a ^. to f ≡ f a

>>> a ^.to f
f a

>>> ("hello","world")^.to snd
"world"

>>> 5^.to succ
6

>>> (0, -5)^._2.to abs
5

to :: (s -> a) -> IndexPreservingGetter s a

ito :: (Indexable i p, Contravariant f) => (s -> (i, a)) -> Over' p f s a #

ito :: (s -> (i, a)) -> IndexedGetter i s a

like :: (Profunctor p, Contravariant f, Functor f) => a -> Optic' p f s a #

Build an constant-valued (index-preserving) Getter from an arbitrary Haskell value.

like a . like b ≡ like b
a ^. like b ≡ b
a ^. like b ≡ a ^. to (const b)

This can be useful as a second case failing a Fold e.g. foo failing like 0

like :: a -> IndexPreservingGetter s a

ilike :: (Indexable i p, Contravariant f, Functor f) => i -> a -> Over' p f s a #

ilike :: i -> a -> IndexedGetter i s a

view :: MonadReader s m => Getting a s a -> m a #

View the value pointed to by a Getter, Iso or Lens or the result of folding over all the results of a Fold or Traversal that points at a monoidal value.

view . to ≡ id

>>> view (to f) a
f a

>>> view _2 (1,"hello")
"hello"

>>> view (to succ) 5
6

>>> view (_2._1) ("hello",("world","!!!"))
"world"

As view is commonly used to access the target of a Getter or obtain a monoidal summary of the targets of a Fold, It may be useful to think of it as having one of these more restricted signatures:

view ::             Getter s a     -> s -> a
view :: Monoid m => Fold s m       -> s -> m
view ::             Iso' s a       -> s -> a
view ::             Lens' s a      -> s -> a
view :: Monoid m => Traversal' s m -> s -> m

In a more general setting, such as when working with a Monad transformer stack you can use:

view :: MonadReader s m             => Getter s a     -> m a
view :: (MonadReader s m, Monoid a) => Fold s a       -> m a
view :: MonadReader s m             => Iso' s a       -> m a
view :: MonadReader s m             => Lens' s a      -> m a
view :: (MonadReader s m, Monoid a) => Traversal' s a -> m a

views :: MonadReader s m => LensLike' (Const r :: Type -> Type) s a -> (a -> r) -> m r #

View a function of the value pointed to by a Getter or Lens or the result of folding over the result of mapping the targets of a Fold or Traversal.

views l f ≡ view (l . to f)

>>> views (to f) g a
g (f a)

>>> views _2 length (1,"hello")
5

As views is commonly used to access the target of a Getter or obtain a monoidal summary of the targets of a Fold, It may be useful to think of it as having one of these more restricted signatures:

views ::             Getter s a     -> (a -> r) -> s -> r
views :: Monoid m => Fold s a       -> (a -> m) -> s -> m
views ::             Iso' s a       -> (a -> r) -> s -> r
views ::             Lens' s a      -> (a -> r) -> s -> r
views :: Monoid m => Traversal' s a -> (a -> m) -> s -> m

In a more general setting, such as when working with a Monad transformer stack you can use:

views :: MonadReader s m             => Getter s a     -> (a -> r) -> m r
views :: (MonadReader s m, Monoid r) => Fold s a       -> (a -> r) -> m r
views :: MonadReader s m             => Iso' s a       -> (a -> r) -> m r
views :: MonadReader s m             => Lens' s a      -> (a -> r) -> m r
views :: (MonadReader s m, Monoid r) => Traversal' s a -> (a -> r) -> m r

views :: MonadReader s m => Getting r s a -> (a -> r) -> m r

(^.) :: s -> Getting a s a -> a infixl 8 #

View the value pointed to by a Getter or Lens or the result of folding over all the results of a Fold or Traversal that points at a monoidal values.

This is the same operation as view with the arguments flipped.

The fixity and semantics are such that subsequent field accesses can be performed with (.).

>>> (a,b)^._2
b

>>> ("hello","world")^._2
"world"

>>> import Data.Complex
>>> ((0, 1 :+ 2), 3)^._1._2.to magnitude
2.23606797749979

(^.) ::             s -> Getter s a     -> a
(^.) :: Monoid m => s -> Fold s m       -> m
(^.) ::             s -> Iso' s a       -> a
(^.) ::             s -> Lens' s a      -> a
(^.) :: Monoid m => s -> Traversal' s m -> m

use :: MonadState s m => Getting a s a -> m a #

Use the target of a Lens, Iso, or Getter in the current state, or use a summary of a Fold or Traversal that points to a monoidal value.

>>> evalState (use _1) (a,b)
a

>>> evalState (use _1) ("hello","world")
"hello"

use :: MonadState s m             => Getter s a     -> m a
use :: (MonadState s m, Monoid r) => Fold s r       -> m r
use :: MonadState s m             => Iso' s a       -> m a
use :: MonadState s m             => Lens' s a      -> m a
use :: (MonadState s m, Monoid r) => Traversal' s r -> m r

uses :: MonadState s m => LensLike' (Const r :: Type -> Type) s a -> (a -> r) -> m r #

Use the target of a Lens, Iso or Getter in the current state, or use a summary of a Fold or Traversal that points to a monoidal value.

>>> evalState (uses _1 length) ("hello","world")
5

uses :: MonadState s m             => Getter s a     -> (a -> r) -> m r
uses :: (MonadState s m, Monoid r) => Fold s a       -> (a -> r) -> m r
uses :: MonadState s m             => Lens' s a      -> (a -> r) -> m r
uses :: MonadState s m             => Iso' s a       -> (a -> r) -> m r
uses :: (MonadState s m, Monoid r) => Traversal' s a -> (a -> r) -> m r

uses :: MonadState s m => Getting r s t a b -> (a -> r) -> m r

listening :: MonadWriter w m => Getting u w u -> m a -> m (a, u) #

This is a generalized form of listen that only extracts the portion of the log that is focused on by a Getter. If given a Fold or a Traversal then a monoidal summary of the parts of the log that are visited will be returned.

listening :: MonadWriter w m             => Getter w u     -> m a -> m (a, u)
listening :: MonadWriter w m             => Lens' w u      -> m a -> m (a, u)
listening :: MonadWriter w m             => Iso' w u       -> m a -> m (a, u)
listening :: (MonadWriter w m, Monoid u) => Fold w u       -> m a -> m (a, u)
listening :: (MonadWriter w m, Monoid u) => Traversal' w u -> m a -> m (a, u)
listening :: (MonadWriter w m, Monoid u) => Prism' w u     -> m a -> m (a, u)

ilistening :: MonadWriter w m => IndexedGetting i (i, u) w u -> m a -> m (a, (i, u)) #

This is a generalized form of listen that only extracts the portion of the log that is focused on by a Getter. If given a Fold or a Traversal then a monoidal summary of the parts of the log that are visited will be returned.

ilistening :: MonadWriter w m             => IndexedGetter i w u     -> m a -> m (a, (i, u))
ilistening :: MonadWriter w m             => IndexedLens' i w u      -> m a -> m (a, (i, u))
ilistening :: (MonadWriter w m, Monoid u) => IndexedFold i w u       -> m a -> m (a, (i, u))
ilistening :: (MonadWriter w m, Monoid u) => IndexedTraversal' i w u -> m a -> m (a, (i, u))

listenings :: MonadWriter w m => Getting v w u -> (u -> v) -> m a -> m (a, v) #

This is a generalized form of listen that only extracts the portion of the log that is focused on by a Getter. If given a Fold or a Traversal then a monoidal summary of the parts of the log that are visited will be returned.

listenings :: MonadWriter w m             => Getter w u     -> (u -> v) -> m a -> m (a, v)
listenings :: MonadWriter w m             => Lens' w u      -> (u -> v) -> m a -> m (a, v)
listenings :: MonadWriter w m             => Iso' w u       -> (u -> v) -> m a -> m (a, v)
listenings :: (MonadWriter w m, Monoid v) => Fold w u       -> (u -> v) -> m a -> m (a, v)
listenings :: (MonadWriter w m, Monoid v) => Traversal' w u -> (u -> v) -> m a -> m (a, v)
listenings :: (MonadWriter w m, Monoid v) => Prism' w u     -> (u -> v) -> m a -> m (a, v)

ilistenings :: MonadWriter w m => IndexedGetting i v w u -> (i -> u -> v) -> m a -> m (a, v) #

This is a generalized form of listen that only extracts the portion of the log that is focused on by a Getter. If given a Fold or a Traversal then a monoidal summary of the parts of the log that are visited will be returned.

ilistenings :: MonadWriter w m             => IndexedGetter w u     -> (i -> u -> v) -> m a -> m (a, v)
ilistenings :: MonadWriter w m             => IndexedLens' w u      -> (i -> u -> v) -> m a -> m (a, v)
ilistenings :: (MonadWriter w m, Monoid v) => IndexedFold w u       -> (i -> u -> v) -> m a -> m (a, v)
ilistenings :: (MonadWriter w m, Monoid v) => IndexedTraversal' w u -> (i -> u -> v) -> m a -> m (a, v)

iview :: MonadReader s m => IndexedGetting i (i, a) s a -> m (i, a) #

View the index and value of an IndexedGetter into the current environment as a pair.

When applied to an IndexedFold the result will most likely be a nonsensical monoidal summary of the indices tupled with a monoidal summary of the values and probably not whatever it is you wanted.

iviews :: MonadReader s m => IndexedGetting i r s a -> (i -> a -> r) -> m r #

View a function of the index and value of an IndexedGetter into the current environment.

When applied to an IndexedFold the result will be a monoidal summary instead of a single answer.

iviews ≡ ifoldMapOf

iuse :: MonadState s m => IndexedGetting i (i, a) s a -> m (i, a) #

Use the index and value of an IndexedGetter into the current state as a pair.

When applied to an IndexedFold the result will most likely be a nonsensical monoidal summary of the indices tupled with a monoidal summary of the values and probably not whatever it is you wanted.

iuses :: MonadState s m => IndexedGetting i r s a -> (i -> a -> r) -> m r #

Use a function of the index and value of an IndexedGetter into the current state.

When applied to an IndexedFold the result will be a monoidal summary instead of a single answer.

(^@.) :: s -> IndexedGetting i (i, a) s a -> (i, a) infixl 8 #

View the index and value of an IndexedGetter or IndexedLens.

This is the same operation as iview with the arguments flipped.

The fixity and semantics are such that subsequent field accesses can be performed with (.).

(^@.) :: s -> IndexedGetter i s a -> (i, a)
(^@.) :: s -> IndexedLens' i s a  -> (i, a)

The result probably doesn't have much meaning when applied to an IndexedFold.

getting :: (Profunctor p, Profunctor q, Functor f, Contravariant f) => Optical p q f s t a b -> Optical' p q f s a #

Coerce a Getter-compatible Optical to an Optical'. This is useful when using a Traversal that is not simple as a Getter or a Fold.

getting :: Traversal s t a b          -> Fold s a
getting :: Lens s t a b               -> Getter s a
getting :: IndexedTraversal i s t a b -> IndexedFold i s a
getting :: IndexedLens i s t a b      -> IndexedGetter i s a

unto :: (Profunctor p, Bifunctor p, Functor f) => (b -> t) -> Optic p f s t a b #

An analogue of to for review.

unto :: (b -> t) -> Review' t b

unto = un . to

un :: (Profunctor p, Bifunctor p, Functor f) => Getting a s a -> Optic' p f a s #

Turn a Getter around to get a Review

un = unto . view
unto = un . to

>>> un (to length) # [1,2,3]
3

re :: AReview t b -> Getter b t #

Turn a Prism or Iso around to build a Getter.

If you have an Iso, from is a more powerful version of this function that will return an Iso instead of a mere Getter.

>>> 5 ^.re _Left
Left 5

>>> 6 ^.re (_Left.unto succ)
Left 7

review  ≡ view  . re
reviews ≡ views . re
reuse   ≡ use   . re
reuses  ≡ uses  . re

re :: Prism s t a b -> Getter b t
re :: Iso s t a b   -> Getter b t

review :: MonadReader b m => AReview t b -> m t #

This can be used to turn an Iso or Prism around and view a value (or the current environment) through it the other way.

review ≡ view . re
review . unto ≡ id

>>> review _Left "mustard"
Left "mustard"

>>> review (unto succ) 5
6

Usually review is used in the (->) Monad with a Prism or Iso, in which case it may be useful to think of it as having one of these more restricted type signatures:

review :: Iso' s a   -> a -> s
review :: Prism' s a -> a -> s

However, when working with a Monad transformer stack, it is sometimes useful to be able to review the current environment, in which case it may be beneficial to think of it as having one of these slightly more liberal type signatures:

review :: MonadReader a m => Iso' s a   -> m s
review :: MonadReader a m => Prism' s a -> m s

reviews :: MonadReader b m => AReview t b -> (t -> r) -> m r #

This can be used to turn an Iso or Prism around and view a value (or the current environment) through it the other way, applying a function.

reviews ≡ views . re
reviews (unto f) g ≡ g . f

>>> reviews _Left isRight "mustard"
False

>>> reviews (unto succ) (*2) 3
8

Usually this function is used in the (->) Monad with a Prism or Iso, in which case it may be useful to think of it as having one of these more restricted type signatures:

reviews :: Iso' s a   -> (s -> r) -> a -> r
reviews :: Prism' s a -> (s -> r) -> a -> r

However, when working with a Monad transformer stack, it is sometimes useful to be able to review the current environment, in which case it may be beneficial to think of it as having one of these slightly more liberal type signatures:

reviews :: MonadReader a m => Iso' s a   -> (s -> r) -> m r
reviews :: MonadReader a m => Prism' s a -> (s -> r) -> m r

reuse :: MonadState b m => AReview t b -> m t #

This can be used to turn an Iso or Prism around and use a value (or the current environment) through it the other way.

reuse ≡ use . re
reuse . unto ≡ gets

>>> evalState (reuse _Left) 5
Left 5

>>> evalState (reuse (unto succ)) 5
6

reuse :: MonadState a m => Prism' s a -> m s
reuse :: MonadState a m => Iso' s a   -> m s

reuses :: MonadState b m => AReview t b -> (t -> r) -> m r #

This can be used to turn an Iso or Prism around and use the current state through it the other way, applying a function.

reuses ≡ uses . re
reuses (unto f) g ≡ gets (g . f)

>>> evalState (reuses _Left isLeft) (5 :: Int)
True

reuses :: MonadState a m => Prism' s a -> (s -> r) -> m r
reuses :: MonadState a m => Iso' s a   -> (s -> r) -> m r

type APrism' s a = APrism s s a a #

type APrism' = Simple APrism

type APrism s t a b = Market a b a (Identity b) -> Market a b s (Identity t) #

If you see this in a signature for a function, the function is expecting a Prism.

withPrism :: APrism s t a b -> ((b -> t) -> (s -> Either t a) -> r) -> r #

Convert APrism to the pair of functions that characterize it.

clonePrism :: APrism s t a b -> Prism s t a b #

Clone a Prism so that you can reuse the same monomorphically typed Prism for different purposes.

See cloneLens and cloneTraversal for examples of why you might want to do this.

prism :: (b -> t) -> (s -> Either t a) -> Prism s t a b #

Build a Prism.

Either t a is used instead of Maybe a to permit the types of s and t to differ.

prism' :: (b -> s) -> (s -> Maybe a) -> Prism s s a b #

This is usually used to build a Prism', when you have to use an operation like cast which already returns a Maybe.

without :: APrism s t a b -> APrism u v c d -> Prism (Either s u) (Either t v) (Either a c) (Either b d) #

Given a pair of prisms, project sums.

Viewing a Prism as a co-Lens, this combinator can be seen to be dual to alongside.

aside :: APrism s t a b -> Prism (e, s) (e, t) (e, a) (e, b) #

Use a Prism to work over part of a structure.

below :: Traversable f => APrism' s a -> Prism' (f s) (f a) #

lift a Prism through a Traversable functor, giving a Prism that matches only if all the elements of the container match the Prism.

>>> [Left 1, Right "foo", Left 4, Right "woot"]^..below _Right
[]

>>> [Right "hail hydra!", Right "foo", Right "blah", Right "woot"]^..below _Right
[["hail hydra!","foo","blah","woot"]]

isn't :: APrism s t a b -> s -> Bool #

Check to see if this Prism doesn't match.

>>> isn't _Left (Right 12)
True

>>> isn't _Left (Left 12)
False

>>> isn't _Empty []
False

matching :: APrism s t a b -> s -> Either t a #

Retrieve the value targeted by a Prism or return the original value while allowing the type to change if it does not match.

>>> matching _Just (Just 12)
Right 12

>>> matching _Just (Nothing :: Maybe Int) :: Either (Maybe Bool) Int
Left Nothing

_Left :: Prism (Either a c) (Either b c) a b #

This Prism provides a Traversal for tweaking the Left half of an Either:

>>> over _Left (+1) (Left 2)
Left 3

>>> over _Left (+1) (Right 2)
Right 2

>>> Right 42 ^._Left :: String
""

>>> Left "hello" ^._Left
"hello"

It also can be turned around to obtain the embedding into the Left half of an Either:

>>> _Left # 5
Left 5

>>> 5^.re _Left
Left 5

_Right :: Prism (Either c a) (Either c b) a b #

This Prism provides a Traversal for tweaking the Right half of an Either:

>>> over _Right (+1) (Left 2)
Left 2

>>> over _Right (+1) (Right 2)
Right 3

>>> Right "hello" ^._Right
"hello"

>>> Left "hello" ^._Right :: [Double]
[]

It also can be turned around to obtain the embedding into the Right half of an Either:

>>> _Right # 5
Right 5

>>> 5^.re _Right
Right 5

_Just :: Prism (Maybe a) (Maybe b) a b #

This Prism provides a Traversal for tweaking the target of the value of Just in a Maybe.

>>> over _Just (+1) (Just 2)
Just 3

Unlike traverse this is a Prism, and so you can use it to inject as well:

>>> _Just # 5
Just 5

>>> 5^.re _Just
Just 5

Interestingly,

m ^? _Just ≡ m

>>> Just x ^? _Just
Just x

>>> Nothing ^? _Just
Nothing

_Nothing :: Prism' (Maybe a) () #

This Prism provides the Traversal of a Nothing in a Maybe.

>>> Nothing ^? _Nothing
Just ()

>>> Just () ^? _Nothing
Nothing

But you can turn it around and use it to construct Nothing as well:

>>> _Nothing # ()
Nothing

_Void :: Prism s s a Void #

Void is a logically uninhabited data type.

This is a Prism that will always fail to match.

only :: Eq a => a -> Prism' a () #

This Prism compares for exact equality with a given value.

>>> only 4 # ()
4

>>> 5 ^? only 4
Nothing

nearly :: a -> (a -> Bool) -> Prism' a () #

This Prism compares for approximate equality with a given value and a predicate for testing, an example where the value is the empty list and the predicate checks that a list is empty (same as _Empty with the AsEmpty list instance):

>>> nearly [] null # ()
[]
>>> [1,2,3,4] ^? nearly [] null
Nothing

nearly [] null :: Prism' [a] ()

To comply with the Prism laws the arguments you supply to nearly a p are somewhat constrained.

We assume p x holds iff x ≡ a. Under that assumption then this is a valid Prism.

This is useful when working with a type where you can test equality for only a subset of its values, and the prism selects such a value.

_Show :: (Read a, Show a) => Prism' String a #

This is an improper prism for text formatting based on Read and Show.

This Prism is "improper" in the sense that it normalizes the text formatting, but round tripping is idempotent given sane 'Read'/'Show' instances.

>>> _Show # 2
"2"

>>> "EQ" ^? _Show :: Maybe Ordering
Just EQ

_Show ≡ prism' show readMaybe

folding :: Foldable f => (s -> f a) -> Fold s a #

Obtain a Fold by lifting an operation that returns a Foldable result.

This can be useful to lift operations from Data.List and elsewhere into a Fold.

>>> [1,2,3,4]^..folding tail
[2,3,4]

ifolding :: (Foldable f, Indexable i p, Contravariant g, Applicative g) => (s -> f (i, a)) -> Over p g s t a b #

foldring :: (Contravariant f, Applicative f) => ((a -> f a -> f a) -> f a -> s -> f a) -> LensLike f s t a b #

Obtain a Fold by lifting foldr like function.

>>> [1,2,3,4]^..foldring foldr
[1,2,3,4]

ifoldring :: (Indexable i p, Contravariant f, Applicative f) => ((i -> a -> f a -> f a) -> f a -> s -> f a) -> Over p f s t a b #

Obtain FoldWithIndex by lifting ifoldr like function.

folded :: Foldable f => IndexedFold Int (f a) a #

Obtain a Fold from any Foldable indexed by ordinal position.

>>> Just 3^..folded
[3]

>>> Nothing^..folded
[]

>>> [(1,2),(3,4)]^..folded.both
[1,2,3,4]

folded64 :: Foldable f => IndexedFold Int64 (f a) a #

Obtain a Fold from any Foldable indexed by ordinal position.

repeated :: Apply f => LensLike' f a a #

Form a Fold1 by repeating the input forever.

repeat ≡ toListOf repeated

>>> timingOut $ 5^..taking 20 repeated
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]

repeated :: Fold1 a a

replicated :: Int -> Fold a a #

A Fold that replicates its input n times.

replicate n ≡ toListOf (replicated n)

>>> 5^..replicated 20
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]

cycled :: Apply f => LensLike f s t a b -> LensLike f s t a b #

Transform a non-empty Fold into a Fold1 that loops over its elements over and over.

>>> timingOut $ [1,2,3]^..taking 7 (cycled traverse)
[1,2,3,1,2,3,1]

cycled :: Fold1 s a -> Fold1 s a

unfolded :: (b -> Maybe (a, b)) -> Fold b a #

Build a Fold that unfolds its values from a seed.

unfoldr ≡ toListOf . unfolded

>>> 10^..unfolded (\b -> if b == 0 then Nothing else Just (b, b-1))
[10,9,8,7,6,5,4,3,2,1]

iterated :: Apply f => (a -> a) -> LensLike' f a a #

x ^. iterated f returns an infinite Fold1 of repeated applications of f to x.

toListOf (iterated f) a ≡ iterate f a

iterated :: (a -> a) -> Fold1 a a

filtered :: (Choice p, Applicative f) => (a -> Bool) -> Optic' p f a a #

Obtain a Fold that can be composed with to filter another Lens, Iso, Getter, Fold (or Traversal).

Note: This is not a legal Traversal, unless you are very careful not to invalidate the predicate on the target.

Note: This is also not a legal Prism, unless you are very careful not to inject a value that matches the predicate.

As a counter example, consider that given evens = filtered even the second Traversal law is violated:

over evens succ . over evens succ /= over evens (succ . succ)

So, in order for this to qualify as a legal Traversal you can only use it for actions that preserve the result of the predicate!

>>> [1..10]^..folded.filtered even
[2,4,6,8,10]

This will preserve an index if it is present.

takingWhile :: (Conjoined p, Applicative f) => (a -> Bool) -> Over p (TakingWhile p f a a) s t a a -> Over p f s t a a #

Obtain a Fold by taking elements from another Fold, Lens, Iso, Getter or Traversal while a predicate holds.

takeWhile p ≡ toListOf (takingWhile p folded)

>>> timingOut $ toListOf (takingWhile (<=3) folded) [1..]
[1,2,3]

takingWhile :: (a -> Bool) -> Fold s a                         -> Fold s a
takingWhile :: (a -> Bool) -> Getter s a                       -> Fold s a
takingWhile :: (a -> Bool) -> Traversal' s a                   -> Fold s a -- * See note below
takingWhile :: (a -> Bool) -> Lens' s a                        -> Fold s a -- * See note below
takingWhile :: (a -> Bool) -> Prism' s a                       -> Fold s a -- * See note below
takingWhile :: (a -> Bool) -> Iso' s a                         -> Fold s a -- * See note below
takingWhile :: (a -> Bool) -> IndexedTraversal' i s a          -> IndexedFold i s a -- * See note below
takingWhile :: (a -> Bool) -> IndexedLens' i s a               -> IndexedFold i s a -- * See note below
takingWhile :: (a -> Bool) -> IndexedFold i s a                -> IndexedFold i s a
takingWhile :: (a -> Bool) -> IndexedGetter i s a              -> IndexedFold i s a

Note: When applied to a Traversal, takingWhile yields something that can be used as if it were a Traversal, but which is not a Traversal per the laws, unless you are careful to ensure that you do not invalidate the predicate when writing back through it.

droppingWhile :: (Conjoined p, Profunctor q, Applicative f) => (a -> Bool) -> Optical p q (Compose (State Bool) f) s t a a -> Optical p q f s t a a #

Obtain a Fold by dropping elements from another Fold, Lens, Iso, Getter or Traversal while a predicate holds.

dropWhile p ≡ toListOf (droppingWhile p folded)

>>> toListOf (droppingWhile (<=3) folded) [1..6]
[4,5,6]

>>> toListOf (droppingWhile (<=3) folded) [1,6,1]
[6,1]

droppingWhile :: (a -> Bool) -> Fold s a                         -> Fold s a
droppingWhile :: (a -> Bool) -> Getter s a                       -> Fold s a
droppingWhile :: (a -> Bool) -> Traversal' s a                   -> Fold s a                -- see notes
droppingWhile :: (a -> Bool) -> Lens' s a                        -> Fold s a                -- see notes
droppingWhile :: (a -> Bool) -> Prism' s a                       -> Fold s a                -- see notes
droppingWhile :: (a -> Bool) -> Iso' s a                         -> Fold s a                -- see notes

droppingWhile :: (a -> Bool) -> IndexPreservingTraversal' s a    -> IndexPreservingFold s a -- see notes
droppingWhile :: (a -> Bool) -> IndexPreservingLens' s a         -> IndexPreservingFold s a -- see notes
droppingWhile :: (a -> Bool) -> IndexPreservingGetter s a        -> IndexPreservingFold s a
droppingWhile :: (a -> Bool) -> IndexPreservingFold s a          -> IndexPreservingFold s a

droppingWhile :: (a -> Bool) -> IndexedTraversal' i s a          -> IndexedFold i s a       -- see notes
droppingWhile :: (a -> Bool) -> IndexedLens' i s a               -> IndexedFold i s a       -- see notes
droppingWhile :: (a -> Bool) -> IndexedGetter i s a              -> IndexedFold i s a
droppingWhile :: (a -> Bool) -> IndexedFold i s a                -> IndexedFold i s a

Note: Many uses of this combinator will yield something that meets the types, but not the laws of a valid Traversal or IndexedTraversal. The Traversal and IndexedTraversal laws are only satisfied if the new values you assign to the first target also does not pass the predicate! Otherwise subsequent traversals will visit fewer elements and Traversal fusion is not sound.

So for any traversal t and predicate p, droppingWhile p t may not be lawful, but (dropping 1 . droppingWhile p) t is. For example:

>>> let l  :: Traversal' [Int] Int; l  = droppingWhile (<= 1) traverse
>>> let l' :: Traversal' [Int] Int; l' = dropping 1 l

l is not a lawful setter because over l f . over l g ≢ over l (f . g):

>>> [1,2,3] & l .~ 0 & l .~ 4
[1,0,0]
>>> [1,2,3] & l .~ 4
[1,4,4]

l' on the other hand behaves lawfully:

>>> [1,2,3] & l' .~ 0 & l' .~ 4
[1,2,4]
>>> [1,2,3] & l' .~ 4
[1,2,4]

worded :: Applicative f => IndexedLensLike' Int f String String #

A Fold over the individual words of a String.

worded :: Fold String String
worded :: Traversal' String String

worded :: IndexedFold Int String String
worded :: IndexedTraversal' Int String String

Note: This function type-checks as a Traversal but it doesn't satisfy the laws. It's only valid to use it when you don't insert any whitespace characters while traversing, and if your original String contains only isolated space characters (and no other characters that count as space, such as non-breaking spaces).

lined :: Applicative f => IndexedLensLike' Int f String String #

A Fold over the individual lines of a String.

lined :: Fold String String
lined :: Traversal' String String

lined :: IndexedFold Int String String
lined :: IndexedTraversal' Int String String

Note: This function type-checks as a Traversal but it doesn't satisfy the laws. It's only valid to use it when you don't insert any newline characters while traversing, and if your original String contains only isolated newline characters.

foldMapOf :: Getting r s a -> (a -> r) -> s -> r #

Map each part of a structure viewed through a Lens, Getter, Fold or Traversal to a monoid and combine the results.

>>> foldMapOf (folded . both . _Just) Sum [(Just 21, Just 21)]
Sum {getSum = 42}

foldMap = foldMapOf folded

foldMapOf ≡ views
ifoldMapOf l = foldMapOf l . Indexed

foldMapOf ::                Getter s a      -> (a -> r) -> s -> r
foldMapOf :: Monoid r    => Fold s a        -> (a -> r) -> s -> r
foldMapOf :: Semigroup r => Fold1 s a       -> (a -> r) -> s -> r
foldMapOf ::                Lens' s a       -> (a -> r) -> s -> r
foldMapOf ::                Iso' s a        -> (a -> r) -> s -> r
foldMapOf :: Monoid r    => Traversal' s a  -> (a -> r) -> s -> r
foldMapOf :: Semigroup r => Traversal1' s a -> (a -> r) -> s -> r
foldMapOf :: Monoid r    => Prism' s a      -> (a -> r) -> s -> r

foldMapOf :: Getting r s a -> (a -> r) -> s -> r

foldOf :: Getting a s a -> s -> a #

Combine the elements of a structure viewed through a Lens, Getter, Fold or Traversal using a monoid.

>>> foldOf (folded.folded) [[Sum 1,Sum 4],[Sum 8, Sum 8],[Sum 21]]
Sum {getSum = 42}

fold = foldOf folded

foldOf ≡ view

foldOf ::             Getter s m     -> s -> m
foldOf :: Monoid m => Fold s m       -> s -> m
foldOf ::             Lens' s m      -> s -> m
foldOf ::             Iso' s m       -> s -> m
foldOf :: Monoid m => Traversal' s m -> s -> m
foldOf :: Monoid m => Prism' s m     -> s -> m

foldrOf :: Getting (Endo r) s a -> (a -> r -> r) -> r -> s -> r #

Right-associative fold of parts of a structure that are viewed through a Lens, Getter, Fold or Traversal.

foldr ≡ foldrOf folded

foldrOf :: Getter s a     -> (a -> r -> r) -> r -> s -> r
foldrOf :: Fold s a       -> (a -> r -> r) -> r -> s -> r
foldrOf :: Lens' s a      -> (a -> r -> r) -> r -> s -> r
foldrOf :: Iso' s a       -> (a -> r -> r) -> r -> s -> r
foldrOf :: Traversal' s a -> (a -> r -> r) -> r -> s -> r
foldrOf :: Prism' s a     -> (a -> r -> r) -> r -> s -> r

ifoldrOf l ≡ foldrOf l . Indexed

foldrOf :: Getting (Endo r) s a -> (a -> r -> r) -> r -> s -> r

foldlOf :: Getting (Dual (Endo r)) s a -> (r -> a -> r) -> r -> s -> r #

Left-associative fold of the parts of a structure that are viewed through a Lens, Getter, Fold or Traversal.

foldl ≡ foldlOf folded

foldlOf :: Getter s a     -> (r -> a -> r) -> r -> s -> r
foldlOf :: Fold s a       -> (r -> a -> r) -> r -> s -> r
foldlOf :: Lens' s a      -> (r -> a -> r) -> r -> s -> r
foldlOf :: Iso' s a       -> (r -> a -> r) -> r -> s -> r
foldlOf :: Traversal' s a -> (r -> a -> r) -> r -> s -> r
foldlOf :: Prism' s a     -> (r -> a -> r) -> r -> s -> r

toListOf :: Getting (Endo [a]) s a -> s -> [a] #

Extract a list of the targets of a Fold. See also (^..).

toList ≡ toListOf folded
(^..) ≡ flip toListOf

toNonEmptyOf :: Getting (NonEmptyDList a) s a -> s -> NonEmpty a #

Extract a NonEmpty of the targets of Fold1.

>>> toNonEmptyOf both1 ("hello", "world")
"hello" :| ["world"]

toNonEmptyOf :: Getter s a      -> s -> NonEmpty a
toNonEmptyOf :: Fold1 s a       -> s -> NonEmpty a
toNonEmptyOf :: Lens' s a       -> s -> NonEmpty a
toNonEmptyOf :: Iso' s a        -> s -> NonEmpty a
toNonEmptyOf :: Traversal1' s a -> s -> NonEmpty a
toNonEmptyOf :: Prism' s a      -> s -> NonEmpty a

(^..) :: s -> Getting (Endo [a]) s a -> [a] infixl 8 #

A convenient infix (flipped) version of toListOf.

>>> [[1,2],[3]]^..id
[[[1,2],[3]]]
>>> [[1,2],[3]]^..traverse
[[1,2],[3]]
>>> [[1,2],[3]]^..traverse.traverse
[1,2,3]

>>> (1,2)^..both
[1,2]

toList xs ≡ xs ^.. folded
(^..) ≡ flip toListOf

(^..) :: s -> Getter s a     -> a :: s -> Fold s a       -> a :: s -> Lens' s a      -> a :: s -> Iso' s a       -> a :: s -> Traversal' s a -> a :: s -> Prism' s a     -> [a]

andOf :: Getting All s Bool -> s -> Bool #

Returns True if every target of a Fold is True.

>>> andOf both (True,False)
False
>>> andOf both (True,True)
True

and ≡ andOf folded

andOf :: Getter s Bool     -> s -> Bool
andOf :: Fold s Bool       -> s -> Bool
andOf :: Lens' s Bool      -> s -> Bool
andOf :: Iso' s Bool       -> s -> Bool
andOf :: Traversal' s Bool -> s -> Bool
andOf :: Prism' s Bool     -> s -> Bool

orOf :: Getting Any s Bool -> s -> Bool #

Returns True if any target of a Fold is True.

>>> orOf both (True,False)
True
>>> orOf both (False,False)
False

or ≡ orOf folded

orOf :: Getter s Bool     -> s -> Bool
orOf :: Fold s Bool       -> s -> Bool
orOf :: Lens' s Bool      -> s -> Bool
orOf :: Iso' s Bool       -> s -> Bool
orOf :: Traversal' s Bool -> s -> Bool
orOf :: Prism' s Bool     -> s -> Bool

anyOf :: Getting Any s a -> (a -> Bool) -> s -> Bool #

Returns True if any target of a Fold satisfies a predicate.

>>> anyOf both (=='x') ('x','y')
True
>>> import Data.Data.Lens
>>> anyOf biplate (== "world") (((),2::Int),"hello",("world",11::Int))
True

any ≡ anyOf folded

ianyOf l ≡ anyOf l . Indexed

anyOf :: Getter s a     -> (a -> Bool) -> s -> Bool
anyOf :: Fold s a       -> (a -> Bool) -> s -> Bool
anyOf :: Lens' s a      -> (a -> Bool) -> s -> Bool
anyOf :: Iso' s a       -> (a -> Bool) -> s -> Bool
anyOf :: Traversal' s a -> (a -> Bool) -> s -> Bool
anyOf :: Prism' s a     -> (a -> Bool) -> s -> Bool

allOf :: Getting All s a -> (a -> Bool) -> s -> Bool #

Returns True if every target of a Fold satisfies a predicate.

>>> allOf both (>=3) (4,5)
True
>>> allOf folded (>=2) [1..10]
False

all ≡ allOf folded

iallOf l = allOf l . Indexed

allOf :: Getter s a     -> (a -> Bool) -> s -> Bool
allOf :: Fold s a       -> (a -> Bool) -> s -> Bool
allOf :: Lens' s a      -> (a -> Bool) -> s -> Bool
allOf :: Iso' s a       -> (a -> Bool) -> s -> Bool
allOf :: Traversal' s a -> (a -> Bool) -> s -> Bool
allOf :: Prism' s a     -> (a -> Bool) -> s -> Bool

noneOf :: Getting Any s a -> (a -> Bool) -> s -> Bool #

Returns True only if no targets of a Fold satisfy a predicate.

>>> noneOf each (is _Nothing) (Just 3, Just 4, Just 5)
True
>>> noneOf (folded.folded) (<10) [[13,99,20],[3,71,42]]
False

inoneOf l = noneOf l . Indexed

noneOf :: Getter s a     -> (a -> Bool) -> s -> Bool
noneOf :: Fold s a       -> (a -> Bool) -> s -> Bool
noneOf :: Lens' s a      -> (a -> Bool) -> s -> Bool
noneOf :: Iso' s a       -> (a -> Bool) -> s -> Bool
noneOf :: Traversal' s a -> (a -> Bool) -> s -> Bool
noneOf :: Prism' s a     -> (a -> Bool) -> s -> Bool

productOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a #

Calculate the Product of every number targeted by a Fold.

>>> productOf both (4,5)
20
>>> productOf folded [1,2,3,4,5]
120

product ≡ productOf folded

This operation may be more strict than you would expect. If you want a lazier version use ala Product . foldMapOf

productOf :: Num a => Getter s a     -> s -> a
productOf :: Num a => Fold s a       -> s -> a
productOf :: Num a => Lens' s a      -> s -> a
productOf :: Num a => Iso' s a       -> s -> a
productOf :: Num a => Traversal' s a -> s -> a
productOf :: Num a => Prism' s a     -> s -> a

sumOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a #

Calculate the Sum of every number targeted by a Fold.

>>> sumOf both (5,6)
11
>>> sumOf folded [1,2,3,4]
10
>>> sumOf (folded.both) [(1,2),(3,4)]
10
>>> import Data.Data.Lens
>>> sumOf biplate [(1::Int,[]),(2,[(3::Int,4::Int)])] :: Int
10

sum ≡ sumOf folded

This operation may be more strict than you would expect. If you want a lazier version use ala Sum . foldMapOf

sumOf _1 :: Num a => (a, b) -> a
sumOf (folded . _1) :: (Foldable f, Num a) => f (a, b) -> a

sumOf :: Num a => Getter s a     -> s -> a
sumOf :: Num a => Fold s a       -> s -> a
sumOf :: Num a => Lens' s a      -> s -> a
sumOf :: Num a => Iso' s a       -> s -> a
sumOf :: Num a => Traversal' s a -> s -> a
sumOf :: Num a => Prism' s a     -> s -> a

traverseOf_ :: Functor f => Getting (Traversed r f) s a -> (a -> f r) -> s -> f () #

Traverse over all of the targets of a Fold (or Getter), computing an Applicative (or Functor)-based answer, but unlike traverseOf do not construct a new structure. traverseOf_ generalizes traverse_ to work over any Fold.

When passed a Getter, traverseOf_ can work over any Functor, but when passed a Fold, traverseOf_ requires an Applicative.

>>> traverseOf_ both putStrLn ("hello","world")
hello
world

traverse_ ≡ traverseOf_ folded

traverseOf_ _2 :: Functor f => (c -> f r) -> (d, c) -> f ()
traverseOf_ _Left :: Applicative f => (a -> f b) -> Either a c -> f ()

itraverseOf_ l ≡ traverseOf_ l . Indexed

The rather specific signature of traverseOf_ allows it to be used as if the signature was any of:

traverseOf_ :: Functor f     => Getter s a     -> (a -> f r) -> s -> f ()
traverseOf_ :: Applicative f => Fold s a       -> (a -> f r) -> s -> f ()
traverseOf_ :: Functor f     => Lens' s a      -> (a -> f r) -> s -> f ()
traverseOf_ :: Functor f     => Iso' s a       -> (a -> f r) -> s -> f ()
traverseOf_ :: Applicative f => Traversal' s a -> (a -> f r) -> s -> f ()
traverseOf_ :: Applicative f => Prism' s a     -> (a -> f r) -> s -> f ()

forOf_ :: Functor f => Getting (Traversed r f) s a -> s -> (a -> f r) -> f () #

Traverse over all of the targets of a Fold (or Getter), computing an Applicative (or Functor)-based answer, but unlike forOf do not construct a new structure. forOf_ generalizes for_ to work over any Fold.

When passed a Getter, forOf_ can work over any Functor, but when passed a Fold, forOf_ requires an Applicative.

for_ ≡ forOf_ folded

>>> forOf_ both ("hello","world") putStrLn
hello
world

The rather specific signature of forOf_ allows it to be used as if the signature was any of:

iforOf_ l s ≡ forOf_ l s . Indexed

forOf_ :: Functor f     => Getter s a     -> s -> (a -> f r) -> f ()
forOf_ :: Applicative f => Fold s a       -> s -> (a -> f r) -> f ()
forOf_ :: Functor f     => Lens' s a      -> s -> (a -> f r) -> f ()
forOf_ :: Functor f     => Iso' s a       -> s -> (a -> f r) -> f ()
forOf_ :: Applicative f => Traversal' s a -> s -> (a -> f r) -> f ()
forOf_ :: Applicative f => Prism' s a     -> s -> (a -> f r) -> f ()

sequenceAOf_ :: Functor f => Getting (Traversed a f) s (f a) -> s -> f () #

Evaluate each action in observed by a Fold on a structure from left to right, ignoring the results.

sequenceA_ ≡ sequenceAOf_ folded

>>> sequenceAOf_ both (putStrLn "hello",putStrLn "world")
hello
world

sequenceAOf_ :: Functor f     => Getter s (f a)     -> s -> f ()
sequenceAOf_ :: Applicative f => Fold s (f a)       -> s -> f ()
sequenceAOf_ :: Functor f     => Lens' s (f a)      -> s -> f ()
sequenceAOf_ :: Functor f     => Iso' s (f a)       -> s -> f ()
sequenceAOf_ :: Applicative f => Traversal' s (f a) -> s -> f ()
sequenceAOf_ :: Applicative f => Prism' s (f a)     -> s -> f ()

traverse1Of_ :: Functor f => Getting (TraversedF r f) s a -> (a -> f r) -> s -> f () #

Traverse over all of the targets of a Fold1, computing an Apply based answer.

As long as you have Applicative or Functor effect you are better using traverseOf_. The traverse1Of_ is useful only when you have genuine Apply effect.

>>> traverse1Of_ both1 (\ks -> Map.fromList [ (k, ()) | k <- ks ]) ("abc", "bcd")
fromList [('b',()),('c',())]

traverse1Of_ :: Apply f => Fold1 s a -> (a -> f r) -> s -> f ()

Since: lens-4.16

for1Of_ :: Functor f => Getting (TraversedF r f) s a -> s -> (a -> f r) -> f () #

See forOf_ and traverse1Of_.

>>> for1Of_ both1 ("abc", "bcd") (\ks -> Map.fromList [ (k, ()) | k <- ks ])
fromList [('b',()),('c',())]

for1Of_ :: Apply f => Fold1 s a -> s -> (a -> f r) -> f ()

Since: lens-4.16

sequence1Of_ :: Functor f => Getting (TraversedF a f) s (f a) -> s -> f () #

See sequenceAOf_ and traverse1Of_.

sequence1Of_ :: Apply f => Fold1 s (f a) -> s -> f ()

Since: lens-4.16

mapMOf_ :: Monad m => Getting (Sequenced r m) s a -> (a -> m r) -> s -> m () #

Map each target of a Fold on a structure to a monadic action, evaluate these actions from left to right, and ignore the results.

>>> mapMOf_ both putStrLn ("hello","world")
hello
world

mapM_ ≡ mapMOf_ folded

mapMOf_ :: Monad m => Getter s a     -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Fold s a       -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Lens' s a      -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Iso' s a       -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Traversal' s a -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Prism' s a     -> (a -> m r) -> s -> m ()

forMOf_ :: Monad m => Getting (Sequenced r m) s a -> s -> (a -> m r) -> m () #

forMOf_ is mapMOf_ with two of its arguments flipped.

>>> forMOf_ both ("hello","world") putStrLn
hello
world

forM_ ≡ forMOf_ folded

forMOf_ :: Monad m => Getter s a     -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Fold s a       -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Lens' s a      -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Iso' s a       -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Traversal' s a -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Prism' s a     -> s -> (a -> m r) -> m ()

sequenceOf_ :: Monad m => Getting (Sequenced a m) s (m a) -> s -> m () #

Evaluate each monadic action referenced by a Fold on the structure from left to right, and ignore the results.

>>> sequenceOf_ both (putStrLn "hello",putStrLn "world")
hello
world

sequence_ ≡ sequenceOf_ folded

sequenceOf_ :: Monad m => Getter s (m a)     -> s -> m ()
sequenceOf_ :: Monad m => Fold s (m a)       -> s -> m ()
sequenceOf_ :: Monad m => Lens' s (m a)      -> s -> m ()
sequenceOf_ :: Monad m => Iso' s (m a)       -> s -> m ()
sequenceOf_ :: Monad m => Traversal' s (m a) -> s -> m ()
sequenceOf_ :: Monad m => Prism' s (m a)     -> s -> m ()

asumOf :: Alternative f => Getting (Endo (f a)) s (f a) -> s -> f a #

The sum of a collection of actions, generalizing concatOf.

>>> asumOf both ("hello","world")
"helloworld"

>>> asumOf each (Nothing, Just "hello", Nothing)
Just "hello"

asum ≡ asumOf folded

asumOf :: Alternative f => Getter s (f a)     -> s -> f a
asumOf :: Alternative f => Fold s (f a)       -> s -> f a
asumOf :: Alternative f => Lens' s (f a)      -> s -> f a
asumOf :: Alternative f => Iso' s (f a)       -> s -> f a
asumOf :: Alternative f => Traversal' s (f a) -> s -> f a
asumOf :: Alternative f => Prism' s (f a)     -> s -> f a

msumOf :: MonadPlus m => Getting (Endo (m a)) s (m a) -> s -> m a #

The sum of a collection of actions, generalizing concatOf.

>>> msumOf both ("hello","world")
"helloworld"

>>> msumOf each (Nothing, Just "hello", Nothing)
Just "hello"

msum ≡ msumOf folded

msumOf :: MonadPlus m => Getter s (m a)     -> s -> m a
msumOf :: MonadPlus m => Fold s (m a)       -> s -> m a
msumOf :: MonadPlus m => Lens' s (m a)      -> s -> m a
msumOf :: MonadPlus m => Iso' s (m a)       -> s -> m a
msumOf :: MonadPlus m => Traversal' s (m a) -> s -> m a
msumOf :: MonadPlus m => Prism' s (m a)     -> s -> m a

elemOf :: Eq a => Getting Any s a -> a -> s -> Bool #

Does the element occur anywhere within a given Fold of the structure?

>>> elemOf both "hello" ("hello","world")
True

elem ≡ elemOf folded

elemOf :: Eq a => Getter s a     -> a -> s -> Bool
elemOf :: Eq a => Fold s a       -> a -> s -> Bool
elemOf :: Eq a => Lens' s a      -> a -> s -> Bool
elemOf :: Eq a => Iso' s a       -> a -> s -> Bool
elemOf :: Eq a => Traversal' s a -> a -> s -> Bool
elemOf :: Eq a => Prism' s a     -> a -> s -> Bool

notElemOf :: Eq a => Getting All s a -> a -> s -> Bool #

Does the element not occur anywhere within a given Fold of the structure?

>>> notElemOf each 'd' ('a','b','c')
True

>>> notElemOf each 'a' ('a','b','c')
False

notElem ≡ notElemOf folded

notElemOf :: Eq a => Getter s a     -> a -> s -> Bool
notElemOf :: Eq a => Fold s a       -> a -> s -> Bool
notElemOf :: Eq a => Iso' s a       -> a -> s -> Bool
notElemOf :: Eq a => Lens' s a      -> a -> s -> Bool
notElemOf :: Eq a => Traversal' s a -> a -> s -> Bool
notElemOf :: Eq a => Prism' s a     -> a -> s -> Bool

concatMapOf :: Getting [r] s a -> (a -> [r]) -> s -> [r] #

Map a function over all the targets of a Fold of a container and concatenate the resulting lists.

>>> concatMapOf both (\x -> [x, x + 1]) (1,3)
[1,2,3,4]

concatMap ≡ concatMapOf folded

concatMapOf :: Getter s a     -> (a -> [r]) -> s -> [r]
concatMapOf :: Fold s a       -> (a -> [r]) -> s -> [r]
concatMapOf :: Lens' s a      -> (a -> [r]) -> s -> [r]
concatMapOf :: Iso' s a       -> (a -> [r]) -> s -> [r]
concatMapOf :: Traversal' s a -> (a -> [r]) -> s -> [r]

concatOf :: Getting [r] s [r] -> s -> [r] #

Concatenate all of the lists targeted by a Fold into a longer list.

>>> concatOf both ("pan","ama")
"panama"

concat ≡ concatOf folded
concatOf ≡ view

concatOf :: Getter s [r]     -> s -> [r]
concatOf :: Fold s [r]       -> s -> [r]
concatOf :: Iso' s [r]       -> s -> [r]
concatOf :: Lens' s [r]      -> s -> [r]
concatOf :: Traversal' s [r] -> s -> [r]

lengthOf :: Getting (Endo (Endo Int)) s a -> s -> Int #

Calculate the number of targets there are for a Fold in a given container.

Note: This can be rather inefficient for large containers and just like length, this will not terminate for infinite folds.

length ≡ lengthOf folded

>>> lengthOf _1 ("hello",())
1

>>> lengthOf traverse [1..10]
10

>>> lengthOf (traverse.traverse) [[1,2],[3,4],[5,6]]
6

lengthOf (folded . folded) :: (Foldable f, Foldable g) => f (g a) -> Int

lengthOf :: Getter s a     -> s -> Int
lengthOf :: Fold s a       -> s -> Int
lengthOf :: Lens' s a      -> s -> Int
lengthOf :: Iso' s a       -> s -> Int
lengthOf :: Traversal' s a -> s -> Int

(^?) :: s -> Getting (First a) s a -> Maybe a infixl 8 #

Perform a safe head of a Fold or Traversal or retrieve Just the result from a Getter or Lens.

When using a Traversal as a partial Lens, or a Fold as a partial Getter this can be a convenient way to extract the optional value.

Note: if you get stack overflows due to this, you may want to use firstOf instead, which can deal more gracefully with heavily left-biased trees.

>>> Left 4 ^?_Left
Just 4

>>> Right 4 ^?_Left
Nothing

>>> "world" ^? ix 3
Just 'l'

>>> "world" ^? ix 20
Nothing

(^?) ≡ flip preview

(^?) :: s -> Getter s a     -> Maybe a
(^?) :: s -> Fold s a       -> Maybe a
(^?) :: s -> Lens' s a      -> Maybe a
(^?) :: s -> Iso' s a       -> Maybe a
(^?) :: s -> Traversal' s a -> Maybe a

(^?!) :: HasCallStack => s -> Getting (Endo a) s a -> a infixl 8 #

Perform an *UNSAFE* head of a Fold or Traversal assuming that it is there.

>>> Left 4 ^?! _Left
4

>>> "world" ^?! ix 3
'l'

(^?!) :: s -> Getter s a     -> a
(^?!) :: s -> Fold s a       -> a
(^?!) :: s -> Lens' s a      -> a
(^?!) :: s -> Iso' s a       -> a
(^?!) :: s -> Traversal' s a -> a

firstOf :: Getting (Leftmost a) s a -> s -> Maybe a #

Retrieve the First entry of a Fold or Traversal or retrieve Just the result from a Getter or Lens.

The answer is computed in a manner that leaks space less than ala First . foldMapOf and gives you back access to the outermost Just constructor more quickly, but may have worse constant factors.

Note: this could been named headOf.

>>> firstOf traverse [1..10]
Just 1

>>> firstOf both (1,2)
Just 1

>>> firstOf ignored ()
Nothing

firstOf :: Getter s a     -> s -> Maybe a
firstOf :: Fold s a       -> s -> Maybe a
firstOf :: Lens' s a      -> s -> Maybe a
firstOf :: Iso' s a       -> s -> Maybe a
firstOf :: Traversal' s a -> s -> Maybe a

first1Of :: Getting (First a) s a -> s -> a #

Retrieve the First entry of a Fold1 or Traversal1 or the result from a Getter or Lens.

>>> first1Of traverse1 (1 :| [2..10])
1

>>> first1Of both1 (1,2)
1

Note: this is different from ^..

>>> first1Of traverse1 ([1,2] :| [[3,4],[5,6]])
[1,2]

>>> ([1,2] :| [[3,4],[5,6]]) ^. traverse1
[1,2,3,4,5,6]

first1Of :: Getter s a      -> s -> a
first1Of :: Fold1 s a       -> s -> a
first1Of :: Lens' s a       -> s -> a
first1Of :: Iso' s a        -> s -> a
first1Of :: Traversal1' s a -> s -> a

lastOf :: Getting (Rightmost a) s a -> s -> Maybe a #

Retrieve the Last entry of a Fold or Traversal or retrieve Just the result from a Getter or Lens.

The answer is computed in a manner that leaks space less than ala Last . foldMapOf and gives you back access to the outermost Just constructor more quickly, but may have worse constant factors.

>>> lastOf traverse [1..10]
Just 10

>>> lastOf both (1,2)
Just 2

>>> lastOf ignored ()
Nothing

lastOf :: Getter s a     -> s -> Maybe a
lastOf :: Fold s a       -> s -> Maybe a
lastOf :: Lens' s a      -> s -> Maybe a
lastOf :: Iso' s a       -> s -> Maybe a
lastOf :: Traversal' s a -> s -> Maybe a

last1Of :: Getting (Last a) s a -> s -> a #

Retrieve the Last entry of a Fold1 or Traversal1 or retrieve the result from a Getter or Lens.o

>>> last1Of traverse1 (1 :| [2..10])
10

>>> last1Of both1 (1,2)
2

last1Of :: Getter s a      -> s -> Maybe a
last1Of :: Fold1 s a       -> s -> Maybe a
last1Of :: Lens' s a       -> s -> Maybe a
last1Of :: Iso' s a        -> s -> Maybe a
last1Of :: Traversal1' s a -> s -> Maybe a

nullOf :: Getting All s a -> s -> Bool #

Returns True if this Fold or Traversal has no targets in the given container.

Note: nullOf on a valid Iso, Lens or Getter should always return False.

null ≡ nullOf folded

This may be rather inefficient compared to the null check of many containers.

>>> nullOf _1 (1,2)
False

>>> nullOf ignored ()
True

>>> nullOf traverse []
True

>>> nullOf (element 20) [1..10]
True

nullOf (folded . _1 . folded) :: (Foldable f, Foldable g) => f (g a, b) -> Bool

nullOf :: Getter s a     -> s -> Bool
nullOf :: Fold s a       -> s -> Bool
nullOf :: Iso' s a       -> s -> Bool
nullOf :: Lens' s a      -> s -> Bool
nullOf :: Traversal' s a -> s -> Bool

notNullOf :: Getting Any s a -> s -> Bool #

Returns True if this Fold or Traversal has any targets in the given container.

A more "conversational" alias for this combinator is has.

Note: notNullOf on a valid Iso, Lens or Getter should always return True.

not . null ≡ notNullOf folded

This may be rather inefficient compared to the not . null check of many containers.

>>> notNullOf _1 (1,2)
True

>>> notNullOf traverse [1..10]
True

>>> notNullOf folded []
False

>>> notNullOf (element 20) [1..10]
False

notNullOf (folded . _1 . folded) :: (Foldable f, Foldable g) => f (g a, b) -> Bool

notNullOf :: Getter s a     -> s -> Bool
notNullOf :: Fold s a       -> s -> Bool
notNullOf :: Iso' s a       -> s -> Bool
notNullOf :: Lens' s a      -> s -> Bool
notNullOf :: Traversal' s a -> s -> Bool

maximumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a #

Obtain the maximum element (if any) targeted by a Fold or Traversal safely.

Note: maximumOf on a valid Iso, Lens or Getter will always return Just a value.

>>> maximumOf traverse [1..10]
Just 10

>>> maximumOf traverse []
Nothing

>>> maximumOf (folded.filtered even) [1,4,3,6,7,9,2]
Just 6

maximum ≡ fromMaybe (error "empty") . maximumOf folded

In the interest of efficiency, This operation has semantics more strict than strictly necessary. rmap getMax (foldMapOf l Max) has lazier semantics but could leak memory.

maximumOf :: Ord a => Getter s a     -> s -> Maybe a
maximumOf :: Ord a => Fold s a       -> s -> Maybe a
maximumOf :: Ord a => Iso' s a       -> s -> Maybe a
maximumOf :: Ord a => Lens' s a      -> s -> Maybe a
maximumOf :: Ord a => Traversal' s a -> s -> Maybe a

maximum1Of :: Ord a => Getting (Max a) s a -> s -> a #

Obtain the maximum element targeted by a Fold1 or Traversal1.

>>> maximum1Of traverse1 (1 :| [2..10])
10

maximum1Of :: Ord a => Getter s a      -> s -> a
maximum1Of :: Ord a => Fold1 s a       -> s -> a
maximum1Of :: Ord a => Iso' s a        -> s -> a
maximum1Of :: Ord a => Lens' s a       -> s -> a
maximum1Of :: Ord a => Traversal1' s a -> s -> a

minimumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a #

Obtain the minimum element (if any) targeted by a Fold or Traversal safely.

Note: minimumOf on a valid Iso, Lens or Getter will always return Just a value.

>>> minimumOf traverse [1..10]
Just 1

>>> minimumOf traverse []
Nothing

>>> minimumOf (folded.filtered even) [1,4,3,6,7,9,2]
Just 2

minimum ≡ fromMaybe (error "empty") . minimumOf folded

In the interest of efficiency, This operation has semantics more strict than strictly necessary. rmap getMin (foldMapOf l Min) has lazier semantics but could leak memory.

minimumOf :: Ord a => Getter s a     -> s -> Maybe a
minimumOf :: Ord a => Fold s a       -> s -> Maybe a
minimumOf :: Ord a => Iso' s a       -> s -> Maybe a
minimumOf :: Ord a => Lens' s a      -> s -> Maybe a
minimumOf :: Ord a => Traversal' s a -> s -> Maybe a

minimum1Of :: Ord a => Getting (Min a) s a -> s -> a #

Obtain the minimum element targeted by a Fold1 or Traversal1.

>>> minimum1Of traverse1 (1 :| [2..10])
1

minimum1Of :: Ord a => Getter s a      -> s -> a
minimum1Of :: Ord a => Fold1 s a       -> s -> a
minimum1Of :: Ord a => Iso' s a        -> s -> a
minimum1Of :: Ord a => Lens' s a       -> s -> a
minimum1Of :: Ord a => Traversal1' s a -> s -> a

maximumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a #

Obtain the maximum element (if any) targeted by a Fold, Traversal, Lens, Iso, or Getter according to a user supplied Ordering.

>>> maximumByOf traverse (compare `on` length) ["mustard","relish","ham"]
Just "mustard"

In the interest of efficiency, This operation has semantics more strict than strictly necessary.

maximumBy cmp ≡ fromMaybe (error "empty") . maximumByOf folded cmp

maximumByOf :: Getter s a     -> (a -> a -> Ordering) -> s -> Maybe a
maximumByOf :: Fold s a       -> (a -> a -> Ordering) -> s -> Maybe a
maximumByOf :: Iso' s a       -> (a -> a -> Ordering) -> s -> Maybe a
maximumByOf :: Lens' s a      -> (a -> a -> Ordering) -> s -> Maybe a
maximumByOf :: Traversal' s a -> (a -> a -> Ordering) -> s -> Maybe a

minimumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a #

Obtain the minimum element (if any) targeted by a Fold, Traversal, Lens, Iso or Getter according to a user supplied Ordering.

In the interest of efficiency, This operation has semantics more strict than strictly necessary.

>>> minimumByOf traverse (compare `on` length) ["mustard","relish","ham"]
Just "ham"

minimumBy cmp ≡ fromMaybe (error "empty") . minimumByOf folded cmp

minimumByOf :: Getter s a     -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Fold s a       -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Iso' s a       -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Lens' s a      -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Traversal' s a -> (a -> a -> Ordering) -> s -> Maybe a

findOf :: Getting (Endo (Maybe a)) s a -> (a -> Bool) -> s -> Maybe a #

The findOf function takes a Lens (or Getter, Iso, Fold, or Traversal), a predicate and a structure and returns the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

>>> findOf each even (1,3,4,6)
Just 4

>>> findOf folded even [1,3,5,7]
Nothing

findOf :: Getter s a     -> (a -> Bool) -> s -> Maybe a
findOf :: Fold s a       -> (a -> Bool) -> s -> Maybe a
findOf :: Iso' s a       -> (a -> Bool) -> s -> Maybe a
findOf :: Lens' s a      -> (a -> Bool) -> s -> Maybe a
findOf :: Traversal' s a -> (a -> Bool) -> s -> Maybe a

find ≡ findOf folded
ifindOf l ≡ findOf l . Indexed

A simpler version that didn't permit indexing, would be:

findOf :: Getting (Endo (Maybe a)) s a -> (a -> Bool) -> s -> Maybe a
findOf l p = foldrOf l (a y -> if p a then Just a else y) Nothing

findMOf :: Monad m => Getting (Endo (m (Maybe a))) s a -> (a -> m Bool) -> s -> m (Maybe a) #

The findMOf function takes a Lens (or Getter, Iso, Fold, or Traversal), a monadic predicate and a structure and returns in the monad the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

>>> findMOf each ( \x -> print ("Checking " ++ show x) >> return (even x)) (1,3,4,6)
"Checking 1"
"Checking 3"
"Checking 4"
Just 4

>>> findMOf each ( \x -> print ("Checking " ++ show x) >> return (even x)) (1,3,5,7)
"Checking 1"
"Checking 3"
"Checking 5"
"Checking 7"
Nothing

findMOf :: (Monad m, Getter s a)     -> (a -> m Bool) -> s -> m (Maybe a)
findMOf :: (Monad m, Fold s a)       -> (a -> m Bool) -> s -> m (Maybe a)
findMOf :: (Monad m, Iso' s a)       -> (a -> m Bool) -> s -> m (Maybe a)
findMOf :: (Monad m, Lens' s a)      -> (a -> m Bool) -> s -> m (Maybe a)
findMOf :: (Monad m, Traversal' s a) -> (a -> m Bool) -> s -> m (Maybe a)

findMOf folded :: (Monad m, Foldable f) => (a -> m Bool) -> f a -> m (Maybe a)
ifindMOf l ≡ findMOf l . Indexed

A simpler version that didn't permit indexing, would be:

findMOf :: Monad m => Getting (Endo (m (Maybe a))) s a -> (a -> m Bool) -> s -> m (Maybe a)
findMOf l p = foldrOf l (a y -> p a >>= x -> if x then return (Just a) else y) $ return Nothing

lookupOf :: Eq k => Getting (Endo (Maybe v)) s (k, v) -> k -> s -> Maybe v #

The lookupOf function takes a Fold (or Getter, Traversal, Lens, Iso, etc.), a key, and a structure containing key/value pairs. It returns the first value corresponding to the given key. This function generalizes lookup to work on an arbitrary Fold instead of lists.

>>> lookupOf folded 4 [(2, 'a'), (4, 'b'), (4, 'c')]
Just 'b'

>>> lookupOf each 2 [(2, 'a'), (4, 'b'), (4, 'c')]
Just 'a'

lookupOf :: Eq k => Fold s (k,v) -> k -> s -> Maybe v

foldr1Of :: HasCallStack => Getting (Endo (Maybe a)) s a -> (a -> a -> a) -> s -> a #

A variant of foldrOf that has no base case and thus may only be applied to lenses and structures such that the Lens views at least one element of the structure.

>>> foldr1Of each (+) (1,2,3,4)
10

foldr1Of l f ≡ foldr1 f . toListOf l
foldr1 ≡ foldr1Of folded

foldr1Of :: Getter s a     -> (a -> a -> a) -> s -> a
foldr1Of :: Fold s a       -> (a -> a -> a) -> s -> a
foldr1Of :: Iso' s a       -> (a -> a -> a) -> s -> a
foldr1Of :: Lens' s a      -> (a -> a -> a) -> s -> a
foldr1Of :: Traversal' s a -> (a -> a -> a) -> s -> a

foldl1Of :: HasCallStack => Getting (Dual (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a #

A variant of foldlOf that has no base case and thus may only be applied to lenses and structures such that the Lens views at least one element of the structure.

>>> foldl1Of each (+) (1,2,3,4)
10

foldl1Of l f ≡ foldl1 f . toListOf l
foldl1 ≡ foldl1Of folded

foldl1Of :: Getter s a     -> (a -> a -> a) -> s -> a
foldl1Of :: Fold s a       -> (a -> a -> a) -> s -> a
foldl1Of :: Iso' s a       -> (a -> a -> a) -> s -> a
foldl1Of :: Lens' s a      -> (a -> a -> a) -> s -> a
foldl1Of :: Traversal' s a -> (a -> a -> a) -> s -> a

foldrOf' :: Getting (Dual (Endo (Endo r))) s a -> (a -> r -> r) -> r -> s -> r #

Strictly fold right over the elements of a structure.

foldr' ≡ foldrOf' folded

foldrOf' :: Getter s a     -> (a -> r -> r) -> r -> s -> r
foldrOf' :: Fold s a       -> (a -> r -> r) -> r -> s -> r
foldrOf' :: Iso' s a       -> (a -> r -> r) -> r -> s -> r
foldrOf' :: Lens' s a      -> (a -> r -> r) -> r -> s -> r
foldrOf' :: Traversal' s a -> (a -> r -> r) -> r -> s -> r

foldlOf' :: Getting (Endo (Endo r)) s a -> (r -> a -> r) -> r -> s -> r #

Fold over the elements of a structure, associating to the left, but strictly.

foldl' ≡ foldlOf' folded

foldlOf' :: Getter s a     -> (r -> a -> r) -> r -> s -> r
foldlOf' :: Fold s a       -> (r -> a -> r) -> r -> s -> r
foldlOf' :: Iso' s a       -> (r -> a -> r) -> r -> s -> r
foldlOf' :: Lens' s a      -> (r -> a -> r) -> r -> s -> r
foldlOf' :: Traversal' s a -> (r -> a -> r) -> r -> s -> r

foldr1Of' :: HasCallStack => Getting (Dual (Endo (Endo (Maybe a)))) s a -> (a -> a -> a) -> s -> a #

A variant of foldrOf' that has no base case and thus may only be applied to folds and structures such that the fold views at least one element of the structure.

foldr1Of l f ≡ foldr1 f . toListOf l

foldr1Of' :: Getter s a     -> (a -> a -> a) -> s -> a
foldr1Of' :: Fold s a       -> (a -> a -> a) -> s -> a
foldr1Of' :: Iso' s a       -> (a -> a -> a) -> s -> a
foldr1Of' :: Lens' s a      -> (a -> a -> a) -> s -> a
foldr1Of' :: Traversal' s a -> (a -> a -> a) -> s -> a

foldl1Of' :: HasCallStack => Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a #

A variant of foldlOf' that has no base case and thus may only be applied to folds and structures such that the fold views at least one element of the structure.

foldl1Of' l f ≡ foldl1' f . toListOf l

foldl1Of' :: Getter s a     -> (a -> a -> a) -> s -> a
foldl1Of' :: Fold s a       -> (a -> a -> a) -> s -> a
foldl1Of' :: Iso' s a       -> (a -> a -> a) -> s -> a
foldl1Of' :: Lens' s a      -> (a -> a -> a) -> s -> a
foldl1Of' :: Traversal' s a -> (a -> a -> a) -> s -> a

foldrMOf :: Monad m => Getting (Dual (Endo (r -> m r))) s a -> (a -> r -> m r) -> r -> s -> m r #

Monadic fold over the elements of a structure, associating to the right, i.e. from right to left.

foldrM ≡ foldrMOf folded

foldrMOf :: Monad m => Getter s a     -> (a -> r -> m r) -> r -> s -> m r
foldrMOf :: Monad m => Fold s a       -> (a -> r -> m r) -> r -> s -> m r
foldrMOf :: Monad m => Iso' s a       -> (a -> r -> m r) -> r -> s -> m r
foldrMOf :: Monad m => Lens' s a      -> (a -> r -> m r) -> r -> s -> m r
foldrMOf :: Monad m => Traversal' s a -> (a -> r -> m r) -> r -> s -> m r

foldlMOf :: Monad m => Getting (Endo (r -> m r)) s a -> (r -> a -> m r) -> r -> s -> m r #

Monadic fold over the elements of a structure, associating to the left, i.e. from left to right.

foldlM ≡ foldlMOf folded

foldlMOf :: Monad m => Getter s a     -> (r -> a -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Fold s a       -> (r -> a -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Iso' s a       -> (r -> a -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Lens' s a      -> (r -> a -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Traversal' s a -> (r -> a -> m r) -> r -> s -> m r

has :: Getting Any s a -> s -> Bool #

Check to see if this Fold or Traversal matches 1 or more entries.

>>> has (element 0) []
False

>>> has _Left (Left 12)
True

>>> has _Right (Left 12)
False

This will always return True for a Lens or Getter.

>>> has _1 ("hello","world")
True

has :: Getter s a     -> s -> Bool
has :: Fold s a       -> s -> Bool
has :: Iso' s a       -> s -> Bool
has :: Lens' s a      -> s -> Bool
has :: Traversal' s a -> s -> Bool

hasn't :: Getting All s a -> s -> Bool #

Check to see if this Fold or Traversal has no matches.

>>> hasn't _Left (Right 12)
True

>>> hasn't _Left (Left 12)
False

pre :: Getting (First a) s a -> IndexPreservingGetter s (Maybe a) #

This converts a Fold to a IndexPreservingGetter that returns the first element, if it exists, as a Maybe.

pre :: Getter s a     -> IndexPreservingGetter s (Maybe a)
pre :: Fold s a       -> IndexPreservingGetter s (Maybe a)
pre :: Traversal' s a -> IndexPreservingGetter s (Maybe a)
pre :: Lens' s a      -> IndexPreservingGetter s (Maybe a)
pre :: Iso' s a       -> IndexPreservingGetter s (Maybe a)
pre :: Prism' s a     -> IndexPreservingGetter s (Maybe a)

ipre :: IndexedGetting i (First (i, a)) s a -> IndexPreservingGetter s (Maybe (i, a)) #

This converts an IndexedFold to an IndexPreservingGetter that returns the first index and element, if they exist, as a Maybe.

ipre :: IndexedGetter i s a     -> IndexPreservingGetter s (Maybe (i, a))
ipre :: IndexedFold i s a       -> IndexPreservingGetter s (Maybe (i, a))
ipre :: IndexedTraversal' i s a -> IndexPreservingGetter s (Maybe (i, a))
ipre :: IndexedLens' i s a      -> IndexPreservingGetter s (Maybe (i, a))

preview :: MonadReader s m => Getting (First a) s a -> m (Maybe a) #

Retrieve the first value targeted by a Fold or Traversal (or Just the result from a Getter or Lens). See also (^?).

listToMaybe . toList ≡ preview folded

This is usually applied in the Reader Monad (->) s.

preview = view . pre

preview :: Getter s a     -> s -> Maybe a
preview :: Fold s a       -> s -> Maybe a
preview :: Lens' s a      -> s -> Maybe a
preview :: Iso' s a       -> s -> Maybe a
preview :: Traversal' s a -> s -> Maybe a

However, it may be useful to think of its full generality when working with a Monad transformer stack:

preview :: MonadReader s m => Getter s a     -> m (Maybe a)
preview :: MonadReader s m => Fold s a       -> m (Maybe a)
preview :: MonadReader s m => Lens' s a      -> m (Maybe a)
preview :: MonadReader s m => Iso' s a       -> m (Maybe a)
preview :: MonadReader s m => Traversal' s a -> m (Maybe a)

ipreview :: MonadReader s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a)) #

Retrieve the first index and value targeted by a Fold or Traversal (or Just the result from a Getter or Lens). See also (^@?).

ipreview = view . ipre

This is usually applied in the Reader Monad (->) s.

ipreview :: IndexedGetter i s a     -> s -> Maybe (i, a)
ipreview :: IndexedFold i s a       -> s -> Maybe (i, a)
ipreview :: IndexedLens' i s a      -> s -> Maybe (i, a)
ipreview :: IndexedTraversal' i s a -> s -> Maybe (i, a)

However, it may be useful to think of its full generality when working with a Monad transformer stack:

ipreview :: MonadReader s m => IndexedGetter s a     -> m (Maybe (i, a))
ipreview :: MonadReader s m => IndexedFold s a       -> m (Maybe (i, a))
ipreview :: MonadReader s m => IndexedLens' s a      -> m (Maybe (i, a))
ipreview :: MonadReader s m => IndexedTraversal' s a -> m (Maybe (i, a))

previews :: MonadReader s m => Getting (First r) s a -> (a -> r) -> m (Maybe r) #

Retrieve a function of the first value targeted by a Fold or Traversal (or Just the result from a Getter or Lens).

This is usually applied in the Reader Monad (->) s.

ipreviews :: MonadReader s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r) #

Retrieve a function of the first index and value targeted by an IndexedFold or IndexedTraversal (or Just the result from an IndexedGetter or IndexedLens). See also (^@?).

ipreviews = views . ipre

This is usually applied in the Reader Monad (->) s.

ipreviews :: IndexedGetter i s a     -> (i -> a -> r) -> s -> Maybe r
ipreviews :: IndexedFold i s a       -> (i -> a -> r) -> s -> Maybe r
ipreviews :: IndexedLens' i s a      -> (i -> a -> r) -> s -> Maybe r
ipreviews :: IndexedTraversal' i s a -> (i -> a -> r) -> s -> Maybe r

However, it may be useful to think of its full generality when working with a Monad transformer stack:

ipreviews :: MonadReader s m => IndexedGetter i s a     -> (i -> a -> r) -> m (Maybe r)
ipreviews :: MonadReader s m => IndexedFold i s a       -> (i -> a -> r) -> m (Maybe r)
ipreviews :: MonadReader s m => IndexedLens' i s a      -> (i -> a -> r) -> m (Maybe r)
ipreviews :: MonadReader s m => IndexedTraversal' i s a -> (i -> a -> r) -> m (Maybe r)

preuse :: MonadState s m => Getting (First a) s a -> m (Maybe a) #

Retrieve the first value targeted by a Fold or Traversal (or Just the result from a Getter or Lens) into the current state.

preuse = use . pre

preuse :: MonadState s m => Getter s a     -> m (Maybe a)
preuse :: MonadState s m => Fold s a       -> m (Maybe a)
preuse :: MonadState s m => Lens' s a      -> m (Maybe a)
preuse :: MonadState s m => Iso' s a       -> m (Maybe a)
preuse :: MonadState s m => Traversal' s a -> m (Maybe a)

ipreuse :: MonadState s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a)) #

Retrieve the first index and value targeted by an IndexedFold or IndexedTraversal (or Just the index and result from an IndexedGetter or IndexedLens) into the current state.

ipreuse = use . ipre

ipreuse :: MonadState s m => IndexedGetter i s a     -> m (Maybe (i, a))
ipreuse :: MonadState s m => IndexedFold i s a       -> m (Maybe (i, a))
ipreuse :: MonadState s m => IndexedLens' i s a      -> m (Maybe (i, a))
ipreuse :: MonadState s m => IndexedTraversal' i s a -> m (Maybe (i, a))

preuses :: MonadState s m => Getting (First r) s a -> (a -> r) -> m (Maybe r) #

Retrieve a function of the first value targeted by a Fold or Traversal (or Just the result from a Getter or Lens) into the current state.

preuses = uses . pre

preuses :: MonadState s m => Getter s a     -> (a -> r) -> m (Maybe r)
preuses :: MonadState s m => Fold s a       -> (a -> r) -> m (Maybe r)
preuses :: MonadState s m => Lens' s a      -> (a -> r) -> m (Maybe r)
preuses :: MonadState s m => Iso' s a       -> (a -> r) -> m (Maybe r)
preuses :: MonadState s m => Traversal' s a -> (a -> r) -> m (Maybe r)

ipreuses :: MonadState s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r) #

Retrieve a function of the first index and value targeted by an IndexedFold or IndexedTraversal (or a function of Just the index and result from an IndexedGetter or IndexedLens) into the current state.

ipreuses = uses . ipre

ipreuses :: MonadState s m => IndexedGetter i s a     -> (i -> a -> r) -> m (Maybe r)
ipreuses :: MonadState s m => IndexedFold i s a       -> (i -> a -> r) -> m (Maybe r)
ipreuses :: MonadState s m => IndexedLens' i s a      -> (i -> a -> r) -> m (Maybe r)
ipreuses :: MonadState s m => IndexedTraversal' i s a -> (i -> a -> r) -> m (Maybe r)

ifoldMapOf :: IndexedGetting i m s a -> (i -> a -> m) -> s -> m #

Fold an IndexedFold or IndexedTraversal by mapping indices and values to an arbitrary Monoid with access to the i.

When you don't need access to the index then foldMapOf is more flexible in what it accepts.

foldMapOf l ≡ ifoldMapOf l . const

ifoldMapOf ::             IndexedGetter i s a     -> (i -> a -> m) -> s -> m
ifoldMapOf :: Monoid m => IndexedFold i s a       -> (i -> a -> m) -> s -> m
ifoldMapOf ::             IndexedLens' i s a      -> (i -> a -> m) -> s -> m
ifoldMapOf :: Monoid m => IndexedTraversal' i s a -> (i -> a -> m) -> s -> m

ifoldrOf :: IndexedGetting i (Endo r) s a -> (i -> a -> r -> r) -> r -> s -> r #

Right-associative fold of parts of a structure that are viewed through an IndexedFold or IndexedTraversal with access to the i.

When you don't need access to the index then foldrOf is more flexible in what it accepts.

foldrOf l ≡ ifoldrOf l . const

ifoldrOf :: IndexedGetter i s a     -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf :: IndexedFold i s a       -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf :: IndexedLens' i s a      -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf :: IndexedTraversal' i s a -> (i -> a -> r -> r) -> r -> s -> r

ifoldlOf :: IndexedGetting i (Dual (Endo r)) s a -> (i -> r -> a -> r) -> r -> s -> r #

Left-associative fold of the parts of a structure that are viewed through an IndexedFold or IndexedTraversal with access to the i.

When you don't need access to the index then foldlOf is more flexible in what it accepts.

foldlOf l ≡ ifoldlOf l . const

ifoldlOf :: IndexedGetter i s a     -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf :: IndexedFold i s a       -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf :: IndexedLens' i s a      -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf :: IndexedTraversal' i s a -> (i -> r -> a -> r) -> r -> s -> r

ianyOf :: IndexedGetting i Any s a -> (i -> a -> Bool) -> s -> Bool #

Return whether or not any element viewed through an IndexedFold or IndexedTraversal satisfy a predicate, with access to the i.

When you don't need access to the index then anyOf is more flexible in what it accepts.

anyOf l ≡ ianyOf l . const

ianyOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Bool
ianyOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Bool
ianyOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Bool
ianyOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Bool

iallOf :: IndexedGetting i All s a -> (i -> a -> Bool) -> s -> Bool #

Return whether or not all elements viewed through an IndexedFold or IndexedTraversal satisfy a predicate, with access to the i.

When you don't need access to the index then allOf is more flexible in what it accepts.

allOf l ≡ iallOf l . const

iallOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Bool
iallOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Bool
iallOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Bool
iallOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Bool

inoneOf :: IndexedGetting i Any s a -> (i -> a -> Bool) -> s -> Bool #

Return whether or not none of the elements viewed through an IndexedFold or IndexedTraversal satisfy a predicate, with access to the i.

When you don't need access to the index then noneOf is more flexible in what it accepts.

noneOf l ≡ inoneOf l . const

inoneOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Bool
inoneOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Bool
inoneOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Bool
inoneOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Bool

itraverseOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> (i -> a -> f r) -> s -> f () #

Traverse the targets of an IndexedFold or IndexedTraversal with access to the i, discarding the results.

When you don't need access to the index then traverseOf_ is more flexible in what it accepts.

traverseOf_ l ≡ itraverseOf l . const

itraverseOf_ :: Functor f     => IndexedGetter i s a     -> (i -> a -> f r) -> s -> f ()
itraverseOf_ :: Applicative f => IndexedFold i s a       -> (i -> a -> f r) -> s -> f ()
itraverseOf_ :: Functor f     => IndexedLens' i s a      -> (i -> a -> f r) -> s -> f ()
itraverseOf_ :: Applicative f => IndexedTraversal' i s a -> (i -> a -> f r) -> s -> f ()

iforOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> s -> (i -> a -> f r) -> f () #

Traverse the targets of an IndexedFold or IndexedTraversal with access to the index, discarding the results (with the arguments flipped).

iforOf_ ≡ flip . itraverseOf_

When you don't need access to the index then forOf_ is more flexible in what it accepts.

forOf_ l a ≡ iforOf_ l a . const

iforOf_ :: Functor f     => IndexedGetter i s a     -> s -> (i -> a -> f r) -> f ()
iforOf_ :: Applicative f => IndexedFold i s a       -> s -> (i -> a -> f r) -> f ()
iforOf_ :: Functor f     => IndexedLens' i s a      -> s -> (i -> a -> f r) -> f ()
iforOf_ :: Applicative f => IndexedTraversal' i s a -> s -> (i -> a -> f r) -> f ()

imapMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> (i -> a -> m r) -> s -> m () #

Run monadic actions for each target of an IndexedFold or IndexedTraversal with access to the index, discarding the results.

When you don't need access to the index then mapMOf_ is more flexible in what it accepts.

mapMOf_ l ≡ imapMOf l . const

imapMOf_ :: Monad m => IndexedGetter i s a     -> (i -> a -> m r) -> s -> m ()
imapMOf_ :: Monad m => IndexedFold i s a       -> (i -> a -> m r) -> s -> m ()
imapMOf_ :: Monad m => IndexedLens' i s a      -> (i -> a -> m r) -> s -> m ()
imapMOf_ :: Monad m => IndexedTraversal' i s a -> (i -> a -> m r) -> s -> m ()

iforMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> s -> (i -> a -> m r) -> m () #

Run monadic actions for each target of an IndexedFold or IndexedTraversal with access to the index, discarding the results (with the arguments flipped).

iforMOf_ ≡ flip . imapMOf_

When you don't need access to the index then forMOf_ is more flexible in what it accepts.

forMOf_ l a ≡ iforMOf l a . const

iforMOf_ :: Monad m => IndexedGetter i s a     -> s -> (i -> a -> m r) -> m ()
iforMOf_ :: Monad m => IndexedFold i s a       -> s -> (i -> a -> m r) -> m ()
iforMOf_ :: Monad m => IndexedLens' i s a      -> s -> (i -> a -> m r) -> m ()
iforMOf_ :: Monad m => IndexedTraversal' i s a -> s -> (i -> a -> m r) -> m ()

iconcatMapOf :: IndexedGetting i [r] s a -> (i -> a -> [r]) -> s -> [r] #

Concatenate the results of a function of the elements of an IndexedFold or IndexedTraversal with access to the index.

When you don't need access to the index then concatMapOf is more flexible in what it accepts.

concatMapOf l ≡ iconcatMapOf l . const
iconcatMapOf ≡ ifoldMapOf

iconcatMapOf :: IndexedGetter i s a     -> (i -> a -> [r]) -> s -> [r]
iconcatMapOf :: IndexedFold i s a       -> (i -> a -> [r]) -> s -> [r]
iconcatMapOf :: IndexedLens' i s a      -> (i -> a -> [r]) -> s -> [r]
iconcatMapOf :: IndexedTraversal' i s a -> (i -> a -> [r]) -> s -> [r]

ifindOf :: IndexedGetting i (Endo (Maybe a)) s a -> (i -> a -> Bool) -> s -> Maybe a #

The ifindOf function takes an IndexedFold or IndexedTraversal, a predicate that is also supplied the index, a structure and returns the left-most element of the structure matching the predicate, or Nothing if there is no such element.

When you don't need access to the index then findOf is more flexible in what it accepts.

findOf l ≡ ifindOf l . const

ifindOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Maybe a
ifindOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Maybe a
ifindOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Maybe a
ifindOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Maybe a

ifindMOf :: Monad m => IndexedGetting i (Endo (m (Maybe a))) s a -> (i -> a -> m Bool) -> s -> m (Maybe a) #

The ifindMOf function takes an IndexedFold or IndexedTraversal, a monadic predicate that is also supplied the index, a structure and returns in the monad the left-most element of the structure matching the predicate, or Nothing if there is no such element.

When you don't need access to the index then findMOf is more flexible in what it accepts.

findMOf l ≡ ifindMOf l . const

ifindMOf :: Monad m => IndexedGetter i s a     -> (i -> a -> m Bool) -> s -> m (Maybe a)
ifindMOf :: Monad m => IndexedFold i s a       -> (i -> a -> m Bool) -> s -> m (Maybe a)
ifindMOf :: Monad m => IndexedLens' i s a      -> (i -> a -> m Bool) -> s -> m (Maybe a)
ifindMOf :: Monad m => IndexedTraversal' i s a -> (i -> a -> m Bool) -> s -> m (Maybe a)

ifoldrOf' :: IndexedGetting i (Dual (Endo (r -> r))) s a -> (i -> a -> r -> r) -> r -> s -> r #

Strictly fold right over the elements of a structure with an index.

When you don't need access to the index then foldrOf' is more flexible in what it accepts.

foldrOf' l ≡ ifoldrOf' l . const

ifoldrOf' :: IndexedGetter i s a     -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf' :: IndexedFold i s a       -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf' :: IndexedLens' i s a      -> (i -> a -> r -> r) -> r -> s -> r
ifoldrOf' :: IndexedTraversal' i s a -> (i -> a -> r -> r) -> r -> s -> r

ifoldlOf' :: IndexedGetting i (Endo (r -> r)) s a -> (i -> r -> a -> r) -> r -> s -> r #

Fold over the elements of a structure with an index, associating to the left, but strictly.

When you don't need access to the index then foldlOf' is more flexible in what it accepts.

foldlOf' l ≡ ifoldlOf' l . const

ifoldlOf' :: IndexedGetter i s a       -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf' :: IndexedFold i s a         -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf' :: IndexedLens' i s a        -> (i -> r -> a -> r) -> r -> s -> r
ifoldlOf' :: IndexedTraversal' i s a   -> (i -> r -> a -> r) -> r -> s -> r

ifoldrMOf :: Monad m => IndexedGetting i (Dual (Endo (r -> m r))) s a -> (i -> a -> r -> m r) -> r -> s -> m r #

Monadic fold right over the elements of a structure with an index.

When you don't need access to the index then foldrMOf is more flexible in what it accepts.

foldrMOf l ≡ ifoldrMOf l . const

ifoldrMOf :: Monad m => IndexedGetter i s a     -> (i -> a -> r -> m r) -> r -> s -> m r
ifoldrMOf :: Monad m => IndexedFold i s a       -> (i -> a -> r -> m r) -> r -> s -> m r
ifoldrMOf :: Monad m => IndexedLens' i s a      -> (i -> a -> r -> m r) -> r -> s -> m r
ifoldrMOf :: Monad m => IndexedTraversal' i s a -> (i -> a -> r -> m r) -> r -> s -> m r

ifoldlMOf :: Monad m => IndexedGetting i (Endo (r -> m r)) s a -> (i -> r -> a -> m r) -> r -> s -> m r #

Monadic fold over the elements of a structure with an index, associating to the left.

When you don't need access to the index then foldlMOf is more flexible in what it accepts.

foldlMOf l ≡ ifoldlMOf l . const

ifoldlMOf :: Monad m => IndexedGetter i s a     -> (i -> r -> a -> m r) -> r -> s -> m r
ifoldlMOf :: Monad m => IndexedFold i s a       -> (i -> r -> a -> m r) -> r -> s -> m r
ifoldlMOf :: Monad m => IndexedLens' i s a      -> (i -> r -> a -> m r) -> r -> s -> m r
ifoldlMOf :: Monad m => IndexedTraversal' i s a -> (i -> r -> a -> m r) -> r -> s -> m r

itoListOf :: IndexedGetting i (Endo [(i, a)]) s a -> s -> [(i, a)] #

Extract the key-value pairs from a structure.

When you don't need access to the indices in the result, then toListOf is more flexible in what it accepts.

toListOf l ≡ map snd . itoListOf l

itoListOf :: IndexedGetter i s a     -> s -> [(i,a)]
itoListOf :: IndexedFold i s a       -> s -> [(i,a)]
itoListOf :: IndexedLens' i s a      -> s -> [(i,a)]
itoListOf :: IndexedTraversal' i s a -> s -> [(i,a)]

(^@..) :: s -> IndexedGetting i (Endo [(i, a)]) s a -> [(i, a)] infixl 8 #

An infix version of itoListOf.

(^@?) :: s -> IndexedGetting i (Endo (Maybe (i, a))) s a -> Maybe (i, a) infixl 8 #

Perform a safe head (with index) of an IndexedFold or IndexedTraversal or retrieve Just the index and result from an IndexedGetter or IndexedLens.

When using a IndexedTraversal as a partial IndexedLens, or an IndexedFold as a partial IndexedGetter this can be a convenient way to extract the optional value.

(^@?) :: s -> IndexedGetter i s a     -> Maybe (i, a)
(^@?) :: s -> IndexedFold i s a       -> Maybe (i, a)
(^@?) :: s -> IndexedLens' i s a      -> Maybe (i, a)
(^@?) :: s -> IndexedTraversal' i s a -> Maybe (i, a)

(^@?!) :: HasCallStack => s -> IndexedGetting i (Endo (i, a)) s a -> (i, a) infixl 8 #

Perform an *UNSAFE* head (with index) of an IndexedFold or IndexedTraversal assuming that it is there.

(^@?!) :: s -> IndexedGetter i s a     -> (i, a)
(^@?!) :: s -> IndexedFold i s a       -> (i, a)
(^@?!) :: s -> IndexedLens' i s a      -> (i, a)
(^@?!) :: s -> IndexedTraversal' i s a -> (i, a)

elemIndexOf :: Eq a => IndexedGetting i (First i) s a -> a -> s -> Maybe i #

Retrieve the index of the first value targeted by a IndexedFold or IndexedTraversal which is equal to a given value.

elemIndex ≡ elemIndexOf folded

elemIndexOf :: Eq a => IndexedFold i s a       -> a -> s -> Maybe i
elemIndexOf :: Eq a => IndexedTraversal' i s a -> a -> s -> Maybe i

elemIndicesOf :: Eq a => IndexedGetting i (Endo [i]) s a -> a -> s -> [i] #

Retrieve the indices of the values targeted by a IndexedFold or IndexedTraversal which are equal to a given value.

elemIndices ≡ elemIndicesOf folded

elemIndicesOf :: Eq a => IndexedFold i s a       -> a -> s -> [i]
elemIndicesOf :: Eq a => IndexedTraversal' i s a -> a -> s -> [i]

findIndexOf :: IndexedGetting i (First i) s a -> (a -> Bool) -> s -> Maybe i #

Retrieve the index of the first value targeted by a IndexedFold or IndexedTraversal which satisfies a predicate.

findIndex ≡ findIndexOf folded

findIndexOf :: IndexedFold i s a       -> (a -> Bool) -> s -> Maybe i
findIndexOf :: IndexedTraversal' i s a -> (a -> Bool) -> s -> Maybe i

findIndicesOf :: IndexedGetting i (Endo [i]) s a -> (a -> Bool) -> s -> [i] #

Retrieve the indices of the values targeted by a IndexedFold or IndexedTraversal which satisfy a predicate.

findIndices ≡ findIndicesOf folded

findIndicesOf :: IndexedFold i s a       -> (a -> Bool) -> s -> [i]
findIndicesOf :: IndexedTraversal' i s a -> (a -> Bool) -> s -> [i]

ifiltered :: (Indexable i p, Applicative f) => (i -> a -> Bool) -> Optical' p (Indexed i) f a a #

Filter an IndexedFold or IndexedGetter, obtaining an IndexedFold.

>>> [0,0,0,5,5,5]^..traversed.ifiltered (\i a -> i <= a)
[0,5,5,5]

Compose with ifiltered to filter another IndexedLens, IndexedIso, IndexedGetter, IndexedFold (or IndexedTraversal) with access to both the value and the index.

Note: As with filtered, this is not a legal IndexedTraversal, unless you are very careful not to invalidate the predicate on the target!

itakingWhile :: (Indexable i p, Profunctor q, Contravariant f, Applicative f) => (i -> a -> Bool) -> Optical' (Indexed i) q (Const (Endo (f s)) :: Type -> Type) s a -> Optical' p q f s a #

Obtain an IndexedFold by taking elements from another IndexedFold, IndexedLens, IndexedGetter or IndexedTraversal while a predicate holds.

itakingWhile :: (i -> a -> Bool) -> IndexedFold i s a          -> IndexedFold i s a
itakingWhile :: (i -> a -> Bool) -> IndexedTraversal' i s a    -> IndexedFold i s a
itakingWhile :: (i -> a -> Bool) -> IndexedLens' i s a         -> IndexedFold i s a
itakingWhile :: (i -> a -> Bool) -> IndexedGetter i s a        -> IndexedFold i s a

Note: Applying itakingWhile to an IndexedLens or IndexedTraversal will still allow you to use it as a pseudo-IndexedTraversal, but if you change the value of any target to one where the predicate returns False, then you will break the Traversal laws and Traversal fusion will no longer be sound.

idroppingWhile :: (Indexable i p, Profunctor q, Applicative f) => (i -> a -> Bool) -> Optical (Indexed i) q (Compose (State Bool) f) s t a a -> Optical p q f s t a a #

Obtain an IndexedFold by dropping elements from another IndexedFold, IndexedLens, IndexedGetter or IndexedTraversal while a predicate holds.

idroppingWhile :: (i -> a -> Bool) -> IndexedFold i s a          -> IndexedFold i s a
idroppingWhile :: (i -> a -> Bool) -> IndexedTraversal' i s a    -> IndexedFold i s a -- see notes
idroppingWhile :: (i -> a -> Bool) -> IndexedLens' i s a         -> IndexedFold i s a -- see notes
idroppingWhile :: (i -> a -> Bool) -> IndexedGetter i s a        -> IndexedFold i s a

Note: As with droppingWhile applying idroppingWhile to an IndexedLens or IndexedTraversal will still allow you to use it as a pseudo-IndexedTraversal, but if you change the value of the first target to one where the predicate returns True, then you will break the Traversal laws and Traversal fusion will no longer be sound.

foldByOf :: Fold s a -> (a -> a -> a) -> a -> s -> a #

Fold a value using a specified Fold and Monoid operations. This is like foldBy where the Foldable instance can be manually specified.

foldByOf folded ≡ foldBy

foldByOf :: Getter s a     -> (a -> a -> a) -> a -> s -> a
foldByOf :: Fold s a       -> (a -> a -> a) -> a -> s -> a
foldByOf :: Lens' s a      -> (a -> a -> a) -> a -> s -> a
foldByOf :: Traversal' s a -> (a -> a -> a) -> a -> s -> a
foldByOf :: Iso' s a       -> (a -> a -> a) -> a -> s -> a

>>> foldByOf both (++) [] ("hello","world")
"helloworld"

foldMapByOf :: Fold s a -> (r -> r -> r) -> r -> (a -> r) -> s -> r #

Fold a value using a specified Fold and Monoid operations. This is like foldMapBy where the Foldable instance can be manually specified.

foldMapByOf folded ≡ foldMapBy

foldMapByOf :: Getter s a     -> (r -> r -> r) -> r -> (a -> r) -> s -> r
foldMapByOf :: Fold s a       -> (r -> r -> r) -> r -> (a -> r) -> s -> r
foldMapByOf :: Traversal' s a -> (r -> r -> r) -> r -> (a -> r) -> s -> r
foldMapByOf :: Lens' s a      -> (r -> r -> r) -> r -> (a -> r) -> s -> r
foldMapByOf :: Iso' s a       -> (r -> r -> r) -> r -> (a -> r) -> s -> r

>>> foldMapByOf both (+) 0 length ("hello","world")
10

class Ord k => TraverseMax k (m :: Type -> Type) | m -> k where #

Allows IndexedTraversal of the value at the largest index.

Methods

traverseMax :: IndexedTraversal' k (m v) v #

IndexedTraversal of the element at the largest index.

Instances

TraverseMax Int IntMap
Instance details Defined in Control.Lens.Traversal Methods traverseMax :: IndexedTraversal' Int (IntMap v) v #
Ord k => TraverseMax k (Map k)
Instance details Defined in Control.Lens.Traversal Methods traverseMax :: IndexedTraversal' k (Map k v) v #

class Ord k => TraverseMin k (m :: Type -> Type) | m -> k where #

Allows IndexedTraversal the value at the smallest index.

Methods

traverseMin :: IndexedTraversal' k (m v) v #

IndexedTraversal of the element with the smallest index.

Instances

TraverseMin Int IntMap
Instance details Defined in Control.Lens.Traversal Methods traverseMin :: IndexedTraversal' Int (IntMap v) v #
Ord k => TraverseMin k (Map k)
Instance details Defined in Control.Lens.Traversal Methods traverseMin :: IndexedTraversal' k (Map k v) v #

type Traversing1' (p :: Type -> Type -> Type) (f :: Type -> Type) s a = Traversing1 p f s s a a #

type Traversing' (p :: Type -> Type -> Type) (f :: Type -> Type) s a = Traversing p f s s a a #

type Traversing' f = Simple (Traversing f)

type Traversing1 (p :: Type -> Type -> Type) (f :: Type -> Type) s t a b = Over p (BazaarT1 p f a b) s t a b #

type Traversing (p :: Type -> Type -> Type) (f :: Type -> Type) s t a b = Over p (BazaarT p f a b) s t a b #

When you see this as an argument to a function, it expects

to be indexed if p is an instance of Indexed i,
to be unindexed if p is (->),
a Traversal if f is Applicative,
a Getter if f is only a Functor and Contravariant,
a Lens if f is only a Functor,
a Fold if f is Applicative and Contravariant.

type AnIndexedTraversal1' i s a = AnIndexedTraversal1 i s s a a #

type AnIndexedTraversal1' = Simple (AnIndexedTraversal1 i)

type AnIndexedTraversal' i s a = AnIndexedTraversal i s s a a #

type AnIndexedTraversal' = Simple (AnIndexedTraversal i)

type AnIndexedTraversal1 i s t a b = Over (Indexed i) (Bazaar1 (Indexed i) a b) s t a b #

When you see this as an argument to a function, it expects an IndexedTraversal1.

type AnIndexedTraversal i s t a b = Over (Indexed i) (Bazaar (Indexed i) a b) s t a b #

When you see this as an argument to a function, it expects an IndexedTraversal.

type ATraversal1' s a = ATraversal1 s s a a #

type ATraversal1' = Simple ATraversal1

type ATraversal1 s t a b = LensLike (Bazaar1 ((->) :: Type -> Type -> Type) a b) s t a b #

When you see this as an argument to a function, it expects a Traversal1.

type ATraversal' s a = ATraversal s s a a #

type ATraversal' = Simple ATraversal

type ATraversal s t a b = LensLike (Bazaar ((->) :: Type -> Type -> Type) a b) s t a b #

When you see this as an argument to a function, it expects a Traversal.

traverseOf :: LensLike f s t a b -> (a -> f b) -> s -> f t #

Map each element of a structure targeted by a Lens or Traversal, evaluate these actions from left to right, and collect the results.

This function is only provided for consistency, id is strictly more general.

>>> traverseOf each print (1,2,3)
1
2
3
((),(),())

traverseOf ≡ id
itraverseOf l ≡ traverseOf l . Indexed
itraverseOf itraversed ≡ itraverse

This yields the obvious law:

traverse ≡ traverseOf traverse

traverseOf :: Functor f     => Iso s t a b        -> (a -> f b) -> s -> f t
traverseOf :: Functor f     => Lens s t a b       -> (a -> f b) -> s -> f t
traverseOf :: Apply f       => Traversal1 s t a b -> (a -> f b) -> s -> f t
traverseOf :: Applicative f => Traversal s t a b  -> (a -> f b) -> s -> f t

forOf :: LensLike f s t a b -> s -> (a -> f b) -> f t #

A version of traverseOf with the arguments flipped, such that:

>>> forOf each (1,2,3) print
1
2
3
((),(),())

This function is only provided for consistency, flip is strictly more general.

forOf ≡ flip
forOf ≡ flip . traverseOf

for ≡ forOf traverse
ifor l s ≡ for l s . Indexed

forOf :: Functor f => Iso s t a b -> s -> (a -> f b) -> f t
forOf :: Functor f => Lens s t a b -> s -> (a -> f b) -> f t
forOf :: Applicative f => Traversal s t a b -> s -> (a -> f b) -> f t

sequenceAOf :: LensLike f s t (f b) b -> s -> f t #

Evaluate each action in the structure from left to right, and collect the results.

>>> sequenceAOf both ([1,2],[3,4])
[(1,3),(1,4),(2,3),(2,4)]

sequenceA ≡ sequenceAOf traverse ≡ traverse id
sequenceAOf l ≡ traverseOf l id ≡ l id

sequenceAOf :: Functor f => Iso s t (f b) b       -> s -> f t
sequenceAOf :: Functor f => Lens s t (f b) b      -> s -> f t
sequenceAOf :: Applicative f => Traversal s t (f b) b -> s -> f t

mapMOf :: LensLike (WrappedMonad m) s t a b -> (a -> m b) -> s -> m t #

Map each element of a structure targeted by a Lens to a monadic action, evaluate these actions from left to right, and collect the results.

>>> mapMOf both (\x -> [x, x + 1]) (1,3)
[(1,3),(1,4),(2,3),(2,4)]

mapM ≡ mapMOf traverse
imapMOf l ≡ forM l . Indexed

mapMOf :: Monad m => Iso s t a b       -> (a -> m b) -> s -> m t
mapMOf :: Monad m => Lens s t a b      -> (a -> m b) -> s -> m t
mapMOf :: Monad m => Traversal s t a b -> (a -> m b) -> s -> m t

forMOf :: LensLike (WrappedMonad m) s t a b -> s -> (a -> m b) -> m t #

forMOf is a flipped version of mapMOf, consistent with the definition of forM.

>>> forMOf both (1,3) $ \x -> [x, x + 1]
[(1,3),(1,4),(2,3),(2,4)]

forM ≡ forMOf traverse
forMOf l ≡ flip (mapMOf l)
iforMOf l s ≡ forM l s . Indexed

forMOf :: Monad m => Iso s t a b       -> s -> (a -> m b) -> m t
forMOf :: Monad m => Lens s t a b      -> s -> (a -> m b) -> m t
forMOf :: Monad m => Traversal s t a b -> s -> (a -> m b) -> m t

sequenceOf :: LensLike (WrappedMonad m) s t (m b) b -> s -> m t #

Sequence the (monadic) effects targeted by a Lens in a container from left to right.

>>> sequenceOf each ([1,2],[3,4],[5,6])
[(1,3,5),(1,3,6),(1,4,5),(1,4,6),(2,3,5),(2,3,6),(2,4,5),(2,4,6)]

sequence ≡ sequenceOf traverse
sequenceOf l ≡ mapMOf l id
sequenceOf l ≡ unwrapMonad . l WrapMonad

sequenceOf :: Monad m => Iso s t (m b) b       -> s -> m t
sequenceOf :: Monad m => Lens s t (m b) b      -> s -> m t
sequenceOf :: Monad m => Traversal s t (m b) b -> s -> m t

transposeOf :: LensLike ZipList s t [a] a -> s -> [t] #

This generalizes transpose to an arbitrary Traversal.

Note: transpose handles ragged inputs more intelligently, but for non-ragged inputs:

>>> transposeOf traverse [[1,2,3],[4,5,6]]
[[1,4],[2,5],[3,6]]

transpose ≡ transposeOf traverse

Since every Lens is a Traversal, we can use this as a form of monadic strength as well:

transposeOf _2 :: (b, [a]) -> [(b, a)]

mapAccumROf :: LensLike (Backwards (State acc)) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t) #

This generalizes mapAccumR to an arbitrary Traversal.

mapAccumR ≡ mapAccumROf traverse

mapAccumROf accumulates State from right to left.

mapAccumROf :: Iso s t a b       -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumROf :: Lens s t a b      -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumROf :: Traversal s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)

mapAccumROf :: LensLike (Backwards (State acc)) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)

mapAccumLOf :: LensLike (State acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t) #

This generalizes mapAccumL to an arbitrary Traversal.

mapAccumL ≡ mapAccumLOf traverse

mapAccumLOf accumulates State from left to right.

mapAccumLOf :: Iso s t a b       -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumLOf :: Lens s t a b      -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumLOf :: Traversal s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)

mapAccumLOf :: LensLike (State acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumLOf l f acc0 s = swap (runState (l (a -> state (acc -> swap (f acc a))) s) acc0)

scanr1Of :: LensLike (Backwards (State (Maybe a))) s t a a -> (a -> a -> a) -> s -> t #

This permits the use of scanr1 over an arbitrary Traversal or Lens.

scanr1 ≡ scanr1Of traverse

scanr1Of :: Iso s t a a       -> (a -> a -> a) -> s -> t
scanr1Of :: Lens s t a a      -> (a -> a -> a) -> s -> t
scanr1Of :: Traversal s t a a -> (a -> a -> a) -> s -> t

scanl1Of :: LensLike (State (Maybe a)) s t a a -> (a -> a -> a) -> s -> t #

This permits the use of scanl1 over an arbitrary Traversal or Lens.

scanl1 ≡ scanl1Of traverse

scanl1Of :: Iso s t a a       -> (a -> a -> a) -> s -> t
scanl1Of :: Lens s t a a      -> (a -> a -> a) -> s -> t
scanl1Of :: Traversal s t a a -> (a -> a -> a) -> s -> t

loci :: Traversal (Bazaar ((->) :: Type -> Type -> Type) a c s) (Bazaar ((->) :: Type -> Type -> Type) b c s) a b #

This Traversal allows you to traverse the individual stores in a Bazaar.

iloci :: IndexedTraversal i (Bazaar (Indexed i) a c s) (Bazaar (Indexed i) b c s) a b #

This IndexedTraversal allows you to traverse the individual stores in a Bazaar with access to their indices.

partsOf :: Functor f => Traversing ((->) :: Type -> Type -> Type) f s t a a -> LensLike f s t [a] [a] #

partsOf turns a Traversal into a Lens that resembles an early version of the uniplate (or biplate) type.

Note: You should really try to maintain the invariant of the number of children in the list.

>>> (a,b,c) & partsOf each .~ [x,y,z]
(x,y,z)

Any extras will be lost. If you do not supply enough, then the remainder will come from the original structure.

>>> (a,b,c) & partsOf each .~ [w,x,y,z]
(w,x,y)

>>> (a,b,c) & partsOf each .~ [x,y]
(x,y,c)

>>> ('b', 'a', 'd', 'c') & partsOf each %~ sort
('a','b','c','d')

So technically, this is only a Lens if you do not change the number of results it returns.

When applied to a Fold the result is merely a Getter.

partsOf :: Iso' s a       -> Lens' s [a]
partsOf :: Lens' s a      -> Lens' s [a]
partsOf :: Traversal' s a -> Lens' s [a]
partsOf :: Fold s a       -> Getter s [a]
partsOf :: Getter s a     -> Getter s [a]

ipartsOf :: (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a a -> Over p f s t [a] [a] #

An indexed version of partsOf that receives the entire list of indices as its index.

partsOf' :: ATraversal s t a a -> Lens s t [a] [a] #

A type-restricted version of partsOf that can only be used with a Traversal.

ipartsOf' :: (Indexable [i] p, Functor f) => Over (Indexed i) (Bazaar' (Indexed i) a) s t a a -> Over p f s t [a] [a] #

A type-restricted version of ipartsOf that can only be used with an IndexedTraversal.

unsafePartsOf :: Functor f => Traversing ((->) :: Type -> Type -> Type) f s t a b -> LensLike f s t [a] [b] #

unsafePartsOf turns a Traversal into a uniplate (or biplate) family.

If you do not need the types of s and t to be different, it is recommended that you use partsOf.

It is generally safer to traverse with the Bazaar rather than use this combinator. However, it is sometimes convenient.

This is unsafe because if you don't supply at least as many b's as you were given a's, then the reconstruction of t will result in an error!

When applied to a Fold the result is merely a Getter (and becomes safe).

unsafePartsOf :: Iso s t a b       -> Lens s t [a] [b]
unsafePartsOf :: Lens s t a b      -> Lens s t [a] [b]
unsafePartsOf :: Traversal s t a b -> Lens s t [a] [b]
unsafePartsOf :: Fold s a          -> Getter s [a]
unsafePartsOf :: Getter s a        -> Getter s [a]

iunsafePartsOf :: (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a b -> Over p f s t [a] [b] #

An indexed version of unsafePartsOf that receives the entire list of indices as its index.

unsafePartsOf' :: ATraversal s t a b -> Lens s t [a] [b] #

iunsafePartsOf' :: Over (Indexed i) (Bazaar (Indexed i) a b) s t a b -> IndexedLens [i] s t [a] [b] #

unsafeSingular :: (HasCallStack, Conjoined p, Functor f) => Traversing p f s t a b -> Over p f s t a b #

This converts a Traversal that you "know" will target only one element to a Lens. It can also be used to transform a Fold into a Getter.

The resulting Lens or Getter will be partial if the Traversal targets nothing or more than one element.

>>> Left (ErrorCall "unsafeSingular: empty traversal") <- try (evaluate ([] & unsafeSingular traverse .~ 0)) :: IO (Either ErrorCall [Integer])

unsafeSingular :: Traversal s t a b          -> Lens s t a b
unsafeSingular :: Fold s a                   -> Getter s a
unsafeSingular :: IndexedTraversal i s t a b -> IndexedLens i s t a b
unsafeSingular :: IndexedFold i s a          -> IndexedGetter i s a

holesOf :: Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t] #

The one-level version of contextsOf. This extracts a list of the immediate children according to a given Traversal as editable contexts.

Given a context you can use pos to see the values, peek at what the structure would be like with an edited result, or simply extract the original structure.

propChildren l x = toListOf l x == map pos (holesOf l x)
propId l x = all (== x) [extract w | w <- holesOf l x]

holesOf :: Iso' s a                -> s -> [Pretext' (->) a s]
holesOf :: Lens' s a               -> s -> [Pretext' (->) a s]
holesOf :: Traversal' s a          -> s -> [Pretext' (->) a s]
holesOf :: IndexedLens' i s a      -> s -> [Pretext' (Indexed i) a s]
holesOf :: IndexedTraversal' i s a -> s -> [Pretext' (Indexed i) a s]

holes1Of :: Conjoined p => Over p (Bazaar1 p a a) s t a a -> s -> NonEmpty (Pretext p a a t) #

The non-empty version of holesOf. This extract a non-empty list of immediate children accroding to a given Traversal1 as editable contexts.

>>> let head1 f s = runPretext (NonEmpty.head $ holes1Of traversed1 s) f
>>> ('a' :| "bc") ^. head1
'a'

>>> ('a' :| "bc") & head1 %~ toUpper
'A' :| "bc"

holes1Of :: Iso' s a                 -> s -> NonEmpty (Pretext' (->) a s)
holes1Of :: Lens' s a                -> s -> NonEmpty (Pretext' (->) a s)
holes1Of :: Traversal1' s a          -> s -> NonEmpty (Pretext' (->) a s)
holes1Of :: IndexedLens' i s a       -> s -> NonEmpty (Pretext' (Indexed i) a s)
holes1Of :: IndexedTraversal1' i s a -> s -> NonEmpty (Pretext' (Indexed i) a s)

both :: Bitraversable r => Traversal (r a a) (r b b) a b #

Traverse both parts of a Bitraversable container with matching types.

Usually that type will be a pair.

>>> (1,2) & both *~ 10
(10,20)

>>> over both length ("hello","world")
(5,5)

>>> ("hello","world")^.both
"helloworld"

both :: Traversal (a, a)       (b, b)       a b
both :: Traversal (Either a a) (Either b b) a b

both1 :: Bitraversable1 r => Traversal1 (r a a) (r b b) a b #

Traverse both parts of a Bitraversable1 container with matching types.

Usually that type will be a pair.

both1 :: Traversal1 (a, a)       (b, b)       a b
both1 :: Traversal1 (Either a a) (Either b b) a b

taking :: (Conjoined p, Applicative f) => Int -> Traversing p f s t a a -> Over p f s t a a #

Visit the first n targets of a Traversal, Fold, Getter or Lens.

>>> [("hello","world"),("!!!","!!!")]^.. taking 2 (traverse.both)
["hello","world"]

>>> timingOut $ [1..] ^.. taking 3 traverse
[1,2,3]

>>> over (taking 5 traverse) succ "hello world"
"ifmmp world"

taking :: Int -> Traversal' s a                   -> Traversal' s a
taking :: Int -> Lens' s a                        -> Traversal' s a
taking :: Int -> Iso' s a                         -> Traversal' s a
taking :: Int -> Prism' s a                       -> Traversal' s a
taking :: Int -> Getter s a                       -> Fold s a
taking :: Int -> Fold s a                         -> Fold s a
taking :: Int -> IndexedTraversal' i s a          -> IndexedTraversal' i s a
taking :: Int -> IndexedLens' i s a               -> IndexedTraversal' i s a
taking :: Int -> IndexedGetter i s a              -> IndexedFold i s a
taking :: Int -> IndexedFold i s a                -> IndexedFold i s a

dropping :: (Conjoined p, Applicative f) => Int -> Over p (Indexing f) s t a a -> Over p f s t a a #

Visit all but the first n targets of a Traversal, Fold, Getter or Lens.

>>> ("hello","world") ^? dropping 1 both
Just "world"

Dropping works on infinite traversals as well:

>>> [1..] ^? dropping 1 folded
Just 2

dropping :: Int -> Traversal' s a                   -> Traversal' s a
dropping :: Int -> Lens' s a                        -> Traversal' s a
dropping :: Int -> Iso' s a                         -> Traversal' s a
dropping :: Int -> Prism' s a                       -> Traversal' s a
dropping :: Int -> Getter s a                       -> Fold s a
dropping :: Int -> Fold s a                         -> Fold s a
dropping :: Int -> IndexedTraversal' i s a          -> IndexedTraversal' i s a
dropping :: Int -> IndexedLens' i s a               -> IndexedTraversal' i s a
dropping :: Int -> IndexedGetter i s a              -> IndexedFold i s a
dropping :: Int -> IndexedFold i s a                -> IndexedFold i s a

cloneTraversal :: ATraversal s t a b -> Traversal s t a b #

A Traversal is completely characterized by its behavior on a Bazaar.

Cloning a Traversal is one way to make sure you aren't given something weaker, such as a Fold and can be used as a way to pass around traversals that have to be monomorphic in f.

Note: This only accepts a proper Traversal (or Lens). To clone a Lens as such, use cloneLens.

Note: It is usually better to use ReifiedTraversal and runTraversal than to cloneTraversal. The former can execute at full speed, while the latter needs to round trip through the Bazaar.

>>> let foo l a = (view (getting (cloneTraversal l)) a, set (cloneTraversal l) 10 a)
>>> foo both ("hello","world")
("helloworld",(10,10))

cloneTraversal :: LensLike (Bazaar (->) a b) s t a b -> Traversal s t a b

cloneIndexPreservingTraversal :: ATraversal s t a b -> IndexPreservingTraversal s t a b #

Clone a Traversal yielding an IndexPreservingTraversal that passes through whatever index it is composed with.

cloneIndexedTraversal :: AnIndexedTraversal i s t a b -> IndexedTraversal i s t a b #

Clone an IndexedTraversal yielding an IndexedTraversal with the same index.

cloneTraversal1 :: ATraversal1 s t a b -> Traversal1 s t a b #

A Traversal1 is completely characterized by its behavior on a Bazaar1.

cloneIndexPreservingTraversal1 :: ATraversal1 s t a b -> IndexPreservingTraversal1 s t a b #

Clone a Traversal1 yielding an IndexPreservingTraversal1 that passes through whatever index it is composed with.

cloneIndexedTraversal1 :: AnIndexedTraversal1 i s t a b -> IndexedTraversal1 i s t a b #

Clone an IndexedTraversal1 yielding an IndexedTraversal1 with the same index.

itraverseOf :: (Indexed i a (f b) -> s -> f t) -> (i -> a -> f b) -> s -> f t #

Traversal with an index.

NB: When you don't need access to the index then you can just apply your IndexedTraversal directly as a function!

itraverseOf ≡ withIndex
traverseOf l = itraverseOf l . const = id

itraverseOf :: Functor f     => IndexedLens i s t a b       -> (i -> a -> f b) -> s -> f t
itraverseOf :: Applicative f => IndexedTraversal i s t a b  -> (i -> a -> f b) -> s -> f t
itraverseOf :: Apply f       => IndexedTraversal1 i s t a b -> (i -> a -> f b) -> s -> f t

iforOf :: (Indexed i a (f b) -> s -> f t) -> s -> (i -> a -> f b) -> f t #

Traverse with an index (and the arguments flipped).

forOf l a ≡ iforOf l a . const
iforOf ≡ flip . itraverseOf

iforOf :: Functor f     => IndexedLens i s t a b       -> s -> (i -> a -> f b) -> f t
iforOf :: Applicative f => IndexedTraversal i s t a b  -> s -> (i -> a -> f b) -> f t
iforOf :: Apply f       => IndexedTraversal1 i s t a b -> s -> (i -> a -> f b) -> f t

imapMOf :: Over (Indexed i) (WrappedMonad m) s t a b -> (i -> a -> m b) -> s -> m t #

Map each element of a structure targeted by a Lens to a monadic action, evaluate these actions from left to right, and collect the results, with access its position.

When you don't need access to the index mapMOf is more liberal in what it can accept.

mapMOf l ≡ imapMOf l . const

imapMOf :: Monad m => IndexedLens       i s t a b -> (i -> a -> m b) -> s -> m t
imapMOf :: Monad m => IndexedTraversal  i s t a b -> (i -> a -> m b) -> s -> m t
imapMOf :: Bind  m => IndexedTraversal1 i s t a b -> (i -> a -> m b) -> s -> m t

iforMOf :: (Indexed i a (WrappedMonad m b) -> s -> WrappedMonad m t) -> s -> (i -> a -> m b) -> m t #

Map each element of a structure targeted by a Lens to a monadic action, evaluate these actions from left to right, and collect the results, with access its position (and the arguments flipped).

forMOf l a ≡ iforMOf l a . const
iforMOf ≡ flip . imapMOf

iforMOf :: Monad m => IndexedLens i s t a b      -> s -> (i -> a -> m b) -> m t
iforMOf :: Monad m => IndexedTraversal i s t a b -> s -> (i -> a -> m b) -> m t

imapAccumROf :: Over (Indexed i) (Backwards (State acc)) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t) #

Generalizes mapAccumR to an arbitrary IndexedTraversal with access to the index.

imapAccumROf accumulates state from right to left.

mapAccumROf l ≡ imapAccumROf l . const

imapAccumROf :: IndexedLens i s t a b      -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
imapAccumROf :: IndexedTraversal i s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)

imapAccumLOf :: Over (Indexed i) (State acc) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t) #

Generalizes mapAccumL to an arbitrary IndexedTraversal with access to the index.

imapAccumLOf accumulates state from left to right.

mapAccumLOf l ≡ imapAccumLOf l . const

imapAccumLOf :: IndexedLens i s t a b      -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
imapAccumLOf :: IndexedTraversal i s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)

traversed :: Traversable f => IndexedTraversal Int (f a) (f b) a b #

Traverse any Traversable container. This is an IndexedTraversal that is indexed by ordinal position.

traversed1 :: Traversable1 f => IndexedTraversal1 Int (f a) (f b) a b #

Traverse any Traversable1 container. This is an IndexedTraversal1 that is indexed by ordinal position.

traversed64 :: Traversable f => IndexedTraversal Int64 (f a) (f b) a b #

Traverse any Traversable container. This is an IndexedTraversal that is indexed by ordinal position.

ignored :: Applicative f => pafb -> s -> f s #

This is the trivial empty Traversal.

ignored :: IndexedTraversal i s s a b

ignored ≡ const pure

>>> 6 & ignored %~ absurd
6

elementOf :: Applicative f => LensLike (Indexing f) s t a a -> Int -> IndexedLensLike Int f s t a a #

Traverse the nth elementOf a Traversal, Lens or Iso if it exists.

>>> [[1],[3,4]] & elementOf (traverse.traverse) 1 .~ 5
[[1],[5,4]]

>>> [[1],[3,4]] ^? elementOf (folded.folded) 1
Just 3

>>> timingOut $ ['a'..] ^?! elementOf folded 5
'f'

>>> timingOut $ take 10 $ elementOf traverse 3 .~ 16 $ [0..]
[0,1,2,16,4,5,6,7,8,9]

elementOf :: Traversal' s a -> Int -> IndexedTraversal' Int s a
elementOf :: Fold s a       -> Int -> IndexedFold Int s a

element :: Traversable t => Int -> IndexedTraversal' Int (t a) a #

Traverse the nth element of a Traversable container.

element ≡ elementOf traverse

elementsOf :: Applicative f => LensLike (Indexing f) s t a a -> (Int -> Bool) -> IndexedLensLike Int f s t a a #

Traverse (or fold) selected elements of a Traversal (or Fold) where their ordinal positions match a predicate.

elementsOf :: Traversal' s a -> (Int -> Bool) -> IndexedTraversal' Int s a
elementsOf :: Fold s a       -> (Int -> Bool) -> IndexedFold Int s a

elements :: Traversable t => (Int -> Bool) -> IndexedTraversal' Int (t a) a #

Traverse elements of a Traversable container where their ordinal positions match a predicate.

elements ≡ elementsOf traverse

failover :: Alternative m => LensLike ((,) Any) s t a b -> (a -> b) -> s -> m t #

Try to map a function over this Traversal, failing if the Traversal has no targets.

>>> failover (element 3) (*2) [1,2] :: Maybe [Int]
Nothing

>>> failover _Left (*2) (Right 4) :: Maybe (Either Int Int)
Nothing

>>> failover _Right (*2) (Right 4) :: Maybe (Either Int Int)
Just (Right 8)

failover :: Alternative m => Traversal s t a b -> (a -> b) -> s -> m t

ifailover :: Alternative m => Over (Indexed i) ((,) Any) s t a b -> (i -> a -> b) -> s -> m t #

Try to map a function which uses the index over this IndexedTraversal, failing if the IndexedTraversal has no targets.

ifailover :: Alternative m => IndexedTraversal i s t a b -> (i -> a -> b) -> s -> m t

failing :: (Conjoined p, Applicative f) => Traversing p f s t a b -> Over p f s t a b -> Over p f s t a b infixl 5 #

Try the first Traversal (or Fold), falling back on the second Traversal (or Fold) if it returns no entries.

This is only a valid Traversal if the second Traversal is disjoint from the result of the first or returns exactly the same results. These conditions are trivially met when given a Lens, Iso, Getter, Prism or "affine" Traversal -- one that has 0 or 1 target.

Mutatis mutandis for Fold.

>>> [0,1,2,3] ^? failing (ix 1) (ix 2)
Just 1

>>> [0,1,2,3] ^? failing (ix 42) (ix 2)
Just 2

failing :: Traversal s t a b -> Traversal s t a b -> Traversal s t a b
failing :: Prism s t a b     -> Prism s t a b     -> Traversal s t a b
failing :: Fold s a          -> Fold s a          -> Fold s a

These cases are also supported, trivially, but are boring, because the left hand side always succeeds.

failing :: Lens s t a b      -> Traversal s t a b -> Traversal s t a b
failing :: Iso s t a b       -> Traversal s t a b -> Traversal s t a b
failing :: Equality s t a b  -> Traversal s t a b -> Traversal s t a b
failing :: Getter s a        -> Fold s a          -> Fold s a

If both of the inputs are indexed, the result is also indexed, so you can apply this to a pair of indexed traversals or indexed folds, obtaining an indexed traversal or indexed fold.

failing :: IndexedTraversal i s t a b -> IndexedTraversal i s t a b -> IndexedTraversal i s t a b
failing :: IndexedFold i s a          -> IndexedFold i s a          -> IndexedFold i s a

These cases are also supported, trivially, but are boring, because the left hand side always succeeds.

failing :: IndexedLens i s t a b      -> IndexedTraversal i s t a b -> IndexedTraversal i s t a b
failing :: IndexedGetter i s a        -> IndexedGetter i s a        -> IndexedFold i s a

deepOf :: (Conjoined p, Applicative f) => LensLike f s t s t -> Traversing p f s t a b -> Over p f s t a b #

Try the second traversal. If it returns no entries, try again with all entries from the first traversal, recursively.

deepOf :: Fold s s          -> Fold s a                   -> Fold s a
deepOf :: Traversal' s s    -> Traversal' s a             -> Traversal' s a
deepOf :: Traversal s t s t -> Traversal s t a b          -> Traversal s t a b
deepOf :: Fold s s          -> IndexedFold i s a          -> IndexedFold i s a
deepOf :: Traversal s t s t -> IndexedTraversal i s t a b -> IndexedTraversal i s t a b

confusing :: Applicative f => LensLike (Curried (Yoneda f) (Yoneda f)) s t a b -> LensLike f s t a b #

Fuse a Traversal by reassociating all of the (<*>) operations to the left and fusing all of the fmap calls into one. This is particularly useful when constructing a Traversal using operations from GHC.Generics.

Given a pair of Traversals foo and bar,

confusing (foo.bar) = foo.bar

However, foo and bar are each going to use the Applicative they are given.

confusing exploits the Yoneda lemma to merge their separate uses of fmap into a single fmap. and it further exploits an interesting property of the right Kan lift (or Curried) to left associate all of the uses of (<*>) to make it possible to fuse together more fmaps.

This is particularly effective when the choice of functor f is unknown at compile time or when the Traversal foo.bar in the above description is recursive or complex enough to prevent inlining.

fusing is a version of this combinator suitable for fusing lenses.

confusing :: Traversal s t a b -> Traversal s t a b

traverseByOf :: Traversal s t a b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> s -> f t #

Traverse a container using a specified Applicative.

This is like traverseBy where the Traversable instance can be specified by any Traversal

traverseByOf traverse ≡ traverseBy

sequenceByOf :: Traversal s t (f b) b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> s -> f t #

Sequence a container using a specified Applicative.

This is like traverseBy where the Traversable instance can be specified by any Traversal

sequenceByOf traverse ≡ sequenceBy

ilevels :: Applicative f => Traversing (Indexed i) f s t a b -> IndexedLensLike Int f s t (Level i a) (Level j b) #

This provides a breadth-first Traversal or Fold of the individual levels of any other Traversal or Fold via iterative deepening depth-first search. The levels are returned to you in a compressed format.

This is similar to levels, but retains the index of the original IndexedTraversal, so you can access it when traversing the levels later on.

>>> ["dog","cat"]^@..ilevels (traversed<.>traversed).itraversed
[((0,0),'d'),((0,1),'o'),((1,0),'c'),((0,2),'g'),((1,1),'a'),((1,2),'t')]

The resulting Traversal of the levels which is indexed by the depth of each Level.

>>> ["dog","cat"]^@..ilevels (traversed<.>traversed)<.>itraversed
[((2,(0,0)),'d'),((3,(0,1)),'o'),((3,(1,0)),'c'),((4,(0,2)),'g'),((4,(1,1)),'a'),((5,(1,2)),'t')]

ilevels :: IndexedTraversal i s t a b      -> IndexedTraversal Int s t (Level i a) (Level i b)
ilevels :: IndexedFold i s a               -> IndexedFold Int s (Level i a)

Note: Internally this is implemented by using an illegal Applicative, as it extracts information in an order that violates the Applicative laws.

type ReifiedPrism' s a = ReifiedPrism s s a a #

type ReifiedPrism' = Simple ReifiedPrism

newtype ReifiedPrism s t a b #

Reify a ReifiedPrism so it can be stored safely in a container.

Constructors

Prism
Fields runPrism :: Prism s t a b

type ReifiedIso' s a = ReifiedIso s s a a #

type ReifiedIso' = Simple ReifiedIso

newtype ReifiedIso s t a b #

Reify an ReifiedIso so it can be stored safely in a container.

Constructors

Iso
Fields runIso :: Iso s t a b

type ReifiedIndexedSetter' i s a = ReifiedIndexedSetter i s s a a #

type ReifiedIndexedSetter' i = Simple (ReifiedIndexedSetter i)

newtype ReifiedIndexedSetter i s t a b #

Reify an ReifiedIndexedSetter so it can be stored safely in a container.

Constructors

IndexedSetter
Fields runIndexedSetter :: IndexedSetter i s t a b

type ReifiedSetter' s a = ReifiedSetter s s a a #

type ReifiedSetter' = Simple ReifiedSetter

newtype ReifiedSetter s t a b #

Reify a ReifiedSetter so it can be stored safely in a container.

Constructors

Setter
Fields runSetter :: Setter s t a b

newtype ReifiedIndexedFold i s a #

Constructors

IndexedFold
Fields runIndexedFold :: IndexedFold i s a

Instances

Profunctor (ReifiedIndexedFold i)
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedIndexedFold i b c -> ReifiedIndexedFold i a d # lmap :: (a -> b) -> ReifiedIndexedFold i b c -> ReifiedIndexedFold i a c # rmap :: (b -> c) -> ReifiedIndexedFold i a b -> ReifiedIndexedFold i a c # (#.) :: Coercible c b => q b c -> ReifiedIndexedFold i a b -> ReifiedIndexedFold i a c # (.#) :: Coercible b a => ReifiedIndexedFold i b c -> q a b -> ReifiedIndexedFold i a c #
Representable (ReifiedIndexedFold i)
Instance details Defined in Control.Lens.Reified Associated Types type Rep (ReifiedIndexedFold i) :: Type -> Type # Methods tabulate :: (d -> Rep (ReifiedIndexedFold i) c) -> ReifiedIndexedFold i d c #
Strong (ReifiedIndexedFold i)
Instance details Defined in Control.Lens.Reified Methods first' :: ReifiedIndexedFold i a b -> ReifiedIndexedFold i (a, c) (b, c) # second' :: ReifiedIndexedFold i a b -> ReifiedIndexedFold i (c, a) (c, b) #
Sieve (ReifiedIndexedFold i) (Compose [] ((,) i))
Instance details Defined in Control.Lens.Reified Methods sieve :: ReifiedIndexedFold i a b -> a -> Compose [] ((,) i) b #
Functor (ReifiedIndexedFold i s)
Instance details Defined in Control.Lens.Reified Methods fmap :: (a -> b) -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s b # (<$) :: a -> ReifiedIndexedFold i s b -> ReifiedIndexedFold i s a #
Plus (ReifiedIndexedFold i s)
Instance details Defined in Control.Lens.Reified Methods zero :: ReifiedIndexedFold i s a #
Alt (ReifiedIndexedFold i s)
Instance details Defined in Control.Lens.Reified Methods (<!>) :: ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a # some :: Applicative (ReifiedIndexedFold i s) => ReifiedIndexedFold i s a -> ReifiedIndexedFold i s [a] # many :: Applicative (ReifiedIndexedFold i s) => ReifiedIndexedFold i s a -> ReifiedIndexedFold i s [a] #
Semigroup (ReifiedIndexedFold i s a)
Instance details Defined in Control.Lens.Reified Methods (<>) :: ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a # sconcat :: NonEmpty (ReifiedIndexedFold i s a) -> ReifiedIndexedFold i s a # stimes :: Integral b => b -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a #
Monoid (ReifiedIndexedFold i s a)
Instance details Defined in Control.Lens.Reified Methods mempty :: ReifiedIndexedFold i s a # mappend :: ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a -> ReifiedIndexedFold i s a # mconcat :: [ReifiedIndexedFold i s a] -> ReifiedIndexedFold i s a #
type Rep (ReifiedIndexedFold i)
Instance details Defined in Control.Lens.Reified type Rep (ReifiedIndexedFold i) = Compose [] ((,) i)

newtype ReifiedFold s a #

Reify a ReifiedFold so it can be stored safely in a container.

This can also be useful for creatively combining folds as ReifiedFold s is isomorphic to ReaderT s [] and provides similar instances.

>>> ("hello","world")^..runFold ((,) <$> Fold _2 <*> Fold both)
[("world","hello"),("world","world")]

Constructors

Fold
Fields runFold :: Fold s a

Instances

Arrow ReifiedFold
Instance details Defined in Control.Lens.Reified Methods arr :: (b -> c) -> ReifiedFold b c # first :: ReifiedFold b c -> ReifiedFold (b, d) (c, d) # second :: ReifiedFold b c -> ReifiedFold (d, b) (d, c) # (***) :: ReifiedFold b c -> ReifiedFold b' c' -> ReifiedFold (b, b') (c, c') # (&&&) :: ReifiedFold b c -> ReifiedFold b c' -> ReifiedFold b (c, c') #
ArrowChoice ReifiedFold
Instance details Defined in Control.Lens.Reified Methods left :: ReifiedFold b c -> ReifiedFold (Either b d) (Either c d) # right :: ReifiedFold b c -> ReifiedFold (Either d b) (Either d c) # (+++) :: ReifiedFold b c -> ReifiedFold b' c' -> ReifiedFold (Either b b') (Either c c') # (\|\|\|) :: ReifiedFold b d -> ReifiedFold c d -> ReifiedFold (Either b c) d #
ArrowApply ReifiedFold
Instance details Defined in Control.Lens.Reified Methods app :: ReifiedFold (ReifiedFold b c, b) c #
Choice ReifiedFold
Instance details Defined in Control.Lens.Reified Methods left' :: ReifiedFold a b -> ReifiedFold (Either a c) (Either b c) # right' :: ReifiedFold a b -> ReifiedFold (Either c a) (Either c b) #
Profunctor ReifiedFold
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedFold b c -> ReifiedFold a d # lmap :: (a -> b) -> ReifiedFold b c -> ReifiedFold a c # rmap :: (b -> c) -> ReifiedFold a b -> ReifiedFold a c # (#.) :: Coercible c b => q b c -> ReifiedFold a b -> ReifiedFold a c # (.#) :: Coercible b a => ReifiedFold b c -> q a b -> ReifiedFold a c #
Representable ReifiedFold
Instance details Defined in Control.Lens.Reified Associated Types type Rep ReifiedFold :: Type -> Type # Methods tabulate :: (d -> Rep ReifiedFold c) -> ReifiedFold d c #
Strong ReifiedFold
Instance details Defined in Control.Lens.Reified Methods first' :: ReifiedFold a b -> ReifiedFold (a, c) (b, c) # second' :: ReifiedFold a b -> ReifiedFold (c, a) (c, b) #
Sieve ReifiedFold []
Instance details Defined in Control.Lens.Reified Methods sieve :: ReifiedFold a b -> a -> [b] #
MonadReader s (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods ask :: ReifiedFold s s # local :: (s -> s) -> ReifiedFold s a -> ReifiedFold s a # reader :: (s -> a) -> ReifiedFold s a #
Monad (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods (>>=) :: ReifiedFold s a -> (a -> ReifiedFold s b) -> ReifiedFold s b # (>>) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s b # return :: a -> ReifiedFold s a # fail :: String -> ReifiedFold s a #
Functor (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods fmap :: (a -> b) -> ReifiedFold s a -> ReifiedFold s b # (<$) :: a -> ReifiedFold s b -> ReifiedFold s a #
Applicative (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods pure :: a -> ReifiedFold s a # (<>) :: ReifiedFold s (a -> b) -> ReifiedFold s a -> ReifiedFold s b # liftA2 :: (a -> b -> c) -> ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s c # (>) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s b # (<*) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s a #
MonadPlus (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods mzero :: ReifiedFold s a # mplus :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a #
Alternative (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods empty :: ReifiedFold s a # (<\|>) :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a # some :: ReifiedFold s a -> ReifiedFold s [a] # many :: ReifiedFold s a -> ReifiedFold s [a] #
Apply (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods (<.>) :: ReifiedFold s (a -> b) -> ReifiedFold s a -> ReifiedFold s b # (.>) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s b # (<.) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s a # liftF2 :: (a -> b -> c) -> ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s c #
Plus (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods zero :: ReifiedFold s a #
Alt (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods (<!>) :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a # some :: Applicative (ReifiedFold s) => ReifiedFold s a -> ReifiedFold s [a] # many :: Applicative (ReifiedFold s) => ReifiedFold s a -> ReifiedFold s [a] #
Bind (ReifiedFold s)
Instance details Defined in Control.Lens.Reified Methods (>>-) :: ReifiedFold s a -> (a -> ReifiedFold s b) -> ReifiedFold s b # join :: ReifiedFold s (ReifiedFold s a) -> ReifiedFold s a #
Category ReifiedFold
Instance details Defined in Control.Lens.Reified Methods id :: ReifiedFold a a # (.) :: ReifiedFold b c -> ReifiedFold a b -> ReifiedFold a c #
Semigroup (ReifiedFold s a)
Instance details Defined in Control.Lens.Reified Methods (<>) :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a # sconcat :: NonEmpty (ReifiedFold s a) -> ReifiedFold s a # stimes :: Integral b => b -> ReifiedFold s a -> ReifiedFold s a #
Monoid (ReifiedFold s a)
Instance details Defined in Control.Lens.Reified Methods mempty :: ReifiedFold s a # mappend :: ReifiedFold s a -> ReifiedFold s a -> ReifiedFold s a # mconcat :: [ReifiedFold s a] -> ReifiedFold s a #
type Rep ReifiedFold
Instance details Defined in Control.Lens.Reified type Rep ReifiedFold = []

newtype ReifiedIndexedGetter i s a #

Reify an ReifiedIndexedGetter so it can be stored safely in a container.

Constructors

IndexedGetter
Fields runIndexedGetter :: IndexedGetter i s a

Instances

Profunctor (ReifiedIndexedGetter i)
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedIndexedGetter i b c -> ReifiedIndexedGetter i a d # lmap :: (a -> b) -> ReifiedIndexedGetter i b c -> ReifiedIndexedGetter i a c # rmap :: (b -> c) -> ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i a c # (#.) :: Coercible c b => q b c -> ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i a c # (.#) :: Coercible b a => ReifiedIndexedGetter i b c -> q a b -> ReifiedIndexedGetter i a c #
Representable (ReifiedIndexedGetter i)
Instance details Defined in Control.Lens.Reified Associated Types type Rep (ReifiedIndexedGetter i) :: Type -> Type # Methods tabulate :: (d -> Rep (ReifiedIndexedGetter i) c) -> ReifiedIndexedGetter i d c #
Strong (ReifiedIndexedGetter i)
Instance details Defined in Control.Lens.Reified Methods first' :: ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i (a, c) (b, c) # second' :: ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i (c, a) (c, b) #
Sieve (ReifiedIndexedGetter i) ((,) i)
Instance details Defined in Control.Lens.Reified Methods sieve :: ReifiedIndexedGetter i a b -> a -> (i, b) #
Functor (ReifiedIndexedGetter i s)
Instance details Defined in Control.Lens.Reified Methods fmap :: (a -> b) -> ReifiedIndexedGetter i s a -> ReifiedIndexedGetter i s b # (<$) :: a -> ReifiedIndexedGetter i s b -> ReifiedIndexedGetter i s a #
Semigroup i => Apply (ReifiedIndexedGetter i s)
Instance details Defined in Control.Lens.Reified Methods (<.>) :: ReifiedIndexedGetter i s (a -> b) -> ReifiedIndexedGetter i s a -> ReifiedIndexedGetter i s b # (.>) :: ReifiedIndexedGetter i s a -> ReifiedIndexedGetter i s b -> ReifiedIndexedGetter i s b # (<.) :: ReifiedIndexedGetter i s a -> ReifiedIndexedGetter i s b -> ReifiedIndexedGetter i s a # liftF2 :: (a -> b -> c) -> ReifiedIndexedGetter i s a -> ReifiedIndexedGetter i s b -> ReifiedIndexedGetter i s c #
type Rep (ReifiedIndexedGetter i)
Instance details Defined in Control.Lens.Reified type Rep (ReifiedIndexedGetter i) = (,) i

newtype ReifiedGetter s a #

Reify a ReifiedGetter so it can be stored safely in a container.

This can also be useful when combining getters in novel ways, as ReifiedGetter is isomorphic to '(->)' and provides similar instances.

>>> ("hello","world","!!!")^.runGetter ((,) <$> Getter _2 <*> Getter (_1.to length))
("world",5)

Constructors

Getter
Fields runGetter :: Getter s a

Instances

Arrow ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods arr :: (b -> c) -> ReifiedGetter b c # first :: ReifiedGetter b c -> ReifiedGetter (b, d) (c, d) # second :: ReifiedGetter b c -> ReifiedGetter (d, b) (d, c) # (***) :: ReifiedGetter b c -> ReifiedGetter b' c' -> ReifiedGetter (b, b') (c, c') # (&&&) :: ReifiedGetter b c -> ReifiedGetter b c' -> ReifiedGetter b (c, c') #
ArrowChoice ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods left :: ReifiedGetter b c -> ReifiedGetter (Either b d) (Either c d) # right :: ReifiedGetter b c -> ReifiedGetter (Either d b) (Either d c) # (+++) :: ReifiedGetter b c -> ReifiedGetter b' c' -> ReifiedGetter (Either b b') (Either c c') # (\|\|\|) :: ReifiedGetter b d -> ReifiedGetter c d -> ReifiedGetter (Either b c) d #
ArrowApply ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods app :: ReifiedGetter (ReifiedGetter b c, b) c #
ArrowLoop ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods loop :: ReifiedGetter (b, d) (c, d) -> ReifiedGetter b c #
Choice ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods left' :: ReifiedGetter a b -> ReifiedGetter (Either a c) (Either b c) # right' :: ReifiedGetter a b -> ReifiedGetter (Either c a) (Either c b) #
Conjoined ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods distrib :: Functor f => ReifiedGetter a b -> ReifiedGetter (f a) (f b) # conjoined :: ((ReifiedGetter ~ (->)) -> q (a -> b) r) -> q (ReifiedGetter a b) r -> q (ReifiedGetter a b) r #
Profunctor ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedGetter b c -> ReifiedGetter a d # lmap :: (a -> b) -> ReifiedGetter b c -> ReifiedGetter a c # rmap :: (b -> c) -> ReifiedGetter a b -> ReifiedGetter a c # (#.) :: Coercible c b => q b c -> ReifiedGetter a b -> ReifiedGetter a c # (.#) :: Coercible b a => ReifiedGetter b c -> q a b -> ReifiedGetter a c #
Representable ReifiedGetter
Instance details Defined in Control.Lens.Reified Associated Types type Rep ReifiedGetter :: Type -> Type # Methods tabulate :: (d -> Rep ReifiedGetter c) -> ReifiedGetter d c #
Corepresentable ReifiedGetter
Instance details Defined in Control.Lens.Reified Associated Types type Corep ReifiedGetter :: Type -> Type # Methods cotabulate :: (Corep ReifiedGetter d -> c) -> ReifiedGetter d c #
Closed ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods closed :: ReifiedGetter a b -> ReifiedGetter (x -> a) (x -> b) #
Strong ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods first' :: ReifiedGetter a b -> ReifiedGetter (a, c) (b, c) # second' :: ReifiedGetter a b -> ReifiedGetter (c, a) (c, b) #
Costrong ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods unfirst :: ReifiedGetter (a, d) (b, d) -> ReifiedGetter a b # unsecond :: ReifiedGetter (d, a) (d, b) -> ReifiedGetter a b #
Sieve ReifiedGetter Identity
Instance details Defined in Control.Lens.Reified Methods sieve :: ReifiedGetter a b -> a -> Identity b #
Cosieve ReifiedGetter Identity
Instance details Defined in Control.Lens.Reified Methods cosieve :: ReifiedGetter a b -> Identity a -> b #
MonadReader s (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods ask :: ReifiedGetter s s # local :: (s -> s) -> ReifiedGetter s a -> ReifiedGetter s a # reader :: (s -> a) -> ReifiedGetter s a #
Monad (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods (>>=) :: ReifiedGetter s a -> (a -> ReifiedGetter s b) -> ReifiedGetter s b # (>>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b # return :: a -> ReifiedGetter s a # fail :: String -> ReifiedGetter s a #
Functor (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods fmap :: (a -> b) -> ReifiedGetter s a -> ReifiedGetter s b # (<$) :: a -> ReifiedGetter s b -> ReifiedGetter s a #
Applicative (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods pure :: a -> ReifiedGetter s a # (<>) :: ReifiedGetter s (a -> b) -> ReifiedGetter s a -> ReifiedGetter s b # liftA2 :: (a -> b -> c) -> ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s c # (>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b # (<*) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s a #
Apply (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods (<.>) :: ReifiedGetter s (a -> b) -> ReifiedGetter s a -> ReifiedGetter s b # (.>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b # (<.) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s a # liftF2 :: (a -> b -> c) -> ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s c #
Distributive (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods distribute :: Functor f => f (ReifiedGetter s a) -> ReifiedGetter s (f a) # collect :: Functor f => (a -> ReifiedGetter s b) -> f a -> ReifiedGetter s (f b) # distributeM :: Monad m => m (ReifiedGetter s a) -> ReifiedGetter s (m a) # collectM :: Monad m => (a -> ReifiedGetter s b) -> m a -> ReifiedGetter s (m b) #
Monoid s => Comonad (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods extract :: ReifiedGetter s a -> a # duplicate :: ReifiedGetter s a -> ReifiedGetter s (ReifiedGetter s a) # extend :: (ReifiedGetter s a -> b) -> ReifiedGetter s a -> ReifiedGetter s b #
Monoid s => ComonadApply (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods (<@>) :: ReifiedGetter s (a -> b) -> ReifiedGetter s a -> ReifiedGetter s b # (@>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b # (<@) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s a #
Bind (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods (>>-) :: ReifiedGetter s a -> (a -> ReifiedGetter s b) -> ReifiedGetter s b # join :: ReifiedGetter s (ReifiedGetter s a) -> ReifiedGetter s a #
Semigroup s => Extend (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods duplicated :: ReifiedGetter s a -> ReifiedGetter s (ReifiedGetter s a) # extended :: (ReifiedGetter s a -> b) -> ReifiedGetter s a -> ReifiedGetter s b #
Category ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods id :: ReifiedGetter a a # (.) :: ReifiedGetter b c -> ReifiedGetter a b -> ReifiedGetter a c #
type Rep ReifiedGetter
Instance details Defined in Control.Lens.Reified type Rep ReifiedGetter = Identity
type Corep ReifiedGetter
Instance details Defined in Control.Lens.Reified type Corep ReifiedGetter = Identity

type ReifiedTraversal' s a = ReifiedTraversal s s a a #

type ReifiedTraversal' = Simple ReifiedTraversal

newtype ReifiedTraversal s t a b #

A form of ReifiedTraversal that can be stored monomorphically in a container.

Constructors

Traversal
Fields runTraversal :: Traversal s t a b

type ReifiedIndexedTraversal' i s a = ReifiedIndexedTraversal i s s a a #

type ReifiedIndexedTraversal' i = Simple (ReifiedIndexedTraversal i)

newtype ReifiedIndexedTraversal i s t a b #

Reify an ReifiedIndexedTraversal so it can be stored safely in a container.

Constructors

IndexedTraversal
Fields runIndexedTraversal :: IndexedTraversal i s t a b

type ReifiedIndexedLens' i s a = ReifiedIndexedLens i s s a a #

type ReifiedIndexedLens' i = Simple (ReifiedIndexedLens i)

newtype ReifiedIndexedLens i s t a b #

Reify an ReifiedIndexedLens so it can be stored safely in a container.

Constructors

IndexedLens
Fields runIndexedLens :: IndexedLens i s t a b

type ReifiedLens' s a = ReifiedLens s s a a #

type ReifiedLens' = Simple ReifiedLens

newtype ReifiedLens s t a b #

Reify a ReifiedLens so it can be stored safely in a container.

Constructors

Lens
Fields runLens :: Lens s t a b

class (FunctorWithIndex i t, FoldableWithIndex i t, Traversable t) => TraversableWithIndex i (t :: Type -> Type) | t -> i where #

A Traversable with an additional index.

An instance must satisfy a (modified) form of the Traversable laws:

itraverse (const Identity) ≡ Identity
fmap (itraverse f) . itraverse g ≡ getCompose . itraverse (\i -> Compose . fmap (f i) . g i)

Minimal complete definition

Nothing

Methods

itraverse :: Applicative f => (i -> a -> f b) -> t a -> f (t b) #

Traverse an indexed container.

itraverse ≡ itraverseOf itraversed

itraversed :: IndexedTraversal i (t a) (t b) a b #

The IndexedTraversal of a TraversableWithIndex container.

Instances

TraversableWithIndex Int []
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> [a] -> f [b] # itraversed :: IndexedTraversal Int [a] [b] a b #
TraversableWithIndex Int ZipList
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> ZipList a -> f (ZipList b) # itraversed :: IndexedTraversal Int (ZipList a) (ZipList b) a b #
TraversableWithIndex Int NonEmpty
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> NonEmpty a -> f (NonEmpty b) # itraversed :: IndexedTraversal Int (NonEmpty a) (NonEmpty b) a b #
TraversableWithIndex Int Vector
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> Vector a -> f (Vector b) # itraversed :: IndexedTraversal Int (Vector a) (Vector b) a b #
TraversableWithIndex Int IntMap
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> IntMap a -> f (IntMap b) # itraversed :: IndexedTraversal Int (IntMap a) (IntMap b) a b #
TraversableWithIndex Int Seq
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Int -> a -> f b) -> Seq a -> f (Seq b) # itraversed :: IndexedTraversal Int (Seq a) (Seq b) a b #
TraversableWithIndex () Maybe
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (() -> a -> f b) -> Maybe a -> f (Maybe b) # itraversed :: IndexedTraversal () (Maybe a) (Maybe b) a b #
TraversableWithIndex () Par1
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (() -> a -> f b) -> Par1 a -> f (Par1 b) # itraversed :: IndexedTraversal () (Par1 a) (Par1 b) a b #
TraversableWithIndex () Identity
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (() -> a -> f b) -> Identity a -> f (Identity b) # itraversed :: IndexedTraversal () (Identity a) (Identity b) a b #
TraversableWithIndex k (Map k)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (k -> a -> f b) -> Map k a -> f (Map k b) # itraversed :: IndexedTraversal k (Map k a) (Map k b) a b #
TraversableWithIndex k (HashMap k)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (k -> a -> f b) -> HashMap k a -> f (HashMap k b) # itraversed :: IndexedTraversal k (HashMap k a) (HashMap k b) a b #
TraversableWithIndex k ((,) k)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (k -> a -> f b) -> (k, a) -> f (k, b) # itraversed :: IndexedTraversal k (k, a) (k, b) a b #
TraversableWithIndex i (Level i)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (i -> a -> f b) -> Level i a -> f (Level i b) # itraversed :: IndexedTraversal i (Level i a) (Level i b) a b #
Ix i => TraversableWithIndex i (Array i)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (i -> a -> f b) -> Array i a -> f (Array i b) # itraversed :: IndexedTraversal i (Array i a) (Array i b) a b #
TraversableWithIndex Void (V1 :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Void -> a -> f b) -> V1 a -> f (V1 b) # itraversed :: IndexedTraversal Void (V1 a) (V1 b) a b #
TraversableWithIndex Void (U1 :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Void -> a -> f b) -> U1 a -> f (U1 b) # itraversed :: IndexedTraversal Void (U1 a) (U1 b) a b #
TraversableWithIndex Void (Proxy :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Void -> a -> f b) -> Proxy a -> f (Proxy b) # itraversed :: IndexedTraversal Void (Proxy a) (Proxy b) a b #
TraversableWithIndex Int (V n)
Instance details Defined in Linear.V Methods itraverse :: Applicative f => (Int -> a -> f b) -> V n a -> f (V n b) # itraversed :: IndexedTraversal Int (V n a) (V n b) a b #
TraversableWithIndex () (Tagged a)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (() -> a0 -> f b) -> Tagged a a0 -> f (Tagged a b) # itraversed :: IndexedTraversal () (Tagged a a0) (Tagged a b) a0 b #
TraversableWithIndex i f => TraversableWithIndex i (Reverse f)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (i -> a -> f0 b) -> Reverse f a -> f0 (Reverse f b) # itraversed :: IndexedTraversal i (Reverse f a) (Reverse f b) a b #
TraversableWithIndex i f => TraversableWithIndex i (Rec1 f)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (i -> a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) # itraversed :: IndexedTraversal i (Rec1 f a) (Rec1 f b) a b #
TraversableWithIndex i m => TraversableWithIndex i (IdentityT m)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (i -> a -> f b) -> IdentityT m a -> f (IdentityT m b) # itraversed :: IndexedTraversal i (IdentityT m a) (IdentityT m b) a b #
TraversableWithIndex i f => TraversableWithIndex i (Backwards f)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (i -> a -> f0 b) -> Backwards f a -> f0 (Backwards f b) # itraversed :: IndexedTraversal i (Backwards f a) (Backwards f b) a b #
TraversableWithIndex i (Magma i t b)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (i -> a -> f b0) -> Magma i t b a -> f (Magma i t b b0) # itraversed :: IndexedTraversal i (Magma i t b a) (Magma i t b b0) a b0 #
TraversableWithIndex Void (K1 i c :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => (Void -> a -> f b) -> K1 i c a -> f (K1 i c b) # itraversed :: IndexedTraversal Void (K1 i c a) (K1 i c b) a b #
TraversableWithIndex [Int] Tree
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f => ([Int] -> a -> f b) -> Tree a -> f (Tree b) # itraversed :: IndexedTraversal [Int] (Tree a) (Tree b) a b #
TraversableWithIndex (E V2) V2
Instance details Defined in Linear.V2 Methods itraverse :: Applicative f => (E V2 -> a -> f b) -> V2 a -> f (V2 b) # itraversed :: IndexedTraversal (E V2) (V2 a) (V2 b) a b #
TraversableWithIndex (E V3) V3
Instance details Defined in Linear.V3 Methods itraverse :: Applicative f => (E V3 -> a -> f b) -> V3 a -> f (V3 b) # itraversed :: IndexedTraversal (E V3) (V3 a) (V3 b) a b #
TraversableWithIndex (E Plucker) Plucker
Instance details Defined in Linear.Plucker Methods itraverse :: Applicative f => (E Plucker -> a -> f b) -> Plucker a -> f (Plucker b) # itraversed :: IndexedTraversal (E Plucker) (Plucker a) (Plucker b) a b #
TraversableWithIndex (E Quaternion) Quaternion
Instance details Defined in Linear.Quaternion Methods itraverse :: Applicative f => (E Quaternion -> a -> f b) -> Quaternion a -> f (Quaternion b) # itraversed :: IndexedTraversal (E Quaternion) (Quaternion a) (Quaternion b) a b #
TraversableWithIndex (E V0) V0
Instance details Defined in Linear.V0 Methods itraverse :: Applicative f => (E V0 -> a -> f b) -> V0 a -> f (V0 b) # itraversed :: IndexedTraversal (E V0) (V0 a) (V0 b) a b #
TraversableWithIndex (E V4) V4
Instance details Defined in Linear.V4 Methods itraverse :: Applicative f => (E V4 -> a -> f b) -> V4 a -> f (V4 b) # itraversed :: IndexedTraversal (E V4) (V4 a) (V4 b) a b #
TraversableWithIndex (E V1) V1
Instance details Defined in Linear.V1 Methods itraverse :: Applicative f => (E V1 -> a -> f b) -> V1 a -> f (V1 b) # itraversed :: IndexedTraversal (E V1) (V1 a) (V1 b) a b #
TraversableWithIndex i f => TraversableWithIndex [i] (Free f)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => ([i] -> a -> f0 b) -> Free f a -> f0 (Free f b) # itraversed :: IndexedTraversal [i] (Free f a) (Free f b) a b #
TraversableWithIndex i f => TraversableWithIndex [i] (Cofree f)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => ([i] -> a -> f0 b) -> Cofree f a -> f0 (Cofree f b) # itraversed :: IndexedTraversal [i] (Cofree f a) (Cofree f b) a b #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (Sum f g)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> Sum f g a -> f0 (Sum f g b) # itraversed :: IndexedTraversal (Either i j) (Sum f g a) (Sum f g b) a b #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (Product f g)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> Product f g a -> f0 (Product f g b) # itraversed :: IndexedTraversal (Either i j) (Product f g a) (Product f g b) a b #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (f :+: g)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) # itraversed :: IndexedTraversal (Either i j) ((f :+: g) a) ((f :+: g) b) a b #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (f :*: g)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => (Either i j -> a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) # itraversed :: IndexedTraversal (Either i j) ((f :: g) a) ((f :: g) b) a b #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (i, j) (Compose f g)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => ((i, j) -> a -> f0 b) -> Compose f g a -> f0 (Compose f g b) # itraversed :: IndexedTraversal (i, j) (Compose f g a) (Compose f g b) a b #
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (i, j) (f :.: g)
Instance details Defined in Control.Lens.Indexed Methods itraverse :: Applicative f0 => ((i, j) -> a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) # itraversed :: IndexedTraversal (i, j) ((f :.: g) a) ((f :.: g) b) a b #

class Foldable f => FoldableWithIndex i (f :: Type -> Type) | f -> i where #

A container that supports folding with an additional index.

Minimal complete definition

Nothing

Methods

ifoldMap :: Monoid m => (i -> a -> m) -> f a -> m #

Fold a container by mapping value to an arbitrary Monoid with access to the index i.

When you don't need access to the index then foldMap is more flexible in what it accepts.

foldMap ≡ ifoldMap . const

ifolded :: IndexedFold i (f a) a #

The IndexedFold of a FoldableWithIndex container.

ifolded . asIndex is a fold over the keys of a FoldableWithIndex.

>>> Data.Map.fromList [(2, "hello"), (1, "world")]^..ifolded.asIndex
[1,2]

ifoldr :: (i -> a -> b -> b) -> b -> f a -> b #

Right-associative fold of an indexed container with access to the index i.

When you don't need access to the index then foldr is more flexible in what it accepts.

foldr ≡ ifoldr . const

ifoldl :: (i -> b -> a -> b) -> b -> f a -> b #

Left-associative fold of an indexed container with access to the index i.

When you don't need access to the index then foldl is more flexible in what it accepts.

foldl ≡ ifoldl . const

ifoldr' :: (i -> a -> b -> b) -> b -> f a -> b #

Strictly fold right over the elements of a structure with access to the index i.

When you don't need access to the index then Foldable is more flexible in what it accepts.

Foldable ≡ ifoldr' . const

ifoldl' :: (i -> b -> a -> b) -> b -> f a -> b #

Fold over the elements of a structure with an index, associating to the left, but strictly.

When you don't need access to the index then foldlOf' is more flexible in what it accepts.

foldlOf' l ≡ ifoldlOf' l . const

Instances

FoldableWithIndex Int []
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> [a] -> m # ifolded :: IndexedFold Int [a] a # ifoldr :: (Int -> a -> b -> b) -> b -> [a] -> b # ifoldl :: (Int -> b -> a -> b) -> b -> [a] -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> [a] -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> [a] -> b #
FoldableWithIndex Int ZipList
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> ZipList a -> m # ifolded :: IndexedFold Int (ZipList a) a # ifoldr :: (Int -> a -> b -> b) -> b -> ZipList a -> b # ifoldl :: (Int -> b -> a -> b) -> b -> ZipList a -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> ZipList a -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> ZipList a -> b #
FoldableWithIndex Int NonEmpty
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> NonEmpty a -> m # ifolded :: IndexedFold Int (NonEmpty a) a # ifoldr :: (Int -> a -> b -> b) -> b -> NonEmpty a -> b # ifoldl :: (Int -> b -> a -> b) -> b -> NonEmpty a -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> NonEmpty a -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> NonEmpty a -> b #
FoldableWithIndex Int Vector
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> Vector a -> m # ifolded :: IndexedFold Int (Vector a) a # ifoldr :: (Int -> a -> b -> b) -> b -> Vector a -> b # ifoldl :: (Int -> b -> a -> b) -> b -> Vector a -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> Vector a -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> Vector a -> b #
FoldableWithIndex Int IntMap
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> IntMap a -> m # ifolded :: IndexedFold Int (IntMap a) a # ifoldr :: (Int -> a -> b -> b) -> b -> IntMap a -> b # ifoldl :: (Int -> b -> a -> b) -> b -> IntMap a -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> IntMap a -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> IntMap a -> b #
FoldableWithIndex Int Seq
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Int -> a -> m) -> Seq a -> m # ifolded :: IndexedFold Int (Seq a) a # ifoldr :: (Int -> a -> b -> b) -> b -> Seq a -> b # ifoldl :: (Int -> b -> a -> b) -> b -> Seq a -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> Seq a -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> Seq a -> b #
FoldableWithIndex () Maybe
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (() -> a -> m) -> Maybe a -> m # ifolded :: IndexedFold () (Maybe a) a # ifoldr :: (() -> a -> b -> b) -> b -> Maybe a -> b # ifoldl :: (() -> b -> a -> b) -> b -> Maybe a -> b # ifoldr' :: (() -> a -> b -> b) -> b -> Maybe a -> b # ifoldl' :: (() -> b -> a -> b) -> b -> Maybe a -> b #
FoldableWithIndex () Par1
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (() -> a -> m) -> Par1 a -> m # ifolded :: IndexedFold () (Par1 a) a # ifoldr :: (() -> a -> b -> b) -> b -> Par1 a -> b # ifoldl :: (() -> b -> a -> b) -> b -> Par1 a -> b # ifoldr' :: (() -> a -> b -> b) -> b -> Par1 a -> b # ifoldl' :: (() -> b -> a -> b) -> b -> Par1 a -> b #
FoldableWithIndex () Identity
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (() -> a -> m) -> Identity a -> m # ifolded :: IndexedFold () (Identity a) a # ifoldr :: (() -> a -> b -> b) -> b -> Identity a -> b # ifoldl :: (() -> b -> a -> b) -> b -> Identity a -> b # ifoldr' :: (() -> a -> b -> b) -> b -> Identity a -> b # ifoldl' :: (() -> b -> a -> b) -> b -> Identity a -> b #
FoldableWithIndex k (Map k)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (k -> a -> m) -> Map k a -> m # ifolded :: IndexedFold k (Map k a) a # ifoldr :: (k -> a -> b -> b) -> b -> Map k a -> b # ifoldl :: (k -> b -> a -> b) -> b -> Map k a -> b # ifoldr' :: (k -> a -> b -> b) -> b -> Map k a -> b # ifoldl' :: (k -> b -> a -> b) -> b -> Map k a -> b #
FoldableWithIndex k (HashMap k)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (k -> a -> m) -> HashMap k a -> m # ifolded :: IndexedFold k (HashMap k a) a # ifoldr :: (k -> a -> b -> b) -> b -> HashMap k a -> b # ifoldl :: (k -> b -> a -> b) -> b -> HashMap k a -> b # ifoldr' :: (k -> a -> b -> b) -> b -> HashMap k a -> b # ifoldl' :: (k -> b -> a -> b) -> b -> HashMap k a -> b #
FoldableWithIndex k ((,) k)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (k -> a -> m) -> (k, a) -> m # ifolded :: IndexedFold k (k, a) a # ifoldr :: (k -> a -> b -> b) -> b -> (k, a) -> b # ifoldl :: (k -> b -> a -> b) -> b -> (k, a) -> b # ifoldr' :: (k -> a -> b -> b) -> b -> (k, a) -> b # ifoldl' :: (k -> b -> a -> b) -> b -> (k, a) -> b #
FoldableWithIndex i (Level i)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (i -> a -> m) -> Level i a -> m # ifolded :: IndexedFold i (Level i a) a # ifoldr :: (i -> a -> b -> b) -> b -> Level i a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Level i a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Level i a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Level i a -> b #
Ix i => FoldableWithIndex i (Array i)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (i -> a -> m) -> Array i a -> m # ifolded :: IndexedFold i (Array i a) a # ifoldr :: (i -> a -> b -> b) -> b -> Array i a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Array i a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Array i a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Array i a -> b #
FoldableWithIndex Void (V1 :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Void -> a -> m) -> V1 a -> m # ifolded :: IndexedFold Void (V1 a) a # ifoldr :: (Void -> a -> b -> b) -> b -> V1 a -> b # ifoldl :: (Void -> b -> a -> b) -> b -> V1 a -> b # ifoldr' :: (Void -> a -> b -> b) -> b -> V1 a -> b # ifoldl' :: (Void -> b -> a -> b) -> b -> V1 a -> b #
FoldableWithIndex Void (U1 :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Void -> a -> m) -> U1 a -> m # ifolded :: IndexedFold Void (U1 a) a # ifoldr :: (Void -> a -> b -> b) -> b -> U1 a -> b # ifoldl :: (Void -> b -> a -> b) -> b -> U1 a -> b # ifoldr' :: (Void -> a -> b -> b) -> b -> U1 a -> b # ifoldl' :: (Void -> b -> a -> b) -> b -> U1 a -> b #
FoldableWithIndex Void (Proxy :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Void -> a -> m) -> Proxy a -> m # ifolded :: IndexedFold Void (Proxy a) a # ifoldr :: (Void -> a -> b -> b) -> b -> Proxy a -> b # ifoldl :: (Void -> b -> a -> b) -> b -> Proxy a -> b # ifoldr' :: (Void -> a -> b -> b) -> b -> Proxy a -> b # ifoldl' :: (Void -> b -> a -> b) -> b -> Proxy a -> b #
FoldableWithIndex Int (V n)
Instance details Defined in Linear.V Methods ifoldMap :: Monoid m => (Int -> a -> m) -> V n a -> m # ifolded :: IndexedFold Int (V n a) a # ifoldr :: (Int -> a -> b -> b) -> b -> V n a -> b # ifoldl :: (Int -> b -> a -> b) -> b -> V n a -> b # ifoldr' :: (Int -> a -> b -> b) -> b -> V n a -> b # ifoldl' :: (Int -> b -> a -> b) -> b -> V n a -> b #
FoldableWithIndex () (Tagged a)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (() -> a0 -> m) -> Tagged a a0 -> m # ifolded :: IndexedFold () (Tagged a a0) a0 # ifoldr :: (() -> a0 -> b -> b) -> b -> Tagged a a0 -> b # ifoldl :: (() -> b -> a0 -> b) -> b -> Tagged a a0 -> b # ifoldr' :: (() -> a0 -> b -> b) -> b -> Tagged a a0 -> b # ifoldl' :: (() -> b -> a0 -> b) -> b -> Tagged a a0 -> b #
FoldableWithIndex i f => FoldableWithIndex i (Reverse f)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (i -> a -> m) -> Reverse f a -> m # ifolded :: IndexedFold i (Reverse f a) a # ifoldr :: (i -> a -> b -> b) -> b -> Reverse f a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Reverse f a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Reverse f a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Reverse f a -> b #
FoldableWithIndex i f => FoldableWithIndex i (Rec1 f)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (i -> a -> m) -> Rec1 f a -> m # ifolded :: IndexedFold i (Rec1 f a) a # ifoldr :: (i -> a -> b -> b) -> b -> Rec1 f a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Rec1 f a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Rec1 f a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Rec1 f a -> b #
FoldableWithIndex i m => FoldableWithIndex i (IdentityT m)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m0 => (i -> a -> m0) -> IdentityT m a -> m0 # ifolded :: IndexedFold i (IdentityT m a) a # ifoldr :: (i -> a -> b -> b) -> b -> IdentityT m a -> b # ifoldl :: (i -> b -> a -> b) -> b -> IdentityT m a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> IdentityT m a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> IdentityT m a -> b #
FoldableWithIndex i f => FoldableWithIndex i (Backwards f)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (i -> a -> m) -> Backwards f a -> m # ifolded :: IndexedFold i (Backwards f a) a # ifoldr :: (i -> a -> b -> b) -> b -> Backwards f a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Backwards f a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Backwards f a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Backwards f a -> b #
FoldableWithIndex i (Magma i t b)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (i -> a -> m) -> Magma i t b a -> m # ifolded :: IndexedFold i (Magma i t b a) a # ifoldr :: (i -> a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # ifoldl :: (i -> b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 # ifoldr' :: (i -> a -> b0 -> b0) -> b0 -> Magma i t b a -> b0 # ifoldl' :: (i -> b0 -> a -> b0) -> b0 -> Magma i t b a -> b0 #
FoldableWithIndex Void (K1 i c :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Void -> a -> m) -> K1 i c a -> m # ifolded :: IndexedFold Void (K1 i c a) a # ifoldr :: (Void -> a -> b -> b) -> b -> K1 i c a -> b # ifoldl :: (Void -> b -> a -> b) -> b -> K1 i c a -> b # ifoldr' :: (Void -> a -> b -> b) -> b -> K1 i c a -> b # ifoldl' :: (Void -> b -> a -> b) -> b -> K1 i c a -> b #
FoldableWithIndex [Int] Tree
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => ([Int] -> a -> m) -> Tree a -> m # ifolded :: IndexedFold [Int] (Tree a) a # ifoldr :: ([Int] -> a -> b -> b) -> b -> Tree a -> b # ifoldl :: ([Int] -> b -> a -> b) -> b -> Tree a -> b # ifoldr' :: ([Int] -> a -> b -> b) -> b -> Tree a -> b # ifoldl' :: ([Int] -> b -> a -> b) -> b -> Tree a -> b #
FoldableWithIndex (E V2) V2
Instance details Defined in Linear.V2 Methods ifoldMap :: Monoid m => (E V2 -> a -> m) -> V2 a -> m # ifolded :: IndexedFold (E V2) (V2 a) a # ifoldr :: (E V2 -> a -> b -> b) -> b -> V2 a -> b # ifoldl :: (E V2 -> b -> a -> b) -> b -> V2 a -> b # ifoldr' :: (E V2 -> a -> b -> b) -> b -> V2 a -> b # ifoldl' :: (E V2 -> b -> a -> b) -> b -> V2 a -> b #
FoldableWithIndex (E V3) V3
Instance details Defined in Linear.V3 Methods ifoldMap :: Monoid m => (E V3 -> a -> m) -> V3 a -> m # ifolded :: IndexedFold (E V3) (V3 a) a # ifoldr :: (E V3 -> a -> b -> b) -> b -> V3 a -> b # ifoldl :: (E V3 -> b -> a -> b) -> b -> V3 a -> b # ifoldr' :: (E V3 -> a -> b -> b) -> b -> V3 a -> b # ifoldl' :: (E V3 -> b -> a -> b) -> b -> V3 a -> b #
FoldableWithIndex (E Plucker) Plucker
Instance details Defined in Linear.Plucker Methods ifoldMap :: Monoid m => (E Plucker -> a -> m) -> Plucker a -> m # ifolded :: IndexedFold (E Plucker) (Plucker a) a # ifoldr :: (E Plucker -> a -> b -> b) -> b -> Plucker a -> b # ifoldl :: (E Plucker -> b -> a -> b) -> b -> Plucker a -> b # ifoldr' :: (E Plucker -> a -> b -> b) -> b -> Plucker a -> b # ifoldl' :: (E Plucker -> b -> a -> b) -> b -> Plucker a -> b #
FoldableWithIndex (E Quaternion) Quaternion
Instance details Defined in Linear.Quaternion Methods ifoldMap :: Monoid m => (E Quaternion -> a -> m) -> Quaternion a -> m # ifolded :: IndexedFold (E Quaternion) (Quaternion a) a # ifoldr :: (E Quaternion -> a -> b -> b) -> b -> Quaternion a -> b # ifoldl :: (E Quaternion -> b -> a -> b) -> b -> Quaternion a -> b # ifoldr' :: (E Quaternion -> a -> b -> b) -> b -> Quaternion a -> b # ifoldl' :: (E Quaternion -> b -> a -> b) -> b -> Quaternion a -> b #
FoldableWithIndex (E V0) V0
Instance details Defined in Linear.V0 Methods ifoldMap :: Monoid m => (E V0 -> a -> m) -> V0 a -> m # ifolded :: IndexedFold (E V0) (V0 a) a # ifoldr :: (E V0 -> a -> b -> b) -> b -> V0 a -> b # ifoldl :: (E V0 -> b -> a -> b) -> b -> V0 a -> b # ifoldr' :: (E V0 -> a -> b -> b) -> b -> V0 a -> b # ifoldl' :: (E V0 -> b -> a -> b) -> b -> V0 a -> b #
FoldableWithIndex (E V4) V4
Instance details Defined in Linear.V4 Methods ifoldMap :: Monoid m => (E V4 -> a -> m) -> V4 a -> m # ifolded :: IndexedFold (E V4) (V4 a) a # ifoldr :: (E V4 -> a -> b -> b) -> b -> V4 a -> b # ifoldl :: (E V4 -> b -> a -> b) -> b -> V4 a -> b # ifoldr' :: (E V4 -> a -> b -> b) -> b -> V4 a -> b # ifoldl' :: (E V4 -> b -> a -> b) -> b -> V4 a -> b #
FoldableWithIndex (E V1) V1
Instance details Defined in Linear.V1 Methods ifoldMap :: Monoid m => (E V1 -> a -> m) -> V1 a -> m # ifolded :: IndexedFold (E V1) (V1 a) a # ifoldr :: (E V1 -> a -> b -> b) -> b -> V1 a -> b # ifoldl :: (E V1 -> b -> a -> b) -> b -> V1 a -> b # ifoldr' :: (E V1 -> a -> b -> b) -> b -> V1 a -> b # ifoldl' :: (E V1 -> b -> a -> b) -> b -> V1 a -> b #
FoldableWithIndex i f => FoldableWithIndex [i] (Free f)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => ([i] -> a -> m) -> Free f a -> m # ifolded :: IndexedFold [i] (Free f a) a # ifoldr :: ([i] -> a -> b -> b) -> b -> Free f a -> b # ifoldl :: ([i] -> b -> a -> b) -> b -> Free f a -> b # ifoldr' :: ([i] -> a -> b -> b) -> b -> Free f a -> b # ifoldl' :: ([i] -> b -> a -> b) -> b -> Free f a -> b #
FoldableWithIndex i f => FoldableWithIndex [i] (Cofree f)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => ([i] -> a -> m) -> Cofree f a -> m # ifolded :: IndexedFold [i] (Cofree f a) a # ifoldr :: ([i] -> a -> b -> b) -> b -> Cofree f a -> b # ifoldl :: ([i] -> b -> a -> b) -> b -> Cofree f a -> b # ifoldr' :: ([i] -> a -> b -> b) -> b -> Cofree f a -> b # ifoldl' :: ([i] -> b -> a -> b) -> b -> Cofree f a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (Sum f g)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Either i j -> a -> m) -> Sum f g a -> m # ifolded :: IndexedFold (Either i j) (Sum f g a) a # ifoldr :: (Either i j -> a -> b -> b) -> b -> Sum f g a -> b # ifoldl :: (Either i j -> b -> a -> b) -> b -> Sum f g a -> b # ifoldr' :: (Either i j -> a -> b -> b) -> b -> Sum f g a -> b # ifoldl' :: (Either i j -> b -> a -> b) -> b -> Sum f g a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (Product f g)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Either i j -> a -> m) -> Product f g a -> m # ifolded :: IndexedFold (Either i j) (Product f g a) a # ifoldr :: (Either i j -> a -> b -> b) -> b -> Product f g a -> b # ifoldl :: (Either i j -> b -> a -> b) -> b -> Product f g a -> b # ifoldr' :: (Either i j -> a -> b -> b) -> b -> Product f g a -> b # ifoldl' :: (Either i j -> b -> a -> b) -> b -> Product f g a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (f :+: g)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Either i j -> a -> m) -> (f :+: g) a -> m # ifolded :: IndexedFold (Either i j) ((f :+: g) a) a # ifoldr :: (Either i j -> a -> b -> b) -> b -> (f :+: g) a -> b # ifoldl :: (Either i j -> b -> a -> b) -> b -> (f :+: g) a -> b # ifoldr' :: (Either i j -> a -> b -> b) -> b -> (f :+: g) a -> b # ifoldl' :: (Either i j -> b -> a -> b) -> b -> (f :+: g) a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (f :*: g)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => (Either i j -> a -> m) -> (f :: g) a -> m # ifolded :: IndexedFold (Either i j) ((f :: g) a) a # ifoldr :: (Either i j -> a -> b -> b) -> b -> (f :: g) a -> b # ifoldl :: (Either i j -> b -> a -> b) -> b -> (f :: g) a -> b # ifoldr' :: (Either i j -> a -> b -> b) -> b -> (f :: g) a -> b # ifoldl' :: (Either i j -> b -> a -> b) -> b -> (f :: g) a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (i, j) (Compose f g)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => ((i, j) -> a -> m) -> Compose f g a -> m # ifolded :: IndexedFold (i, j) (Compose f g a) a # ifoldr :: ((i, j) -> a -> b -> b) -> b -> Compose f g a -> b # ifoldl :: ((i, j) -> b -> a -> b) -> b -> Compose f g a -> b # ifoldr' :: ((i, j) -> a -> b -> b) -> b -> Compose f g a -> b # ifoldl' :: ((i, j) -> b -> a -> b) -> b -> Compose f g a -> b #
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (i, j) (f :.: g)
Instance details Defined in Control.Lens.Indexed Methods ifoldMap :: Monoid m => ((i, j) -> a -> m) -> (f :.: g) a -> m # ifolded :: IndexedFold (i, j) ((f :.: g) a) a # ifoldr :: ((i, j) -> a -> b -> b) -> b -> (f :.: g) a -> b # ifoldl :: ((i, j) -> b -> a -> b) -> b -> (f :.: g) a -> b # ifoldr' :: ((i, j) -> a -> b -> b) -> b -> (f :.: g) a -> b # ifoldl' :: ((i, j) -> b -> a -> b) -> b -> (f :.: g) a -> b #

class Functor f => FunctorWithIndex i (f :: Type -> Type) | f -> i where #

A Functor with an additional index.

Instances must satisfy a modified form of the Functor laws:

imap f . imap g ≡ imap (\i -> f i . g i)
imap (\_ a -> a) ≡ id

Minimal complete definition

Nothing

Methods

imap :: (i -> a -> b) -> f a -> f b #

Map with access to the index.

imapped :: IndexedSetter i (f a) (f b) a b #

The IndexedSetter for a FunctorWithIndex.

If you don't need access to the index, then mapped is more flexible in what it accepts.

Instances

FunctorWithIndex Int []	The position in the list is available as the index.
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> [a] -> [b] # imapped :: IndexedSetter Int [a] [b] a b #
FunctorWithIndex Int ZipList	Same instance as for `[]`.
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> ZipList a -> ZipList b # imapped :: IndexedSetter Int (ZipList a) (ZipList b) a b #
FunctorWithIndex Int NonEmpty
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> NonEmpty a -> NonEmpty b # imapped :: IndexedSetter Int (NonEmpty a) (NonEmpty b) a b #
FunctorWithIndex Int Vector
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> Vector a -> Vector b # imapped :: IndexedSetter Int (Vector a) (Vector b) a b #
FunctorWithIndex Int IntMap
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> IntMap a -> IntMap b # imapped :: IndexedSetter Int (IntMap a) (IntMap b) a b #
FunctorWithIndex Int Seq	The position in the `Seq` is available as the index.
Instance details Defined in Control.Lens.Indexed Methods imap :: (Int -> a -> b) -> Seq a -> Seq b # imapped :: IndexedSetter Int (Seq a) (Seq b) a b #
FunctorWithIndex () Maybe
Instance details Defined in Control.Lens.Indexed Methods imap :: (() -> a -> b) -> Maybe a -> Maybe b # imapped :: IndexedSetter () (Maybe a) (Maybe b) a b #
FunctorWithIndex () Par1
Instance details Defined in Control.Lens.Indexed Methods imap :: (() -> a -> b) -> Par1 a -> Par1 b # imapped :: IndexedSetter () (Par1 a) (Par1 b) a b #
FunctorWithIndex () Identity
Instance details Defined in Control.Lens.Indexed Methods imap :: (() -> a -> b) -> Identity a -> Identity b # imapped :: IndexedSetter () (Identity a) (Identity b) a b #
FunctorWithIndex k (Map k)
Instance details Defined in Control.Lens.Indexed Methods imap :: (k -> a -> b) -> Map k a -> Map k b # imapped :: IndexedSetter k (Map k a) (Map k b) a b #
FunctorWithIndex k (HashMap k)
Instance details Defined in Control.Lens.Indexed Methods imap :: (k -> a -> b) -> HashMap k a -> HashMap k b # imapped :: IndexedSetter k (HashMap k a) (HashMap k b) a b #
FunctorWithIndex k ((,) k)
Instance details Defined in Control.Lens.Indexed Methods imap :: (k -> a -> b) -> (k, a) -> (k, b) # imapped :: IndexedSetter k (k, a) (k, b) a b #
FunctorWithIndex i (Level i)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b) -> Level i a -> Level i b # imapped :: IndexedSetter i (Level i a) (Level i b) a b #
Ix i => FunctorWithIndex i (Array i)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b) -> Array i a -> Array i b # imapped :: IndexedSetter i (Array i a) (Array i b) a b #
FunctorWithIndex Void (V1 :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Void -> a -> b) -> V1 a -> V1 b # imapped :: IndexedSetter Void (V1 a) (V1 b) a b #
FunctorWithIndex Void (U1 :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Void -> a -> b) -> U1 a -> U1 b # imapped :: IndexedSetter Void (U1 a) (U1 b) a b #
FunctorWithIndex Void (Proxy :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Void -> a -> b) -> Proxy a -> Proxy b # imapped :: IndexedSetter Void (Proxy a) (Proxy b) a b #
FunctorWithIndex Int (V n)
Instance details Defined in Linear.V Methods imap :: (Int -> a -> b) -> V n a -> V n b # imapped :: IndexedSetter Int (V n a) (V n b) a b #
FunctorWithIndex () (Tagged a)
Instance details Defined in Control.Lens.Indexed Methods imap :: (() -> a0 -> b) -> Tagged a a0 -> Tagged a b # imapped :: IndexedSetter () (Tagged a a0) (Tagged a b) a0 b #
FunctorWithIndex i f => FunctorWithIndex i (Reverse f)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b) -> Reverse f a -> Reverse f b # imapped :: IndexedSetter i (Reverse f a) (Reverse f b) a b #
FunctorWithIndex i f => FunctorWithIndex i (Rec1 f)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b) -> Rec1 f a -> Rec1 f b # imapped :: IndexedSetter i (Rec1 f a) (Rec1 f b) a b #
FunctorWithIndex i m => FunctorWithIndex i (IdentityT m)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b) -> IdentityT m a -> IdentityT m b # imapped :: IndexedSetter i (IdentityT m a) (IdentityT m b) a b #
FunctorWithIndex i f => FunctorWithIndex i (Backwards f)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b) -> Backwards f a -> Backwards f b # imapped :: IndexedSetter i (Backwards f a) (Backwards f b) a b #
FunctorWithIndex r ((->) r :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods imap :: (r -> a -> b) -> (r -> a) -> r -> b # imapped :: IndexedSetter r (r -> a) (r -> b) a b #
FunctorWithIndex i (Magma i t b)
Instance details Defined in Control.Lens.Indexed Methods imap :: (i -> a -> b0) -> Magma i t b a -> Magma i t b b0 # imapped :: IndexedSetter i (Magma i t b a) (Magma i t b b0) a b0 #
FunctorWithIndex Void (K1 i c :: Type -> Type)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Void -> a -> b) -> K1 i c a -> K1 i c b # imapped :: IndexedSetter Void (K1 i c a) (K1 i c b) a b #
FunctorWithIndex [Int] Tree
Instance details Defined in Control.Lens.Indexed Methods imap :: ([Int] -> a -> b) -> Tree a -> Tree b # imapped :: IndexedSetter [Int] (Tree a) (Tree b) a b #
FunctorWithIndex (E V2) V2
Instance details Defined in Linear.V2 Methods imap :: (E V2 -> a -> b) -> V2 a -> V2 b # imapped :: IndexedSetter (E V2) (V2 a) (V2 b) a b #
FunctorWithIndex (E V3) V3
Instance details Defined in Linear.V3 Methods imap :: (E V3 -> a -> b) -> V3 a -> V3 b # imapped :: IndexedSetter (E V3) (V3 a) (V3 b) a b #
FunctorWithIndex (E Plucker) Plucker
Instance details Defined in Linear.Plucker Methods imap :: (E Plucker -> a -> b) -> Plucker a -> Plucker b # imapped :: IndexedSetter (E Plucker) (Plucker a) (Plucker b) a b #
FunctorWithIndex (E Quaternion) Quaternion
Instance details Defined in Linear.Quaternion Methods imap :: (E Quaternion -> a -> b) -> Quaternion a -> Quaternion b # imapped :: IndexedSetter (E Quaternion) (Quaternion a) (Quaternion b) a b #
FunctorWithIndex (E V0) V0
Instance details Defined in Linear.V0 Methods imap :: (E V0 -> a -> b) -> V0 a -> V0 b # imapped :: IndexedSetter (E V0) (V0 a) (V0 b) a b #
FunctorWithIndex (E V4) V4
Instance details Defined in Linear.V4 Methods imap :: (E V4 -> a -> b) -> V4 a -> V4 b # imapped :: IndexedSetter (E V4) (V4 a) (V4 b) a b #
FunctorWithIndex (E V1) V1
Instance details Defined in Linear.V1 Methods imap :: (E V1 -> a -> b) -> V1 a -> V1 b # imapped :: IndexedSetter (E V1) (V1 a) (V1 b) a b #
FunctorWithIndex i f => FunctorWithIndex [i] (Free f)
Instance details Defined in Control.Lens.Indexed Methods imap :: ([i] -> a -> b) -> Free f a -> Free f b # imapped :: IndexedSetter [i] (Free f a) (Free f b) a b #
FunctorWithIndex i f => FunctorWithIndex [i] (Cofree f)
Instance details Defined in Control.Lens.Indexed Methods imap :: ([i] -> a -> b) -> Cofree f a -> Cofree f b # imapped :: IndexedSetter [i] (Cofree f a) (Cofree f b) a b #
FunctorWithIndex i w => FunctorWithIndex (s, i) (TracedT s w)
Instance details Defined in Control.Lens.Indexed Methods imap :: ((s, i) -> a -> b) -> TracedT s w a -> TracedT s w b # imapped :: IndexedSetter (s, i) (TracedT s w a) (TracedT s w b) a b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (Sum f g)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Either i j -> a -> b) -> Sum f g a -> Sum f g b # imapped :: IndexedSetter (Either i j) (Sum f g a) (Sum f g b) a b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (Product f g)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Either i j -> a -> b) -> Product f g a -> Product f g b # imapped :: IndexedSetter (Either i j) (Product f g a) (Product f g b) a b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (f :+: g)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Either i j -> a -> b) -> (f :+: g) a -> (f :+: g) b # imapped :: IndexedSetter (Either i j) ((f :+: g) a) ((f :+: g) b) a b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (f :*: g)
Instance details Defined in Control.Lens.Indexed Methods imap :: (Either i j -> a -> b) -> (f :: g) a -> (f :: g) b # imapped :: IndexedSetter (Either i j) ((f :: g) a) ((f :: g) b) a b #
FunctorWithIndex i m => FunctorWithIndex (e, i) (ReaderT e m)
Instance details Defined in Control.Lens.Indexed Methods imap :: ((e, i) -> a -> b) -> ReaderT e m a -> ReaderT e m b # imapped :: IndexedSetter (e, i) (ReaderT e m a) (ReaderT e m b) a b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (i, j) (Compose f g)
Instance details Defined in Control.Lens.Indexed Methods imap :: ((i, j) -> a -> b) -> Compose f g a -> Compose f g b # imapped :: IndexedSetter (i, j) (Compose f g a) (Compose f g b) a b #
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (i, j) (f :.: g)
Instance details Defined in Control.Lens.Indexed Methods imap :: ((i, j) -> a -> b) -> (f :.: g) a -> (f :.: g) b # imapped :: IndexedSetter (i, j) ((f :.: g) a) ((f :.: g) b) a b #

(<.) :: Indexable i p => (Indexed i s t -> r) -> ((a -> b) -> s -> t) -> p a b -> r infixr 9 #

Compose an Indexed function with a non-indexed function.

Mnemonically, the < points to the indexing we want to preserve.

>>> let nestedMap = (fmap Map.fromList . Map.fromList) [(1, [(10, "one,ten"), (20, "one,twenty")]), (2, [(30, "two,thirty"), (40,"two,forty")])]
>>> nestedMap^..(itraversed<.itraversed).withIndex
[(1,"one,ten"),(1,"one,twenty"),(2,"two,thirty"),(2,"two,forty")]

selfIndex :: Indexable a p => p a fb -> a -> fb #

Use a value itself as its own index. This is essentially an indexed version of id.

Note: When used to modify the value, this can break the index requirements assumed by indices and similar, so this is only properly an IndexedGetter, but it can be used as more.

selfIndex :: IndexedGetter a a b

reindexed :: Indexable j p => (i -> j) -> (Indexed i a b -> r) -> p a b -> r #

Remap the index.

icompose :: Indexable p c => (i -> j -> p) -> (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> c a b -> r #

Composition of Indexed functions with a user supplied function for combining indices.

index :: (Indexable i p, Eq i, Applicative f) => i -> Optical' p (Indexed i) f a a #

This allows you to filter an IndexedFold, IndexedGetter, IndexedTraversal or IndexedLens based on an index.

>>> ["hello","the","world","!!!"]^?traversed.index 2
Just "world"

iany :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool #

Return whether or not any element in a container satisfies a predicate, with access to the index i.

When you don't need access to the index then any is more flexible in what it accepts.

any ≡ iany . const

iall :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool #

Return whether or not all elements in a container satisfy a predicate, with access to the index i.

When you don't need access to the index then all is more flexible in what it accepts.

all ≡ iall . const

inone :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool #

Return whether or not none of the elements in a container satisfy a predicate, with access to the index i.

When you don't need access to the index then none is more flexible in what it accepts.

none ≡ inone . const
inone f ≡ not . iany f

itraverse_ :: (FoldableWithIndex i t, Applicative f) => (i -> a -> f b) -> t a -> f () #

Traverse elements with access to the index i, discarding the results.

When you don't need access to the index then traverse_ is more flexible in what it accepts.

traverse_ l = itraverse . const

ifor_ :: (FoldableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f () #

Traverse elements with access to the index i, discarding the results (with the arguments flipped).

ifor_ ≡ flip itraverse_

When you don't need access to the index then for_ is more flexible in what it accepts.

for_ a ≡ ifor_ a . const

imapM_ :: (FoldableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m () #

Run monadic actions for each target of an IndexedFold or IndexedTraversal with access to the index, discarding the results.

When you don't need access to the index then mapMOf_ is more flexible in what it accepts.

mapM_ ≡ imapM . const

iforM_ :: (FoldableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m () #

Run monadic actions for each target of an IndexedFold or IndexedTraversal with access to the index, discarding the results (with the arguments flipped).

iforM_ ≡ flip imapM_

When you don't need access to the index then forMOf_ is more flexible in what it accepts.

forMOf_ l a ≡ iforMOf l a . const

iconcatMap :: FoldableWithIndex i f => (i -> a -> [b]) -> f a -> [b] #

Concatenate the results of a function of the elements of an indexed container with access to the index.

When you don't need access to the index then concatMap is more flexible in what it accepts.

concatMap ≡ iconcatMap . const
iconcatMap ≡ ifoldMap

ifind :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Maybe (i, a) #

Searches a container with a predicate that is also supplied the index, returning the left-most element of the structure matching the predicate, or Nothing if there is no such element.

When you don't need access to the index then find is more flexible in what it accepts.

find ≡ ifind . const

ifoldrM :: (FoldableWithIndex i f, Monad m) => (i -> a -> b -> m b) -> b -> f a -> m b #

Monadic fold right over the elements of a structure with an index.

When you don't need access to the index then foldrM is more flexible in what it accepts.

foldrM ≡ ifoldrM . const

ifoldlM :: (FoldableWithIndex i f, Monad m) => (i -> b -> a -> m b) -> b -> f a -> m b #

Monadic fold over the elements of a structure with an index, associating to the left.

When you don't need access to the index then foldlM is more flexible in what it accepts.

foldlM ≡ ifoldlM . const

itoList :: FoldableWithIndex i f => f a -> [(i, a)] #

Extract the key-value pairs from a structure.

When you don't need access to the indices in the result, then toList is more flexible in what it accepts.

toList ≡ map snd . itoList

ifor :: (TraversableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f (t b) #

Traverse with an index (and the arguments flipped).

for a ≡ ifor a . const
ifor ≡ flip itraverse

imapM :: (TraversableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m (t b) #

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results, with access the index.

When you don't need access to the index mapM is more liberal in what it can accept.

mapM ≡ imapM . const

iforM :: (TraversableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m (t b) #

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results, with access its position (and the arguments flipped).

forM a ≡ iforM a . const
iforM ≡ flip imapM

imapAccumR :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b) #

Generalizes mapAccumR to add access to the index.

imapAccumROf accumulates state from right to left.

mapAccumR ≡ imapAccumR . const

imapAccumL :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b) #

Generalizes mapAccumL to add access to the index.

imapAccumLOf accumulates state from left to right.

mapAccumLOf ≡ imapAccumL . const

ifoldMapBy :: FoldableWithIndex i t => (r -> r -> r) -> r -> (i -> a -> r) -> t a -> r #

ifoldMapByOf :: IndexedFold i t a -> (r -> r -> r) -> r -> (i -> a -> r) -> t -> r #

itraverseBy :: TraversableWithIndex i t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> t a -> f (t b) #

itraverseByOf :: IndexedTraversal i s t a b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> s -> f t #

type AnEquality' (s :: k2) (a :: k2) = AnEquality s s a a #

A Simple AnEquality.

type AnEquality (s :: k1) (t :: k2) (a :: k1) (b :: k2) = Identical a (Proxy b) a (Proxy b) -> Identical a (Proxy b) s (Proxy t) #

When you see this as an argument to a function, it expects an Equality.

data Identical (a :: k) (b :: k1) (s :: k) (t :: k1) :: forall k k1. k -> k1 -> k -> k1 -> Type where #

Provides witness that (s ~ a, b ~ t) holds.

Constructors

Identical :: forall k k1 (a :: k) (b :: k1) (s :: k) (t :: k1). Identical a b a b

runEq :: AnEquality s t a b -> Identical s t a b #

Extract a witness of type Equality.

substEq :: AnEquality s t a b -> ((s ~ a) -> (t ~ b) -> r) -> r #

Substituting types with Equality.

mapEq :: AnEquality s t a b -> f s -> f a #

We can use Equality to do substitution into anything.

fromEq :: AnEquality s t a b -> Equality b a t s #

Equality is symmetric.

simply :: (Optic' p f s a -> r) -> Optic' p f s a -> r #

This is an adverb that can be used to modify many other Lens combinators to make them require simple lenses, simple traversals, simple prisms or simple isos as input.

simple :: Equality' a a #

Composition with this isomorphism is occasionally useful when your Lens, Traversal or Iso has a constraint on an unused argument to force that argument to agree with the type of a used argument and avoid ScopedTypeVariables or other ugliness.

class Strict lazy strict | lazy -> strict, strict -> lazy where #

Ad hoc conversion between "strict" and "lazy" versions of a structure, such as Text or ByteString.

Methods

strict :: Iso' lazy strict #

Instances

Strict ByteString ByteString
Instance details Defined in Control.Lens.Iso Methods strict :: Iso' ByteString ByteString0 #
Strict Text Text
Instance details Defined in Control.Lens.Iso Methods strict :: Iso' Text Text0 #
Strict (ST s a) (ST s a)
Instance details Defined in Control.Lens.Iso Methods strict :: Iso' (ST s a) (ST0 s a) #
Strict (WriterT w m a) (WriterT w m a)
Instance details Defined in Control.Lens.Iso Methods strict :: Iso' (WriterT0 w m a) (WriterT w m a) #
Strict (StateT s m a) (StateT s m a)
Instance details Defined in Control.Lens.Iso Methods strict :: Iso' (StateT s m a) (StateT0 s m a) #
Strict (RWST r w s m a) (RWST r w s m a)
Instance details Defined in Control.Lens.Iso Methods strict :: Iso' (RWST r w s m a) (RWST0 r w s m a) #

class Bifunctor p => Swapped (p :: Type -> Type -> Type) where #

This class provides for symmetric bifunctors.

Methods

swapped :: Iso (p a b) (p c d) (p b a) (p d c) #

swapped . swapped ≡ id
first f . swapped = swapped . second f
second g . swapped = swapped . first g
bimap f g . swapped = swapped . bimap g f

>>> (1,2)^.swapped
(2,1)

Instances

Swapped Either
Instance details Defined in Control.Lens.Iso Methods swapped :: Iso (Either a b) (Either c d) (Either b a) (Either d c) #
Swapped (,)
Instance details Defined in Control.Lens.Iso Methods swapped :: Iso (a, b) (c, d) (b, a) (d, c) #

type AnIso' s a = AnIso s s a a #

A Simple AnIso.

type AnIso s t a b = Exchange a b a (Identity b) -> Exchange a b s (Identity t) #

When you see this as an argument to a function, it expects an Iso.

pattern List :: forall l. IsList l => [Item l] -> l #

pattern Reversed :: forall t. Reversing t => t -> t #

pattern Swapped :: forall (p :: Type -> Type -> Type) c d. Swapped p => p d c -> p c d #

pattern Lazy :: forall t s. Strict t s => t -> s #

pattern Strict :: forall s t. Strict s t => t -> s #

iso :: (s -> a) -> (b -> t) -> Iso s t a b #

Build a simple isomorphism from a pair of inverse functions.

view (iso f g) ≡ f
view (from (iso f g)) ≡ g
over (iso f g) h ≡ g . h . f
over (from (iso f g)) h ≡ f . h . g

from :: AnIso s t a b -> Iso b a t s #

Invert an isomorphism.

from (from l) ≡ l

withIso :: AnIso s t a b -> ((s -> a) -> (b -> t) -> r) -> r #

Extract the two functions, one from s -> a and one from b -> t that characterize an Iso.

cloneIso :: AnIso s t a b -> Iso s t a b #

Convert from AnIso back to any Iso.

This is useful when you need to store an isomorphism as a data type inside a container and later reconstitute it as an overloaded function.

See cloneLens or cloneTraversal for more information on why you might want to do this.

au :: Functor f => AnIso s t a b -> ((b -> t) -> f s) -> f a #

Based on ala from Conor McBride's work on Epigram.

This version is generalized to accept any Iso, not just a newtype.

>>> au (_Wrapping Sum) foldMap [1,2,3,4]
10

You may want to think of this combinator as having the following, simpler type:

au :: AnIso s t a b -> ((b -> t) -> e -> s) -> e -> a

auf :: Optic (Costar f) g s t a b -> (f a -> g b) -> f s -> g t #

Based on ala' from Conor McBride's work on Epigram.

This version is generalized to accept any Iso, not just a newtype.

For a version you pass the name of the newtype constructor to, see alaf.

>>> auf (_Unwrapping Sum) (foldMapOf both) Prelude.length ("hello","world")
10

Mnemonically, the German auf plays a similar role to à la, and the combinator is au with an extra function argument:

auf :: Iso s t a b -> ((r ->  a) -> e -> b) -> (r -> s) -> e -> t

but the signature is general.

under :: AnIso s t a b -> (t -> s) -> b -> a #

The opposite of working over a Setter is working under an isomorphism.

under ≡ over . from

under :: Iso s t a b -> (t -> s) -> b -> a

enum :: Enum a => Iso' Int a #

This isomorphism can be used to convert to or from an instance of Enum.

>>> LT^.from enum
0

>>> 97^.enum :: Char
'a'

Note: this is only an isomorphism from the numeric range actually used and it is a bit of a pleasant fiction, since there are questionable Enum instances for Double, and Float that exist solely for [1.0 .. 4.0] sugar and the instances for those and Integer don't cover all values in their range.

mapping :: (Functor f, Functor g) => AnIso s t a b -> Iso (f s) (g t) (f a) (g b) #

This can be used to lift any Iso into an arbitrary Functor.

non :: Eq a => a -> Iso' (Maybe a) a #

If v is an element of a type a, and a' is a sans the element v, then non v is an isomorphism from Maybe a' to a.

non ≡ non' . only

Keep in mind this is only a real isomorphism if you treat the domain as being Maybe (a sans v).

This is practically quite useful when you want to have a Map where all the entries should have non-zero values.

>>> Map.fromList [("hello",1)] & at "hello" . non 0 +~ 2
fromList [("hello",3)]

>>> Map.fromList [("hello",1)] & at "hello" . non 0 -~ 1
fromList []

>>> Map.fromList [("hello",1)] ^. at "hello" . non 0
1

>>> Map.fromList [] ^. at "hello" . non 0
0

This combinator is also particularly useful when working with nested maps.

e.g. When you want to create the nested Map when it is missing:

>>> Map.empty & at "hello" . non Map.empty . at "world" ?~ "!!!"
fromList [("hello",fromList [("world","!!!")])]

and when have deleting the last entry from the nested Map mean that we should delete its entry from the surrounding one:

>>> fromList [("hello",fromList [("world","!!!")])] & at "hello" . non Map.empty . at "world" .~ Nothing
fromList []

It can also be used in reverse to exclude a given value:

>>> non 0 # rem 10 4
Just 2

>>> non 0 # rem 10 5
Nothing

non' :: APrism' a () -> Iso' (Maybe a) a #

non' p generalizes non (p # ()) to take any unit Prism

This function generates an isomorphism between Maybe (a | isn't p a) and a.

>>> Map.singleton "hello" Map.empty & at "hello" . non' _Empty . at "world" ?~ "!!!"
fromList [("hello",fromList [("world","!!!")])]

>>> fromList [("hello",fromList [("world","!!!")])] & at "hello" . non' _Empty . at "world" .~ Nothing
fromList []

anon :: a -> (a -> Bool) -> Iso' (Maybe a) a #

anon a p generalizes non a to take any value and a predicate.

This function assumes that p a holds True and generates an isomorphism between Maybe (a | not (p a)) and a.

>>> Map.empty & at "hello" . anon Map.empty Map.null . at "world" ?~ "!!!"
fromList [("hello",fromList [("world","!!!")])]

>>> fromList [("hello",fromList [("world","!!!")])] & at "hello" . anon Map.empty Map.null . at "world" .~ Nothing
fromList []

curried :: Iso ((a, b) -> c) ((d, e) -> f) (a -> b -> c) (d -> e -> f) #

The canonical isomorphism for currying and uncurrying a function.

curried = iso curry uncurry

>>> (fst^.curried) 3 4
3

>>> view curried fst 3 4
3

uncurried :: Iso (a -> b -> c) (d -> e -> f) ((a, b) -> c) ((d, e) -> f) #

The canonical isomorphism for uncurrying and currying a function.

uncurried = iso uncurry curry

uncurried = from curried

>>> ((+)^.uncurried) (1,2)
3

flipped :: Iso (a -> b -> c) (a' -> b' -> c') (b -> a -> c) (b' -> a' -> c') #

The isomorphism for flipping a function.

>>> ((,)^.flipped) 1 2
(2,1)

lazy :: Strict lazy strict => Iso' strict lazy #

An Iso between the strict variant of a structure and its lazy counterpart.

lazy = from strict

See http://hackage.haskell.org/package/strict-base-types for an example use.

reversed :: Reversing a => Iso' a a #

An Iso between a list, ByteString, Text fragment, etc. and its reversal.

>>> "live" ^. reversed
"evil"

>>> "live" & reversed %~ ('d':)
"lived"

involuted :: (a -> a) -> Iso' a a #

Given a function that is its own inverse, this gives you an Iso using it in both directions.

involuted ≡ join iso

>>> "live" ^. involuted reverse
"evil"

>>> "live" & involuted reverse %~ ('d':)
"lived"

magma :: LensLike (Mafic a b) s t a b -> Iso s u (Magma Int t b a) (Magma j u c c) #

This isomorphism can be used to inspect a Traversal to see how it associates the structure and it can also be used to bake the Traversal into a Magma so that you can traverse over it multiple times.

imagma :: Over (Indexed i) (Molten i a b) s t a b -> Iso s t' (Magma i t b a) (Magma j t' c c) #

This isomorphism can be used to inspect an IndexedTraversal to see how it associates the structure and it can also be used to bake the IndexedTraversal into a Magma so that you can traverse over it multiple times with access to the original indices.

contramapping :: Contravariant f => AnIso s t a b -> Iso (f a) (f b) (f s) (f t) #

Lift an Iso into a Contravariant functor.

contramapping :: Contravariant f => Iso s t a b -> Iso (f a) (f b) (f s) (f t)
contramapping :: Contravariant f => Iso' s a -> Iso' (f a) (f s)

dimapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> AnIso s' t' a' b' -> Iso (p a s') (q b t') (p s a') (q t b') #

Lift two Isos into both arguments of a Profunctor simultaneously.

dimapping :: Profunctor p => Iso s t a b -> Iso s' t' a' b' -> Iso (p a s') (p b t') (p s a') (p t b')
dimapping :: Profunctor p => Iso' s a -> Iso' s' a' -> Iso' (p a s') (p s a')

lmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso (p a x) (q b y) (p s x) (q t y) #

Lift an Iso contravariantly into the left argument of a Profunctor.

lmapping :: Profunctor p => Iso s t a b -> Iso (p a x) (p b y) (p s x) (p t y)
lmapping :: Profunctor p => Iso' s a -> Iso' (p a x) (p s x)

rmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso (p x s) (q y t) (p x a) (q y b) #

Lift an Iso covariantly into the right argument of a Profunctor.

rmapping :: Profunctor p => Iso s t a b -> Iso (p x s) (p y t) (p x a) (p y b)
rmapping :: Profunctor p => Iso' s a -> Iso' (p x s) (p x a)

bimapping :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> AnIso s' t' a' b' -> Iso (f s s') (g t t') (f a a') (g b b') #

Lift two Isos into both arguments of a Bifunctor.

bimapping :: Bifunctor p => Iso s t a b -> Iso s' t' a' b' -> Iso (p s s') (p t t') (p a a') (p b b')
bimapping :: Bifunctor p => Iso' s a -> Iso' s' a' -> Iso' (p s s') (p a a')

firsting :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso (f s x) (g t y) (f a x) (g b y) #

Lift an Iso into the first argument of a Bifunctor.

firsting :: Bifunctor p => Iso s t a b -> Iso (p s x) (p t y) (p a x) (p b y)
firsting :: Bifunctor p => Iso' s a -> Iso' (p s x) (p a x)

seconding :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso (f x s) (g y t) (f x a) (g y b) #

Lift an Iso into the second argument of a Bifunctor. This is essentially the same as mapping, but it takes a 'Bifunctor p' constraint instead of a 'Functor (p a)' one.

seconding :: Bifunctor p => Iso s t a b -> Iso (p x s) (p y t) (p x a) (p y b)
seconding :: Bifunctor p => Iso' s a -> Iso' (p x s) (p x a)

coerced :: (Coercible s a, Coercible t b) => Iso s t a b #

Data types that are representationally equal are isomorphic.

This is only available on GHC 7.8+

Since: lens-4.13

class AsEmpty a where #

Minimal complete definition

Nothing

Methods

_Empty :: Prism' a () #

>>> isn't _Empty [1,2,3]
True

Instances

AsEmpty Ordering
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Ordering () #
AsEmpty ()
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' () () #
AsEmpty ByteString
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' ByteString () #
AsEmpty ByteString
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' ByteString () #
AsEmpty Text
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Text () #
AsEmpty Text
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Text () #
AsEmpty Event
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Event () #
AsEmpty All
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' All () #
AsEmpty Any
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' Any () #
AsEmpty IntSet
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' IntSet () #
AsEmpty [a]
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' [a] () #
AsEmpty (Maybe a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Maybe a) () #
AsEmpty (Set a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Set a) () #
AsEmpty (ZipList a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (ZipList a) () #
Storable a => AsEmpty (Vector a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Vector a) () #
AsEmpty (First a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (First a) () #
AsEmpty (Last a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Last a) () #
AsEmpty a => AsEmpty (Dual a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Dual a) () #
(Eq a, Num a) => AsEmpty (Sum a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Sum a) () #
(Eq a, Num a) => AsEmpty (Product a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Product a) () #
AsEmpty (Vector a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Vector a) () #
AsEmpty (IntMap a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (IntMap a) () #
AsEmpty (Seq a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Seq a) () #
Unbox a => AsEmpty (Vector a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Vector a) () #
AsEmpty (Clip n)
Instance details Defined in Diagrams.TwoD.Path Methods _Empty :: Prism' (Clip n) () #
AsEmpty (HashSet a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (HashSet a) () #
(AsEmpty a, AsEmpty b) => AsEmpty (a, b)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (a, b) () #
AsEmpty (Map k a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (Map k a) () #
AsEmpty (HashMap k a)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (HashMap k a) () #
AsEmpty (BoundingBox v n)
Instance details Defined in Diagrams.BoundingBox Methods _Empty :: Prism' (BoundingBox v n) () #
AsEmpty (Path v n)
Instance details Defined in Diagrams.Path Methods _Empty :: Prism' (Path v n) () #
(Metric v, OrderedField n) => AsEmpty (Trail v n)
Instance details Defined in Diagrams.Trail Methods _Empty :: Prism' (Trail v n) () #
(AsEmpty a, AsEmpty b, AsEmpty c) => AsEmpty (a, b, c)
Instance details Defined in Control.Lens.Empty Methods _Empty :: Prism' (a, b, c) () #
(Metric v, OrderedField n) => AsEmpty (Trail' Line v n)
Instance details Defined in Diagrams.Trail Methods _Empty :: Prism' (Trail' Line v n) () #

pattern Empty :: forall s. AsEmpty s => s #

class Snoc s t a b | s -> a, t -> b, s b -> t, t a -> s where #

This class provides a way to attach or detach elements on the right side of a structure in a flexible manner.

Methods

_Snoc :: Prism s t (s, a) (t, b) #

_Snoc :: Prism [a] [b] ([a], a) ([b], b)
_Snoc :: Prism (Seq a) (Seq b) (Seq a, a) (Seq b, b)
_Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b)
_Snoc :: Prism' String (String, Char)
_Snoc :: Prism' Text (Text, Char)
_Snoc :: Prism' ByteString (ByteString, Word8)

Instances

Snoc ByteString ByteString Word8 Word8
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism ByteString ByteString (ByteString, Word8) (ByteString, Word8) #
Snoc ByteString ByteString Word8 Word8
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism ByteString ByteString (ByteString, Word8) (ByteString, Word8) #
Snoc Text Text Char Char
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism Text Text (Text, Char) (Text, Char) #
Snoc Text Text Char Char
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism Text Text (Text, Char) (Text, Char) #
Snoc [a] [b] a b
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism [a] [b] ([a], a) ([b], b) #
Snoc (ZipList a) (ZipList b) a b
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (ZipList a) (ZipList b) (ZipList a, a) (ZipList b, b) #
(Storable a, Storable b) => Snoc (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b) #
Snoc (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b) #
Snoc (Seq a) (Seq b) a b
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Seq a) (Seq b) (Seq a, a) (Seq b, b) #
(Unbox a, Unbox b) => Snoc (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b) #
(Prim a, Prim b) => Snoc (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Snoc :: Prism (Vector a) (Vector b) (Vector a, a) (Vector b, b) #
Snoc (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))
Instance details Defined in Diagrams.Path Methods _Snoc :: Prism (Path v n) (Path v' n') (Path v n, Located (Trail v n)) (Path v' n', Located (Trail v' n')) #
(Metric v, OrderedField n, Metric u, OrderedField n') => Snoc (SegTree v n) (SegTree u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Snoc :: Prism (SegTree v n) (SegTree u n') (SegTree v n, Segment Closed v n) (SegTree u n', Segment Closed u n') #
(Metric v, OrderedField n, Metric u, OrderedField n') => Snoc (Trail' Line v n) (Trail' Line u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Snoc :: Prism (Trail' Line v n) (Trail' Line u n') (Trail' Line v n, Segment Closed v n) (Trail' Line u n', Segment Closed u n') #

class Cons s t a b | s -> a, t -> b, s b -> t, t a -> s where #

This class provides a way to attach or detach elements on the left side of a structure in a flexible manner.

Methods

_Cons :: Prism s t (a, s) (b, t) #

_Cons :: Prism [a] [b] (a, [a]) (b, [b])
_Cons :: Prism (Seq a) (Seq b) (a, Seq a) (b, Seq b)
_Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b)
_Cons :: Prism' String (Char, String)
_Cons :: Prism' Text (Char, Text)
_Cons :: Prism' ByteString (Word8, ByteString)

Instances

Cons ByteString ByteString Word8 Word8
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism ByteString ByteString (Word8, ByteString) (Word8, ByteString) #
Cons ByteString ByteString Word8 Word8
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism ByteString ByteString (Word8, ByteString) (Word8, ByteString) #
Cons Text Text Char Char
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism Text Text (Char, Text) (Char, Text) #
Cons Text Text Char Char
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism Text Text (Char, Text) (Char, Text) #
Cons [a] [b] a b
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism [a] [b] (a, [a]) (b, [b]) #
Cons (ZipList a) (ZipList b) a b
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (ZipList a) (ZipList b) (a, ZipList a) (b, ZipList b) #
(Storable a, Storable b) => Cons (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b) #
Cons (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b) #
Cons (Seq a) (Seq b) a b
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Seq a) (Seq b) (a, Seq a) (b, Seq b) #
(Unbox a, Unbox b) => Cons (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b) #
(Prim a, Prim b) => Cons (Vector a) (Vector b) a b
Instance details Defined in Control.Lens.Cons Methods _Cons :: Prism (Vector a) (Vector b) (a, Vector a) (b, Vector b) #
Cons (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))
Instance details Defined in Diagrams.Path Methods _Cons :: Prism (Path v n) (Path v' n') (Located (Trail v n), Path v n) (Located (Trail v' n'), Path v' n') #
(Metric v, OrderedField n, Metric u, OrderedField n') => Cons (SegTree v n) (SegTree u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Cons :: Prism (SegTree v n) (SegTree u n') (Segment Closed v n, SegTree v n) (Segment Closed u n', SegTree u n') #
(Metric v, OrderedField n, Metric u, OrderedField n') => Cons (Trail' Line v n) (Trail' Line u n') (Segment Closed v n) (Segment Closed u n')
Instance details Defined in Diagrams.Trail Methods _Cons :: Prism (Trail' Line v n) (Trail' Line u n') (Segment Closed v n, Trail' Line v n) (Segment Closed u n', Trail' Line u n') #

pattern (:>) :: forall a b. Snoc a a b b => a -> b -> a infixl 5 #

pattern (:<) :: forall b a. Cons b b a a => a -> b -> b infixr 5 #

(<|) :: Cons s s a a => a -> s -> s infixr 5 #

cons an element onto a container.

This is an infix alias for cons.

>>> a <| []
[a]

>>> a <| [b, c]
[a,b,c]

>>> a <| Seq.fromList []
fromList [a]

>>> a <| Seq.fromList [b, c]
fromList [a,b,c]

cons :: Cons s s a a => a -> s -> s infixr 5 #

cons an element onto a container.

>>> cons a []
[a]

>>> cons a [b, c]
[a,b,c]

>>> cons a (Seq.fromList [])
fromList [a]

>>> cons a (Seq.fromList [b, c])
fromList [a,b,c]

uncons :: Cons s s a a => s -> Maybe (a, s) #

Attempt to extract the left-most element from a container, and a version of the container without that element.

>>> uncons []
Nothing

>>> uncons [a, b, c]
Just (a,[b,c])

_head :: Cons s s a a => Traversal' s a #

A Traversal reading and writing to the head of a non-empty container.

>>> [a,b,c]^? _head
Just a

>>> [a,b,c] & _head .~ d
[d,b,c]

>>> [a,b,c] & _head %~ f
[f a,b,c]

>>> [] & _head %~ f
[]

>>> [1,2,3]^?!_head
1

>>> []^?_head
Nothing

>>> [1,2]^?_head
Just 1

>>> [] & _head .~ 1
[]

>>> [0] & _head .~ 2
[2]

>>> [0,1] & _head .~ 2
[2,1]

This isn't limited to lists.

For instance you can also traverse the head of a Seq:

>>> Seq.fromList [a,b,c,d] & _head %~ f
fromList [f a,b,c,d]

>>> Seq.fromList [] ^? _head
Nothing

>>> Seq.fromList [a,b,c,d] ^? _head
Just a

_head :: Traversal' [a] a
_head :: Traversal' (Seq a) a
_head :: Traversal' (Vector a) a

_tail :: Cons s s a a => Traversal' s s #

A Traversal reading and writing to the tail of a non-empty container.

>>> [a,b] & _tail .~ [c,d,e]
[a,c,d,e]

>>> [] & _tail .~ [a,b]
[]

>>> [a,b,c,d,e] & _tail.traverse %~ f
[a,f b,f c,f d,f e]

>>> [1,2] & _tail .~ [3,4,5]
[1,3,4,5]

>>> [] & _tail .~ [1,2]
[]

>>> [a,b,c]^?_tail
Just [b,c]

>>> [1,2]^?!_tail
[2]

>>> "hello"^._tail
"ello"

>>> ""^._tail
""

This isn't limited to lists. For instance you can also traverse the tail of a Seq.

>>> Seq.fromList [a,b] & _tail .~ Seq.fromList [c,d,e]
fromList [a,c,d,e]

>>> Seq.fromList [a,b,c] ^? _tail
Just (fromList [b,c])

>>> Seq.fromList [] ^? _tail
Nothing

_tail :: Traversal' [a] [a]
_tail :: Traversal' (Seq a) (Seq a)
_tail :: Traversal' (Vector a) (Vector a)

_init :: Snoc s s a a => Traversal' s s #

A Traversal reading and replacing all but the a last element of a non-empty container.

>>> [a,b,c,d]^?_init
Just [a,b,c]

>>> []^?_init
Nothing

>>> [a,b] & _init .~ [c,d,e]
[c,d,e,b]

>>> [] & _init .~ [a,b]
[]

>>> [a,b,c,d] & _init.traverse %~ f
[f a,f b,f c,d]

>>> [1,2,3]^?_init
Just [1,2]

>>> [1,2,3,4]^?!_init
[1,2,3]

>>> "hello"^._init
"hell"

>>> ""^._init
""

_init :: Traversal' [a] [a]
_init :: Traversal' (Seq a) (Seq a)
_init :: Traversal' (Vector a) (Vector a)

_last :: Snoc s s a a => Traversal' s a #

A Traversal reading and writing to the last element of a non-empty container.

>>> [a,b,c]^?!_last
c

>>> []^?_last
Nothing

>>> [a,b,c] & _last %~ f
[a,b,f c]

>>> [1,2]^?_last
Just 2

>>> [] & _last .~ 1
[]

>>> [0] & _last .~ 2
[2]

>>> [0,1] & _last .~ 2
[0,2]

This Traversal is not limited to lists, however. We can also work with other containers, such as a Vector.

>>> Vector.fromList "abcde" ^? _last
Just 'e'

>>> Vector.empty ^? _last
Nothing

>>> (Vector.fromList "abcde" & _last .~ 'Q') == Vector.fromList "abcdQ"
True

_last :: Traversal' [a] a
_last :: Traversal' (Seq a) a
_last :: Traversal' (Vector a) a

(|>) :: Snoc s s a a => s -> a -> s infixl 5 #

snoc an element onto the end of a container.

This is an infix alias for snoc.

>>> Seq.fromList [] |> a
fromList [a]

>>> Seq.fromList [b, c] |> a
fromList [b,c,a]

>>> LazyT.pack "hello" |> '!'
"hello!"

snoc :: Snoc s s a a => s -> a -> s infixl 5 #

snoc an element onto the end of a container.

>>> snoc (Seq.fromList []) a
fromList [a]

>>> snoc (Seq.fromList [b, c]) a
fromList [b,c,a]

>>> snoc (LazyT.pack "hello") '!'
"hello!"

unsnoc :: Snoc s s a a => s -> Maybe (s, a) #

Attempt to extract the right-most element from a container, and a version of the container without that element.

>>> unsnoc (LazyT.pack "hello!")
Just ("hello",'!')

>>> unsnoc (LazyT.pack "")
Nothing

>>> unsnoc (Seq.fromList [b,c,a])
Just (fromList [b,c],a)

>>> unsnoc (Seq.fromList [])
Nothing

class (Rewrapped s t, Rewrapped t s) => Rewrapping s t #

Instances

(Rewrapped s t, Rewrapped t s) => Rewrapping s t
Instance details Defined in Control.Lens.Wrapped

class Wrapped s => Rewrapped s t #

Instances

t ~ PatternMatchFail => Rewrapped PatternMatchFail t
Instance details Defined in Control.Lens.Wrapped
t ~ RecSelError => Rewrapped RecSelError t
Instance details Defined in Control.Lens.Wrapped
t ~ RecConError => Rewrapped RecConError t
Instance details Defined in Control.Lens.Wrapped
t ~ RecUpdError => Rewrapped RecUpdError t
Instance details Defined in Control.Lens.Wrapped
t ~ NoMethodError => Rewrapped NoMethodError t
Instance details Defined in Control.Lens.Wrapped
t ~ TypeError => Rewrapped TypeError t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CDev t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CIno t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CMode t
Instance details Defined in Control.Lens.Wrapped
Rewrapped COff t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CPid t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSsize t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CGid t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CNlink t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUid t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CCc t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSpeed t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CTcflag t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CRLim t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CBlkSize t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CBlkCnt t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CClockId t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CFsBlkCnt t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CFsFilCnt t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CId t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CKey t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CTimer t
Instance details Defined in Control.Lens.Wrapped
Rewrapped Fd t
Instance details Defined in Control.Lens.Wrapped
Rewrapped Errno t
Instance details Defined in Control.Lens.Wrapped
t ~ CompactionFailed => Rewrapped CompactionFailed t
Instance details Defined in Control.Lens.Wrapped
t ~ AssertionFailed => Rewrapped AssertionFailed t
Instance details Defined in Control.Lens.Wrapped
t ~ ErrorCall => Rewrapped ErrorCall t
Instance details Defined in Control.Lens.Wrapped
t ~ All => Rewrapped All t
Instance details Defined in Control.Lens.Wrapped
t ~ Any => Rewrapped Any t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CChar t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSChar t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUChar t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CShort t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUShort t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CInt t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUInt t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CLong t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CULong t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CLLong t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CULLong t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CBool t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CFloat t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CDouble t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CPtrdiff t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSize t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CWchar t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSigAtomic t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CClock t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CTime t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUSeconds t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CSUSeconds t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CIntPtr t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUIntPtr t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CIntMax t
Instance details Defined in Control.Lens.Wrapped
Rewrapped CUIntMax t
Instance details Defined in Control.Lens.Wrapped
t ~ IntSet => Rewrapped IntSet t	Use `wrapping fromList`. unwrapping returns a sorted list.
Instance details Defined in Control.Lens.Wrapped
Rewrapped Name Name
Instance details Defined in Diagrams.Core.Names
Rewrapped SegCount SegCount
Instance details Defined in Diagrams.Segment
t ~ Par1 p' => Rewrapped (Par1 p) t
Instance details Defined in Control.Lens.Wrapped
(t ~ Set a', Ord a) => Rewrapped (Set a) t	Use `wrapping fromList`. unwrapping returns a sorted list.
Instance details Defined in Control.Lens.Wrapped
t ~ Identity b => Rewrapped (Identity a) t
Instance details Defined in Control.Lens.Wrapped
t ~ ZipList b => Rewrapped (ZipList a) t
Instance details Defined in Control.Lens.Wrapped
(Storable a, t ~ Vector a') => Rewrapped (Vector a) t
Instance details Defined in Control.Lens.Wrapped
Active a1 ~ t => Rewrapped (Active a2) t
Instance details Defined in Data.Active
Duration n1 ~ t => Rewrapped (Duration n2) t
Instance details Defined in Data.Active
Time n1 ~ t => Rewrapped (Time n2) t
Instance details Defined in Data.Active
t ~ Predicate b => Rewrapped (Predicate a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Comparison b => Rewrapped (Comparison a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Equivalence b => Rewrapped (Equivalence a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Min b => Rewrapped (Min a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Max b => Rewrapped (Max a) t
Instance details Defined in Control.Lens.Wrapped
t ~ First b => Rewrapped (First a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Last b => Rewrapped (Last a) t
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedMonoid b => Rewrapped (WrappedMonoid a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Option b => Rewrapped (Option a) t
Instance details Defined in Control.Lens.Wrapped
t ~ First b => Rewrapped (First a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Last b => Rewrapped (Last a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Dual b => Rewrapped (Dual a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Endo b => Rewrapped (Endo a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Sum b => Rewrapped (Sum a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Product b => Rewrapped (Product a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Down b => Rewrapped (Down a) t
Instance details Defined in Control.Lens.Wrapped
t ~ NonEmpty b => Rewrapped (NonEmpty a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Vector a' => Rewrapped (Vector a) t
Instance details Defined in Control.Lens.Wrapped
t ~ IntMap a' => Rewrapped (IntMap a) t	Use `wrapping fromList`. unwrapping returns a sorted list.
Instance details Defined in Control.Lens.Wrapped
t ~ Seq a' => Rewrapped (Seq a) t
Instance details Defined in Control.Lens.Wrapped
(Unbox a, t ~ Vector a') => Rewrapped (Vector a) t
Instance details Defined in Control.Lens.Wrapped
Clip n1 ~ t => Rewrapped (Clip n2) t
Instance details Defined in Diagrams.TwoD.Path
(Prim a, t ~ Vector a') => Rewrapped (Vector a) t
Instance details Defined in Control.Lens.Wrapped
(t ~ HashSet a', Hashable a, Eq a) => Rewrapped (HashSet a) t	Use `wrapping fromList`. Unwrapping returns some permutation of the list.
Instance details Defined in Control.Lens.Wrapped
Rewrapped (TransInv t) (TransInv t')
Instance details Defined in Diagrams.Core.Transform
Rewrapped (ArcLength n) (ArcLength n')
Instance details Defined in Diagrams.Segment
(t ~ Map k' a', Ord k) => Rewrapped (Map k a) t	Use `wrapping fromList`. unwrapping returns a sorted list.
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedMonad m' a' => Rewrapped (WrappedMonad m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Op a' b' => Rewrapped (Op a b) t
Instance details Defined in Control.Lens.Wrapped
(t ~ HashMap k' a', Hashable k, Eq k) => Rewrapped (HashMap k a) t	Use `wrapping fromList`. Unwrapping returns some permutation of the list.
Instance details Defined in Control.Lens.Wrapped
t ~ ArrowMonad m' a' => Rewrapped (ArrowMonad m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Point g b => Rewrapped (Point f a) t
Instance details Defined in Linear.Affine
t ~ MaybeT n b => Rewrapped (MaybeT m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ CatchT m' a' => Rewrapped (CatchT m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ CoiterT w' a' => Rewrapped (CoiterT w a) t
Instance details Defined in Control.Lens.Wrapped
t ~ IterT m' a' => Rewrapped (IterT m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Alt f' a' => Rewrapped (Alt f a) t
Instance details Defined in Control.Lens.Wrapped
t ~ ListT n b => Rewrapped (ListT m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedApplicative f' a' => Rewrapped (WrappedApplicative f a) t
Instance details Defined in Control.Lens.Wrapped
t ~ MaybeApply f' a' => Rewrapped (MaybeApply f a) t
Instance details Defined in Control.Lens.Wrapped
Rewrapped (Envelope v n) (Envelope v' n')
Instance details Defined in Diagrams.Core.Envelope
Rewrapped (Trace v n) (Trace v' n')
Instance details Defined in Diagrams.Core.Trace
Rewrapped (Style v n) (Style v' n')
Instance details Defined in Diagrams.Core.Style
Rewrapped (Path v n) (Path v' n')
Instance details Defined in Diagrams.Path
Rewrapped (SegTree v n) (SegTree v' n')
Instance details Defined in Diagrams.Trail
Rewrapped (Trail v n) (Trail v' n')
Instance details Defined in Diagrams.Trail
Rewrapped (TotalOffset v n) (TotalOffset v' n')
Instance details Defined in Diagrams.Segment
t ~ Rec1 f' p' => Rewrapped (Rec1 f p) t
Instance details Defined in Control.Lens.Wrapped
t ~ IdentityT n b => Rewrapped (IdentityT m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Const a' x' => Rewrapped (Const a x) t
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedArrow a' b' c' => Rewrapped (WrappedArrow a b c) t
Instance details Defined in Control.Lens.Wrapped
t ~ Kleisli m' a' b' => Rewrapped (Kleisli m a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Ap g b => Rewrapped (Ap f a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Alt g b => Rewrapped (Alt f a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Join p' a' => Rewrapped (Join p a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Fix p' a' => Rewrapped (Fix p a) t
Instance details Defined in Control.Lens.Wrapped
t ~ TracedT m' w' a' => Rewrapped (TracedT m w a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Compose f' g' a' => Rewrapped (Compose f g a) t
Instance details Defined in Control.Lens.Wrapped
t ~ ComposeFC f' g' a' => Rewrapped (ComposeFC f g a) t
Instance details Defined in Control.Lens.Wrapped
t ~ ComposeCF f' g' a' => Rewrapped (ComposeCF f g a) t
Instance details Defined in Control.Lens.Wrapped
t ~ ExceptT e' m' a' => Rewrapped (ExceptT e m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ FreeT f' m' a' => Rewrapped (FreeT f m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ CofreeT f' w' a' => Rewrapped (CofreeT f w a) t
Instance details Defined in Control.Lens.Wrapped
t ~ ApT f' g' a' => Rewrapped (ApT f g a) t
Instance details Defined in Control.Lens.Wrapped
t ~ ErrorT e' m' a' => Rewrapped (ErrorT e m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ StateT s' m' a' => Rewrapped (StateT s m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Backwards g b => Rewrapped (Backwards f a) t
Instance details Defined in Control.Lens.Wrapped
t ~ WriterT w' m' a' => Rewrapped (WriterT w m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ StateT s' m' a' => Rewrapped (StateT s m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ WriterT w' m' a' => Rewrapped (WriterT w m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Star f' d' c' => Rewrapped (Star f d c) t
Instance details Defined in Control.Lens.Wrapped
t ~ Costar f' d' c' => Rewrapped (Costar f d c) t
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedArrow p' a' b' => Rewrapped (WrappedArrow p a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Forget r' a' b' => Rewrapped (Forget r a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Static f' a' b' => Rewrapped (Static f a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Tagged s' a' => Rewrapped (Tagged s a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Reverse g b => Rewrapped (Reverse f a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Constant a' b' => Rewrapped (Constant a b) t
Instance details Defined in Control.Lens.Wrapped
Rewrapped (Query v a m) (Query v' a' m')
Instance details Defined in Diagrams.Core.Query
Rewrapped (Trail' Line v n) (Trail' Line v' n')
Instance details Defined in Diagrams.Trail
t ~ K1 i' c' p' => Rewrapped (K1 i c p) t
Instance details Defined in Control.Lens.Wrapped
t ~ ReaderT s n b => Rewrapped (ReaderT r m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ ContT r' m' a' => Rewrapped (ContT r m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Cayley f' p' a' b' => Rewrapped (Cayley f p a b) t
Instance details Defined in Control.Lens.Wrapped
Rewrapped (QDiagram b v n m) (QDiagram b' v' n' m')
Instance details Defined in Diagrams.Core.Types
Rewrapped (SubMap b v n m) (SubMap b' v' n' m')
Instance details Defined in Diagrams.Core.Types
t ~ M1 i' c' f' p' => Rewrapped (M1 i c f p) t
Instance details Defined in Control.Lens.Wrapped
t ~ (f' :.: g') p' => Rewrapped ((f :.: g) p) t
Instance details Defined in Control.Lens.Wrapped
t ~ Compose f' g' a' => Rewrapped (Compose f g a) t
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedBifunctor p' a' b' => Rewrapped (WrappedBifunctor p a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Joker g' a' b' => Rewrapped (Joker g a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Flip p' a' b' => Rewrapped (Flip p a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Clown f' a' b' => Rewrapped (Clown f a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ RWST r' w' s' m' a' => Rewrapped (RWST r w s m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ RWST r' w' s' m' a' => Rewrapped (RWST r w s m a) t
Instance details Defined in Control.Lens.Wrapped
t ~ Dual k' a' b' => Rewrapped (Dual k6 a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ WrappedCategory k' a' b' => Rewrapped (WrappedCategory k6 a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Semi m' a' b' => Rewrapped (Semi m a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Tannen f' p' a' b' => Rewrapped (Tannen f p a b) t
Instance details Defined in Control.Lens.Wrapped
t ~ Biff p' f' g' a' b' => Rewrapped (Biff p f g a b) t
Instance details Defined in Control.Lens.Wrapped

class Wrapped s where #

Wrapped provides isomorphisms to wrap and unwrap newtypes or data types with one constructor.

Minimal complete definition

Nothing

Associated Types

type Unwrapped s :: Type #

Methods

_Wrapped' :: Iso' s (Unwrapped s) #

An isomorphism between s and a.

If your type has a Generic instance, _Wrapped' will default to _GWrapped', and you can choose to not override it with your own definition.

Instances

Wrapped PatternMatchFail
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped PatternMatchFail :: Type # Methods _Wrapped' :: Iso' PatternMatchFail (Unwrapped PatternMatchFail) #
Wrapped RecSelError
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped RecSelError :: Type # Methods _Wrapped' :: Iso' RecSelError (Unwrapped RecSelError) #
Wrapped RecConError
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped RecConError :: Type # Methods _Wrapped' :: Iso' RecConError (Unwrapped RecConError) #
Wrapped RecUpdError
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped RecUpdError :: Type # Methods _Wrapped' :: Iso' RecUpdError (Unwrapped RecUpdError) #
Wrapped NoMethodError
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped NoMethodError :: Type # Methods _Wrapped' :: Iso' NoMethodError (Unwrapped NoMethodError) #
Wrapped TypeError
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped TypeError :: Type # Methods _Wrapped' :: Iso' TypeError (Unwrapped TypeError) #
Wrapped CDev
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CDev :: Type # Methods _Wrapped' :: Iso' CDev (Unwrapped CDev) #
Wrapped CIno
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CIno :: Type # Methods _Wrapped' :: Iso' CIno (Unwrapped CIno) #
Wrapped CMode
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CMode :: Type # Methods _Wrapped' :: Iso' CMode (Unwrapped CMode) #
Wrapped COff
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped COff :: Type # Methods _Wrapped' :: Iso' COff (Unwrapped COff) #
Wrapped CPid
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CPid :: Type # Methods _Wrapped' :: Iso' CPid (Unwrapped CPid) #
Wrapped CSsize
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSsize :: Type # Methods _Wrapped' :: Iso' CSsize (Unwrapped CSsize) #
Wrapped CGid
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CGid :: Type # Methods _Wrapped' :: Iso' CGid (Unwrapped CGid) #
Wrapped CNlink
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CNlink :: Type # Methods _Wrapped' :: Iso' CNlink (Unwrapped CNlink) #
Wrapped CUid
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUid :: Type # Methods _Wrapped' :: Iso' CUid (Unwrapped CUid) #
Wrapped CCc
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CCc :: Type # Methods _Wrapped' :: Iso' CCc (Unwrapped CCc) #
Wrapped CSpeed
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSpeed :: Type # Methods _Wrapped' :: Iso' CSpeed (Unwrapped CSpeed) #
Wrapped CTcflag
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CTcflag :: Type # Methods _Wrapped' :: Iso' CTcflag (Unwrapped CTcflag) #
Wrapped CRLim
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CRLim :: Type # Methods _Wrapped' :: Iso' CRLim (Unwrapped CRLim) #
Wrapped CBlkSize
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CBlkSize :: Type # Methods _Wrapped' :: Iso' CBlkSize (Unwrapped CBlkSize) #
Wrapped CBlkCnt
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CBlkCnt :: Type # Methods _Wrapped' :: Iso' CBlkCnt (Unwrapped CBlkCnt) #
Wrapped CClockId
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CClockId :: Type # Methods _Wrapped' :: Iso' CClockId (Unwrapped CClockId) #
Wrapped CFsBlkCnt
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CFsBlkCnt :: Type # Methods _Wrapped' :: Iso' CFsBlkCnt (Unwrapped CFsBlkCnt) #
Wrapped CFsFilCnt
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CFsFilCnt :: Type # Methods _Wrapped' :: Iso' CFsFilCnt (Unwrapped CFsFilCnt) #
Wrapped CId
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CId :: Type # Methods _Wrapped' :: Iso' CId (Unwrapped CId) #
Wrapped CKey
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CKey :: Type # Methods _Wrapped' :: Iso' CKey (Unwrapped CKey) #
Wrapped CTimer
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CTimer :: Type # Methods _Wrapped' :: Iso' CTimer (Unwrapped CTimer) #
Wrapped Fd
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped Fd :: Type # Methods _Wrapped' :: Iso' Fd (Unwrapped Fd) #
Wrapped Errno
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped Errno :: Type # Methods _Wrapped' :: Iso' Errno (Unwrapped Errno) #
Wrapped CompactionFailed
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CompactionFailed :: Type # Methods _Wrapped' :: Iso' CompactionFailed (Unwrapped CompactionFailed) #
Wrapped AssertionFailed
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped AssertionFailed :: Type # Methods _Wrapped' :: Iso' AssertionFailed (Unwrapped AssertionFailed) #
Wrapped ErrorCall
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped ErrorCall :: Type # Methods _Wrapped' :: Iso' ErrorCall (Unwrapped ErrorCall) #
Wrapped All
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped All :: Type # Methods _Wrapped' :: Iso' All (Unwrapped All) #
Wrapped Any
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped Any :: Type # Methods _Wrapped' :: Iso' Any (Unwrapped Any) #
Wrapped CChar
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CChar :: Type # Methods _Wrapped' :: Iso' CChar (Unwrapped CChar) #
Wrapped CSChar
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSChar :: Type # Methods _Wrapped' :: Iso' CSChar (Unwrapped CSChar) #
Wrapped CUChar
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUChar :: Type # Methods _Wrapped' :: Iso' CUChar (Unwrapped CUChar) #
Wrapped CShort
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CShort :: Type # Methods _Wrapped' :: Iso' CShort (Unwrapped CShort) #
Wrapped CUShort
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUShort :: Type # Methods _Wrapped' :: Iso' CUShort (Unwrapped CUShort) #
Wrapped CInt
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CInt :: Type # Methods _Wrapped' :: Iso' CInt (Unwrapped CInt) #
Wrapped CUInt
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUInt :: Type # Methods _Wrapped' :: Iso' CUInt (Unwrapped CUInt) #
Wrapped CLong
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CLong :: Type # Methods _Wrapped' :: Iso' CLong (Unwrapped CLong) #
Wrapped CULong
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CULong :: Type # Methods _Wrapped' :: Iso' CULong (Unwrapped CULong) #
Wrapped CLLong
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CLLong :: Type # Methods _Wrapped' :: Iso' CLLong (Unwrapped CLLong) #
Wrapped CULLong
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CULLong :: Type # Methods _Wrapped' :: Iso' CULLong (Unwrapped CULLong) #
Wrapped CBool
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CBool :: Type # Methods _Wrapped' :: Iso' CBool (Unwrapped CBool) #
Wrapped CFloat
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CFloat :: Type # Methods _Wrapped' :: Iso' CFloat (Unwrapped CFloat) #
Wrapped CDouble
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CDouble :: Type # Methods _Wrapped' :: Iso' CDouble (Unwrapped CDouble) #
Wrapped CPtrdiff
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CPtrdiff :: Type # Methods _Wrapped' :: Iso' CPtrdiff (Unwrapped CPtrdiff) #
Wrapped CSize
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSize :: Type # Methods _Wrapped' :: Iso' CSize (Unwrapped CSize) #
Wrapped CWchar
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CWchar :: Type # Methods _Wrapped' :: Iso' CWchar (Unwrapped CWchar) #
Wrapped CSigAtomic
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSigAtomic :: Type # Methods _Wrapped' :: Iso' CSigAtomic (Unwrapped CSigAtomic) #
Wrapped CClock
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CClock :: Type # Methods _Wrapped' :: Iso' CClock (Unwrapped CClock) #
Wrapped CTime
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CTime :: Type # Methods _Wrapped' :: Iso' CTime (Unwrapped CTime) #
Wrapped CUSeconds
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUSeconds :: Type # Methods _Wrapped' :: Iso' CUSeconds (Unwrapped CUSeconds) #
Wrapped CSUSeconds
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CSUSeconds :: Type # Methods _Wrapped' :: Iso' CSUSeconds (Unwrapped CSUSeconds) #
Wrapped CIntPtr
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CIntPtr :: Type # Methods _Wrapped' :: Iso' CIntPtr (Unwrapped CIntPtr) #
Wrapped CUIntPtr
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUIntPtr :: Type # Methods _Wrapped' :: Iso' CUIntPtr (Unwrapped CUIntPtr) #
Wrapped CIntMax
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CIntMax :: Type # Methods _Wrapped' :: Iso' CIntMax (Unwrapped CIntMax) #
Wrapped CUIntMax
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped CUIntMax :: Type # Methods _Wrapped' :: Iso' CUIntMax (Unwrapped CUIntMax) #
Wrapped IntSet
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped IntSet :: Type # Methods _Wrapped' :: Iso' IntSet (Unwrapped IntSet) #
Wrapped Name
Instance details Defined in Diagrams.Core.Names Associated Types type Unwrapped Name :: Type # Methods _Wrapped' :: Iso' Name (Unwrapped Name) #
Wrapped SegCount
Instance details Defined in Diagrams.Segment Associated Types type Unwrapped SegCount :: Type # Methods _Wrapped' :: Iso' SegCount (Unwrapped SegCount) #
Wrapped (Par1 p)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Par1 p) :: Type # Methods _Wrapped' :: Iso' (Par1 p) (Unwrapped (Par1 p)) #
Ord a => Wrapped (Set a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Set a) :: Type # Methods _Wrapped' :: Iso' (Set a) (Unwrapped (Set a)) #
Wrapped (Identity a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Identity a) :: Type # Methods _Wrapped' :: Iso' (Identity a) (Unwrapped (Identity a)) #
Wrapped (ZipList a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ZipList a) :: Type # Methods _Wrapped' :: Iso' (ZipList a) (Unwrapped (ZipList a)) #
Storable a => Wrapped (Vector a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Vector a) :: Type # Methods _Wrapped' :: Iso' (Vector a) (Unwrapped (Vector a)) #
Wrapped (Active a)
Instance details Defined in Data.Active Associated Types type Unwrapped (Active a) :: Type # Methods _Wrapped' :: Iso' (Active a) (Unwrapped (Active a)) #
Wrapped (Duration n)
Instance details Defined in Data.Active Associated Types type Unwrapped (Duration n) :: Type # Methods _Wrapped' :: Iso' (Duration n) (Unwrapped (Duration n)) #
Wrapped (Time n)
Instance details Defined in Data.Active Associated Types type Unwrapped (Time n) :: Type # Methods _Wrapped' :: Iso' (Time n) (Unwrapped (Time n)) #
Wrapped (Predicate a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Predicate a) :: Type # Methods _Wrapped' :: Iso' (Predicate a) (Unwrapped (Predicate a)) #
Wrapped (Comparison a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Comparison a) :: Type # Methods _Wrapped' :: Iso' (Comparison a) (Unwrapped (Comparison a)) #
Wrapped (Equivalence a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Equivalence a) :: Type # Methods _Wrapped' :: Iso' (Equivalence a) (Unwrapped (Equivalence a)) #
Wrapped (Min a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Min a) :: Type # Methods _Wrapped' :: Iso' (Min a) (Unwrapped (Min a)) #
Wrapped (Max a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Max a) :: Type # Methods _Wrapped' :: Iso' (Max a) (Unwrapped (Max a)) #
Wrapped (First a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (First a) :: Type # Methods _Wrapped' :: Iso' (First a) (Unwrapped (First a)) #
Wrapped (Last a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Last a) :: Type # Methods _Wrapped' :: Iso' (Last a) (Unwrapped (Last a)) #
Wrapped (WrappedMonoid a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedMonoid a) :: Type # Methods _Wrapped' :: Iso' (WrappedMonoid a) (Unwrapped (WrappedMonoid a)) #
Wrapped (Option a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Option a) :: Type # Methods _Wrapped' :: Iso' (Option a) (Unwrapped (Option a)) #
Wrapped (First a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (First a) :: Type # Methods _Wrapped' :: Iso' (First a) (Unwrapped (First a)) #
Wrapped (Last a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Last a) :: Type # Methods _Wrapped' :: Iso' (Last a) (Unwrapped (Last a)) #
Wrapped (Dual a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Dual a) :: Type # Methods _Wrapped' :: Iso' (Dual a) (Unwrapped (Dual a)) #
Wrapped (Endo a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Endo a) :: Type # Methods _Wrapped' :: Iso' (Endo a) (Unwrapped (Endo a)) #
Wrapped (Sum a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Sum a) :: Type # Methods _Wrapped' :: Iso' (Sum a) (Unwrapped (Sum a)) #
Wrapped (Product a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Product a) :: Type # Methods _Wrapped' :: Iso' (Product a) (Unwrapped (Product a)) #
Wrapped (Down a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Down a) :: Type # Methods _Wrapped' :: Iso' (Down a) (Unwrapped (Down a)) #
Wrapped (NonEmpty a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (NonEmpty a) :: Type # Methods _Wrapped' :: Iso' (NonEmpty a) (Unwrapped (NonEmpty a)) #
Wrapped (Vector a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Vector a) :: Type # Methods _Wrapped' :: Iso' (Vector a) (Unwrapped (Vector a)) #
Wrapped (IntMap a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (IntMap a) :: Type # Methods _Wrapped' :: Iso' (IntMap a) (Unwrapped (IntMap a)) #
Wrapped (Seq a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Seq a) :: Type # Methods _Wrapped' :: Iso' (Seq a) (Unwrapped (Seq a)) #
Wrapped (TransInv t)
Instance details Defined in Diagrams.Core.Transform Associated Types type Unwrapped (TransInv t) :: Type # Methods _Wrapped' :: Iso' (TransInv t) (Unwrapped (TransInv t)) #
Unbox a => Wrapped (Vector a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Vector a) :: Type # Methods _Wrapped' :: Iso' (Vector a) (Unwrapped (Vector a)) #
Wrapped (Clip n)
Instance details Defined in Diagrams.TwoD.Path Associated Types type Unwrapped (Clip n) :: Type # Methods _Wrapped' :: Iso' (Clip n) (Unwrapped (Clip n)) #
Wrapped (ArcLength n)
Instance details Defined in Diagrams.Segment Associated Types type Unwrapped (ArcLength n) :: Type # Methods _Wrapped' :: Iso' (ArcLength n) (Unwrapped (ArcLength n)) #
Prim a => Wrapped (Vector a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Vector a) :: Type # Methods _Wrapped' :: Iso' (Vector a) (Unwrapped (Vector a)) #
(Hashable a, Eq a) => Wrapped (HashSet a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (HashSet a) :: Type # Methods _Wrapped' :: Iso' (HashSet a) (Unwrapped (HashSet a)) #
Ord k => Wrapped (Map k a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Map k a) :: Type # Methods _Wrapped' :: Iso' (Map k a) (Unwrapped (Map k a)) #
Wrapped (WrappedMonad m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedMonad m a) :: Type # Methods _Wrapped' :: Iso' (WrappedMonad m a) (Unwrapped (WrappedMonad m a)) #
Wrapped (Op a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Op a b) :: Type # Methods _Wrapped' :: Iso' (Op a b) (Unwrapped (Op a b)) #
(Hashable k, Eq k) => Wrapped (HashMap k a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (HashMap k a) :: Type # Methods _Wrapped' :: Iso' (HashMap k a) (Unwrapped (HashMap k a)) #
Wrapped (ArrowMonad m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ArrowMonad m a) :: Type # Methods _Wrapped' :: Iso' (ArrowMonad m a) (Unwrapped (ArrowMonad m a)) #
Wrapped (Envelope v n)
Instance details Defined in Diagrams.Core.Envelope Associated Types type Unwrapped (Envelope v n) :: Type # Methods _Wrapped' :: Iso' (Envelope v n) (Unwrapped (Envelope v n)) #
Wrapped (Trace v n)
Instance details Defined in Diagrams.Core.Trace Associated Types type Unwrapped (Trace v n) :: Type # Methods _Wrapped' :: Iso' (Trace v n) (Unwrapped (Trace v n)) #
Wrapped (Style v n)
Instance details Defined in Diagrams.Core.Style Associated Types type Unwrapped (Style v n) :: Type # Methods _Wrapped' :: Iso' (Style v n) (Unwrapped (Style v n)) #
Wrapped (Point f a)
Instance details Defined in Linear.Affine Associated Types type Unwrapped (Point f a) :: Type # Methods _Wrapped' :: Iso' (Point f a) (Unwrapped (Point f a)) #
Wrapped (MaybeT m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (MaybeT m a) :: Type # Methods _Wrapped' :: Iso' (MaybeT m a) (Unwrapped (MaybeT m a)) #
Wrapped (Path v n)
Instance details Defined in Diagrams.Path Associated Types type Unwrapped (Path v n) :: Type # Methods _Wrapped' :: Iso' (Path v n) (Unwrapped (Path v n)) #
Wrapped (SegTree v n)
Instance details Defined in Diagrams.Trail Associated Types type Unwrapped (SegTree v n) :: Type # Methods _Wrapped' :: Iso' (SegTree v n) (Unwrapped (SegTree v n)) #
Wrapped (Trail v n)
Instance details Defined in Diagrams.Trail Associated Types type Unwrapped (Trail v n) :: Type # Methods _Wrapped' :: Iso' (Trail v n) (Unwrapped (Trail v n)) #
Wrapped (TotalOffset v n)
Instance details Defined in Diagrams.Segment Associated Types type Unwrapped (TotalOffset v n) :: Type # Methods _Wrapped' :: Iso' (TotalOffset v n) (Unwrapped (TotalOffset v n)) #
Wrapped (CatchT m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (CatchT m a) :: Type # Methods _Wrapped' :: Iso' (CatchT m a) (Unwrapped (CatchT m a)) #
Wrapped (CoiterT w a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (CoiterT w a) :: Type # Methods _Wrapped' :: Iso' (CoiterT w a) (Unwrapped (CoiterT w a)) #
Wrapped (IterT m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (IterT m a) :: Type # Methods _Wrapped' :: Iso' (IterT m a) (Unwrapped (IterT m a)) #
Wrapped (Alt f a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Alt f a) :: Type # Methods _Wrapped' :: Iso' (Alt f a) (Unwrapped (Alt f a)) #
Wrapped (ListT m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ListT m a) :: Type # Methods _Wrapped' :: Iso' (ListT m a) (Unwrapped (ListT m a)) #
Wrapped (WrappedApplicative f a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedApplicative f a) :: Type # Methods _Wrapped' :: Iso' (WrappedApplicative f a) (Unwrapped (WrappedApplicative f a)) #
Wrapped (MaybeApply f a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (MaybeApply f a) :: Type # Methods _Wrapped' :: Iso' (MaybeApply f a) (Unwrapped (MaybeApply f a)) #
Wrapped (Rec1 f p)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Rec1 f p) :: Type # Methods _Wrapped' :: Iso' (Rec1 f p) (Unwrapped (Rec1 f p)) #
Wrapped (IdentityT m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (IdentityT m a) :: Type # Methods _Wrapped' :: Iso' (IdentityT m a) (Unwrapped (IdentityT m a)) #
Wrapped (Const a x)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Const a x) :: Type # Methods _Wrapped' :: Iso' (Const a x) (Unwrapped (Const a x)) #
Wrapped (WrappedArrow a b c)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedArrow a b c) :: Type # Methods _Wrapped' :: Iso' (WrappedArrow a b c) (Unwrapped (WrappedArrow a b c)) #
Wrapped (Kleisli m a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Kleisli m a b) :: Type # Methods _Wrapped' :: Iso' (Kleisli m a b) (Unwrapped (Kleisli m a b)) #
Wrapped (Ap f a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Ap f a) :: Type # Methods _Wrapped' :: Iso' (Ap f a) (Unwrapped (Ap f a)) #
Wrapped (Alt f a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Alt f a) :: Type # Methods _Wrapped' :: Iso' (Alt f a) (Unwrapped (Alt f a)) #
Wrapped (Join p a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Join p a) :: Type # Methods _Wrapped' :: Iso' (Join p a) (Unwrapped (Join p a)) #
Wrapped (Fix p a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Fix p a) :: Type # Methods _Wrapped' :: Iso' (Fix p a) (Unwrapped (Fix p a)) #
Wrapped (TracedT m w a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (TracedT m w a) :: Type # Methods _Wrapped' :: Iso' (TracedT m w a) (Unwrapped (TracedT m w a)) #
Wrapped (Compose f g a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Compose f g a) :: Type # Methods _Wrapped' :: Iso' (Compose f g a) (Unwrapped (Compose f g a)) #
Wrapped (ComposeFC f g a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ComposeFC f g a) :: Type # Methods _Wrapped' :: Iso' (ComposeFC f g a) (Unwrapped (ComposeFC f g a)) #
Wrapped (ComposeCF f g a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ComposeCF f g a) :: Type # Methods _Wrapped' :: Iso' (ComposeCF f g a) (Unwrapped (ComposeCF f g a)) #
Wrapped (Query v n m)
Instance details Defined in Diagrams.Core.Query Associated Types type Unwrapped (Query v n m) :: Type # Methods _Wrapped' :: Iso' (Query v n m) (Unwrapped (Query v n m)) #
Wrapped (Trail' Line v n)
Instance details Defined in Diagrams.Trail Associated Types type Unwrapped (Trail' Line v n) :: Type # Methods _Wrapped' :: Iso' (Trail' Line v n) (Unwrapped (Trail' Line v n)) #
Wrapped (ExceptT e m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ExceptT e m a) :: Type # Methods _Wrapped' :: Iso' (ExceptT e m a) (Unwrapped (ExceptT e m a)) #
Wrapped (FreeT f m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (FreeT f m a) :: Type # Methods _Wrapped' :: Iso' (FreeT f m a) (Unwrapped (FreeT f m a)) #
Wrapped (CofreeT f w a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (CofreeT f w a) :: Type # Methods _Wrapped' :: Iso' (CofreeT f w a) (Unwrapped (CofreeT f w a)) #
Wrapped (ApT f g a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ApT f g a) :: Type # Methods _Wrapped' :: Iso' (ApT f g a) (Unwrapped (ApT f g a)) #
Wrapped (ErrorT e m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ErrorT e m a) :: Type # Methods _Wrapped' :: Iso' (ErrorT e m a) (Unwrapped (ErrorT e m a)) #
Wrapped (StateT s m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (StateT s m a) :: Type # Methods _Wrapped' :: Iso' (StateT s m a) (Unwrapped (StateT s m a)) #
Wrapped (Backwards f a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Backwards f a) :: Type # Methods _Wrapped' :: Iso' (Backwards f a) (Unwrapped (Backwards f a)) #
Wrapped (WriterT w m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WriterT w m a) :: Type # Methods _Wrapped' :: Iso' (WriterT w m a) (Unwrapped (WriterT w m a)) #
Wrapped (StateT s m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (StateT s m a) :: Type # Methods _Wrapped' :: Iso' (StateT s m a) (Unwrapped (StateT s m a)) #
Wrapped (WriterT w m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WriterT w m a) :: Type # Methods _Wrapped' :: Iso' (WriterT w m a) (Unwrapped (WriterT w m a)) #
Wrapped (Star f d c)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Star f d c) :: Type # Methods _Wrapped' :: Iso' (Star f d c) (Unwrapped (Star f d c)) #
Wrapped (Costar f d c)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Costar f d c) :: Type # Methods _Wrapped' :: Iso' (Costar f d c) (Unwrapped (Costar f d c)) #
Wrapped (WrappedArrow p a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedArrow p a b) :: Type # Methods _Wrapped' :: Iso' (WrappedArrow p a b) (Unwrapped (WrappedArrow p a b)) #
Wrapped (Forget r a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Forget r a b) :: Type # Methods _Wrapped' :: Iso' (Forget r a b) (Unwrapped (Forget r a b)) #
Wrapped (Static f a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Static f a b) :: Type # Methods _Wrapped' :: Iso' (Static f a b) (Unwrapped (Static f a b)) #
Wrapped (Tagged s a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Tagged s a) :: Type # Methods _Wrapped' :: Iso' (Tagged s a) (Unwrapped (Tagged s a)) #
Wrapped (Reverse f a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Reverse f a) :: Type # Methods _Wrapped' :: Iso' (Reverse f a) (Unwrapped (Reverse f a)) #
Wrapped (Constant a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Constant a b) :: Type # Methods _Wrapped' :: Iso' (Constant a b) (Unwrapped (Constant a b)) #
Wrapped (K1 i c p)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (K1 i c p) :: Type # Methods _Wrapped' :: Iso' (K1 i c p) (Unwrapped (K1 i c p)) #
Wrapped (QDiagram b v n m)
Instance details Defined in Diagrams.Core.Types Associated Types type Unwrapped (QDiagram b v n m) :: Type # Methods _Wrapped' :: Iso' (QDiagram b v n m) (Unwrapped (QDiagram b v n m)) #
Wrapped (SubMap b v n m)
Instance details Defined in Diagrams.Core.Types Associated Types type Unwrapped (SubMap b v n m) :: Type # Methods _Wrapped' :: Iso' (SubMap b v n m) (Unwrapped (SubMap b v n m)) #
Wrapped (ReaderT r m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ReaderT r m a) :: Type # Methods _Wrapped' :: Iso' (ReaderT r m a) (Unwrapped (ReaderT r m a)) #
Wrapped (ContT r m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (ContT r m a) :: Type # Methods _Wrapped' :: Iso' (ContT r m a) (Unwrapped (ContT r m a)) #
Wrapped (Cayley f p a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Cayley f p a b) :: Type # Methods _Wrapped' :: Iso' (Cayley f p a b) (Unwrapped (Cayley f p a b)) #
Wrapped (M1 i c f p)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (M1 i c f p) :: Type # Methods _Wrapped' :: Iso' (M1 i c f p) (Unwrapped (M1 i c f p)) #
Wrapped ((f :.: g) p)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped ((f :.: g) p) :: Type # Methods _Wrapped' :: Iso' ((f :.: g) p) (Unwrapped ((f :.: g) p)) #
Wrapped (Compose f g a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Compose f g a) :: Type # Methods _Wrapped' :: Iso' (Compose f g a) (Unwrapped (Compose f g a)) #
Wrapped (WrappedBifunctor p a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedBifunctor p a b) :: Type # Methods _Wrapped' :: Iso' (WrappedBifunctor p a b) (Unwrapped (WrappedBifunctor p a b)) #
Wrapped (Joker g a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Joker g a b) :: Type # Methods _Wrapped' :: Iso' (Joker g a b) (Unwrapped (Joker g a b)) #
Wrapped (Flip p a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Flip p a b) :: Type # Methods _Wrapped' :: Iso' (Flip p a b) (Unwrapped (Flip p a b)) #
Wrapped (Clown f a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Clown f a b) :: Type # Methods _Wrapped' :: Iso' (Clown f a b) (Unwrapped (Clown f a b)) #
Wrapped (RWST r w s m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (RWST r w s m a) :: Type # Methods _Wrapped' :: Iso' (RWST r w s m a) (Unwrapped (RWST r w s m a)) #
Wrapped (RWST r w s m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (RWST r w s m a) :: Type # Methods _Wrapped' :: Iso' (RWST r w s m a) (Unwrapped (RWST r w s m a)) #
Wrapped (Dual k3 a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Dual k3 a b) :: Type # Methods _Wrapped' :: Iso' (Dual k3 a b) (Unwrapped (Dual k3 a b)) #
Wrapped (WrappedCategory k3 a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (WrappedCategory k3 a b) :: Type # Methods _Wrapped' :: Iso' (WrappedCategory k3 a b) (Unwrapped (WrappedCategory k3 a b)) #
Wrapped (Semi m a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Semi m a b) :: Type # Methods _Wrapped' :: Iso' (Semi m a b) (Unwrapped (Semi m a b)) #
Wrapped (Tannen f p a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Tannen f p a b) :: Type # Methods _Wrapped' :: Iso' (Tannen f p a b) (Unwrapped (Tannen f p a b)) #
Wrapped (Biff p f g a b)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (Biff p f g a b) :: Type # Methods _Wrapped' :: Iso' (Biff p f g a b) (Unwrapped (Biff p f g a b)) #

pattern Unwrapped :: forall t. Rewrapped t t => t -> Unwrapped t #

pattern Wrapped :: forall s. Rewrapped s s => Unwrapped s -> s #

_GWrapped' :: (Generic s, D1 d (C1 c (S1 s' (Rec0 a))) ~ Rep s, Unwrapped s ~ GUnwrapped (Rep s)) => Iso' s (Unwrapped s) #

Implement the _Wrapped operation for a type using its Generic instance.

_Unwrapped' :: Wrapped s => Iso' (Unwrapped s) s #

_Wrapped :: Rewrapping s t => Iso s t (Unwrapped s) (Unwrapped t) #

Work under a newtype wrapper.

>>> Const "hello" & _Wrapped %~ Prelude.length & getConst
5

_Wrapped   ≡ from _Unwrapped
_Unwrapped ≡ from _Wrapped

_Unwrapped :: Rewrapping s t => Iso (Unwrapped t) (Unwrapped s) t s #

op :: Wrapped s => (Unwrapped s -> s) -> s -> Unwrapped s #

Given the constructor for a Wrapped type, return a deconstructor that is its inverse.

Assuming the Wrapped instance is legal, these laws hold:

op f . f ≡ id
f . op f ≡ id

>>> op Identity (Identity 4)
4

>>> op Const (Const "hello")
"hello"

_Wrapping' :: Wrapped s => (Unwrapped s -> s) -> Iso' s (Unwrapped s) #

This is a convenient version of _Wrapped with an argument that's ignored.

The user supplied function is ignored, merely its type is used.

_Unwrapping' :: Wrapped s => (Unwrapped s -> s) -> Iso' (Unwrapped s) s #

This is a convenient version of _Wrapped with an argument that's ignored.

The user supplied function is ignored, merely its type is used.

_Wrapping :: Rewrapping s t => (Unwrapped s -> s) -> Iso s t (Unwrapped s) (Unwrapped t) #

This is a convenient version of _Wrapped with an argument that's ignored.

The user supplied function is ignored, merely its types are used.

_Unwrapping :: Rewrapping s t => (Unwrapped s -> s) -> Iso (Unwrapped t) (Unwrapped s) t s #

This is a convenient version of _Unwrapped with an argument that's ignored.

The user supplied function is ignored, merely its types are used.

ala :: (Functor f, Rewrapping s t) => (Unwrapped s -> s) -> ((Unwrapped t -> t) -> f s) -> f (Unwrapped s) #

This combinator is based on ala from Conor McBride's work on Epigram.

As with _Wrapping, the user supplied function for the newtype is ignored.

>>> ala Sum foldMap [1,2,3,4]
10

>>> ala All foldMap [True,True]
True

>>> ala All foldMap [True,False]
False

>>> ala Any foldMap [False,False]
False

>>> ala Any foldMap [True,False]
True

>>> ala Product foldMap [1,2,3,4]
24

You may want to think of this combinator as having the following, simpler, type.

ala :: Rewrapping s t => (Unwrapped s -> s) -> ((Unwrapped t -> t) -> e -> s) -> e -> Unwrapped s

alaf :: (Functor f, Functor g, Rewrapping s t) => (Unwrapped s -> s) -> (f t -> g s) -> f (Unwrapped t) -> g (Unwrapped s) #

This combinator is based on ala' from Conor McBride's work on Epigram.

As with _Wrapping, the user supplied function for the newtype is ignored.

alaf :: Rewrapping s t => (Unwrapped s -> s) -> ((r ->  t) -> e -> s) -> (r -> Unwrapped t) -> e -> Unwrapped s

>>> alaf Sum foldMap Prelude.length ["hello","world"]
10

class (Magnified m ~ Magnified n, MonadReader b m, MonadReader a n) => Magnify (m :: Type -> Type) (n :: Type -> Type) b a | m -> b, n -> a, m a -> n, n b -> m where #

This class allows us to use magnify part of the environment, changing the environment supplied by many different Monad transformers. Unlike zoom this can change the environment of a deeply nested Monad transformer.

Also, unlike zoom, this can be used with any valid Getter, but cannot be used with a Traversal or Fold.

Methods

magnify :: LensLike' (Magnified m c) a b -> m c -> n c infixr 2 #

Run a monadic action in a larger environment than it was defined in, using a Getter.

This acts like local, but can in many cases change the type of the environment as well.

This is commonly used to lift actions in a simpler Reader Monad into a Monad with a larger environment type.

This can be used to edit pretty much any Monad transformer stack with an environment in it:

>>> (1,2) & magnify _2 (+1)
3

>>> flip Reader.runReader (1,2) $ magnify _1 Reader.ask
1

>>> flip Reader.runReader (1,2,[10..20]) $ magnify (_3._tail) Reader.ask
[11,12,13,14,15,16,17,18,19,20]

magnify :: Getter s a -> (a -> r) -> s -> r
magnify :: Monoid r => Fold s a   -> (a -> r) -> s -> r

magnify :: Monoid w                 => Getter s t -> RWS t w st c -> RWS s w st c
magnify :: (Monoid w, Monoid c) => Fold s a   -> RWS a w st c -> RWS s w st c
...

Instances

Magnify m n b a => Magnify (IdentityT m) (IdentityT n) b a
Instance details Defined in Control.Lens.Zoom Methods magnify :: LensLike' (Magnified (IdentityT m) c) a b -> IdentityT m c -> IdentityT n c #
Magnify ((->) b :: Type -> Type) ((->) a :: Type -> Type) b a	`magnify` = `views`
Instance details Defined in Control.Lens.Zoom Methods magnify :: LensLike' (Magnified ((->) b) c) a b -> (b -> c) -> a -> c #
Monad m => Magnify (ReaderT b m) (ReaderT a m) b a
Instance details Defined in Control.Lens.Zoom Methods magnify :: LensLike' (Magnified (ReaderT b m) c) a b -> ReaderT b m c -> ReaderT a m c #
(Monad m, Monoid w) => Magnify (RWST b w s m) (RWST a w s m) b a
Instance details Defined in Control.Lens.Zoom Methods magnify :: LensLike' (Magnified (RWST b w s m) c) a b -> RWST b w s m c -> RWST a w s m c #
(Monad m, Monoid w) => Magnify (RWST b w s m) (RWST a w s m) b a
Instance details Defined in Control.Lens.Zoom Methods magnify :: LensLike' (Magnified (RWST b w s m) c) a b -> RWST b w s m c -> RWST a w s m c #

class (MonadState s m, MonadState t n) => Zoom (m :: Type -> Type) (n :: Type -> Type) s t | m -> s, n -> t, m t -> n, n s -> m where #

This class allows us to use zoom in, changing the State supplied by many different Monad transformers, potentially quite deep in a Monad transformer stack.

Methods

zoom :: LensLike' (Zoomed m c) t s -> m c -> n c infixr 2 #

Run a monadic action in a larger State than it was defined in, using a Lens' or Traversal'.

This is commonly used to lift actions in a simpler State Monad into a State Monad with a larger State type.

When applied to a Traversal' over multiple values, the actions for each target are executed sequentially and the results are aggregated.

This can be used to edit pretty much any Monad transformer stack with a State in it!

>>> flip State.evalState (a,b) $ zoom _1 $ use id
a

>>> flip State.execState (a,b) $ zoom _1 $ id .= c
(c,b)

>>> flip State.execState [(a,b),(c,d)] $ zoom traverse $ _2 %= f
[(a,f b),(c,f d)]

>>> flip State.runState [(a,b),(c,d)] $ zoom traverse $ _2 <%= f
(f b <> f d <> mempty,[(a,f b),(c,f d)])

>>> flip State.evalState (a,b) $ zoom both (use id)
a <> b

zoom :: Monad m             => Lens' s t      -> StateT t m a -> StateT s m a
zoom :: (Monad m, Monoid c) => Traversal' s t -> StateT t m c -> StateT s m c
zoom :: (Monad m, Monoid w)             => Lens' s t      -> RWST r w t m c -> RWST r w s m c
zoom :: (Monad m, Monoid w, Monoid c) => Traversal' s t -> RWST r w t m c -> RWST r w s m c
zoom :: (Monad m, Monoid w, Error e)  => Lens' s t      -> ErrorT e (RWST r w t m) c -> ErrorT e (RWST r w s m) c
zoom :: (Monad m, Monoid w, Monoid c, Error e) => Traversal' s t -> ErrorT e (RWST r w t m) c -> ErrorT e (RWST r w s m) c
...

Instances

Zoom m n s t => Zoom (MaybeT m) (MaybeT n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (MaybeT m) c) t s -> MaybeT m c -> MaybeT n c #
Zoom m n s t => Zoom (ListT m) (ListT n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (ListT m) c) t s -> ListT m c -> ListT n c #
Zoom m n s t => Zoom (IdentityT m) (IdentityT n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (IdentityT m) c) t s -> IdentityT m c -> IdentityT n c #
Zoom m n s t => Zoom (ExceptT e m) (ExceptT e n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (ExceptT e m) c) t s -> ExceptT e m c -> ExceptT e n c #
(Functor f, Zoom m n s t) => Zoom (FreeT f m) (FreeT f n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (FreeT f m) c) t s -> FreeT f m c -> FreeT f n c #
(Error e, Zoom m n s t) => Zoom (ErrorT e m) (ErrorT e n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (ErrorT e m) c) t s -> ErrorT e m c -> ErrorT e n c #
Monad z => Zoom (StateT s z) (StateT t z) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (StateT s z) c) t s -> StateT s z c -> StateT t z c #
(Monoid w, Zoom m n s t) => Zoom (WriterT w m) (WriterT w n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (WriterT w m) c) t s -> WriterT w m c -> WriterT w n c #
Monad z => Zoom (StateT s z) (StateT t z) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (StateT s z) c) t s -> StateT s z c -> StateT t z c #
(Monoid w, Zoom m n s t) => Zoom (WriterT w m) (WriterT w n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (WriterT w m) c) t s -> WriterT w m c -> WriterT w n c #
Zoom m n s t => Zoom (ReaderT e m) (ReaderT e n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (ReaderT e m) c) t s -> ReaderT e m c -> ReaderT e n c #
(Monoid w, Monad z) => Zoom (RWST r w s z) (RWST r w t z) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (RWST r w s z) c) t s -> RWST r w s z c -> RWST r w t z c #
(Monoid w, Monad z) => Zoom (RWST r w s z) (RWST r w t z) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (RWST r w s z) c) t s -> RWST r w s z c -> RWST r w t z c #

type family Magnified (m :: Type -> Type) :: Type -> Type -> Type #

This type family is used by Magnify to describe the common effect type.

Instances

type Magnified (IdentityT m)
Instance details Defined in Control.Lens.Zoom type Magnified (IdentityT m) = Magnified m
type Magnified ((->) b :: Type -> Type)
Instance details Defined in Control.Lens.Zoom type Magnified ((->) b :: Type -> Type) = (Const :: Type -> Type -> Type)
type Magnified (ReaderT b m)
Instance details Defined in Control.Lens.Zoom type Magnified (ReaderT b m) = Effect m
type Magnified (RWST a w s m)
Instance details Defined in Control.Lens.Zoom type Magnified (RWST a w s m) = EffectRWS w s m
type Magnified (RWST a w s m)
Instance details Defined in Control.Lens.Zoom type Magnified (RWST a w s m) = EffectRWS w s m

type family Zoomed (m :: Type -> Type) :: Type -> Type -> Type #

This type family is used by Zoom to describe the common effect type.

Instances

type Zoomed (MaybeT m)
Instance details Defined in Control.Lens.Zoom type Zoomed (MaybeT m) = FocusingMay (Zoomed m)
type Zoomed (ListT m)
Instance details Defined in Control.Lens.Zoom type Zoomed (ListT m) = FocusingOn [] (Zoomed m)
type Zoomed (IdentityT m)
Instance details Defined in Control.Lens.Zoom type Zoomed (IdentityT m) = Zoomed m
type Zoomed (ExceptT e m)
Instance details Defined in Control.Lens.Zoom type Zoomed (ExceptT e m) = FocusingErr e (Zoomed m)
type Zoomed (FreeT f m)
Instance details Defined in Control.Lens.Zoom type Zoomed (FreeT f m) = FocusingFree f m (Zoomed m)
type Zoomed (ErrorT e m)
Instance details Defined in Control.Lens.Zoom type Zoomed (ErrorT e m) = FocusingErr e (Zoomed m)
type Zoomed (StateT s z)
Instance details Defined in Control.Lens.Zoom type Zoomed (StateT s z) = Focusing z
type Zoomed (WriterT w m)
Instance details Defined in Control.Lens.Zoom type Zoomed (WriterT w m) = FocusingPlus w (Zoomed m)
type Zoomed (StateT s z)
Instance details Defined in Control.Lens.Zoom type Zoomed (StateT s z) = Focusing z
type Zoomed (WriterT w m)
Instance details Defined in Control.Lens.Zoom type Zoomed (WriterT w m) = FocusingPlus w (Zoomed m)
type Zoomed (ReaderT e m)
Instance details Defined in Control.Lens.Zoom type Zoomed (ReaderT e m) = Zoomed m
type Zoomed (RWST r w s z)
Instance details Defined in Control.Lens.Zoom type Zoomed (RWST r w s z) = FocusingWith w z
type Zoomed (RWST r w s z)
Instance details Defined in Control.Lens.Zoom type Zoomed (RWST r w s z) = FocusingWith w z

class GPlated1 (f :: k -> Type) (g :: k -> Type) #

Minimal complete definition

gplate1'

Instances

GPlated1 (f :: k -> Type) (V1 :: k -> Type)	ignored
Instance details Defined in Control.Lens.Plated Methods gplate1' :: Traversal' (V1 a) (f a)
GPlated1 (f :: k -> Type) (U1 :: k -> Type)	ignored
Instance details Defined in Control.Lens.Plated Methods gplate1' :: Traversal' (U1 a) (f a)
GPlated1 (f :: k -> Type) (URec a :: k -> Type)	ignored
Instance details Defined in Control.Lens.Plated Methods gplate1' :: Traversal' (URec a a0) (f a0)
GPlated1 (f :: k -> Type) (Rec1 f :: k -> Type)	match
Instance details Defined in Control.Lens.Plated Methods gplate1' :: Traversal' (Rec1 f a) (f a)
GPlated1 (f :: k -> Type) (Rec1 g :: k -> Type)	ignored
Instance details Defined in Control.Lens.Plated Methods gplate1' :: Traversal' (Rec1 g a) (f a)
GPlated1 (f :: k -> Type) (K1 i a :: k -> Type)	ignored
Instance details Defined in Control.Lens.Plated Methods gplate1' :: Traversal' (K1 i a a0) (f a0)
(GPlated1 f g, GPlated1 f h) => GPlated1 (f :: k -> Type) (g :+: h :: k -> Type)	recursive match
Instance details Defined in Control.Lens.Plated Methods gplate1' :: Traversal' ((g :+: h) a) (f a)
(GPlated1 f g, GPlated1 f h) => GPlated1 (f :: k -> Type) (g :*: h :: k -> Type)	recursive match
Instance details Defined in Control.Lens.Plated Methods gplate1' :: Traversal' ((g :*: h) a) (f a)
GPlated1 f g => GPlated1 (f :: k -> Type) (M1 i c g :: k -> Type)	recursive match
Instance details Defined in Control.Lens.Plated Methods gplate1' :: Traversal' (M1 i c g a) (f a)
(Traversable t, GPlated1 f g) => GPlated1 (f :: k1 -> Type) (t :.: g :: k1 -> Type)	recursive match under outer `Traversable` instance
Instance details Defined in Control.Lens.Plated Methods gplate1' :: Traversal' ((t :.: g) a) (f a)
GPlated1 (f :: Type -> Type) Par1	ignored
Instance details Defined in Control.Lens.Plated Methods gplate1' :: Traversal' (Par1 a) (f a)

class GPlated a (g :: k -> Type) #

Minimal complete definition

gplate'

Instances

GPlated a (V1 :: k -> Type)
Instance details Defined in Control.Lens.Plated Methods gplate' :: Traversal' (V1 p) a
GPlated a (U1 :: k -> Type)
Instance details Defined in Control.Lens.Plated Methods gplate' :: Traversal' (U1 p) a
GPlated a (URec b :: k -> Type)
Instance details Defined in Control.Lens.Plated Methods gplate' :: Traversal' (URec b p) a
GPlated a (K1 i a :: k -> Type)
Instance details Defined in Control.Lens.Plated Methods gplate' :: Traversal' (K1 i a p) a
GPlated a (K1 i b :: k -> Type)
Instance details Defined in Control.Lens.Plated Methods gplate' :: Traversal' (K1 i b p) a
(GPlated a f, GPlated a g) => GPlated a (f :+: g :: k -> Type)
Instance details Defined in Control.Lens.Plated Methods gplate' :: Traversal' ((f :+: g) p) a
(GPlated a f, GPlated a g) => GPlated a (f :*: g :: k -> Type)
Instance details Defined in Control.Lens.Plated Methods gplate' :: Traversal' ((f :*: g) p) a
GPlated a f => GPlated a (M1 i c f :: k -> Type)
Instance details Defined in Control.Lens.Plated Methods gplate' :: Traversal' (M1 i c f p) a

class Plated a where #

A Plated type is one where we know how to extract its immediate self-similar children.

Example 1:

import Control.Applicative
import Control.Lens
import Control.Lens.Plated
import Data.Data
import Data.Data.Lens (uniplate)

data Expr
  = Val Int
  | Neg Expr
  | Add Expr Expr
  deriving (Eq,Ord,Show,Read,Data,Typeable)

instance Plated Expr where
  plate f (Neg e) = Neg <$> f e
  plate f (Add a b) = Add <$> f a <*> f b
  plate _ a = pure a

or

instance Plated Expr where
  plate = uniplate

Example 2:

import Control.Applicative
import Control.Lens
import Control.Lens.Plated
import Data.Data
import Data.Data.Lens (uniplate)

data Tree a
  = Bin (Tree a) (Tree a)
  | Tip a
  deriving (Eq,Ord,Show,Read,Data,Typeable)

instance Plated (Tree a) where
  plate f (Bin l r) = Bin <$> f l <*> f r
  plate _ t = pure t

or

instance Data a => Plated (Tree a) where
  plate = uniplate

Note the big distinction between these two implementations.

The former will only treat children directly in this tree as descendents, the latter will treat trees contained in the values under the tips also as descendants!

When in doubt, pick a Traversal and just use the various ...Of combinators rather than pollute Plated with orphan instances!

If you want to find something unplated and non-recursive with biplate use the ...OnOf variant with ignored, though those usecases are much better served in most cases by using the existing Lens combinators! e.g.

toListOf biplate ≡ universeOnOf biplate ignored

This same ability to explicitly pass the Traversal in question is why there is no analogue to uniplate's Biplate.

Moreover, since we can allow custom traversals, we implement reasonable defaults for polymorphic data types, that only traverse into themselves, and not their polymorphic arguments.

Minimal complete definition

Nothing

Methods

plate :: Traversal' a a #

Traversal of the immediate children of this structure.

If you're using GHC 7.2 or newer and your type has a Data instance, plate will default to uniplate and you can choose to not override it with your own definition.

Instances

Plated Exp
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Exp Exp #
Plated Pat
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Pat Pat #
Plated Type
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Type Type #
Plated Dec
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Dec Dec #
Plated Con
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Con Con #
Plated Stmt
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' Stmt Stmt #
Plated [a]
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' [a] [a] #
Plated (Tree a)
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (Tree a) (Tree a) #
Traversable f => Plated (Cofree f a)
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (Cofree f a) (Cofree f a) #
Traversable f => Plated (F f a)
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (F f a) (F f a) #
Traversable f => Plated (Free f a)
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (Free f a) (Free f a) #
(Traversable f, Traversable m) => Plated (FreeT f m a)
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (FreeT f m a) (FreeT f m a) #
(Traversable f, Traversable w) => Plated (CofreeT f w a)
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (CofreeT f w a) (CofreeT f w a) #

deep :: (Conjoined p, Applicative f, Plated s) => Traversing p f s s a b -> Over p f s s a b #

Try to apply a traversal to all transitive descendants of a Plated container, but do not recurse through matching descendants.

deep :: Plated s => Fold s a                 -> Fold s a
deep :: Plated s => IndexedFold s a          -> IndexedFold s a
deep :: Plated s => Traversal s s a b        -> Traversal s s a b
deep :: Plated s => IndexedTraversal s s a b -> IndexedTraversal s s a b

rewrite :: Plated a => (a -> Maybe a) -> a -> a #

Rewrite by applying a rule everywhere you can. Ensures that the rule cannot be applied anywhere in the result:

propRewrite r x = all (isNothing . r) (universe (rewrite r x))

Usually transform is more appropriate, but rewrite can give better compositionality. Given two single transformations f and g, you can construct \a -> f a <|> g a which performs both rewrites until a fixed point.

rewriteOf :: ASetter a b a b -> (b -> Maybe a) -> a -> b #

Rewrite by applying a rule everywhere you can. Ensures that the rule cannot be applied anywhere in the result:

propRewriteOf l r x = all (isNothing . r) (universeOf l (rewriteOf l r x))

Usually transformOf is more appropriate, but rewriteOf can give better compositionality. Given two single transformations f and g, you can construct \a -> f a <|> g a which performs both rewrites until a fixed point.

rewriteOf :: Iso' a a       -> (a -> Maybe a) -> a -> a
rewriteOf :: Lens' a a      -> (a -> Maybe a) -> a -> a
rewriteOf :: Traversal' a a -> (a -> Maybe a) -> a -> a
rewriteOf :: Setter' a a    -> (a -> Maybe a) -> a -> a

rewriteOn :: Plated a => ASetter s t a a -> (a -> Maybe a) -> s -> t #

Rewrite recursively over part of a larger structure.

rewriteOn :: Plated a => Iso' s a       -> (a -> Maybe a) -> s -> s
rewriteOn :: Plated a => Lens' s a      -> (a -> Maybe a) -> s -> s
rewriteOn :: Plated a => Traversal' s a -> (a -> Maybe a) -> s -> s
rewriteOn :: Plated a => ASetter' s a   -> (a -> Maybe a) -> s -> s

rewriteOnOf :: ASetter s t a b -> ASetter a b a b -> (b -> Maybe a) -> s -> t #

Rewrite recursively over part of a larger structure using a specified Setter.

rewriteOnOf :: Iso' s a       -> Iso' a a       -> (a -> Maybe a) -> s -> s
rewriteOnOf :: Lens' s a      -> Lens' a a      -> (a -> Maybe a) -> s -> s
rewriteOnOf :: Traversal' s a -> Traversal' a a -> (a -> Maybe a) -> s -> s
rewriteOnOf :: Setter' s a    -> Setter' a a    -> (a -> Maybe a) -> s -> s

rewriteM :: (Monad m, Plated a) => (a -> m (Maybe a)) -> a -> m a #

Rewrite by applying a monadic rule everywhere you can. Ensures that the rule cannot be applied anywhere in the result.

rewriteMOf :: Monad m => LensLike (WrappedMonad m) a b a b -> (b -> m (Maybe a)) -> a -> m b #

Rewrite by applying a monadic rule everywhere you recursing with a user-specified Traversal. Ensures that the rule cannot be applied anywhere in the result.

rewriteMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m (Maybe a)) -> s -> m t #

Rewrite by applying a monadic rule everywhere inside of a structure located by a user-specified Traversal. Ensures that the rule cannot be applied anywhere in the result.

rewriteMOnOf :: Monad m => LensLike (WrappedMonad m) s t a b -> LensLike (WrappedMonad m) a b a b -> (b -> m (Maybe a)) -> s -> m t #

Rewrite by applying a monadic rule everywhere inside of a structure located by a user-specified Traversal, using a user-specified Traversal for recursion. Ensures that the rule cannot be applied anywhere in the result.

universe :: Plated a => a -> [a] #

Retrieve all of the transitive descendants of a Plated container, including itself.

universeOf :: Getting [a] a a -> a -> [a] #

Given a Fold that knows how to locate immediate children, retrieve all of the transitive descendants of a node, including itself.

universeOf :: Fold a a -> a -> [a]

universeOn :: Plated a => Getting [a] s a -> s -> [a] #

Given a Fold that knows how to find Plated parts of a container retrieve them and all of their descendants, recursively.

universeOnOf :: Getting [a] s a -> Getting [a] a a -> s -> [a] #

Given a Fold that knows how to locate immediate children, retrieve all of the transitive descendants of a node, including itself that lie in a region indicated by another Fold.

toListOf l ≡ universeOnOf l ignored

cosmos :: Plated a => Fold a a #

Fold over all transitive descendants of a Plated container, including itself.

cosmosOf :: (Applicative f, Contravariant f) => LensLike' f a a -> LensLike' f a a #

Given a Fold that knows how to locate immediate children, fold all of the transitive descendants of a node, including itself.

cosmosOf :: Fold a a -> Fold a a

cosmosOn :: (Applicative f, Contravariant f, Plated a) => LensLike' f s a -> LensLike' f s a #

Given a Fold that knows how to find Plated parts of a container fold them and all of their descendants, recursively.

cosmosOn :: Plated a => Fold s a -> Fold s a

cosmosOnOf :: (Applicative f, Contravariant f) => LensLike' f s a -> LensLike' f a a -> LensLike' f s a #

Given a Fold that knows how to locate immediate children, fold all of the transitive descendants of a node, including itself that lie in a region indicated by another Fold.

cosmosOnOf :: Fold s a -> Fold a a -> Fold s a

transformOn :: Plated a => ASetter s t a a -> (a -> a) -> s -> t #

Transform every element in the tree in a bottom-up manner over a region indicated by a Setter.

transformOn :: Plated a => Traversal' s a -> (a -> a) -> s -> s
transformOn :: Plated a => Setter' s a    -> (a -> a) -> s -> s

transformOf :: ASetter a b a b -> (b -> b) -> a -> b #

Transform every element by recursively applying a given Setter in a bottom-up manner.

transformOf :: Traversal' a a -> (a -> a) -> a -> a
transformOf :: Setter' a a    -> (a -> a) -> a -> a

transformOnOf :: ASetter s t a b -> ASetter a b a b -> (b -> b) -> s -> t #

Transform every element in a region indicated by a Setter by recursively applying another Setter in a bottom-up manner.

transformOnOf :: Setter' s a -> Traversal' a a -> (a -> a) -> s -> s
transformOnOf :: Setter' s a -> Setter' a a    -> (a -> a) -> s -> s

transformM :: (Monad m, Plated a) => (a -> m a) -> a -> m a #

Transform every element in the tree, in a bottom-up manner, monadically.

transformMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m a) -> s -> m t #

Transform every element in the tree in a region indicated by a supplied Traversal, in a bottom-up manner, monadically.

transformMOn :: (Monad m, Plated a) => Traversal' s a -> (a -> m a) -> s -> m s

transformMOf :: Monad m => LensLike (WrappedMonad m) a b a b -> (b -> m b) -> a -> m b #

Transform every element in a tree using a user supplied Traversal in a bottom-up manner with a monadic effect.

transformMOf :: Monad m => Traversal' a a -> (a -> m a) -> a -> m a

transformMOnOf :: Monad m => LensLike (WrappedMonad m) s t a b -> LensLike (WrappedMonad m) a b a b -> (b -> m b) -> s -> m t #

Transform every element in a tree that lies in a region indicated by a supplied Traversal, walking with a user supplied Traversal in a bottom-up manner with a monadic effect.

transformMOnOf :: Monad m => Traversal' s a -> Traversal' a a -> (a -> m a) -> s -> m s

contexts :: Plated a => a -> [Context a a a] #

Return a list of all of the editable contexts for every location in the structure, recursively.

propUniverse x = universe x == map pos (contexts x)
propId x = all (== x) [extract w | w <- contexts x]

contexts ≡ contextsOf plate

contextsOf :: ATraversal' a a -> a -> [Context a a a] #

Return a list of all of the editable contexts for every location in the structure, recursively, using a user-specified Traversal to walk each layer.

propUniverse l x = universeOf l x == map pos (contextsOf l x)
propId l x = all (== x) [extract w | w <- contextsOf l x]

contextsOf :: Traversal' a a -> a -> [Context a a a]

contextsOn :: Plated a => ATraversal s t a a -> s -> [Context a a t] #

Return a list of all of the editable contexts for every location in the structure in an areas indicated by a user supplied Traversal, recursively using plate.

contextsOn b ≡ contextsOnOf b plate

contextsOn :: Plated a => Traversal' s a -> s -> [Context a a s]

contextsOnOf :: ATraversal s t a a -> ATraversal' a a -> s -> [Context a a t] #

Return a list of all of the editable contexts for every location in the structure in an areas indicated by a user supplied Traversal, recursively using another user-supplied Traversal to walk each layer.

contextsOnOf :: Traversal' s a -> Traversal' a a -> s -> [Context a a s]

holes :: Plated a => a -> [Pretext ((->) :: Type -> Type -> Type) a a a] #

The one-level version of context. This extracts a list of the immediate children as editable contexts.

Given a context you can use pos to see the values, peek at what the structure would be like with an edited result, or simply extract the original structure.

propChildren x = children l x == map pos (holes l x)
propId x = all (== x) [extract w | w <- holes l x]

holes = holesOf plate

holesOn :: Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t] #

An alias for holesOf, provided for consistency with the other combinators.

holesOn ≡ holesOf

holesOn :: Iso' s a                -> s -> [Pretext (->) a a s]
holesOn :: Lens' s a               -> s -> [Pretext (->) a a s]
holesOn :: Traversal' s a          -> s -> [Pretext (->) a a s]
holesOn :: IndexedLens' i s a      -> s -> [Pretext (Indexed i) a a s]
holesOn :: IndexedTraversal' i s a -> s -> [Pretext (Indexed i) a a s]

holesOnOf :: Conjoined p => LensLike (Bazaar p r r) s t a b -> Over p (Bazaar p r r) a b r r -> s -> [Pretext p r r t] #

Extract one level of holes from a container in a region specified by one Traversal, using another.

holesOnOf b l ≡ holesOf (b . l)

holesOnOf :: Iso' s a       -> Iso' a a                -> s -> [Pretext (->) a a s]
holesOnOf :: Lens' s a      -> Lens' a a               -> s -> [Pretext (->) a a s]
holesOnOf :: Traversal' s a -> Traversal' a a          -> s -> [Pretext (->) a a s]
holesOnOf :: Lens' s a      -> IndexedLens' i a a      -> s -> [Pretext (Indexed i) a a s]
holesOnOf :: Traversal' s a -> IndexedTraversal' i a a -> s -> [Pretext (Indexed i) a a s]

paraOf :: Getting (Endo [a]) a a -> (a -> [r] -> r) -> a -> r #

Perform a fold-like computation on each value, technically a paramorphism.

paraOf :: Fold a a -> (a -> [r] -> r) -> a -> r

para :: Plated a => (a -> [r] -> r) -> a -> r #

Perform a fold-like computation on each value, technically a paramorphism.

para ≡ paraOf plate

composOpFold :: Plated a => b -> (b -> b -> b) -> (a -> b) -> a -> b #

Fold the immediate children of a Plated container.

composOpFold z c f = foldrOf plate (c . f) z

parts :: Plated a => Lens' a [a] #

The original uniplate combinator, implemented in terms of Plated as a Lens.

parts ≡ partsOf plate

The resulting Lens is safer to use as it ignores 'over-application' and deals gracefully with under-application, but it is only a proper Lens if you don't change the list length!

gplate :: (Generic a, GPlated a (Rep a)) => Traversal' a a #

Implement plate operation for a type using its Generic instance.

gplate1 :: (Generic1 f, GPlated1 f (Rep1 f)) => Traversal' (f a) (f a) #

Implement plate operation for a type using its Generic1 instance.

class Each s t a b | s -> a, t -> b, s b -> t, t a -> s where #

Extract each element of a (potentially monomorphic) container.

Notably, when applied to a tuple, this generalizes both to arbitrary homogeneous tuples.

>>> (1,2,3) & each *~ 10
(10,20,30)

It can also be used on monomorphic containers like Text or ByteString.

>>> over each Char.toUpper ("hello"^.Text.packed)
"HELLO"

>>> ("hello","world") & each.each %~ Char.toUpper
("HELLO","WORLD")

Minimal complete definition

Nothing

Methods

each :: Traversal s t a b #

Instances

(a ~ Word8, b ~ Word8) => Each ByteString ByteString a b	`each` :: `Traversal` `ByteString` `ByteString` `Word8` `Word8`
Instance details Defined in Control.Lens.Each Methods each :: Traversal ByteString ByteString a b #
(a ~ Word8, b ~ Word8) => Each ByteString ByteString a b	`each` :: `Traversal` `ByteString` `ByteString` `Word8` `Word8`
Instance details Defined in Control.Lens.Each Methods each :: Traversal ByteString ByteString a b #
(a ~ Char, b ~ Char) => Each Text Text a b	`each` :: `Traversal` `Text` `Text` `Char` `Char`
Instance details Defined in Control.Lens.Each Methods each :: Traversal Text Text a b #
(a ~ Char, b ~ Char) => Each Text Text a b	`each` :: `Traversal` `Text` `Text` `Char` `Char`
Instance details Defined in Control.Lens.Each Methods each :: Traversal Text Text a b #
Each Name Name AName AName
Instance details Defined in Diagrams.Core.Names Methods each :: Traversal Name Name AName AName #
Each [a] [b] a b	`each` :: `Traversal` [a] [b] a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal [a] [b] a b #
Each (Maybe a) (Maybe b) a b	`each` :: `Traversal` (`Maybe` a) (`Maybe` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Maybe a) (Maybe b) a b #
Each (Identity a) (Identity b) a b	`each` :: `Traversal` (`Identity` a) (`Identity` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Identity a) (Identity b) a b #
(Storable a, Storable b) => Each (Vector a) (Vector b) a b	`each` :: (`Storable` a, `Storable` b) => `Traversal` (`Vector` a) (`Vector` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Vector a) (Vector b) a b #
Each (Complex a) (Complex b) a b	`each` :: (`RealFloat` a, `RealFloat` b) => `Traversal` (`Complex` a) (`Complex` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Complex a) (Complex b) a b #
Each (NonEmpty a) (NonEmpty b) a b	`each` :: `Traversal` (NonEmpty a) (NonEmpty b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (NonEmpty a) (NonEmpty b) a b #
Each (Vector a) (Vector b) a b	`each` :: `Traversal` (`Vector` a) (`Vector` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Vector a) (Vector b) a b #
Each (IntMap a) (IntMap b) a b	`each` :: `Traversal` (`Map` c a) (`Map` c b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (IntMap a) (IntMap b) a b #
Each (Tree a) (Tree b) a b	`each` :: `Traversal` (`Tree` a) (`Tree` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Tree a) (Tree b) a b #
Each (Seq a) (Seq b) a b	`each` :: `Traversal` (`Seq` a) (`Seq` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Seq a) (Seq b) a b #
(Unbox a, Unbox b) => Each (Vector a) (Vector b) a b	`each` :: (`Unbox` a, `Unbox` b) => `Traversal` (`Vector` a) (`Vector` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Vector a) (Vector b) a b #
Each (V2 a) (V2 b) a b
Instance details Defined in Linear.V2 Methods each :: Traversal (V2 a) (V2 b) a b #
Each (V3 a) (V3 b) a b
Instance details Defined in Linear.V3 Methods each :: Traversal (V3 a) (V3 b) a b #
(Prim a, Prim b) => Each (Vector a) (Vector b) a b	`each` :: (`Prim` a, `Prim` b) => `Traversal` (`Vector` a) (`Vector` b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Vector a) (Vector b) a b #
Each (Plucker a) (Plucker b) a b
Instance details Defined in Linear.Plucker Methods each :: Traversal (Plucker a) (Plucker b) a b #
Each (Quaternion a) (Quaternion b) a b
Instance details Defined in Linear.Quaternion Methods each :: Traversal (Quaternion a) (Quaternion b) a b #
Each (V0 a) (V0 b) a b
Instance details Defined in Linear.V0 Methods each :: Traversal (V0 a) (V0 b) a b #
Each (V4 a) (V4 b) a b
Instance details Defined in Linear.V4 Methods each :: Traversal (V4 a) (V4 b) a b #
Each (V1 a) (V1 b) a b
Instance details Defined in Linear.V1 Methods each :: Traversal (V1 a) (V1 b) a b #
(a ~ a', b ~ b') => Each (a, a') (b, b') a b	`each` :: `Traversal` (a,a) (b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a') (b, b') a b #
c ~ d => Each (Map c a) (Map d b) a b	`each` :: `Traversal` (`Map` c a) (`Map` c b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Map c a) (Map d b) a b #
c ~ d => Each (HashMap c a) (HashMap d b) a b	`each` :: `Traversal` (`HashMap` c a) (`HashMap` c b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (HashMap c a) (HashMap d b) a b #
(Ix i, IArray UArray a, IArray UArray b, i ~ j) => Each (UArray i a) (UArray j b) a b	`each` :: (`Ix` i, `IArray` `UArray` a, `IArray` `UArray` b) => `Traversal` (`Array` i a) (`Array` i b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (UArray i a) (UArray j b) a b #
(Ix i, i ~ j) => Each (Array i a) (Array j b) a b	`each` :: `Ix` i => `Traversal` (`Array` i a) (`Array` i b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (Array i a) (Array j b) a b #
Traversable f => Each (Point f a) (Point f b) a b
Instance details Defined in Linear.Affine Methods each :: Traversal (Point f a) (Point f b) a b #
Each (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n'))
Instance details Defined in Diagrams.Path Methods each :: Traversal (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n')) #
Each (Style v n) (Style v' n') (Attribute v n) (Attribute v' n')
Instance details Defined in Diagrams.Core.Style Methods each :: Traversal (Style v n) (Style v' n') (Attribute v n) (Attribute v' n') #
(Additive v', Foldable v', Ord n') => Each (BoundingBox v n) (BoundingBox v' n') (Point v n) (Point v' n')	Only valid if the second point is not smaller than the first.
Instance details Defined in Diagrams.BoundingBox Methods each :: Traversal (BoundingBox v n) (BoundingBox v' n') (Point v n) (Point v' n') #
Each (FixedSegment v n) (FixedSegment v' n') (Point v n) (Point v' n')
Instance details Defined in Diagrams.Segment Methods each :: Traversal (FixedSegment v n) (FixedSegment v' n') (Point v n) (Point v' n') #
(a ~ a2, a ~ a3, b ~ b2, b ~ b3) => Each (a, a2, a3) (b, b2, b3) a b	`each` :: `Traversal` (a,a,a) (b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3) (b, b2, b3) a b #
Each (V n a) (V n b) a b
Instance details Defined in Linear.V Methods each :: Traversal (V n a) (V n b) a b #
Each (Offset c v n) (Offset c v' n') (v n) (v' n')
Instance details Defined in Diagrams.Segment Methods each :: Traversal (Offset c v n) (Offset c v' n') (v n) (v' n') #
Each (Segment c v n) (Segment c v' n') (v n) (v' n')
Instance details Defined in Diagrams.Segment Methods each :: Traversal (Segment c v n) (Segment c v' n') (v n) (v' n') #
(a ~ a2, a ~ a3, a ~ a4, b ~ b2, b ~ b3, b ~ b4) => Each (a, a2, a3, a4) (b, b2, b3, b4) a b	`each` :: `Traversal` (a,a,a,a) (b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4) (b, b2, b3, b4) a b #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, b ~ b2, b ~ b3, b ~ b4, b ~ b5) => Each (a, a2, a3, a4, a5) (b, b2, b3, b4, b5) a b	`each` :: `Traversal` (a,a,a,a,a) (b,b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4, a5) (b, b2, b3, b4, b5) a b #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, b ~ b2, b ~ b3, b ~ b4, b ~ b5, b ~ b6) => Each (a, a2, a3, a4, a5, a6) (b, b2, b3, b4, b5, b6) a b	`each` :: `Traversal` (a,a,a,a,a,a) (b,b,b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4, a5, a6) (b, b2, b3, b4, b5, b6) a b #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, b ~ b2, b ~ b3, b ~ b4, b ~ b5, b ~ b6, b ~ b7) => Each (a, a2, a3, a4, a5, a6, a7) (b, b2, b3, b4, b5, b6, b7) a b	`each` :: `Traversal` (a,a,a,a,a,a,a) (b,b,b,b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4, a5, a6, a7) (b, b2, b3, b4, b5, b6, b7) a b #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, a ~ a8, b ~ b2, b ~ b3, b ~ b4, b ~ b5, b ~ b6, b ~ b7, b ~ b8) => Each (a, a2, a3, a4, a5, a6, a7, a8) (b, b2, b3, b4, b5, b6, b7, b8) a b	`each` :: `Traversal` (a,a,a,a,a,a,a,a) (b,b,b,b,b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4, a5, a6, a7, a8) (b, b2, b3, b4, b5, b6, b7, b8) a b #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, a ~ a8, a ~ a9, b ~ b2, b ~ b3, b ~ b4, b ~ b5, b ~ b6, b ~ b7, b ~ b8, b ~ b9) => Each (a, a2, a3, a4, a5, a6, a7, a8, a9) (b, b2, b3, b4, b5, b6, b7, b8, b9) a b	`each` :: `Traversal` (a,a,a,a,a,a,a,a,a) (b,b,b,b,b,b,b,b,b) a b
Instance details Defined in Control.Lens.Each Methods each :: Traversal (a, a2, a3, a4, a5, a6, a7, a8, a9) (b, b2, b3, b4, b5, b6, b7, b8, b9) a b #

class Ixed m => At m #

At provides a Lens that can be used to read, write or delete the value associated with a key in a Map-like container on an ad hoc basis.

An instance of At should satisfy:

ix k ≡ at k . traverse

Minimal complete definition

at

Instances

At IntSet
Instance details Defined in Control.Lens.At Methods at :: Index IntSet -> Lens' IntSet (Maybe (IxValue IntSet)) #
At (Maybe a)
Instance details Defined in Control.Lens.At Methods at :: Index (Maybe a) -> Lens' (Maybe a) (Maybe (IxValue (Maybe a))) #
Ord k => At (Set k)
Instance details Defined in Control.Lens.At Methods at :: Index (Set k) -> Lens' (Set k) (Maybe (IxValue (Set k))) #
At (IntMap a)
Instance details Defined in Control.Lens.At Methods at :: Index (IntMap a) -> Lens' (IntMap a) (Maybe (IxValue (IntMap a))) #
(Eq k, Hashable k) => At (HashSet k)
Instance details Defined in Control.Lens.At Methods at :: Index (HashSet k) -> Lens' (HashSet k) (Maybe (IxValue (HashSet k))) #
Ord k => At (Map k a)
Instance details Defined in Control.Lens.At Methods at :: Index (Map k a) -> Lens' (Map k a) (Maybe (IxValue (Map k a))) #
(Eq k, Hashable k) => At (HashMap k a)
Instance details Defined in Control.Lens.At Methods at :: Index (HashMap k a) -> Lens' (HashMap k a) (Maybe (IxValue (HashMap k a))) #
At (Style v n)
Instance details Defined in Diagrams.Core.Style Methods at :: Index (Style v n) -> Lens' (Style v n) (Maybe (IxValue (Style v n))) #

class Ixed m where #

Provides a simple Traversal lets you traverse the value at a given key in a Map or element at an ordinal position in a list or Seq.

Minimal complete definition

Nothing

Methods

ix :: Index m -> Traversal' m (IxValue m) #

NB: Setting the value of this Traversal will only set the value in at if it is already present.

If you want to be able to insert missing values, you want at.

>>> Seq.fromList [a,b,c,d] & ix 2 %~ f
fromList [a,b,f c,d]

>>> Seq.fromList [a,b,c,d] & ix 2 .~ e
fromList [a,b,e,d]

>>> Seq.fromList [a,b,c,d] ^? ix 2
Just c

>>> Seq.fromList [] ^? ix 2
Nothing

Instances

Ixed ByteString
Instance details Defined in Control.Lens.At Methods ix :: Index ByteString -> Traversal' ByteString (IxValue ByteString) #
Ixed ByteString
Instance details Defined in Control.Lens.At Methods ix :: Index ByteString -> Traversal' ByteString (IxValue ByteString) #
Ixed Text
Instance details Defined in Control.Lens.At Methods ix :: Index Text -> Traversal' Text (IxValue Text) #
Ixed Text
Instance details Defined in Control.Lens.At Methods ix :: Index Text -> Traversal' Text (IxValue Text) #
Ixed IntSet
Instance details Defined in Control.Lens.At Methods ix :: Index IntSet -> Traversal' IntSet (IxValue IntSet) #
Ixed [a]
Instance details Defined in Control.Lens.At Methods ix :: Index [a] -> Traversal' [a] (IxValue [a]) #
Ixed (Maybe a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Maybe a) -> Traversal' (Maybe a) (IxValue (Maybe a)) #
Ord k => Ixed (Set k)
Instance details Defined in Control.Lens.At Methods ix :: Index (Set k) -> Traversal' (Set k) (IxValue (Set k)) #
Ixed (Identity a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Identity a) -> Traversal' (Identity a) (IxValue (Identity a)) #
Storable a => Ixed (Vector a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a)) #
Ixed (NonEmpty a)
Instance details Defined in Control.Lens.At Methods ix :: Index (NonEmpty a) -> Traversal' (NonEmpty a) (IxValue (NonEmpty a)) #
Ixed (Vector a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a)) #
Ixed (IntMap a)
Instance details Defined in Control.Lens.At Methods ix :: Index (IntMap a) -> Traversal' (IntMap a) (IxValue (IntMap a)) #
Ixed (Tree a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Tree a) -> Traversal' (Tree a) (IxValue (Tree a)) #
Ixed (Seq a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Seq a) -> Traversal' (Seq a) (IxValue (Seq a)) #
Unbox a => Ixed (Vector a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a)) #
Ixed (V2 a)
Instance details Defined in Linear.V2 Methods ix :: Index (V2 a) -> Traversal' (V2 a) (IxValue (V2 a)) #
Ixed (V3 a)
Instance details Defined in Linear.V3 Methods ix :: Index (V3 a) -> Traversal' (V3 a) (IxValue (V3 a)) #
Prim a => Ixed (Vector a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Vector a) -> Traversal' (Vector a) (IxValue (Vector a)) #
(Eq k, Hashable k) => Ixed (HashSet k)
Instance details Defined in Control.Lens.At Methods ix :: Index (HashSet k) -> Traversal' (HashSet k) (IxValue (HashSet k)) #
Ixed (Plucker a)
Instance details Defined in Linear.Plucker Methods ix :: Index (Plucker a) -> Traversal' (Plucker a) (IxValue (Plucker a)) #
Ixed (Quaternion a)
Instance details Defined in Linear.Quaternion Methods ix :: Index (Quaternion a) -> Traversal' (Quaternion a) (IxValue (Quaternion a)) #
Ixed (V0 a)
Instance details Defined in Linear.V0 Methods ix :: Index (V0 a) -> Traversal' (V0 a) (IxValue (V0 a)) #
Ixed (V4 a)
Instance details Defined in Linear.V4 Methods ix :: Index (V4 a) -> Traversal' (V4 a) (IxValue (V4 a)) #
Ixed (V1 a)
Instance details Defined in Linear.V1 Methods ix :: Index (V1 a) -> Traversal' (V1 a) (IxValue (V1 a)) #
Eq e => Ixed (e -> a)
Instance details Defined in Control.Lens.At Methods ix :: Index (e -> a) -> Traversal' (e -> a) (IxValue (e -> a)) #
a ~ a2 => Ixed (a, a2)
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2) -> Traversal' (a, a2) (IxValue (a, a2)) #
Ord k => Ixed (Map k a)
Instance details Defined in Control.Lens.At Methods ix :: Index (Map k a) -> Traversal' (Map k a) (IxValue (Map k a)) #
(Eq k, Hashable k) => Ixed (HashMap k a)
Instance details Defined in Control.Lens.At Methods ix :: Index (HashMap k a) -> Traversal' (HashMap k a) (IxValue (HashMap k a)) #
(IArray UArray e, Ix i) => Ixed (UArray i e)	arr `!` i ≡ arr `^.` `ix` i arr `//` [(i,e)] ≡ `ix` i `.~` e `$` arr
Instance details Defined in Control.Lens.At Methods ix :: Index (UArray i e) -> Traversal' (UArray i e) (IxValue (UArray i e)) #
Ix i => Ixed (Array i e)	arr `!` i ≡ arr `^.` `ix` i arr `//` [(i,e)] ≡ `ix` i `.~` e `$` arr
Instance details Defined in Control.Lens.At Methods ix :: Index (Array i e) -> Traversal' (Array i e) (IxValue (Array i e)) #
Ixed (Style v n)
Instance details Defined in Diagrams.Core.Style Methods ix :: Index (Style v n) -> Traversal' (Style v n) (IxValue (Style v n)) #
Ixed (f a) => Ixed (Point f a)
Instance details Defined in Linear.Affine Methods ix :: Index (Point f a) -> Traversal' (Point f a) (IxValue (Point f a)) #
(a ~ a2, a ~ a3) => Ixed (a, a2, a3)
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3) -> Traversal' (a, a2, a3) (IxValue (a, a2, a3)) #
Ixed (V n a)
Instance details Defined in Linear.V Methods ix :: Index (V n a) -> Traversal' (V n a) (IxValue (V n a)) #
(a ~ a2, a ~ a3, a ~ a4) => Ixed (a, a2, a3, a4)
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4) -> Traversal' (a, a2, a3, a4) (IxValue (a, a2, a3, a4)) #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5) => Ixed (a, a2, a3, a4, a5)
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4, a5) -> Traversal' (a, a2, a3, a4, a5) (IxValue (a, a2, a3, a4, a5)) #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6) => Ixed (a, a2, a3, a4, a5, a6)
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4, a5, a6) -> Traversal' (a, a2, a3, a4, a5, a6) (IxValue (a, a2, a3, a4, a5, a6)) #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7) => Ixed (a, a2, a3, a4, a5, a6, a7)
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4, a5, a6, a7) -> Traversal' (a, a2, a3, a4, a5, a6, a7) (IxValue (a, a2, a3, a4, a5, a6, a7)) #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, a ~ a8) => Ixed (a, a2, a3, a4, a5, a6, a7, a8)
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4, a5, a6, a7, a8) -> Traversal' (a, a2, a3, a4, a5, a6, a7, a8) (IxValue (a, a2, a3, a4, a5, a6, a7, a8)) #
(a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, a ~ a8, a ~ a9) => Ixed (a, a2, a3, a4, a5, a6, a7, a8, a9)
Instance details Defined in Control.Lens.At Methods ix :: Index (a, a2, a3, a4, a5, a6, a7, a8, a9) -> Traversal' (a, a2, a3, a4, a5, a6, a7, a8, a9) (IxValue (a, a2, a3, a4, a5, a6, a7, a8, a9)) #

type family IxValue m :: Type #

This provides a common notion of a value at an index that is shared by both Ixed and At.

Instances

type IxValue ByteString
Instance details Defined in Control.Lens.At type IxValue ByteString = Word8
type IxValue ByteString
Instance details Defined in Control.Lens.At type IxValue ByteString = Word8
type IxValue Text
Instance details Defined in Control.Lens.At type IxValue Text = Char
type IxValue Text
Instance details Defined in Control.Lens.At type IxValue Text = Char
type IxValue IntSet
Instance details Defined in Control.Lens.At type IxValue IntSet = ()
type IxValue [a]
Instance details Defined in Control.Lens.At type IxValue [a] = a
type IxValue (Maybe a)
Instance details Defined in Control.Lens.At type IxValue (Maybe a) = a
type IxValue (Set k)
Instance details Defined in Control.Lens.At type IxValue (Set k) = ()
type IxValue (Identity a)
Instance details Defined in Control.Lens.At type IxValue (Identity a) = a
type IxValue (Vector a)
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type IxValue (NonEmpty a)
Instance details Defined in Control.Lens.At type IxValue (NonEmpty a) = a
type IxValue (Vector a)
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type IxValue (IntMap a)
Instance details Defined in Control.Lens.At type IxValue (IntMap a) = a
type IxValue (Tree a)
Instance details Defined in Control.Lens.At type IxValue (Tree a) = a
type IxValue (Seq a)
Instance details Defined in Control.Lens.At type IxValue (Seq a) = a
type IxValue (Vector a)
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type IxValue (V2 a)
Instance details Defined in Linear.V2 type IxValue (V2 a) = a
type IxValue (V3 a)
Instance details Defined in Linear.V3 type IxValue (V3 a) = a
type IxValue (Vector a)
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type IxValue (HashSet k)
Instance details Defined in Control.Lens.At type IxValue (HashSet k) = ()
type IxValue (Plucker a)
Instance details Defined in Linear.Plucker type IxValue (Plucker a) = a
type IxValue (Quaternion a)
Instance details Defined in Linear.Quaternion type IxValue (Quaternion a) = a
type IxValue (V0 a)
Instance details Defined in Linear.V0 type IxValue (V0 a) = a
type IxValue (V4 a)
Instance details Defined in Linear.V4 type IxValue (V4 a) = a
type IxValue (V1 a)
Instance details Defined in Linear.V1 type IxValue (V1 a) = a
type IxValue (e -> a)
Instance details Defined in Control.Lens.At type IxValue (e -> a) = a
type IxValue (a, a2)	`ix` :: `Int` -> `Traversal'` (a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2) = a
type IxValue (Map k a)
Instance details Defined in Control.Lens.At type IxValue (Map k a) = a
type IxValue (HashMap k a)
Instance details Defined in Control.Lens.At type IxValue (HashMap k a) = a
type IxValue (UArray i e)
Instance details Defined in Control.Lens.At type IxValue (UArray i e) = e
type IxValue (Array i e)
Instance details Defined in Control.Lens.At type IxValue (Array i e) = e
type IxValue (Style v n)
Instance details Defined in Diagrams.Core.Style type IxValue (Style v n) = Attribute v n
type IxValue (Point f a)
Instance details Defined in Linear.Affine type IxValue (Point f a) = IxValue (f a)
type IxValue (a, a2, a3)	`ix` :: `Int` -> `Traversal'` (a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3) = a
type IxValue (V n a)
Instance details Defined in Linear.V type IxValue (V n a) = a
type IxValue (a, a2, a3, a4)	`ix` :: `Int` -> `Traversal'` (a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4) = a
type IxValue (a, a2, a3, a4, a5)	`ix` :: `Int` -> `Traversal'` (a,a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5) = a
type IxValue (a, a2, a3, a4, a5, a6)	`ix` :: `Int` -> `Traversal'` (a,a,a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6) = a
type IxValue (a, a2, a3, a4, a5, a6, a7)	`ix` :: `Int` -> `Traversal'` (a,a,a,a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6, a7) = a
type IxValue (a, a2, a3, a4, a5, a6, a7, a8)	`ix` :: `Int` -> `Traversal'` (a,a,a,a,a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6, a7, a8) = a
type IxValue (a, a2, a3, a4, a5, a6, a7, a8, a9)	`ix` :: `Int` -> `Traversal'` (a,a,a,a,a,a,a,a,a) a
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6, a7, a8, a9) = a

class Contains m #

This class provides a simple Lens that lets you view (and modify) information about whether or not a container contains a given Index.

Minimal complete definition

contains

Instances

Contains IntSet
Instance details Defined in Control.Lens.At Methods contains :: Index IntSet -> Lens' IntSet Bool #
Ord a => Contains (Set a)
Instance details Defined in Control.Lens.At Methods contains :: Index (Set a) -> Lens' (Set a) Bool #
(Eq a, Hashable a) => Contains (HashSet a)
Instance details Defined in Control.Lens.At Methods contains :: Index (HashSet a) -> Lens' (HashSet a) Bool #

type family Index s :: Type #

Instances

type Index ByteString
Instance details Defined in Control.Lens.At type Index ByteString = Int
type Index ByteString
Instance details Defined in Control.Lens.At type Index ByteString = Int64
type Index Text
Instance details Defined in Control.Lens.At type Index Text = Int
type Index Text
Instance details Defined in Control.Lens.At type Index Text = Int64
type Index IntSet
Instance details Defined in Control.Lens.At type Index IntSet = Int
type Index [a]
Instance details Defined in Control.Lens.At type Index [a] = Int
type Index (Maybe a)
Instance details Defined in Control.Lens.At type Index (Maybe a) = ()
type Index (Set a)
Instance details Defined in Control.Lens.At type Index (Set a) = a
type Index (Identity a)
Instance details Defined in Control.Lens.At type Index (Identity a) = ()
type Index (Vector a)
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
type Index (Complex a)
Instance details Defined in Control.Lens.At type Index (Complex a) = Int
type Index (NonEmpty a)
Instance details Defined in Control.Lens.At type Index (NonEmpty a) = Int
type Index (Vector a)
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
type Index (IntMap a)
Instance details Defined in Control.Lens.At type Index (IntMap a) = Int
type Index (Tree a)
Instance details Defined in Control.Lens.At type Index (Tree a) = [Int]
type Index (Seq a)
Instance details Defined in Control.Lens.At type Index (Seq a) = Int
type Index (Vector a)
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
type Index (V2 a)
Instance details Defined in Linear.V2 type Index (V2 a) = E V2
type Index (V3 a)
Instance details Defined in Linear.V3 type Index (V3 a) = E V3
type Index (Vector a)
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
type Index (HashSet a)
Instance details Defined in Control.Lens.At type Index (HashSet a) = a
type Index (Plucker a)
Instance details Defined in Linear.Plucker type Index (Plucker a) = E Plucker
type Index (Quaternion a)
Instance details Defined in Linear.Quaternion type Index (Quaternion a) = E Quaternion
type Index (V0 a)
Instance details Defined in Linear.V0 type Index (V0 a) = E V0
type Index (V4 a)
Instance details Defined in Linear.V4 type Index (V4 a) = E V4
type Index (V1 a)
Instance details Defined in Linear.V1 type Index (V1 a) = E V1
type Index (e -> a)
Instance details Defined in Control.Lens.At type Index (e -> a) = e
type Index (a, b)
Instance details Defined in Control.Lens.At type Index (a, b) = Int
type Index (Map k a)
Instance details Defined in Control.Lens.At type Index (Map k a) = k
type Index (HashMap k a)
Instance details Defined in Control.Lens.At type Index (HashMap k a) = k
type Index (UArray i e)
Instance details Defined in Control.Lens.At type Index (UArray i e) = i
type Index (Array i e)
Instance details Defined in Control.Lens.At type Index (Array i e) = i
type Index (Style v n)
Instance details Defined in Diagrams.Core.Style type Index (Style v n) = TypeRep
type Index (Point f a)
Instance details Defined in Linear.Affine type Index (Point f a) = Index (f a)
type Index (a, b, c)
Instance details Defined in Control.Lens.At type Index (a, b, c) = Int
type Index (V n a)
Instance details Defined in Linear.V type Index (V n a) = Int
type Index (a, b, c, d)
Instance details Defined in Control.Lens.At type Index (a, b, c, d) = Int
type Index (a, b, c, d, e)
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e) = Int
type Index (a, b, c, d, e, f)
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e, f) = Int
type Index (a, b, c, d, e, f, g)
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e, f, g) = Int
type Index (a, b, c, d, e, f, g, h)
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e, f, g, h) = Int
type Index (a, b, c, d, e, f, g, h, i)
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e, f, g, h, i) = Int

icontains :: Contains m => Index m -> IndexedLens' (Index m) m Bool #

An indexed version of contains.

>>> IntSet.fromList [1,2,3,4] ^@. icontains 3
(3,True)

>>> IntSet.fromList [1,2,3,4] ^@. icontains 5
(5,False)

>>> IntSet.fromList [1,2,3,4] & icontains 3 %@~ \i x -> if odd i then not x else x
fromList [1,2,4]

>>> IntSet.fromList [1,2,3,4] & icontains 3 %@~ \i x -> if even i then not x else x
fromList [1,2,3,4]

iix :: Ixed m => Index m -> IndexedTraversal' (Index m) m (IxValue m) #

An indexed version of ix.

>>> Seq.fromList [a,b,c,d] & iix 2 %@~ f'
fromList [a,b,f' 2 c,d]

>>> Seq.fromList [a,b,c,d] & iix 2 .@~ h
fromList [a,b,h 2,d]

>>> Seq.fromList [a,b,c,d] ^@? iix 2
Just (2,c)

>>> Seq.fromList [] ^@? iix 2
Nothing

ixAt :: At m => Index m -> Traversal' m (IxValue m) #

A definition of ix for types with an At instance. This is the default if you don't specify a definition for ix.

sans :: At m => Index m -> m -> m #

Delete the value associated with a key in a Map-like container

sans k = at k .~ Nothing

iat :: At m => Index m -> IndexedLens' (Index m) m (Maybe (IxValue m)) #

An indexed version of at.

>>> Map.fromList [(1,"world")] ^@. iat 1
(1,Just "world")

>>> iat 1 %@~ (\i x -> if odd i then Just "hello" else Nothing) $ Map.empty
fromList [(1,"hello")]

>>> iat 2 %@~ (\i x -> if odd i then Just "hello" else Nothing) $ Map.empty
fromList []

makePrisms #

Arguments

:: Name	Type constructor name
-> DecsQ

Generate a Prism for each constructor of a data type. Isos generated when possible. Reviews are created for constructors with existentially quantified constructors and GADTs.

e.g.

data FooBarBaz a
  = Foo Int
  | Bar a
  | Baz Int Char
makePrisms ''FooBarBaz

will create

_Foo :: Prism' (FooBarBaz a) Int
_Bar :: Prism (FooBarBaz a) (FooBarBaz b) a b
_Baz :: Prism' (FooBarBaz a) (Int, Char)

makeClassyPrisms #

Arguments

:: Name	Type constructor name
-> DecsQ

Generate a Prism for each constructor of a data type and combine them into a single class. No Isos are created. Reviews are created for constructors with existentially quantified constructors and GADTs.

e.g.

data FooBarBaz a
  = Foo Int
  | Bar a
  | Baz Int Char
makeClassyPrisms ''FooBarBaz

will create

class AsFooBarBaz s a | s -> a where
  _FooBarBaz :: Prism' s (FooBarBaz a)
  _Foo :: Prism' s Int
  _Bar :: Prism' s a
  _Baz :: Prism' s (Int,Char)

  _Foo = _FooBarBaz . _Foo
  _Bar = _FooBarBaz . _Bar
  _Baz = _FooBarBaz . _Baz

instance AsFooBarBaz (FooBarBaz a) a

Generate an As class of prisms. Names are selected by prefixing the constructor name with an underscore. Constructors with multiple fields will construct Prisms to tuples of those fields.

type ClassyNamer #

Arguments

= Name	Name of the data type that lenses are being generated for.
-> Maybe (Name, Name)	Names of the class and the main method it generates, respectively.

The optional rule to create a class and method around a monomorphic data type. If this naming convention is provided, it generates a "classy" lens.

data DefName #

Name to give to generated field optics.

Constructors

TopName Name	Simple top-level definiton name
MethodName Name Name	makeFields-style class name and method name

Instances

Eq DefName
Instance details Defined in Control.Lens.Internal.FieldTH Methods (==) :: DefName -> DefName -> Bool # (/=) :: DefName -> DefName -> Bool #
Ord DefName
Instance details Defined in Control.Lens.Internal.FieldTH Methods compare :: DefName -> DefName -> Ordering # (<) :: DefName -> DefName -> Bool # (<=) :: DefName -> DefName -> Bool # (>) :: DefName -> DefName -> Bool # (>=) :: DefName -> DefName -> Bool # max :: DefName -> DefName -> DefName # min :: DefName -> DefName -> DefName #
Show DefName
Instance details Defined in Control.Lens.Internal.FieldTH Methods showsPrec :: Int -> DefName -> ShowS # show :: DefName -> String # showList :: [DefName] -> ShowS #

type FieldNamer #

Arguments

= Name	Name of the data type that lenses are being generated for.
-> [Name]	Names of all fields (including the field being named) in the data type.
-> Name	Name of the field being named.
-> [DefName]	Name(s) of the lens functions. If empty, no lens is created for that field.

The rule to create function names of lenses for data fields.

Although it's sometimes useful, you won't need the first two arguments most of the time.

data LensRules #

Rules to construct lenses for data fields.

simpleLenses :: Lens' LensRules Bool #

Generate "simple" optics even when type-changing optics are possible. (e.g. Lens' instead of Lens)

generateSignatures :: Lens' LensRules Bool #

Indicate whether or not to supply the signatures for the generated lenses.

Disabling this can be useful if you want to provide a more restricted type signature or if you want to supply hand-written haddocks.

generateUpdateableOptics :: Lens' LensRules Bool #

Generate "updateable" optics when True. When False, Folds will be generated instead of Traversals and Getters will be generated instead of Lenses. This mode is intended to be used for types with invariants which must be maintained by "smart" constructors.

generateLazyPatterns :: Lens' LensRules Bool #

Generate optics using lazy pattern matches. This can allow fields of an undefined value to be initialized with lenses:

data Foo = Foo {_x :: Int, _y :: Bool}
  deriving Show

makeLensesWith (lensRules & generateLazyPatterns .~ True) ''Foo

> undefined & x .~ 8 & y .~ True
Foo {_x = 8, _y = True}

The downside of this flag is that it can lead to space-leaks and code-size/compile-time increases when generated for large records. By default this flag is turned off, and strict optics are generated.

When using lazy optics the strict optic can be recovered by composing with $!:

strictOptic = ($!) . lazyOptic

createClass :: Lens' LensRules Bool #

Create the class if the constructor is Simple and the lensClass rule matches.

lensField :: Lens' LensRules FieldNamer #

Lens' to access the convention for naming fields in our LensRules.

lensClass :: Lens' LensRules ClassyNamer #

Lens' to access the option for naming "classy" lenses.

lensRules :: LensRules #

Rules for making fairly simple partial lenses, ignoring the special cases for isomorphisms and traversals, and not making any classes. It uses underscoreNoPrefixNamer.

underscoreNoPrefixNamer :: FieldNamer #

A FieldNamer that strips the _ off of the field name, lowercases the name, and skips the field if it doesn't start with an '_'.

lensRulesFor #

Arguments

:: [(String, String)]	(Field Name, Definition Name)
-> LensRules

Construct a LensRules value for generating top-level definitions using the given map from field names to definition names.

lookingupNamer :: [(String, String)] -> FieldNamer #

Create a FieldNamer from explicit pairings of (fieldName, lensName).

mappingNamer #

Arguments

:: (String -> [String])	A function that maps a `fieldName` to `lensName`s.
-> FieldNamer

Create a FieldNamer from a mapping function. If the function returns [], it creates no lens for the field.

classyRules :: LensRules #

Rules for making lenses and traversals that precompose another Lens.

classyRules_ :: LensRules #

A LensRules used by makeClassy_.

makeLenses :: Name -> DecsQ #

Build lenses (and traversals) with a sensible default configuration.

e.g.

data FooBar
  = Foo { _x, _y :: Int }
  | Bar { _x :: Int }
makeLenses ''FooBar

will create

x :: Lens' FooBar Int
x f (Foo a b) = (\a' -> Foo a' b) <$> f a
x f (Bar a)   = Bar <$> f a
y :: Traversal' FooBar Int
y f (Foo a b) = (\b' -> Foo a  b') <$> f b
y _ c@(Bar _) = pure c

makeLenses = makeLensesWith lensRules

makeClassy :: Name -> DecsQ #

Make lenses and traversals for a type, and create a class when the type has no arguments.

e.g.

data Foo = Foo { _fooX, _fooY :: Int }
makeClassy ''Foo

will create

class HasFoo t where
  foo :: Lens' t Foo
  fooX :: Lens' t Int
  fooX = foo . go where go f (Foo x y) = (\x' -> Foo x' y) <$> f x
  fooY :: Lens' t Int
  fooY = foo . go where go f (Foo x y) = (\y' -> Foo x y') <$> f y
instance HasFoo Foo where
  foo = id

makeClassy = makeLensesWith classyRules

makeClassy_ :: Name -> DecsQ #

Make lenses and traversals for a type, and create a class when the type has no arguments. Works the same as makeClassy except that (a) it expects that record field names do not begin with an underscore, (b) all record fields are made into lenses, and (c) the resulting lens is prefixed with an underscore.

makeLensesFor :: [(String, String)] -> Name -> DecsQ #

Derive lenses and traversals, specifying explicit pairings of (fieldName, lensName).

If you map multiple names to the same label, and it is present in the same constructor then this will generate a Traversal.

e.g.

makeLensesFor [("_foo", "fooLens"), ("baz", "lbaz")] ''Foo
makeLensesFor [("_barX", "bar"), ("_barY", "bar")] ''Bar

makeClassyFor :: String -> String -> [(String, String)] -> Name -> DecsQ #

Derive lenses and traversals, using a named wrapper class, and specifying explicit pairings of (fieldName, traversalName).

Example usage:

makeClassyFor "HasFoo" "foo" [("_foo", "fooLens"), ("bar", "lbar")] ''Foo

makeLensesWith :: LensRules -> Name -> DecsQ #

Build lenses with a custom configuration.

declareLenses :: DecsQ -> DecsQ #

Make lenses for all records in the given declaration quote. All record syntax in the input will be stripped off.

e.g.

declareLenses [d|
  data Foo = Foo { fooX, fooY :: Int }
    deriving Show
  |]

will create

data Foo = Foo Int Int deriving Show
fooX, fooY :: Lens' Foo Int

declareLensesFor :: [(String, String)] -> DecsQ -> DecsQ #

Similar to makeLensesFor, but takes a declaration quote.

declareClassy :: DecsQ -> DecsQ #

For each record in the declaration quote, make lenses and traversals for it, and create a class when the type has no arguments. All record syntax in the input will be stripped off.

e.g.

declareClassy [d|
  data Foo = Foo { fooX, fooY :: Int }
    deriving Show
  |]

will create

data Foo = Foo Int Int deriving Show
class HasFoo t where
  foo :: Lens' t Foo
instance HasFoo Foo where foo = id
fooX, fooY :: HasFoo t => Lens' t Int

declareClassyFor :: [(String, (String, String))] -> [(String, String)] -> DecsQ -> DecsQ #

Similar to makeClassyFor, but takes a declaration quote.

declarePrisms :: DecsQ -> DecsQ #

Generate a Prism for each constructor of each data type.

e.g.

declarePrisms [d|
  data Exp = Lit Int | Var String | Lambda{ bound::String, body::Exp }
  |]

will create

data Exp = Lit Int | Var String | Lambda { bound::String, body::Exp }
_Lit :: Prism' Exp Int
_Var :: Prism' Exp String
_Lambda :: Prism' Exp (String, Exp)

declareWrapped :: DecsQ -> DecsQ #

Build Wrapped instance for each newtype.

declareFields :: DecsQ -> DecsQ #

 declareFields = declareLensesWith defaultFieldRules

declareLensesWith :: LensRules -> DecsQ -> DecsQ #

Declare lenses for each records in the given declarations, using the specified LensRules. Any record syntax in the input will be stripped off.

makeWrapped :: Name -> DecsQ #

Build Wrapped instance for a given newtype

underscoreFields :: LensRules #

Field rules for fields in the form _prefix_fieldname

underscoreNamer :: FieldNamer #

A FieldNamer for underscoreFields.

camelCaseFields :: LensRules #

Field rules for fields in the form prefixFieldname or _prefixFieldname If you want all fields to be lensed, then there is no reason to use an _ before the prefix. If any of the record fields leads with an _ then it is assume a field without an _ should not have a lens created.

Note: The prefix must be the same as the typename (with the first letter lowercased). This is a change from lens versions before lens 4.5. If you want the old behaviour, use makeLensesWith abbreviatedFields

camelCaseNamer :: FieldNamer #

A FieldNamer for camelCaseFields.

classUnderscoreNoPrefixFields :: LensRules #

Field rules for fields in the form _fieldname (the leading underscore is mandatory).

Note: The primary difference to camelCaseFields is that for classUnderscoreNoPrefixFields the field names are not expected to be prefixed with the type name. This might be the desired behaviour when the DuplicateRecordFields extension is enabled.

classUnderscoreNoPrefixNamer :: FieldNamer #

A FieldNamer for classUnderscoreNoPrefixFields.

abbreviatedFields :: LensRules #

Field rules fields in the form prefixFieldname or _prefixFieldname If you want all fields to be lensed, then there is no reason to use an _ before the prefix. If any of the record fields leads with an _ then it is assume a field without an _ should not have a lens created.

Note that prefix may be any string of characters that are not uppercase letters. (In particular, it may be arbitrary string of lowercase letters and numbers) This is the behavior that defaultFieldRules had in lens 4.4 and earlier.

abbreviatedNamer :: FieldNamer #

A FieldNamer for abbreviatedFields.

makeFields :: Name -> DecsQ #

Generate overloaded field accessors.

e.g

data Foo a = Foo { _fooX :: Int, _fooY :: a }
newtype Bar = Bar { _barX :: Char }
makeFields ''Foo
makeFields ''Bar

will create

_fooXLens :: Lens' (Foo a) Int
_fooYLens :: Lens (Foo a) (Foo b) a b
class HasX s a | s -> a where
  x :: Lens' s a
instance HasX (Foo a) Int where
  x = _fooXLens
class HasY s a | s -> a where
  y :: Lens' s a
instance HasY (Foo a) a where
  y = _fooYLens
_barXLens :: Iso' Bar Char
instance HasX Bar Char where
  x = _barXLens

For details, see camelCaseFields.

makeFields = makeLensesWith defaultFieldRules

makeFieldsNoPrefix :: Name -> DecsQ #

Generate overloaded field accessors based on field names which are only prefixed with an underscore (e.g. _name), not additionally with the type name (e.g. _fooName).

This might be the desired behaviour in case the DuplicateRecordFields language extension is used in order to get rid of the necessity to prefix each field name with the type name.

As an example:

data Foo a  = Foo { _x :: Int, _y :: a }
newtype Bar = Bar { _x :: Char }
makeFieldsNoPrefix ''Foo
makeFieldsNoPrefix ''Bar

will create classes

class HasX s a | s -> a where
  x :: Lens' s a
class HasY s a | s -> a where
  y :: Lens' s a

together with instances

instance HasX (Foo a) Int
instance HasY (Foo a) a where
instance HasX Bar Char where

For details, see classUnderscoreNoPrefixFields.

makeFieldsNoPrefix = makeLensesWith classUnderscoreNoPrefixFields

defaultFieldRules :: LensRules #

class Profunctor (p :: Type -> Type -> Type) where #

Formally, the class Profunctor represents a profunctor from Hask -> Hask.

Intuitively it is a bifunctor where the first argument is contravariant and the second argument is covariant.

You can define a Profunctor by either defining dimap or by defining both lmap and rmap.

If you supply dimap, you should ensure that:

dimap id id ≡ id

If you supply lmap and rmap, ensure:

lmap id ≡ id
rmap id ≡ id

If you supply both, you should also ensure:

dimap f g ≡ lmap f . rmap g

These ensure by parametricity:

dimap (f . g) (h . i) ≡ dimap g h . dimap f i
lmap (f . g) ≡ lmap g . lmap f
rmap (f . g) ≡ rmap f . rmap g

Minimal complete definition

dimap | lmap, rmap

Methods

dimap :: (a -> b) -> (c -> d) -> p b c -> p a d #

Map over both arguments at the same time.

dimap f g ≡ lmap f . rmap g

lmap :: (a -> b) -> p b c -> p a c #

Map the first argument contravariantly.

lmap f ≡ dimap f id

rmap :: (b -> c) -> p a b -> p a c #

Map the second argument covariantly.

rmap ≡ dimap id

Instances

Profunctor Measured
Instance details Defined in Diagrams.Core.Measure Methods dimap :: (a -> b) -> (c -> d) -> Measured b c -> Measured a d # lmap :: (a -> b) -> Measured b c -> Measured a c # rmap :: (b -> c) -> Measured a b -> Measured a c # (#.) :: Coercible c b => q b c -> Measured a b -> Measured a c # (.#) :: Coercible b a => Measured b c -> q a b -> Measured a c #
Profunctor ReifiedFold
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedFold b c -> ReifiedFold a d # lmap :: (a -> b) -> ReifiedFold b c -> ReifiedFold a c # rmap :: (b -> c) -> ReifiedFold a b -> ReifiedFold a c # (#.) :: Coercible c b => q b c -> ReifiedFold a b -> ReifiedFold a c # (.#) :: Coercible b a => ReifiedFold b c -> q a b -> ReifiedFold a c #
Profunctor ReifiedGetter
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedGetter b c -> ReifiedGetter a d # lmap :: (a -> b) -> ReifiedGetter b c -> ReifiedGetter a c # rmap :: (b -> c) -> ReifiedGetter a b -> ReifiedGetter a c # (#.) :: Coercible c b => q b c -> ReifiedGetter a b -> ReifiedGetter a c # (.#) :: Coercible b a => ReifiedGetter b c -> q a b -> ReifiedGetter a c #
Monad m => Profunctor (Kleisli m)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Kleisli m b c -> Kleisli m a d # lmap :: (a -> b) -> Kleisli m b c -> Kleisli m a c # rmap :: (b -> c) -> Kleisli m a b -> Kleisli m a c # (#.) :: Coercible c b => q b c -> Kleisli m a b -> Kleisli m a c # (.#) :: Coercible b a => Kleisli m b c -> q a b -> Kleisli m a c #
Functor h => Profunctor (OneColonnade h)
Instance details Defined in Colonnade.Encode Methods dimap :: (a -> b) -> (c -> d) -> OneColonnade h b c -> OneColonnade h a d # lmap :: (a -> b) -> OneColonnade h b c -> OneColonnade h a c # rmap :: (b -> c) -> OneColonnade h a b -> OneColonnade h a c # (#.) :: Coercible c b => q b c -> OneColonnade h a b -> OneColonnade h a c # (.#) :: Coercible b a => OneColonnade h b c -> q a b -> OneColonnade h a c #
Functor h => Profunctor (Colonnade h)
Instance details Defined in Colonnade.Encode Methods dimap :: (a -> b) -> (c -> d) -> Colonnade h b c -> Colonnade h a d # lmap :: (a -> b) -> Colonnade h b c -> Colonnade h a c # rmap :: (b -> c) -> Colonnade h a b -> Colonnade h a c # (#.) :: Coercible c b => q b c -> Colonnade h a b -> Colonnade h a c # (.#) :: Coercible b a => Colonnade h b c -> q a b -> Colonnade h a c #
Functor v => Profunctor (Query v)
Instance details Defined in Diagrams.Core.Query Methods dimap :: (a -> b) -> (c -> d) -> Query v b c -> Query v a d # lmap :: (a -> b) -> Query v b c -> Query v a c # rmap :: (b -> c) -> Query v a b -> Query v a c # (#.) :: Coercible c b => q b c -> Query v a b -> Query v a c # (.#) :: Coercible b a => Query v b c -> q a b -> Query v a c #
Profunctor (Indexed i)
Instance details Defined in Control.Lens.Internal.Indexed Methods dimap :: (a -> b) -> (c -> d) -> Indexed i b c -> Indexed i a d # lmap :: (a -> b) -> Indexed i b c -> Indexed i a c # rmap :: (b -> c) -> Indexed i a b -> Indexed i a c # (#.) :: Coercible c b => q b c -> Indexed i a b -> Indexed i a c # (.#) :: Coercible b a => Indexed i b c -> q a b -> Indexed i a c #
Profunctor (ReifiedIndexedFold i)
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedIndexedFold i b c -> ReifiedIndexedFold i a d # lmap :: (a -> b) -> ReifiedIndexedFold i b c -> ReifiedIndexedFold i a c # rmap :: (b -> c) -> ReifiedIndexedFold i a b -> ReifiedIndexedFold i a c # (#.) :: Coercible c b => q b c -> ReifiedIndexedFold i a b -> ReifiedIndexedFold i a c # (.#) :: Coercible b a => ReifiedIndexedFold i b c -> q a b -> ReifiedIndexedFold i a c #
Profunctor (ReifiedIndexedGetter i)
Instance details Defined in Control.Lens.Reified Methods dimap :: (a -> b) -> (c -> d) -> ReifiedIndexedGetter i b c -> ReifiedIndexedGetter i a d # lmap :: (a -> b) -> ReifiedIndexedGetter i b c -> ReifiedIndexedGetter i a c # rmap :: (b -> c) -> ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i a c # (#.) :: Coercible c b => q b c -> ReifiedIndexedGetter i a b -> ReifiedIndexedGetter i a c # (.#) :: Coercible b a => ReifiedIndexedGetter i b c -> q a b -> ReifiedIndexedGetter i a c #
Profunctor p => Profunctor (TambaraSum p)
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> TambaraSum p b c -> TambaraSum p a d # lmap :: (a -> b) -> TambaraSum p b c -> TambaraSum p a c # rmap :: (b -> c) -> TambaraSum p a b -> TambaraSum p a c # (#.) :: Coercible c b => q b c -> TambaraSum p a b -> TambaraSum p a c # (.#) :: Coercible b a => TambaraSum p b c -> q a b -> TambaraSum p a c #
Profunctor (PastroSum p)
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> PastroSum p b c -> PastroSum p a d # lmap :: (a -> b) -> PastroSum p b c -> PastroSum p a c # rmap :: (b -> c) -> PastroSum p a b -> PastroSum p a c # (#.) :: Coercible c b => q b c -> PastroSum p a b -> PastroSum p a c # (.#) :: Coercible b a => PastroSum p b c -> q a b -> PastroSum p a c #
Profunctor (CotambaraSum p)
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> CotambaraSum p b c -> CotambaraSum p a d # lmap :: (a -> b) -> CotambaraSum p b c -> CotambaraSum p a c # rmap :: (b -> c) -> CotambaraSum p a b -> CotambaraSum p a c # (#.) :: Coercible c b => q b c -> CotambaraSum p a b -> CotambaraSum p a c # (.#) :: Coercible b a => CotambaraSum p b c -> q a b -> CotambaraSum p a c #
Profunctor (CopastroSum p)
Instance details Defined in Data.Profunctor.Choice Methods dimap :: (a -> b) -> (c -> d) -> CopastroSum p b c -> CopastroSum p a d # lmap :: (a -> b) -> CopastroSum p b c -> CopastroSum p a c # rmap :: (b -> c) -> CopastroSum p a b -> CopastroSum p a c # (#.) :: Coercible c b => q b c -> CopastroSum p a b -> CopastroSum p a c # (.#) :: Coercible b a => CopastroSum p b c -> q a b -> CopastroSum p a c #
Profunctor p => Profunctor (Tambara p)
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Tambara p b c -> Tambara p a d # lmap :: (a -> b) -> Tambara p b c -> Tambara p a c # rmap :: (b -> c) -> Tambara p a b -> Tambara p a c # (#.) :: Coercible c b => q b c -> Tambara p a b -> Tambara p a c # (.#) :: Coercible b a => Tambara p b c -> q a b -> Tambara p a c #
Profunctor (Pastro p)
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Pastro p b c -> Pastro p a d # lmap :: (a -> b) -> Pastro p b c -> Pastro p a c # rmap :: (b -> c) -> Pastro p a b -> Pastro p a c # (#.) :: Coercible c b => q b c -> Pastro p a b -> Pastro p a c # (.#) :: Coercible b a => Pastro p b c -> q a b -> Pastro p a c #
Profunctor (Cotambara p)
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Cotambara p b c -> Cotambara p a d # lmap :: (a -> b) -> Cotambara p b c -> Cotambara p a c # rmap :: (b -> c) -> Cotambara p a b -> Cotambara p a c # (#.) :: Coercible c b => q b c -> Cotambara p a b -> Cotambara p a c # (.#) :: Coercible b a => Cotambara p b c -> q a b -> Cotambara p a c #
Profunctor (Copastro p)
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Copastro p b c -> Copastro p a d # lmap :: (a -> b) -> Copastro p b c -> Copastro p a c # rmap :: (b -> c) -> Copastro p a b -> Copastro p a c # (#.) :: Coercible c b => q b c -> Copastro p a b -> Copastro p a c # (.#) :: Coercible b a => Copastro p b c -> q a b -> Copastro p a c #
Functor f => Profunctor (Star f)
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Star f b c -> Star f a d # lmap :: (a -> b) -> Star f b c -> Star f a c # rmap :: (b -> c) -> Star f a b -> Star f a c # (#.) :: Coercible c b => q b c -> Star f a b -> Star f a c # (.#) :: Coercible b a => Star f b c -> q a b -> Star f a c #
Functor f => Profunctor (Costar f)
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Costar f b c -> Costar f a d # lmap :: (a -> b) -> Costar f b c -> Costar f a c # rmap :: (b -> c) -> Costar f a b -> Costar f a c # (#.) :: Coercible c b => q b c -> Costar f a b -> Costar f a c # (.#) :: Coercible b a => Costar f b c -> q a b -> Costar f a c #
Arrow p => Profunctor (WrappedArrow p)
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> WrappedArrow p b c -> WrappedArrow p a d # lmap :: (a -> b) -> WrappedArrow p b c -> WrappedArrow p a c # rmap :: (b -> c) -> WrappedArrow p a b -> WrappedArrow p a c # (#.) :: Coercible c b => q b c -> WrappedArrow p a b -> WrappedArrow p a c # (.#) :: Coercible b a => WrappedArrow p b c -> q a b -> WrappedArrow p a c #
Profunctor (Forget r)
Instance details Defined in Data.Profunctor.Types Methods dimap :: (a -> b) -> (c -> d) -> Forget r b c -> Forget r a d # lmap :: (a -> b) -> Forget r b c -> Forget r a c # rmap :: (b -> c) -> Forget r a b -> Forget r a c # (#.) :: Coercible c b => q b c -> Forget r a b -> Forget r a c # (.#) :: Coercible b a => Forget r b c -> q a b -> Forget r a c #
Profunctor (Tagged :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Tagged b c -> Tagged a d # lmap :: (a -> b) -> Tagged b c -> Tagged a c # rmap :: (b -> c) -> Tagged a b -> Tagged a c # (#.) :: Coercible c b => q b c -> Tagged a b -> Tagged a c # (.#) :: Coercible b a => Tagged b c -> q a b -> Tagged a c #
Profunctor ((->) :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> (b -> c) -> a -> d # lmap :: (a -> b) -> (b -> c) -> a -> c # rmap :: (b -> c) -> (a -> b) -> a -> c # (#.) :: Coercible c b => q b c -> (a -> b) -> a -> c # (.#) :: Coercible b a => (b -> c) -> q a b -> a -> c #
Functor h => Profunctor (Cornice h p)
Instance details Defined in Colonnade.Encode Methods dimap :: (a -> b) -> (c -> d) -> Cornice h p b c -> Cornice h p a d # lmap :: (a -> b) -> Cornice h p b c -> Cornice h p a c # rmap :: (b -> c) -> Cornice h p a b -> Cornice h p a c # (#.) :: Coercible c b => q b c -> Cornice h p a b -> Cornice h p a c # (.#) :: Coercible b a => Cornice h p b c -> q a b -> Cornice h p a c #
Functor w => Profunctor (Cokleisli w)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Cokleisli w b c -> Cokleisli w a d # lmap :: (a -> b) -> Cokleisli w b c -> Cokleisli w a c # rmap :: (b -> c) -> Cokleisli w a b -> Cokleisli w a c # (#.) :: Coercible c b => q b c -> Cokleisli w a b -> Cokleisli w a c # (.#) :: Coercible b a => Cokleisli w b c -> q a b -> Cokleisli w a c #
Profunctor (Exchange a b)
Instance details Defined in Control.Lens.Internal.Iso Methods dimap :: (a0 -> b0) -> (c -> d) -> Exchange a b b0 c -> Exchange a b a0 d # lmap :: (a0 -> b0) -> Exchange a b b0 c -> Exchange a b a0 c # rmap :: (b0 -> c) -> Exchange a b a0 b0 -> Exchange a b a0 c # (#.) :: Coercible c b0 => q b0 c -> Exchange a b a0 b0 -> Exchange a b a0 c # (.#) :: Coercible b0 a0 => Exchange a b b0 c -> q a0 b0 -> Exchange a b a0 c #
(Profunctor p, Profunctor q) => Profunctor (Procompose p q)
Instance details Defined in Data.Profunctor.Composition Methods dimap :: (a -> b) -> (c -> d) -> Procompose p q b c -> Procompose p q a d # lmap :: (a -> b) -> Procompose p q b c -> Procompose p q a c # rmap :: (b -> c) -> Procompose p q a b -> Procompose p q a c # (#.) :: Coercible c b => q0 b c -> Procompose p q a b -> Procompose p q a c # (.#) :: Coercible b a => Procompose p q b c -> q0 a b -> Procompose p q a c #
(Profunctor p, Profunctor q) => Profunctor (Rift p q)
Instance details Defined in Data.Profunctor.Composition Methods dimap :: (a -> b) -> (c -> d) -> Rift p q b c -> Rift p q a d # lmap :: (a -> b) -> Rift p q b c -> Rift p q a c # rmap :: (b -> c) -> Rift p q a b -> Rift p q a c # (#.) :: Coercible c b => q0 b c -> Rift p q a b -> Rift p q a c # (.#) :: Coercible b a => Rift p q b c -> q0 a b -> Rift p q a c #
Functor f => Profunctor (Joker f :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Joker f b c -> Joker f a d # lmap :: (a -> b) -> Joker f b c -> Joker f a c # rmap :: (b -> c) -> Joker f a b -> Joker f a c # (#.) :: Coercible c b => q b c -> Joker f a b -> Joker f a c # (.#) :: Coercible b a => Joker f b c -> q a b -> Joker f a c #
Contravariant f => Profunctor (Clown f :: Type -> Type -> Type)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Clown f b c -> Clown f a d # lmap :: (a -> b) -> Clown f b c -> Clown f a c # rmap :: (b -> c) -> Clown f a b -> Clown f a c # (#.) :: Coercible c b => q b c -> Clown f a b -> Clown f a c # (.#) :: Coercible b a => Clown f b c -> q a b -> Clown f a c #
(Profunctor p, Profunctor q) => Profunctor (Sum p q)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Sum p q b c -> Sum p q a d # lmap :: (a -> b) -> Sum p q b c -> Sum p q a c # rmap :: (b -> c) -> Sum p q a b -> Sum p q a c # (#.) :: Coercible c b => q0 b c -> Sum p q a b -> Sum p q a c # (.#) :: Coercible b a => Sum p q b c -> q0 a b -> Sum p q a c #
(Profunctor p, Profunctor q) => Profunctor (Product p q)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Product p q b c -> Product p q a d # lmap :: (a -> b) -> Product p q b c -> Product p q a c # rmap :: (b -> c) -> Product p q a b -> Product p q a c # (#.) :: Coercible c b => q0 b c -> Product p q a b -> Product p q a c # (.#) :: Coercible b a => Product p q b c -> q0 a b -> Product p q a c #
(Functor f, Profunctor p) => Profunctor (Tannen f p)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Tannen f p b c -> Tannen f p a d # lmap :: (a -> b) -> Tannen f p b c -> Tannen f p a c # rmap :: (b -> c) -> Tannen f p a b -> Tannen f p a c # (#.) :: Coercible c b => q b c -> Tannen f p a b -> Tannen f p a c # (.#) :: Coercible b a => Tannen f p b c -> q a b -> Tannen f p a c #
(Profunctor p, Functor f, Functor g) => Profunctor (Biff p f g)
Instance details Defined in Data.Profunctor.Unsafe Methods dimap :: (a -> b) -> (c -> d) -> Biff p f g b c -> Biff p f g a d # lmap :: (a -> b) -> Biff p f g b c -> Biff p f g a c # rmap :: (b -> c) -> Biff p f g a b -> Biff p f g a c # (#.) :: Coercible c b => q b c -> Biff p f g a b -> Biff p f g a c # (.#) :: Coercible b a => Biff p f g b c -> q a b -> Biff p f g a c #

aspect :: (CameraLens l, Floating n) => l n -> n #

The natural aspect ratio of the projection.

module Diagrams.Backend.SVG