| Copyright | (c) 2011-2015 diagrams-lib team (see LICENSE) |
|---|---|
| License | BSD-style (see LICENSE) |
| Maintainer | diagrams-discuss@googlegroups.com |
| Safe Haskell | None |
| Language | Haskell2010 |
Diagrams.Prelude
Description
A module to re-export most of the functionality of the diagrams core and standard library.
Synopsis
- module Diagrams
- module Data.Default.Class
- 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
- 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)
- black :: Num a => Colour a
- module Data.Colour.SRGB
- module Data.Semigroup
- module Linear.Vector
- module Linear.Affine
- module Linear.Metric
- module Data.Active
- class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where
- traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
- class Contravariant (f :: Type -> Type) where
- class Bifunctor (p :: Type -> Type -> Type) where
- bimap :: (a -> b) -> (c -> d) -> p a c -> p b d
- newtype Identity a = Identity {
- runIdentity :: a
- newtype Const a (b :: k) :: forall k. Type -> k -> Type = Const {
- getConst :: a
- data (a :: k) :~: (b :: k) :: forall k. k -> k -> Type where
- (&) :: a -> (a -> b) -> b
- (<&>) :: Functor f => f a -> (a -> b) -> f b
- class Profunctor (p :: Type -> Type -> Type) where
- defaultFieldRules :: LensRules
- makeFieldsNoPrefix :: Name -> DecsQ
- makeFields :: Name -> DecsQ
- abbreviatedNamer :: FieldNamer
- abbreviatedFields :: LensRules
- classUnderscoreNoPrefixNamer :: FieldNamer
- classUnderscoreNoPrefixFields :: LensRules
- camelCaseNamer :: FieldNamer
- camelCaseFields :: LensRules
- underscoreNamer :: FieldNamer
- underscoreFields :: LensRules
- makeWrapped :: Name -> DecsQ
- declareLensesWith :: LensRules -> DecsQ -> DecsQ
- declareFields :: DecsQ -> DecsQ
- declareWrapped :: DecsQ -> DecsQ
- declarePrisms :: DecsQ -> DecsQ
- declareClassyFor :: [(String, (String, String))] -> [(String, String)] -> DecsQ -> DecsQ
- declareClassy :: DecsQ -> DecsQ
- declareLensesFor :: [(String, String)] -> DecsQ -> DecsQ
- declareLenses :: DecsQ -> DecsQ
- makeLensesWith :: LensRules -> Name -> DecsQ
- makeClassyFor :: String -> String -> [(String, String)] -> Name -> DecsQ
- makeLensesFor :: [(String, String)] -> Name -> DecsQ
- makeClassy_ :: Name -> DecsQ
- makeClassy :: Name -> DecsQ
- makeLenses :: Name -> DecsQ
- classyRules_ :: LensRules
- classyRules :: LensRules
- mappingNamer :: (String -> [String]) -> FieldNamer
- lookingupNamer :: [(String, String)] -> FieldNamer
- lensRulesFor :: [(String, String)] -> LensRules
- underscoreNoPrefixNamer :: FieldNamer
- lensRules :: LensRules
- lensClass :: Lens' LensRules ClassyNamer
- lensField :: Lens' LensRules FieldNamer
- createClass :: Lens' LensRules Bool
- generateLazyPatterns :: Lens' LensRules Bool
- generateUpdateableOptics :: Lens' LensRules Bool
- generateSignatures :: Lens' LensRules Bool
- simpleLenses :: Lens' LensRules Bool
- data LensRules
- type FieldNamer = Name -> [Name] -> Name -> [DefName]
- data DefName
- type ClassyNamer = Name -> Maybe (Name, Name)
- makeClassyPrisms :: Name -> DecsQ
- makePrisms :: Name -> DecsQ
- iat :: At m => Index m -> IndexedLens' (Index m) m (Maybe (IxValue m))
- sans :: At m => Index m -> m -> m
- ixAt :: At m => Index m -> Traversal' m (IxValue m)
- iix :: Ixed m => Index m -> IndexedTraversal' (Index m) m (IxValue m)
- icontains :: Contains m => Index m -> IndexedLens' (Index m) m Bool
- type family Index s :: Type
- class Contains m
- type family IxValue m :: Type
- class Ixed m where
- ix :: Index m -> Traversal' m (IxValue m)
- class Ixed m => At m
- class Each s t a b | s -> a, t -> b, s b -> t, t a -> s where
- gplate1 :: (Generic1 f, GPlated1 f (Rep1 f)) => Traversal' (f a) (f a)
- gplate :: (Generic a, GPlated a (Rep a)) => Traversal' a a
- parts :: Plated a => Lens' a [a]
- composOpFold :: Plated a => b -> (b -> b -> b) -> (a -> b) -> a -> b
- para :: Plated a => (a -> [r] -> r) -> a -> r
- paraOf :: Getting (Endo [a]) a a -> (a -> [r] -> r) -> a -> r
- 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]
- holesOn :: Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t]
- holes :: Plated a => a -> [Pretext ((->) :: Type -> Type -> Type) a a a]
- contextsOnOf :: ATraversal s t a a -> ATraversal' a a -> s -> [Context a a t]
- contextsOn :: Plated a => ATraversal s t a a -> s -> [Context a a t]
- contextsOf :: ATraversal' a a -> a -> [Context a a a]
- contexts :: Plated a => a -> [Context a a a]
- transformMOnOf :: Monad m => LensLike (WrappedMonad m) s t a b -> LensLike (WrappedMonad m) a b a b -> (b -> m b) -> s -> m t
- transformMOf :: Monad m => LensLike (WrappedMonad m) a b a b -> (b -> m b) -> a -> m b
- transformMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m a) -> s -> m t
- transformM :: (Monad m, Plated a) => (a -> m a) -> a -> m a
- transformOnOf :: ASetter s t a b -> ASetter a b a b -> (b -> b) -> s -> t
- transformOf :: ASetter a b a b -> (b -> b) -> a -> b
- transformOn :: Plated a => ASetter s t a a -> (a -> a) -> s -> t
- cosmosOnOf :: (Applicative f, Contravariant f) => LensLike' f s a -> LensLike' f a a -> LensLike' f s a
- cosmosOn :: (Applicative f, Contravariant f, Plated a) => LensLike' f s a -> LensLike' f s a
- cosmosOf :: (Applicative f, Contravariant f) => LensLike' f a a -> LensLike' f a a
- cosmos :: Plated a => Fold a a
- universeOnOf :: Getting [a] s a -> Getting [a] a a -> s -> [a]
- universeOn :: Plated a => Getting [a] s a -> s -> [a]
- universeOf :: Getting [a] a a -> a -> [a]
- universe :: Plated a => a -> [a]
- rewriteMOnOf :: Monad m => LensLike (WrappedMonad m) s t a b -> LensLike (WrappedMonad m) a b a b -> (b -> m (Maybe a)) -> s -> m t
- rewriteMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m (Maybe a)) -> s -> m t
- rewriteMOf :: Monad m => LensLike (WrappedMonad m) a b a b -> (b -> m (Maybe a)) -> a -> m b
- rewriteM :: (Monad m, Plated a) => (a -> m (Maybe a)) -> a -> m a
- rewriteOnOf :: ASetter s t a b -> ASetter a b a b -> (b -> Maybe a) -> s -> t
- rewriteOn :: Plated a => ASetter s t a a -> (a -> Maybe a) -> s -> t
- rewriteOf :: ASetter a b a b -> (b -> Maybe a) -> a -> b
- rewrite :: Plated a => (a -> Maybe a) -> a -> a
- deep :: (Conjoined p, Applicative f, Plated s) => Traversing p f s s a b -> Over p f s s a b
- class Plated a where
- plate :: Traversal' a a
- class GPlated a (g :: k -> Type)
- class GPlated1 (f :: k -> Type) (g :: k -> Type)
- type family Zoomed (m :: Type -> Type) :: Type -> Type -> Type
- type family Magnified (m :: Type -> Type) :: Type -> Type -> Type
- 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
- 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
- alaf :: (Functor f, Functor g, Rewrapping s t) => (Unwrapped s -> s) -> (f t -> g s) -> f (Unwrapped t) -> g (Unwrapped s)
- ala :: (Functor f, Rewrapping s t) => (Unwrapped s -> s) -> ((Unwrapped t -> t) -> f s) -> f (Unwrapped s)
- _Unwrapping :: Rewrapping s t => (Unwrapped s -> s) -> Iso (Unwrapped t) (Unwrapped s) t s
- _Wrapping :: Rewrapping s t => (Unwrapped s -> s) -> Iso s t (Unwrapped s) (Unwrapped t)
- _Unwrapping' :: Wrapped s => (Unwrapped s -> s) -> Iso' (Unwrapped s) s
- _Wrapping' :: Wrapped s => (Unwrapped s -> s) -> Iso' s (Unwrapped s)
- op :: Wrapped s => (Unwrapped s -> s) -> s -> Unwrapped s
- _Unwrapped :: Rewrapping s t => Iso (Unwrapped t) (Unwrapped s) t s
- _Wrapped :: Rewrapping s t => Iso s t (Unwrapped s) (Unwrapped t)
- _Unwrapped' :: Wrapped s => Iso' (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)
- pattern Wrapped :: forall s. Rewrapped s s => Unwrapped s -> s
- pattern Unwrapped :: forall t. Rewrapped t t => t -> Unwrapped t
- class Wrapped s where
- class Wrapped s => Rewrapped s t
- class (Rewrapped s t, Rewrapped t s) => Rewrapping s t
- unsnoc :: Snoc s s a a => s -> Maybe (s, a)
- snoc :: Snoc s s a a => s -> a -> s
- (|>) :: Snoc s s a a => s -> a -> s
- _last :: Snoc s s a a => Traversal' s a
- _init :: Snoc s s a a => Traversal' s s
- _tail :: Cons s s a a => Traversal' s s
- _head :: Cons s s a a => Traversal' s a
- uncons :: Cons s s a a => s -> Maybe (a, s)
- cons :: Cons s s a a => a -> s -> s
- (<|) :: Cons s s a a => a -> s -> s
- pattern (:<) :: forall b a. Cons b b a a => a -> b -> b
- pattern (:>) :: forall a b. Snoc a a b b => a -> b -> a
- class Cons s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Snoc s t a b | s -> a, t -> b, s b -> t, t a -> s where
- pattern Empty :: forall s. AsEmpty s => s
- class AsEmpty a where
- coerced :: (Coercible s a, Coercible t b) => Iso s t a b
- seconding :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso (f x s) (g y t) (f x a) (g y b)
- firsting :: (Bifunctor f, Bifunctor g) => AnIso s t a b -> Iso (f s x) (g t y) (f a x) (g b y)
- 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')
- rmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso (p x s) (q y t) (p x a) (q y b)
- lmapping :: (Profunctor p, Profunctor q) => AnIso s t a b -> Iso (p a x) (q b y) (p s x) (q t y)
- 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')
- contramapping :: Contravariant f => AnIso s t a b -> Iso (f a) (f b) (f s) (f t)
- 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)
- magma :: LensLike (Mafic a b) s t a b -> Iso s u (Magma Int t b a) (Magma j u c c)
- involuted :: (a -> a) -> Iso' a a
- reversed :: Reversing a => Iso' a a
- lazy :: Strict lazy strict => Iso' strict lazy
- flipped :: Iso (a -> b -> c) (a' -> b' -> c') (b -> a -> c) (b' -> a' -> c')
- uncurried :: Iso (a -> b -> c) (d -> e -> f) ((a, b) -> c) ((d, e) -> f)
- curried :: Iso ((a, b) -> c) ((d, e) -> f) (a -> b -> c) (d -> e -> f)
- anon :: a -> (a -> Bool) -> Iso' (Maybe a) a
- non' :: APrism' a () -> Iso' (Maybe a) a
- non :: Eq a => a -> Iso' (Maybe a) a
- mapping :: (Functor f, Functor g) => AnIso s t a b -> Iso (f s) (g t) (f a) (g b)
- enum :: Enum a => Iso' Int a
- under :: AnIso s t a b -> (t -> s) -> b -> a
- xplatf :: Optic (Costar f) g s t a b -> (f a -> g b) -> f s -> g t
- xplat :: Optic (Costar ((->) s :: Type -> Type)) g s t a b -> ((s -> a) -> g b) -> g t
- auf :: (Functor f, Functor g) => AnIso s t a b -> (f t -> g s) -> f b -> g a
- au :: Functor f => AnIso s t a b -> ((b -> t) -> f s) -> f a
- cloneIso :: AnIso s t a b -> Iso s t a b
- withIso :: AnIso s t a b -> ((s -> a) -> (b -> t) -> r) -> r
- from :: AnIso s t a b -> Iso b a t s
- iso :: (s -> a) -> (b -> t) -> Iso s t a b
- pattern Strict :: forall s t. Strict s t => t -> s
- pattern Lazy :: forall t s. Strict t s => t -> s
- pattern Swapped :: forall (p :: Type -> Type -> Type) c d. Swapped p => p d c -> p c d
- pattern Reversed :: forall t. Reversing t => t -> t
- pattern List :: forall l. IsList l => [Item l] -> l
- type AnIso s t a b = Exchange a b a (Identity b) -> Exchange a b s (Identity t)
- type AnIso' s a = AnIso s s a a
- class Bifunctor p => Swapped (p :: Type -> Type -> Type) where
- class Strict lazy strict | lazy -> strict, strict -> lazy where
- withEquality :: AnEquality s t a b -> ((s :~: a) -> (b :~: t) -> r) -> r
- fromLeibniz' :: ((s :~: s) -> s :~: a) -> Equality' s a
- fromLeibniz :: (Identical a b a b -> Identical a b s t) -> Equality s t a b
- underEquality :: AnEquality s t a b -> p t s -> p b a
- overEquality :: AnEquality s t a b -> p a b -> p s t
- equality' :: (a :~: b) -> Equality' a b
- equality :: (s :~: a) -> (b :~: t) -> Equality s t a b
- cloneEquality :: AnEquality s t a b -> Equality s t a b
- simple :: Equality' a a
- simply :: (Optic' p f s a -> r) -> Optic' p f s a -> r
- fromEq :: AnEquality s t a b -> Equality b a t s
- mapEq :: AnEquality s t a b -> f s -> f a
- substEq :: AnEquality s t a b -> ((s ~ a) -> (t ~ b) -> r) -> r
- runEq :: AnEquality s t a b -> Identical s t a b
- data Identical (a :: k) (b :: k1) (s :: k) (t :: k1) :: forall k k1. k -> k1 -> k -> k1 -> Type where
- type AnEquality (s :: k1) (t :: k2) (a :: k1) (b :: k2) = Identical a (Proxy b) a (Proxy b) -> Identical a (Proxy b) s (Proxy t)
- type AnEquality' (s :: k2) (a :: k2) = AnEquality s s a a
- 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
- 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)
- ifoldMapByOf :: IndexedFold i t a -> (r -> r -> r) -> r -> (i -> a -> r) -> t -> r
- ifoldMapBy :: FoldableWithIndex i t => (r -> r -> r) -> r -> (i -> a -> r) -> t a -> r
- imapAccumL :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b)
- imapAccumR :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b)
- iforM :: (TraversableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m (t b)
- imapM :: (TraversableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m (t b)
- ifor :: (TraversableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f (t b)
- itoList :: FoldableWithIndex i f => f a -> [(i, a)]
- ifoldlM :: (FoldableWithIndex i f, Monad m) => (i -> b -> a -> m b) -> b -> f a -> m b
- ifoldrM :: (FoldableWithIndex i f, Monad m) => (i -> a -> b -> m b) -> b -> f a -> m b
- ifind :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Maybe (i, a)
- iconcatMap :: FoldableWithIndex i f => (i -> a -> [b]) -> f a -> [b]
- iforM_ :: (FoldableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m ()
- imapM_ :: (FoldableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m ()
- ifor_ :: (FoldableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f ()
- itraverse_ :: (FoldableWithIndex i t, Applicative f) => (i -> a -> f b) -> t a -> f ()
- inone :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
- iall :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
- iany :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
- index :: (Indexable i p, Eq i, Applicative f) => i -> Optical' p (Indexed i) f a a
- icompose :: Indexable p c => (i -> j -> p) -> (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> c a b -> r
- reindexed :: Indexable j p => (i -> j) -> (Indexed i a b -> r) -> p a b -> r
- selfIndex :: Indexable a p => p a fb -> a -> fb
- (<.) :: Indexable i p => (Indexed i s t -> r) -> ((a -> b) -> s -> t) -> p a b -> r
- 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
- class Foldable f => FoldableWithIndex i (f :: Type -> Type) | f -> i where
- 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
- newtype ReifiedLens s t a b = Lens {}
- type ReifiedLens' s a = ReifiedLens s s a a
- newtype ReifiedIndexedLens i s t a b = IndexedLens {
- runIndexedLens :: IndexedLens i s t a b
- type ReifiedIndexedLens' i s a = ReifiedIndexedLens i s s a a
- newtype ReifiedIndexedTraversal i s t a b = IndexedTraversal {
- runIndexedTraversal :: IndexedTraversal i s t a b
- type ReifiedIndexedTraversal' i s a = ReifiedIndexedTraversal i s s a a
- newtype ReifiedTraversal s t a b = Traversal {
- runTraversal :: Traversal s t a b
- type ReifiedTraversal' s a = ReifiedTraversal s s a a
- newtype ReifiedGetter s a = Getter {}
- newtype ReifiedIndexedGetter i s a = IndexedGetter {
- runIndexedGetter :: IndexedGetter i s a
- newtype ReifiedFold s a = Fold {}
- newtype ReifiedIndexedFold i s a = IndexedFold {
- runIndexedFold :: IndexedFold i s a
- newtype ReifiedSetter s t a b = Setter {}
- type ReifiedSetter' s a = ReifiedSetter s s a a
- newtype ReifiedIndexedSetter i s t a b = IndexedSetter {
- runIndexedSetter :: IndexedSetter i s t a b
- type ReifiedIndexedSetter' i s a = ReifiedIndexedSetter i s s a a
- newtype ReifiedIso s t a b = Iso {}
- type ReifiedIso' s a = ReifiedIso s s a a
- newtype ReifiedPrism s t a b = Prism {}
- type ReifiedPrism' s a = ReifiedPrism s s a a
- ilevels :: Applicative f => Traversing (Indexed i) f s t a b -> IndexedLensLike Int f s t (Level i a) (Level j b)
- 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
- 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
- confusing :: Applicative f => LensLike (Curried (Yoneda f) (Yoneda f)) s t a b -> LensLike 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
- 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
- ifailover :: Alternative m => Over (Indexed i) ((,) Any) s t a b -> (i -> a -> b) -> s -> m t
- failover :: Alternative m => LensLike ((,) Any) s t a b -> (a -> b) -> s -> m t
- elements :: Traversable t => (Int -> Bool) -> IndexedTraversal' Int (t a) a
- elementsOf :: Applicative f => LensLike (Indexing f) s t a a -> (Int -> Bool) -> IndexedLensLike Int f s t a a
- element :: Traversable t => Int -> IndexedTraversal' Int (t a) a
- elementOf :: Applicative f => LensLike (Indexing f) s t a a -> Int -> IndexedLensLike Int f s t a a
- ignored :: Applicative f => pafb -> s -> f s
- traversed64 :: Traversable f => IndexedTraversal Int64 (f a) (f b) a b
- traversed1 :: Traversable1 f => IndexedTraversal1 Int (f a) (f b) a b
- traversed :: Traversable f => IndexedTraversal Int (f a) (f b) a b
- imapAccumLOf :: Over (Indexed i) (State acc) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
- imapAccumROf :: Over (Indexed i) (Backwards (State acc)) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
- iforMOf :: (Indexed i a (WrappedMonad m b) -> s -> WrappedMonad m t) -> s -> (i -> a -> m b) -> m t
- imapMOf :: Over (Indexed i) (WrappedMonad m) s t a b -> (i -> a -> m b) -> s -> m t
- iforOf :: (Indexed i a (f b) -> s -> f t) -> s -> (i -> a -> f b) -> f t
- itraverseOf :: (Indexed i a (f b) -> s -> f t) -> (i -> a -> f b) -> s -> f t
- cloneIndexedTraversal1 :: AnIndexedTraversal1 i s t a b -> IndexedTraversal1 i s t a b
- cloneIndexPreservingTraversal1 :: ATraversal1 s t a b -> IndexPreservingTraversal1 s t a b
- cloneTraversal1 :: ATraversal1 s t a b -> Traversal1 s t a b
- cloneIndexedTraversal :: AnIndexedTraversal i s t a b -> IndexedTraversal i s t a b
- cloneIndexPreservingTraversal :: ATraversal s t a b -> IndexPreservingTraversal s t a b
- cloneTraversal :: ATraversal s t a b -> Traversal s t a b
- dropping :: (Conjoined p, Applicative f) => Int -> Over p (Indexing f) s t a a -> Over p f s t a a
- taking :: (Conjoined p, Applicative f) => Int -> Traversing p f s t a a -> Over p f s t a a
- both1 :: Bitraversable1 r => Traversal1 (r a a) (r b b) a b
- both :: Bitraversable r => Traversal (r a a) (r b b) a b
- holes1Of :: Conjoined p => Over p (Bazaar1 p a a) s t a a -> s -> NonEmpty (Pretext p a a t)
- holesOf :: Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t]
- unsafeSingular :: (HasCallStack, Conjoined p, Functor f) => Traversing p f s t a b -> Over p f s t a b
- iunsafePartsOf' :: Over (Indexed i) (Bazaar (Indexed i) a b) s t a b -> IndexedLens [i] s t [a] [b]
- unsafePartsOf' :: ATraversal s t a b -> Lens 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 :: Functor f => Traversing ((->) :: Type -> Type -> Type) f s t a b -> LensLike f s t [a] [b]
- ipartsOf' :: (Indexable [i] p, Functor f) => Over (Indexed i) (Bazaar' (Indexed i) a) 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) => Traversing (Indexed i) f s t a a -> Over p f s t [a] [a]
- partsOf :: Functor f => Traversing ((->) :: Type -> Type -> Type) f s t a a -> LensLike f s t [a] [a]
- iloci :: IndexedTraversal i (Bazaar (Indexed i) a c s) (Bazaar (Indexed i) b c s) a b
- loci :: Traversal (Bazaar ((->) :: Type -> Type -> Type) a c s) (Bazaar ((->) :: Type -> Type -> Type) b c s) a b
- scanl1Of :: LensLike (State (Maybe a)) s t a a -> (a -> a -> a) -> s -> t
- scanr1Of :: LensLike (Backwards (State (Maybe a))) s t a a -> (a -> a -> a) -> s -> t
- mapAccumLOf :: LensLike (State acc) 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)
- transposeOf :: LensLike ZipList s t [a] a -> s -> [t]
- sequenceOf :: LensLike (WrappedMonad m) s t (m b) b -> s -> m t
- forMOf :: LensLike (WrappedMonad m) s t a b -> s -> (a -> m b) -> m t
- mapMOf :: LensLike (WrappedMonad m) s t a b -> (a -> m b) -> s -> m t
- sequenceAOf :: LensLike f s t (f b) b -> s -> f t
- forOf :: LensLike f s t a b -> s -> (a -> f b) -> f t
- traverseOf :: LensLike f s t a b -> (a -> f b) -> s -> f t
- type ATraversal s t a b = LensLike (Bazaar ((->) :: Type -> Type -> Type) a b) s t a b
- type ATraversal' s a = ATraversal s s a a
- type ATraversal1 s t a b = LensLike (Bazaar1 ((->) :: Type -> Type -> Type) a b) s t a b
- type ATraversal1' s a = ATraversal1 s s a a
- type AnIndexedTraversal i s t a b = Over (Indexed i) (Bazaar (Indexed i) a b) s t a b
- type AnIndexedTraversal1 i s t a b = Over (Indexed i) (Bazaar1 (Indexed i) a b) s t a b
- type AnIndexedTraversal' i s a = AnIndexedTraversal i s s a a
- type AnIndexedTraversal1' i s a = AnIndexedTraversal1 i s s a a
- 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 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 a = Traversing p f s s a a
- type Traversing1' (p :: Type -> Type -> Type) (f :: Type -> Type) s a = Traversing1 p f s s a a
- class Ord k => TraverseMin k (m :: Type -> Type) | m -> k where
- traverseMin :: IndexedTraversal' k (m v) v
- class Ord k => TraverseMax k (m :: Type -> Type) | m -> k where
- traverseMax :: IndexedTraversal' k (m v) v
- foldMapByOf :: Fold s a -> (r -> r -> r) -> r -> (a -> r) -> s -> r
- foldByOf :: Fold s a -> (a -> a -> a) -> a -> 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
- 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
- ifiltered :: (Indexable i p, Applicative f) => (i -> a -> Bool) -> Optical' p (Indexed i) f a a
- findIndicesOf :: IndexedGetting i (Endo [i]) s a -> (a -> Bool) -> s -> [i]
- findIndexOf :: IndexedGetting i (First i) s a -> (a -> Bool) -> s -> Maybe i
- elemIndicesOf :: Eq a => IndexedGetting i (Endo [i]) s a -> a -> s -> [i]
- elemIndexOf :: Eq a => IndexedGetting i (First i) s a -> a -> s -> Maybe i
- (^@?!) :: HasCallStack => s -> IndexedGetting i (Endo (i, a)) s a -> (i, a)
- (^@?) :: s -> IndexedGetting i (Endo (Maybe (i, a))) s a -> Maybe (i, a)
- (^@..) :: s -> IndexedGetting i (Endo [(i, a)]) s a -> [(i, a)]
- itoListOf :: IndexedGetting i (Endo [(i, a)]) s a -> s -> [(i, a)]
- ifoldlMOf :: Monad m => IndexedGetting i (Endo (r -> m r)) s a -> (i -> r -> a -> m r) -> r -> s -> m r
- ifoldrMOf :: Monad m => IndexedGetting i (Dual (Endo (r -> m r))) s a -> (i -> a -> r -> m r) -> r -> s -> m r
- ifoldlOf' :: IndexedGetting i (Endo (r -> r)) s a -> (i -> r -> a -> r) -> r -> s -> r
- ifoldrOf' :: IndexedGetting i (Dual (Endo (r -> r))) s a -> (i -> a -> r -> r) -> r -> s -> r
- ifindMOf :: Monad m => IndexedGetting i (Endo (m (Maybe a))) s a -> (i -> a -> m Bool) -> s -> m (Maybe a)
- ifindOf :: IndexedGetting i (Endo (Maybe a)) s a -> (i -> a -> Bool) -> s -> Maybe a
- iconcatMapOf :: IndexedGetting i [r] s a -> (i -> a -> [r]) -> s -> [r]
- iforMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> s -> (i -> a -> m r) -> m ()
- imapMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> (i -> a -> m r) -> s -> m ()
- iforOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> s -> (i -> a -> f r) -> f ()
- itraverseOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> (i -> a -> f r) -> s -> f ()
- inoneOf :: IndexedGetting i Any s a -> (i -> a -> Bool) -> s -> Bool
- iallOf :: IndexedGetting i All s a -> (i -> a -> Bool) -> s -> Bool
- ianyOf :: IndexedGetting i Any s a -> (i -> a -> Bool) -> s -> Bool
- ifoldlOf :: IndexedGetting i (Dual (Endo r)) s a -> (i -> r -> a -> r) -> r -> s -> r
- ifoldrOf :: IndexedGetting i (Endo r) s a -> (i -> a -> r -> r) -> r -> s -> r
- ifoldMapOf :: IndexedGetting i m s a -> (i -> a -> m) -> s -> m
- ipreuses :: MonadState s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r)
- preuses :: MonadState s m => Getting (First r) s a -> (a -> r) -> m (Maybe r)
- ipreuse :: MonadState s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a))
- preuse :: MonadState s m => Getting (First a) s a -> m (Maybe a)
- ipreviews :: MonadReader s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r)
- previews :: MonadReader s m => Getting (First r) s a -> (a -> r) -> m (Maybe r)
- ipreview :: MonadReader s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a))
- preview :: MonadReader s m => Getting (First a) s a -> m (Maybe a)
- ipre :: IndexedGetting i (First (i, a)) s a -> IndexPreservingGetter s (Maybe (i, a))
- pre :: Getting (First a) s a -> IndexPreservingGetter s (Maybe a)
- hasn't :: Getting All s a -> s -> Bool
- has :: Getting Any s a -> s -> Bool
- foldlMOf :: Monad m => Getting (Endo (r -> m r)) s a -> (r -> a -> m r) -> r -> s -> m r
- foldrMOf :: Monad m => Getting (Dual (Endo (r -> m r))) s a -> (a -> r -> m r) -> r -> s -> m r
- foldl1Of' :: HasCallStack => Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a
- foldr1Of' :: HasCallStack => Getting (Dual (Endo (Endo (Maybe a)))) s a -> (a -> a -> a) -> s -> a
- foldlOf' :: Getting (Endo (Endo r)) s a -> (r -> a -> r) -> r -> s -> r
- foldrOf' :: Getting (Dual (Endo (Endo r))) s a -> (a -> r -> r) -> r -> s -> r
- foldl1Of :: HasCallStack => Getting (Dual (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a
- foldr1Of :: HasCallStack => Getting (Endo (Maybe a)) s a -> (a -> a -> a) -> s -> a
- lookupOf :: Eq k => Getting (Endo (Maybe v)) s (k, v) -> k -> s -> Maybe v
- findMOf :: Monad m => Getting (Endo (m (Maybe a))) s a -> (a -> m Bool) -> s -> m (Maybe a)
- findOf :: Getting (Endo (Maybe a)) s a -> (a -> Bool) -> s -> Maybe a
- minimumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a
- maximumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a
- minimum1Of :: Ord a => Getting (Min a) s a -> s -> a
- minimumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a
- maximum1Of :: Ord a => Getting (Max a) s a -> s -> a
- maximumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a
- notNullOf :: Getting Any s a -> s -> Bool
- nullOf :: Getting All s a -> s -> Bool
- last1Of :: Getting (Last a) s a -> s -> a
- lastOf :: Getting (Rightmost a) s a -> s -> Maybe a
- first1Of :: Getting (First a) s a -> s -> a
- firstOf :: Getting (Leftmost a) s a -> s -> Maybe a
- (^?!) :: HasCallStack => s -> Getting (Endo a) s a -> a
- (^?) :: s -> Getting (First a) s a -> Maybe a
- lengthOf :: Getting (Endo (Endo Int)) s a -> s -> Int
- concatOf :: Getting [r] s [r] -> s -> [r]
- concatMapOf :: Getting [r] s a -> (a -> [r]) -> s -> [r]
- notElemOf :: Eq a => Getting All s a -> a -> s -> Bool
- elemOf :: Eq a => Getting Any s a -> a -> s -> Bool
- msumOf :: MonadPlus m => Getting (Endo (m a)) s (m a) -> s -> m a
- asumOf :: Alternative f => Getting (Endo (f a)) s (f a) -> s -> f a
- sequenceOf_ :: Monad m => Getting (Sequenced a m) s (m a) -> s -> m ()
- forMOf_ :: Monad m => Getting (Sequenced r m) s a -> s -> (a -> m r) -> m ()
- mapMOf_ :: Monad m => Getting (Sequenced r m) s a -> (a -> m r) -> s -> m ()
- sequence1Of_ :: Functor f => Getting (TraversedF a f) s (f a) -> s -> f ()
- for1Of_ :: Functor f => Getting (TraversedF r f) s a -> s -> (a -> f r) -> f ()
- traverse1Of_ :: Functor f => Getting (TraversedF r f) s a -> (a -> f r) -> s -> f ()
- sequenceAOf_ :: Functor f => Getting (Traversed a f) s (f a) -> s -> f ()
- forOf_ :: Functor f => Getting (Traversed r f) s a -> s -> (a -> f r) -> f ()
- traverseOf_ :: Functor f => Getting (Traversed r f) s a -> (a -> f r) -> s -> f ()
- sumOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a
- productOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a
- noneOf :: Getting Any s a -> (a -> Bool) -> s -> Bool
- allOf :: Getting All s a -> (a -> Bool) -> s -> Bool
- anyOf :: Getting Any s a -> (a -> Bool) -> s -> Bool
- orOf :: Getting Any s Bool -> s -> Bool
- andOf :: Getting All s Bool -> s -> Bool
- (^..) :: s -> Getting (Endo [a]) s a -> [a]
- toNonEmptyOf :: Getting (NonEmptyDList a) s a -> s -> NonEmpty a
- toListOf :: Getting (Endo [a]) s a -> s -> [a]
- foldlOf :: Getting (Dual (Endo r)) s a -> (r -> a -> r) -> r -> s -> r
- foldrOf :: Getting (Endo r) s a -> (a -> r -> r) -> r -> s -> r
- foldOf :: Getting a s a -> s -> a
- foldMapOf :: Getting r s a -> (a -> r) -> s -> r
- lined :: Applicative f => IndexedLensLike' Int f String String
- worded :: Applicative f => IndexedLensLike' Int f String String
- 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
- 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
- filteredBy :: (Indexable i p, Applicative f) => Getting (First i) a i -> p a (f a) -> a -> f a
- filtered :: (Choice p, Applicative f) => (a -> Bool) -> Optic' p f a a
- iterated :: Apply f => (a -> a) -> LensLike' f a a
- unfolded :: (b -> Maybe (a, b)) -> Fold b a
- cycled :: Apply f => LensLike f s t a b -> LensLike f s t a b
- replicated :: Int -> Fold a a
- repeated :: Apply f => LensLike' f a a
- folded64 :: Foldable f => IndexedFold Int64 (f a) a
- folded :: Foldable f => IndexedFold Int (f a) a
- 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
- foldring :: (Contravariant f, Applicative f) => ((a -> f a -> f a) -> f a -> s -> f a) -> LensLike f s t a b
- ifolding :: (Foldable f, Indexable i p, Contravariant g, Applicative g) => (s -> f (i, a)) -> Over p g s t a b
- folding :: Foldable f => (s -> f a) -> Fold s a
- _Show :: (Read a, Show a) => Prism' String a
- nearly :: a -> (a -> Bool) -> Prism' a ()
- only :: Eq a => a -> Prism' a ()
- _Void :: Prism s s a Void
- _Nothing :: Prism' (Maybe a) ()
- _Just :: Prism (Maybe a) (Maybe b) a b
- _Right :: Prism (Either c a) (Either c b) a b
- _Left :: Prism (Either a c) (Either b c) a b
- matching :: APrism s t a b -> s -> Either t a
- isn't :: APrism s t a b -> s -> Bool
- below :: Traversable f => APrism' s a -> Prism' (f s) (f a)
- aside :: APrism s t a b -> Prism (e, s) (e, t) (e, a) (e, 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)
- prism' :: (b -> s) -> (s -> Maybe a) -> Prism s s a b
- prism :: (b -> t) -> (s -> Either t a) -> Prism s t a b
- clonePrism :: APrism s t a b -> Prism s t a b
- withPrism :: APrism s t a b -> ((b -> t) -> (s -> Either t a) -> r) -> r
- type APrism s t a b = Market a b a (Identity b) -> Market a b s (Identity t)
- type APrism' s a = APrism s s a a
- reuses :: MonadState b m => AReview t b -> (t -> r) -> m r
- reuse :: MonadState b m => AReview t b -> m t
- reviews :: MonadReader b m => AReview t b -> (t -> r) -> m r
- review :: MonadReader b m => AReview t b -> m t
- re :: AReview t b -> Getter b t
- un :: (Profunctor p, Bifunctor p, Functor f) => Getting a s a -> Optic' p f a s
- unto :: (Profunctor p, Bifunctor p, Functor f) => (b -> t) -> Optic p f s t a b
- getting :: (Profunctor p, Profunctor q, Functor f, Contravariant f) => Optical p q f s t a b -> Optical' p q f s a
- (^@.) :: s -> IndexedGetting i (i, a) s a -> (i, a)
- iuses :: MonadState 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)
- iviews :: MonadReader s m => IndexedGetting i r s a -> (i -> a -> r) -> m r
- iview :: MonadReader s m => IndexedGetting i (i, a) s a -> m (i, a)
- ilistenings :: MonadWriter w m => IndexedGetting i v w u -> (i -> u -> v) -> m a -> m (a, v)
- listenings :: MonadWriter w m => Getting v w u -> (u -> v) -> m a -> m (a, v)
- ilistening :: MonadWriter w m => IndexedGetting i (i, u) w u -> m a -> m (a, (i, u))
- listening :: MonadWriter w m => Getting u w u -> m a -> m (a, u)
- uses :: MonadState s m => LensLike' (Const r :: Type -> Type) s a -> (a -> r) -> m r
- use :: MonadState s m => Getting a s a -> m a
- (^.) :: s -> Getting a s a -> a
- views :: MonadReader s m => LensLike' (Const r :: Type -> Type) s a -> (a -> r) -> m r
- view :: MonadReader s m => Getting a s a -> m a
- ilike :: (Indexable i p, Contravariant f, Functor f) => i -> a -> Over' p f s a
- like :: (Profunctor p, Contravariant f, Functor f) => a -> Optic' p f s a
- ito :: (Indexable i p, Contravariant f) => (s -> (i, a)) -> Over' p f s a
- to :: (Profunctor p, Contravariant f) => (s -> a) -> Optic' p f s a
- type Getting r s a = (a -> Const r a) -> s -> Const r s
- type IndexedGetting i m s a = Indexed i a (Const m a) -> s -> Const m s
- type Accessing (p :: Type -> Type -> Type) m s a = p a (Const m a) -> s -> Const m s
- _19' :: Field19 s t a b => Lens s t a b
- _18' :: Field18 s t a b => Lens s t a b
- _17' :: Field17 s t a b => Lens s t a b
- _16' :: Field16 s t a b => Lens s t a b
- _15' :: Field15 s t a b => Lens s t a b
- _14' :: Field14 s t a b => Lens s t a b
- _13' :: Field13 s t a b => Lens s t a b
- _12' :: Field12 s t a b => Lens s t a b
- _11' :: Field11 s t a b => Lens s t a b
- _10' :: Field10 s t a b => Lens s t a b
- _9' :: Field9 s t a b => Lens s t a b
- _8' :: Field8 s t a b => Lens s t a b
- _7' :: Field7 s t a b => Lens s t a b
- _6' :: Field6 s t a b => Lens s t a b
- _5' :: Field5 s t a b => Lens s t a b
- _4' :: Field4 s t a b => Lens s t a b
- _3' :: Field3 s t a b => Lens s t a b
- _2' :: Field2 s t a b => Lens s t a b
- _1' :: Field1 s t a b => Lens s t a b
- class Field1 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field2 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field3 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field4 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field5 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field6 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field7 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field8 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field9 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field10 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field11 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field12 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field13 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field14 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field15 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field16 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field17 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field18 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- class Field19 s t a b | s -> a, t -> b, s b -> t, t a -> s where
- fusing :: Functor f => LensLike (Yoneda f) s t a b -> LensLike f s t a b
- last1 :: Traversable1 t => Lens' (t a) a
- head1 :: Traversable1 t => Lens' (t a) a
- united :: Lens' a ()
- devoid :: Over p f Void Void a b
- (<#=) :: MonadState s m => ALens s s a b -> b -> m b
- (<#~) :: ALens s t a b -> b -> s -> (b, t)
- (#%%=) :: MonadState s m => ALens s s a b -> (a -> (r, b)) -> m r
- (<#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m b
- (<#%~) :: ALens s t a b -> (a -> b) -> s -> (b, t)
- (#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m ()
- (#=) :: MonadState s m => ALens s s a b -> b -> m ()
- (#%%~) :: Functor f => ALens s t a b -> (a -> f b) -> s -> f t
- (#%~) :: ALens s t a b -> (a -> b) -> s -> t
- (#~) :: ALens s t a b -> b -> s -> t
- storing :: ALens s t a b -> b -> s -> t
- (^#) :: s -> ALens s t a b -> a
- (<<%@=) :: MonadState s m => Over (Indexed i) ((,) a) s s a b -> (i -> a -> b) -> m a
- (<%@=) :: MonadState s m => Over (Indexed i) ((,) b) s s a b -> (i -> a -> b) -> m b
- (%%@=) :: MonadState s m => Over (Indexed i) ((,) r) s s a b -> (i -> a -> (r, b)) -> m r
- (%%@~) :: Over (Indexed i) f s t a b -> (i -> a -> f b) -> s -> f t
- (<<%@~) :: Over (Indexed i) ((,) a) s t a b -> (i -> a -> b) -> s -> (a, t)
- (<%@~) :: Over (Indexed i) ((,) b) s t a b -> (i -> a -> b) -> s -> (b, t)
- overA :: Arrow ar => LensLike (Context a b) s t a b -> ar a b -> ar s t
- (<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r
- (<<>~) :: Monoid m => LensLike ((,) m) s t m m -> m -> s -> (m, t)
- (<<~) :: MonadState s m => ALens s s a b -> m b -> m b
- (<<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r
- (<<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
- (<<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
- (<<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m a
- (<<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a
- (<<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a
- (<<//=) :: (MonadState s m, Fractional 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, Num a) => LensLike' ((,) a) s a -> a -> m a
- (<<?=) :: MonadState s m => LensLike ((,) a) s s a (Maybe b) -> b -> m a
- (<<.=) :: MonadState s m => LensLike ((,) a) s s a b -> b -> m a
- (<<%=) :: (Strong p, MonadState s m) => Over p ((,) a) s s a b -> p a b -> 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, Floating a) => LensLike' ((,) a) s a -> a -> m a
- (<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a
- (<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a
- (<//=) :: (MonadState s m, Fractional 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, Num a) => LensLike' ((,) a) s a -> a -> m a
- (<%=) :: MonadState s m => LensLike ((,) b) s s a b -> (a -> b) -> m b
- (<<<>~) :: Monoid r => LensLike' ((,) r) s r -> r -> s -> (r, s)
- (<<&&~) :: LensLike' ((,) Bool) s Bool -> Bool -> s -> (Bool, s)
- (<<||~) :: LensLike' ((,) Bool) s Bool -> Bool -> s -> (Bool, s)
- (<<**~) :: Floating a => LensLike' ((,) a) s a -> a -> s -> (a, s)
- (<<^^~) :: (Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> s -> (a, s)
- (<<^~) :: (Num a, Integral e) => LensLike' ((,) a) s a -> e -> s -> (a, s)
- (<<//~) :: Fractional 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)
- (<<+~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s)
- (<<?~) :: LensLike ((,) a) s t a (Maybe b) -> b -> s -> (a, t)
- (<<.~) :: LensLike ((,) a) s t a b -> b -> s -> (a, t)
- (<<%~) :: LensLike ((,) a) s t a b -> (a -> b) -> s -> (a, t)
- (<&&~) :: LensLike ((,) Bool) s t Bool Bool -> Bool -> s -> (Bool, t)
- (<||~) :: LensLike ((,) Bool) s t Bool Bool -> Bool -> s -> (Bool, t)
- (<**~) :: Floating a => LensLike ((,) a) s t a a -> a -> s -> (a, t)
- (<^^~) :: (Fractional a, Integral e) => LensLike ((,) a) s t a a -> e -> s -> (a, t)
- (<^~) :: (Num a, Integral e) => LensLike ((,) a) s t a a -> e -> s -> (a, t)
- (<//~) :: Fractional 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)
- (<+~) :: Num a => LensLike ((,) a) s t a a -> a -> s -> (a, t)
- (<%~) :: LensLike ((,) b) s t a b -> (a -> b) -> s -> (b, t)
- cloneIndexedLens :: AnIndexedLens i s t a b -> IndexedLens i s t a b
- cloneIndexPreservingLens :: ALens s t a b -> IndexPreservingLens s t a b
- cloneLens :: ALens s t a b -> Lens s t a b
- locus :: IndexedComonadStore p => Lens (p a c s) (p b c s) 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')
- chosen :: IndexPreservingLens (Either a a) (Either b b) a 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
- (??) :: Functor f => f (a -> b) -> a -> f b
- (%%=) :: MonadState s m => Over p ((,) r) s s a b -> p a (r, b) -> m r
- (%%~) :: LensLike f s t a b -> (a -> f b) -> s -> f t
- (&~) :: s -> State s a -> s
- ilens :: (s -> (i, a)) -> (s -> b -> t) -> IndexedLens i s t a b
- iplens :: (s -> a) -> (s -> b -> t) -> IndexPreservingLens s t a b
- withLens :: ALens s t a b -> ((s -> a) -> (s -> b -> t) -> r) -> r
- lens :: (s -> a) -> (s -> b -> t) -> Lens s t a b
- type ALens s t a b = LensLike (Pretext ((->) :: Type -> Type -> Type) a b) s t a b
- type ALens' s a = ALens 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 AnIndexedLens' i s a = AnIndexedLens i s s a a
- imapOf :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t
- mapOf :: ASetter s t a b -> (a -> b) -> s -> t
- assignA :: Arrow p => ASetter s t a b -> p s b -> p s t
- (.@=) :: MonadState s m => AnIndexedSetter i s s a b -> (i -> 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 -> a -> b) -> m ()
- (.@~) :: AnIndexedSetter i s t a b -> (i -> b) -> s -> t
- (%@~) :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t
- isets :: ((i -> a -> b) -> s -> t) -> IndexedSetter i s t a b
- iset :: AnIndexedSetter i s t a b -> (i -> b) -> s -> t
- iover :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t
- ilocally :: MonadReader s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m r -> m r
- locally :: MonadReader s m => ASetter s s a b -> (a -> b) -> m r -> m r
- icensoring :: MonadWriter w m => IndexedSetter i w w u v -> (i -> u -> v) -> m a -> m a
- censoring :: MonadWriter w m => Setter w w u v -> (u -> v) -> m a -> m a
- ipassing :: MonadWriter w m => IndexedSetter i w w u v -> m (a, i -> u -> v) -> m a
- passing :: MonadWriter w m => Setter w w u v -> m (a, u -> v) -> m a
- scribe :: (MonadWriter t m, Monoid s) => ASetter s t a b -> b -> m ()
- (<>=) :: (MonadState s m, Monoid a) => ASetter' s a -> a -> m ()
- (<>~) :: Monoid a => ASetter s t a a -> a -> s -> t
- (<?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m b
- (<.=) :: MonadState s m => ASetter s s a b -> b -> m b
- (<~) :: MonadState s m => ASetter s s a b -> m b -> m ()
- (||=) :: MonadState s m => ASetter' s Bool -> Bool -> m ()
- (&&=) :: MonadState s m => ASetter' s Bool -> Bool -> m ()
- (**=) :: (MonadState s m, Floating a) => ASetter' s a -> a -> m ()
- (^^=) :: (MonadState s m, Fractional a, Integral e) => ASetter' s a -> e -> m ()
- (^=) :: (MonadState s m, Num a, Integral e) => ASetter' s a -> e -> m ()
- (//=) :: (MonadState s m, Fractional 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, Num a) => ASetter' s a -> a -> m ()
- (?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m ()
- modifying :: MonadState s m => ASetter s s a b -> (a -> b) -> m ()
- (%=) :: MonadState s m => ASetter s s a b -> (a -> b) -> m ()
- (.=) :: MonadState s m => ASetter s s a b -> b -> m ()
- assign :: MonadState s m => ASetter s s a b -> b -> m ()
- (&&~) :: ASetter s t Bool Bool -> Bool -> s -> t
- (||~) :: ASetter s t Bool Bool -> Bool -> s -> t
- (**~) :: Floating a => ASetter s t a a -> a -> s -> t
- (^^~) :: (Fractional a, Integral e) => ASetter s t a a -> e -> s -> t
- (^~) :: (Num a, Integral e) => ASetter s t a a -> e -> s -> t
- (//~) :: Fractional 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
- (+~) :: Num a => ASetter s t a a -> a -> s -> t
- (<?~) :: ASetter s t a (Maybe b) -> b -> s -> (b, t)
- (<.~) :: ASetter s t a b -> b -> s -> (b, t)
- (?~) :: ASetter s t a (Maybe b) -> b -> s -> t
- (.~) :: ASetter s t a b -> b -> s -> t
- (%~) :: ASetter s t a b -> (a -> b) -> s -> t
- set' :: ASetter' s a -> a -> s -> s
- set :: ASetter s t a b -> b -> s -> t
- over :: ASetter s t a b -> (a -> b) -> s -> t
- cloneIndexedSetter :: AnIndexedSetter i s t a b -> IndexedSetter i s t a b
- cloneIndexPreservingSetter :: ASetter s t a b -> IndexPreservingSetter s t a b
- cloneSetter :: ASetter s t a b -> 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
- setting :: ((a -> b) -> s -> t) -> IndexPreservingSetter s t a b
- contramapped :: Contravariant f => Setter (f b) (f a) a b
- lifted :: Monad m => Setter (m a) (m b) a b
- mapped :: Functor f => Setter (f a) (f b) a b
- type ASetter s t a b = (a -> Identity b) -> s -> Identity t
- type ASetter' s a = ASetter s s a a
- type AnIndexedSetter i s t a b = Indexed i a (Identity b) -> s -> Identity t
- type AnIndexedSetter' i s a = AnIndexedSetter i s s a a
- type Setting (p :: Type -> Type -> Type) s t a b = p a (Identity b) -> s -> Identity t
- type Setting' (p :: Type -> Type -> Type) s a = Setting p s s a a
- type Lens s t a b = forall (f :: Type -> Type). Functor f => (a -> f b) -> s -> f t
- type Lens' s a = Lens 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 IndexedLens' i s a = IndexedLens i 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 IndexPreservingLens' s a = IndexPreservingLens s s a a
- type Traversal s t a b = forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t
- type Traversal' s a = Traversal s s a a
- type Traversal1 s t a b = forall (f :: Type -> Type). Apply f => (a -> f b) -> s -> f t
- type Traversal1' s a = Traversal1 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 IndexedTraversal' i s a = IndexedTraversal 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 IndexedTraversal1' i s a = IndexedTraversal1 i 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 IndexPreservingTraversal' s a = IndexPreservingTraversal 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 IndexPreservingTraversal1' s a = IndexPreservingTraversal1 s s a a
- type Setter s t a b = forall (f :: Type -> Type). Settable f => (a -> f b) -> s -> f t
- type Setter' s a = Setter 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 IndexedSetter' i s a = IndexedSetter i 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 IndexPreservingSetter' s a = IndexPreservingSetter 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 Iso' s a = Iso s s a a
- type Review t b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Choice p, Bifunctor p, Settable f) => Optic' p f t b
- type AReview t b = Optic' (Tagged :: Type -> Type -> Type) Identity t b
- 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 Prism' s a = Prism 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 Equality' (s :: k2) (a :: k2) = Equality s s a a
- type As (a :: k2) = Equality' a a
- type Getter s a = forall (f :: Type -> Type). (Contravariant f, Functor f) => (a -> f a) -> 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 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 Fold s a = forall (f :: Type -> Type). (Contravariant f, Applicative f) => (a -> f a) -> 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 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 Fold1 s a = forall (f :: Type -> Type). (Contravariant f, Apply f) => (a -> f a) -> 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 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 Simple (f :: k -> k -> k1 -> k1 -> k2) (s :: k) (a :: k1) = 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 Optic' (p :: k1 -> k -> Type) (f :: k1 -> k) (s :: k1) (a :: k1) = Optic p 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 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 LensLike (f :: k -> Type) s (t :: k) a (b :: k) = (a -> f b) -> s -> f t
- type LensLike' (f :: Type -> Type) s a = LensLike 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 IndexedLensLike' i (f :: Type -> Type) s a = IndexedLensLike i 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 Over' (p :: Type -> Type -> Type) (f :: Type -> Type) s a = Over p f s s a a
- class (Applicative f, Distributive f, Traversable f) => Settable (f :: Type -> Type)
- retagged :: (Profunctor p, Bifunctor p) => p a b -> p s b
- class (Profunctor p, Bifunctor p) => Reviewable (p :: Type -> Type -> Type)
- data Magma i t b a
- data Level i a
- class Reversing t where
- reversing :: t -> t
- newtype Bazaar (p :: Type -> Type -> Type) a b t = Bazaar {
- runBazaar :: forall (f :: Type -> Type). Applicative f => p a (f b) -> f t
- type Bazaar' (p :: Type -> Type -> Type) a = Bazaar 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 Bazaar1' (p :: Type -> Type -> Type) a = Bazaar1 p a a
- data Context a b t = Context (b -> t) a
- type Context' a = Context a a
- asIndex :: (Indexable i p, Contravariant f, Functor f) => p i (f i) -> Indexed i s (f s)
- withIndex :: (Indexable i p, Functor f) => p (i, s) (f (j, t)) -> Indexed i s (f t)
- indexing64 :: Indexable Int64 p => ((a -> Indexing64 f b) -> s -> Indexing64 f t) -> p a (f b) -> s -> f t
- indexing :: Indexable Int p => ((a -> Indexing f b) -> s -> Indexing f t) -> p a (f b) -> s -> f t
- 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
- class Conjoined p => Indexable i (p :: Type -> Type -> Type)
- newtype Indexed i a b = Indexed {
- runIndexed :: i -> a -> b
- data Traversed a (f :: Type -> Type)
- data Sequenced a (m :: Type -> Type)
- data Leftmost a
- data Rightmost a
- class (Foldable1 t, Traversable t) => Traversable1 (t :: Type -> Type) where
- foldBy :: Foldable t => (a -> a -> a) -> a -> t a -> a
- foldMapBy :: Foldable t => (r -> r -> r) -> r -> (a -> r) -> t a -> r
- 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)
- sequenceBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> t (f a) -> f (t a)
- class Profunctor p => Choice (p :: Type -> Type -> Type) where
- class Functor f => Applicative (f :: Type -> Type) where
- (*>) :: Applicative f => f a -> f b -> f b
- (<*) :: Applicative f => f a -> f b -> f a
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- (<$) :: Functor f => a -> f b -> f a
- liftA :: Applicative f => (a -> b) -> f a -> f b
- liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c
- liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
Diagrams library
Exports from this library for working with diagrams.
module Diagrams
Convenience re-exports from other packages
module Data.Default.Class
For representing and operating on colors.
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.
colourConvert :: (Fractional b, Real a) => Colour a -> Colour b #
Change the type used to represent the colour coordinates.
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 | |
Defined in Data.Colour.Internal | |
| ColourOps Colour | |
| Eq a => Eq (Colour a) | |
| Num a => Semigroup (Colour a) | |
| Num a => Monoid (Colour a) | |
| a ~ Double => Color (Colour a) Source # | |
Defined in Diagrams.Attributes Methods toAlphaColour :: Colour a -> AlphaColour Double Source # fromAlphaColour :: AlphaColour Double -> Colour a Source # | |
| Parseable (Colour Double) Source # | Parse |
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
class ColourOps (f :: Type -> Type) where #
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 | |
| ColourOps AlphaColour | |
Defined in Data.Colour.Internal Methods over :: Num a => AlphaColour a -> AlphaColour a -> AlphaColour a # darken :: Num a => a -> AlphaColour a -> AlphaColour a # | |
A large list of color names.
yellowgreen :: (Ord a, Floating a) => Colour a #
whitesmoke :: (Ord a, Floating a) => Colour a #
springgreen :: (Ord a, Floating a) => Colour a #
sandybrown :: (Ord a, Floating a) => Colour a #
saddlebrown :: (Ord a, Floating a) => Colour a #
powderblue :: (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 #
palegoldenrod :: (Ord a, Floating a) => Colour a #
navajowhite :: (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 #
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 #
lightgreen :: (Ord a, Floating a) => Colour a #
lightgoldenrodyellow :: (Ord a, Floating a) => Colour a #
lightcoral :: (Ord a, Floating a) => Colour a #
lemonchiffon :: (Ord a, Floating a) => Colour a #
lavenderblush :: (Ord a, Floating a) => Colour a #
greenyellow :: (Ord a, Floating a) => Colour a #
ghostwhite :: (Ord a, Floating a) => Colour a #
forestgreen :: (Ord a, Floating a) => Colour a #
floralwhite :: (Ord a, Floating a) => Colour a #
dodgerblue :: (Ord a, Floating a) => Colour a #
deepskyblue :: (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 #
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 #
darkgoldenrod :: (Ord a, Floating a) => Colour a #
cornflowerblue :: (Ord a, Floating a) => Colour a #
chartreuse :: (Ord a, Floating a) => Colour a #
blueviolet :: (Ord a, Floating a) => Colour a #
blanchedalmond :: (Ord a, Floating a) => Colour a #
aquamarine :: (Ord a, Floating a) => Colour a #
antiquewhite :: (Ord a, Floating a) => Colour a #
Specify your own colours.
module Data.Colour.SRGB
Semigroups and monoids show up all over the place, so things from Data.Semigroup and Data.Monoid often come in handy.
module Data.Semigroup
For computing with vectors.
module Linear.Vector
For computing with points and vectors.
module Linear.Affine
For computing with dot products and norm.
module Linear.Metric
For working with Active (i.e. animated) things.
module Data.Active
Most of the lens package. The following functions are not exported from lens because they either conflict with diagrams or may conflict with other libraries:
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 .for every applicative transformationtraversef =traverse(t . f)t- identity
traverseIdentity = Identity- composition
traverse(Compose .fmapg . f) = Compose .fmap(traverseg) .traversef
A definition of sequenceA must satisfy the following laws:
- naturality
t .for every applicative transformationsequenceA=sequenceA.fmaptt- identity
sequenceA.fmapIdentity = Identity- composition
sequenceA.fmapCompose = Compose .fmapsequenceA.sequenceA
where an applicative transformation is a function
t :: (Applicative f, Applicative g) => f a -> g a
preserving the Applicative operations, i.e.
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
Functorinstance,fmapshould be equivalent to traversal with the identity applicative functor (fmapDefault). - In the
Foldableinstance,foldMapshould be equivalent to traversal with a constant applicative functor (foldMapDefault).
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
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
Instances
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:
bimapidid≡id
If you supply first and second, ensure:
firstid≡idsecondid≡id
If you supply both, you should also ensure:
bimapf g ≡firstf.secondg
These ensure by parametricity:
bimap(f.g) (h.i) ≡bimapf h.bimapg ifirst(f.g) ≡firstf.firstgsecond(f.g) ≡secondf.secondg
Since: base-4.8.0.0
Methods
Instances
Identity functor and monad. (a non-strict monad)
Since: base-4.8.0.0
Constructors
| Identity | |
Fields
| |
Instances
newtype Const a (b :: k) :: forall k. Type -> k -> Type #
The Const functor.
Instances
| Generic1 (Const a :: k -> Type) | |
| Bitraversable (Const :: Type -> Type -> Type) | Since: base-4.10.0.0 |
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 |
| Bifunctor (Const :: Type -> Type -> Type) | Since: base-4.8.0.0 |
| Eq2 (Const :: Type -> Type -> Type) | Since: base-4.9.0.0 |
| Ord2 (Const :: Type -> Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
| Read2 (Const :: Type -> Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Const a b) # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Const a b] # liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Const a b) # liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Const a b] # | |
| Show2 (Const :: Type -> Type -> Type) | Since: base-4.9.0.0 |
| Biapplicative (Const :: Type -> Type -> Type) | |
Defined in Data.Biapplicative | |
| Hashable2 (Const :: Type -> Type -> Type) | |
Defined in Data.Hashable.Class | |
| Bitraversable1 (Const :: Type -> Type -> Type) | |
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) | |
| Semigroupoid (Const :: Type -> Type -> Type) | |
| Functor (Const m :: Type -> Type) | Since: base-2.1 |
| Monoid m => Applicative (Const m :: Type -> Type) | Since: base-2.0.1 |
| Foldable (Const m :: Type -> Type) | Since: base-4.7.0.0 |
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 # elem :: Eq a => a -> Const m a -> Bool # maximum :: Ord a => Const m a -> a # minimum :: Ord a => Const m a -> a # | |
| Traversable (Const m :: Type -> Type) | Since: base-4.7.0.0 |
| Semigroup m => Apply (Const m :: Type -> Type) | |
| Contravariant (Const a :: Type -> Type) | |
| Eq a => Eq1 (Const a :: Type -> Type) | Since: base-4.9.0.0 |
| Ord a => Ord1 (Const a :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
| Read a => Read1 (Const a :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Const a a0) # liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Const a a0] # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Const a a0) # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Const a a0] # | |
| Show a => Show1 (Const a :: Type -> Type) | Since: base-4.9.0.0 |
| Hashable a => Hashable1 (Const a :: Type -> Type) | |
Defined in Data.Hashable.Class | |
| Bounded a => Bounded (Const a b) | Since: base-4.9.0.0 |
| Enum a => Enum (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods succ :: Const a b -> Const a b # pred :: Const a b -> 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 |
| Floating a => Floating (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods 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 # | |
| Fractional a => Fractional (Const a b) | Since: base-4.9.0.0 |
| Integral a => Integral (Const a b) | Since: base-4.9.0.0 |
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) # | |
| (Typeable k, Data a, Typeable b) => Data (Const a b) | Since: base-4.10.0.0 |
Defined in Data.Data Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Const a b -> c (Const a b) # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Const a b) # toConstr :: Const a b -> Constr # dataTypeOf :: Const a b -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Const a b)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Const a b)) # gmapT :: (forall b0. Data b0 => b0 -> b0) -> Const a b -> Const a b # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Const a b -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Const a b -> r # gmapQ :: (forall d. Data d => d -> u) -> Const a b -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Const a b -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b) # | |
| Num a => Num (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
| Ord a => Ord (Const a b) | Since: base-4.9.0.0 |
| Read a => Read (Const a b) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Real a => Real (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods toRational :: Const a b -> Rational # | |
| RealFloat a => RealFloat (Const a b) | Since: base-4.9.0.0 |
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 # isInfinite :: Const a b -> Bool # isDenormalized :: Const a b -> Bool # isNegativeZero :: Const a b -> Bool # | |
| RealFrac a => RealFrac (Const a b) | Since: base-4.9.0.0 |
| Show a => Show (Const a b) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Ix a => Ix (Const a b) | Since: base-4.9.0.0 |
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 |
Defined in Data.String Methods fromString :: String -> Const a b # | |
| Generic (Const a b) | |
| Semigroup a => Semigroup (Const a b) | Since: base-4.9.0.0 |
| Monoid a => Monoid (Const a b) | Since: base-4.9.0.0 |
| Storable a => Storable (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
| Bits a => Bits (Const a b) | Since: base-4.9.0.0 |
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 # 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 # 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 # | |
| FiniteBits a => FiniteBits (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods finiteBitSize :: Const a b -> Int # countLeadingZeros :: Const a b -> Int # countTrailingZeros :: Const a b -> Int # | |
| Hashable a => Hashable (Const a b) | |
Defined in Data.Hashable.Class | |
| Prim a => Prim (Const a b) | Since: primitive-0.6.5.0 |
Defined in Data.Primitive.Types Methods sizeOf# :: Const a b -> Int# # alignment# :: Const a b -> Int# # indexByteArray# :: ByteArray# -> Int# -> Const a b # readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (#State# s, Const a b#) # writeByteArray# :: MutableByteArray# s -> Int# -> Const a b -> State# s -> State# s # setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Const a b -> State# s -> State# s # indexOffAddr# :: Addr# -> Int# -> Const a b # readOffAddr# :: Addr# -> Int# -> State# s -> (#State# s, Const a b#) # writeOffAddr# :: Addr# -> Int# -> Const a b -> State# s -> State# s # setOffAddr# :: Addr# -> Int# -> Int# -> Const a b -> State# s -> State# s # | |
| Wrapped (Const a x) | |
| Newtype (Const a x) | |
| t ~ Const a' x' => Rewrapped (Const a x) t | |
Defined in Control.Lens.Wrapped | |
| type Rep1 (Const a :: k -> Type) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
| type Rep (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
| type Unwrapped (Const a x) | |
Defined in Control.Lens.Wrapped | |
| type O (Const a x) | |
Defined in Control.Newtype.Generics | |
data (a :: k) :~: (b :: k) :: forall k. k -> k -> Type where infix 4 #
Propositional equality. If a :~: b is inhabited by some terminating
value, then the type a is the same as the type b. To use this equality
in practice, pattern-match on the a :~: b to get out the Refl constructor;
in the body of the pattern-match, the compiler knows that a ~ b.
Since: base-4.7.0.0
Instances
| Semigroupoid ((:~:) :: k -> k -> Type) | |
| TestEquality ((:~:) a :: k -> Type) | Since: base-4.7.0.0 |
Defined in Data.Type.Equality | |
| a ~ b => Bounded (a :~: b) | Since: base-4.7.0.0 |
| a ~ b => Enum (a :~: b) | Since: base-4.7.0.0 |
Defined in Data.Type.Equality Methods succ :: (a :~: b) -> a :~: b # pred :: (a :~: b) -> a :~: b # fromEnum :: (a :~: b) -> Int # enumFrom :: (a :~: b) -> [a :~: b] # enumFromThen :: (a :~: b) -> (a :~: b) -> [a :~: b] # enumFromTo :: (a :~: b) -> (a :~: b) -> [a :~: b] # enumFromThenTo :: (a :~: b) -> (a :~: b) -> (a :~: b) -> [a :~: b] # | |
| Eq (a :~: b) | Since: base-4.7.0.0 |
| (a ~ b, Data a) => Data (a :~: b) | Since: base-4.7.0.0 |
Defined in Data.Data Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> (a :~: b) -> c (a :~: b) # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (a :~: b) # toConstr :: (a :~: b) -> Constr # dataTypeOf :: (a :~: b) -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (a :~: b)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (a :~: b)) # gmapT :: (forall b0. Data b0 => b0 -> b0) -> (a :~: b) -> a :~: b # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> (a :~: b) -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> (a :~: b) -> r # gmapQ :: (forall d. Data d => d -> u) -> (a :~: b) -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> (a :~: b) -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> (a :~: b) -> m (a :~: b) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> (a :~: b) -> m (a :~: b) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> (a :~: b) -> m (a :~: b) # | |
| Ord (a :~: b) | Since: base-4.7.0.0 |
Defined in Data.Type.Equality | |
| a ~ b => Read (a :~: b) | Since: base-4.7.0.0 |
| Show (a :~: b) | Since: base-4.7.0.0 |
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:
dimapidid≡id
If you supply lmap and rmap, ensure:
lmapid≡idrmapid≡id
If you supply both, you should also ensure:
dimapf g ≡lmapf.rmapg
These ensure by parametricity:
dimap(f.g) (h.i) ≡dimapg h.dimapf ilmap(f.g) ≡lmapg.lmapfrmap(f.g) ≡rmapf.rmapg
Instances
| Profunctor Measured | |
Defined in Diagrams.Core.Measure | |
| Profunctor ReifiedGetter | |
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 # | |
| Profunctor ReifiedFold | |
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 # | |
| Monad m => Profunctor (Kleisli m) | |
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 v => Profunctor (Query v) | |
Defined in Diagrams.Core.Query | |
| Profunctor (ReifiedIndexedGetter i) | |
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 (ReifiedIndexedFold i) | |
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 (Indexed i) | |
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 p => Profunctor (TambaraSum p) | |
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) | |
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) | |
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) | |
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) | |
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) | |
Defined in Data.Profunctor.Strong | |
| Profunctor (Cotambara p) | |
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) | |
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) | |
Defined in Data.Profunctor.Types | |
| Functor f => Profunctor (Costar f) | |
Defined in Data.Profunctor.Types | |
| Arrow p => Profunctor (WrappedArrow p) | |
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) | |
Defined in Data.Profunctor.Types | |
| Profunctor (Tagged :: Type -> Type -> Type) | |
Defined in Data.Profunctor.Unsafe | |
| Profunctor ((->) :: Type -> Type -> Type) | |
| Functor w => Profunctor (Cokleisli w) | |
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 (Market a b) | |
Defined in Control.Lens.Internal.Prism Methods dimap :: (a0 -> b0) -> (c -> d) -> Market a b b0 c -> Market a b a0 d # lmap :: (a0 -> b0) -> Market a b b0 c -> Market a b a0 c # rmap :: (b0 -> c) -> Market a b a0 b0 -> Market a b a0 c # (#.) :: Coercible c b0 => q b0 c -> Market a b a0 b0 -> Market a b a0 c # (.#) :: Coercible b0 a0 => Market a b b0 c -> q a0 b0 -> Market a b a0 c # | |
| Profunctor (Exchange a b) | |
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 # | |
| (Functor f, Profunctor p) => Profunctor (Cayley f p) | |
Defined in Data.Profunctor.Cayley Methods dimap :: (a -> b) -> (c -> d) -> Cayley f p b c -> Cayley f p a d # lmap :: (a -> b) -> Cayley f p b c -> Cayley f p a c # rmap :: (b -> c) -> Cayley f p a b -> Cayley f p a c # (#.) :: Coercible c b => q b c -> Cayley f p a b -> Cayley f p a c # (.#) :: Coercible b a => Cayley f p b c -> q a b -> Cayley f p a c # | |
| (Profunctor p, Profunctor q) => Profunctor (Procompose p q) | |
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) | |
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) | |
Defined in Data.Profunctor.Unsafe | |
| Contravariant f => Profunctor (Clown f :: Type -> Type -> Type) | |
Defined in Data.Profunctor.Unsafe | |
| (Profunctor p, Profunctor q) => Profunctor (Sum p q) | |
Defined in Data.Profunctor.Unsafe | |
| (Profunctor p, Profunctor q) => Profunctor (Product p q) | |
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) | |
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) | |
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 # | |
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 =makeLensesWithclassUnderscoreNoPrefixFields
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 =makeLensesWithdefaultFieldRules
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.
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.
camelCaseNamer :: FieldNamer #
A FieldNamer for camelCaseFields.
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
underscoreNamer :: FieldNamer #
A FieldNamer for underscoreFields.
underscoreFields :: LensRules #
Field rules for fields in the form _prefix_fieldname
makeWrapped :: Name -> DecsQ #
Build Wrapped instance for a given newtype
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.
declareFields :: DecsQ -> DecsQ #
declareFields =declareLensesWithdefaultFieldRules
declareWrapped :: DecsQ -> DecsQ #
Build Wrapped instance for each newtype.
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)
declareClassyFor :: [(String, (String, String))] -> [(String, String)] -> DecsQ -> DecsQ #
Similar to makeClassyFor, 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 = FooIntIntderivingShowclass HasFoo t where foo ::Lens't Foo instance HasFoo Foo where foo =idfooX, fooY :: HasFoo t =>Lens'tInt
declareLensesFor :: [(String, String)] -> DecsQ -> DecsQ #
Similar to makeLensesFor, but takes a declaration quote.
declareLenses :: DecsQ -> DecsQ #
makeLensesWith :: LensRules -> Name -> DecsQ #
Build lenses with a custom configuration.
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
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")] ''FoomakeLensesFor[("_barX", "bar"), ("_barY", "bar")] ''Bar
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.
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'tIntfooX = foo . go where go f (Foo x y) = (\x' -> Foo x' y) <$> f x fooY ::Lens'tIntfooY = foo . go where go f (Foo x y) = (\y' -> Foo x y') <$> f y instance HasFoo Foo where foo = id
makeClassy=makeLensesWithclassyRules
makeLenses :: Name -> DecsQ #
Build lenses (and traversals) with a sensible default configuration.
e.g.
data FooBar
= Foo { _x, _y :: Int }
| Bar { _x :: Int }
makeLenses ''FooBar
will create
x ::Lens'FooBarIntx f (Foo a b) = (\a' -> Foo a' b) <$> f a x f (Bar a) = Bar <$> f a y ::Traversal'FooBarInty f (Foo a b) = (\b' -> Foo a b') <$> f b y _ c@(Bar _) = pure c
makeLenses=makeLensesWithlensRules
A LensRules used by makeClassy_.
Rules for making lenses and traversals that precompose another Lens.
Arguments
| :: (String -> [String]) | A function that maps a |
| -> FieldNamer |
Create a FieldNamer from a mapping function. If the function
returns [], it creates no lens for the field.
lookingupNamer :: [(String, String)] -> FieldNamer #
Create a FieldNamer from explicit pairings of (fieldName, lensName).
Construct a LensRules value for generating top-level definitions
using the given map from field names to definition names.
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 '_'.
Rules for making fairly simple partial lenses, ignoring the special cases
for isomorphisms and traversals, and not making any classes.
It uses underscoreNoPrefixNamer.
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
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.
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.
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 |
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.
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.
In the event that the name of a data type is also the name of one of its
constructors, the name of the Prism generated for the data type will be
prefixed with an extra _ (if the data type name is prefix) or . (if the
name is infix) to disambiguate it from the Prism for the corresponding
constructor. For example, this code:
data Quux = Quux Int | Fred Bool makeClassyPrisms ''Quux
will create:
class AsQuux s where __Quux :: Prism' s Quux -- Data type prism _Quux :: Prism' s Int -- Constructor prism _Fred :: Prism' s Bool _Quux = __Quux . _Quux _Fred = __Quux . _Fred instance AsQuux Quux
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)
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.emptyfromList [(1,"hello")]
>>>iat 2 %@~ (\i x -> if odd i then Just "hello" else Nothing) $ Map.emptyfromList []
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 .@~ hfromList [a,b,h 2,d]
>>>Seq.fromList [a,b,c,d] ^@? iix 2Just (2,c)
>>>Seq.fromList [] ^@? iix 2Nothing
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 xfromList [1,2,4]
>>>IntSet.fromList [1,2,3,4] & icontains 3 %@~ \i x -> if even i then not x else xfromList [1,2,3,4]
Instances
| type Index ByteString | |
Defined in Control.Lens.At | |
| type Index ByteString | |
Defined in Control.Lens.At | |
| type Index IntSet | |
Defined in Control.Lens.At | |
| type Index Text | |
Defined in Control.Lens.At | |
| type Index Text | |
Defined in Control.Lens.At | |
| type Index [a] | |
Defined in Control.Lens.At | |
| type Index (Maybe a) | |
Defined in Control.Lens.At | |
| type Index (Vector a) | |
Defined in Control.Lens.At | |
| type Index (Complex a) | |
Defined in Control.Lens.At | |
| type Index (Identity a) | |
Defined in Control.Lens.At | |
| type Index (NonEmpty a) | |
Defined in Control.Lens.At | |
| type Index (IntMap a) | |
Defined in Control.Lens.At | |
| type Index (Tree a) | |
Defined in Control.Lens.At | |
| type Index (Seq a) | |
Defined in Control.Lens.At | |
| type Index (Set a) | |
Defined in Control.Lens.At | |
| type Index (Vector a) | |
Defined in Control.Lens.At | |
| type Index (Vector a) | |
Defined in Control.Lens.At | |
| type Index (HashSet a) | |
Defined in Control.Lens.At | |
| type Index (Vector a) | |
Defined in Control.Lens.At | |
| type Index (Plucker a) | |
Defined in Linear.Plucker | |
| type Index (Quaternion a) | |
Defined in Linear.Quaternion | |
| type Index (V0 a) | |
| type Index (V4 a) | |
| type Index (V3 a) | |
| type Index (V2 a) | |
| type Index (V1 a) | |
| type Index (e -> a) | |
Defined in Control.Lens.At type Index (e -> a) = e | |
| type Index (a, b) | |
Defined in Control.Lens.At | |
| type Index (UArray i e) | |
Defined in Control.Lens.At | |
| type Index (Array i e) | |
Defined in Control.Lens.At | |
| type Index (Map k a) | |
Defined in Control.Lens.At | |
| type Index (Style v n) | |
Defined in Diagrams.Core.Style | |
| type Index (Point f a) | |
Defined in Linear.Affine | |
| type Index (HashMap k a) | |
Defined in Control.Lens.At | |
| type Index (a, b, c) | |
Defined in Control.Lens.At | |
| type Index (V n a) | |
| type Index (a, b, c, d) | |
Defined in Control.Lens.At | |
| type Index (a, b, c, d, e) | |
Defined in Control.Lens.At | |
| type Index (a, b, c, d, e, f) | |
Defined in Control.Lens.At | |
| type Index (a, b, c, d, e, f, g) | |
Defined in Control.Lens.At | |
| type Index (a, b, c, d, e, f, g, h) | |
Defined in Control.Lens.At | |
| type Index (a, b, c, d, e, f, g, h, i) | |
Defined in Control.Lens.At | |
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
type family IxValue m :: Type #
Instances
| type IxValue ByteString | |
Defined in Control.Lens.At | |
| type IxValue ByteString | |
Defined in Control.Lens.At | |
| type IxValue IntSet | |
Defined in Control.Lens.At | |
| type IxValue Text | |
Defined in Control.Lens.At | |
| type IxValue Text | |
Defined in Control.Lens.At | |
| type IxValue [a] | |
Defined in Control.Lens.At type IxValue [a] = a | |
| type IxValue (Maybe a) | |
Defined in Control.Lens.At | |
| type IxValue (Vector a) | |
Defined in Control.Lens.At | |
| type IxValue (Identity a) | |
Defined in Control.Lens.At | |
| type IxValue (NonEmpty a) | |
Defined in Control.Lens.At | |
| type IxValue (IntMap a) | |
Defined in Control.Lens.At | |
| type IxValue (Tree a) | |
Defined in Control.Lens.At | |
| type IxValue (Seq a) | |
Defined in Control.Lens.At | |
| type IxValue (Set k) | |
Defined in Control.Lens.At | |
| type IxValue (Vector a) | |
Defined in Control.Lens.At | |
| type IxValue (Vector a) | |
Defined in Control.Lens.At | |
| type IxValue (HashSet k) | |
Defined in Control.Lens.At | |
| type IxValue (Vector a) | |
Defined in Control.Lens.At | |
| type IxValue (Plucker a) | |
Defined in Linear.Plucker | |
| type IxValue (Quaternion a) | |
Defined in Linear.Quaternion | |
| type IxValue (V0 a) | |
| type IxValue (V4 a) | |
| type IxValue (V3 a) | |
| type IxValue (V2 a) | |
| type IxValue (V1 a) | |
| type IxValue (e -> a) | |
Defined in Control.Lens.At type IxValue (e -> a) = a | |
| type IxValue (a, a2) |
|
Defined in Control.Lens.At type IxValue (a, a2) = a | |
| type IxValue (UArray i e) | |
Defined in Control.Lens.At | |
| type IxValue (Array i e) | |
Defined in Control.Lens.At | |
| type IxValue (Map k a) | |
Defined in Control.Lens.At | |
| type IxValue (Style v n) | |
Defined in Diagrams.Core.Style | |
| type IxValue (Point f a) | |
Defined in Linear.Affine | |
| type IxValue (HashMap k a) | |
Defined in Control.Lens.At | |
| type IxValue (a, a2, a3) |
|
Defined in Control.Lens.At type IxValue (a, a2, a3) = a | |
| type IxValue (V n a) | |
| type IxValue (a, a2, a3, a4) |
|
Defined in Control.Lens.At type IxValue (a, a2, a3, a4) = a | |
| type IxValue (a, a2, a3, a4, a5) |
|
Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5) = a | |
| type IxValue (a, a2, a3, a4, a5, a6) |
|
Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6) = a | |
| type IxValue (a, a2, a3, a4, a5, a6, a7) |
|
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) |
|
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) |
|
Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6, a7, a8, a9) = a | |
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 %~ ffromList [a,b,f c,d]
>>>Seq.fromList [a,b,c,d] & ix 2 .~ efromList [a,b,e,d]
>>>Seq.fromList [a,b,c,d] ^? ix 2Just c
>>>Seq.fromList [] ^? ix 2Nothing
Instances
| Ixed ByteString | |
Defined in Control.Lens.At Methods ix :: Index ByteString -> Traversal' ByteString (IxValue ByteString) # | |
| Ixed ByteString | |
Defined in Control.Lens.At Methods ix :: Index ByteString -> Traversal' ByteString (IxValue ByteString) # | |
| Ixed IntSet | |
Defined in Control.Lens.At | |
| Ixed Text | |
Defined in Control.Lens.At | |
| Ixed Text | |
Defined in Control.Lens.At | |
| Ixed [a] | |
Defined in Control.Lens.At Methods ix :: Index [a] -> Traversal' [a] (IxValue [a]) # | |
| Ixed (Maybe a) | |
Defined in Control.Lens.At | |
| Storable a => Ixed (Vector a) | |
Defined in Control.Lens.At | |
| Ixed (Identity a) | |
Defined in Control.Lens.At | |
| Ixed (NonEmpty a) | |
Defined in Control.Lens.At | |
| Ixed (IntMap a) | |
Defined in Control.Lens.At | |
| Ixed (Tree a) | |
Defined in Control.Lens.At | |
| Ixed (Seq a) | |
Defined in Control.Lens.At | |
| Ord k => Ixed (Set k) | |
Defined in Control.Lens.At | |
| Prim a => Ixed (Vector a) | |
Defined in Control.Lens.At | |
| Unbox a => Ixed (Vector a) | |
Defined in Control.Lens.At | |
| (Eq k, Hashable k) => Ixed (HashSet k) | |
Defined in Control.Lens.At | |
| Ixed (Vector a) | |
Defined in Control.Lens.At | |
| Ixed (Plucker a) | |
Defined in Linear.Plucker | |
| Ixed (Quaternion a) | |
Defined in Linear.Quaternion Methods ix :: Index (Quaternion a) -> Traversal' (Quaternion a) (IxValue (Quaternion a)) # | |
| Ixed (V0 a) | |
| Ixed (V4 a) | |
| Ixed (V3 a) | |
| Ixed (V2 a) | |
| Ixed (V1 a) | |
| Eq e => Ixed (e -> a) | |
Defined in Control.Lens.At Methods ix :: Index (e -> a) -> Traversal' (e -> a) (IxValue (e -> a)) # | |
| a ~ a2 => Ixed (a, a2) | |
Defined in Control.Lens.At Methods ix :: Index (a, a2) -> Traversal' (a, a2) (IxValue (a, a2)) # | |
| (IArray UArray e, Ix i) => Ixed (UArray i e) | arr |
Defined in Control.Lens.At | |
| Ix i => Ixed (Array i e) | arr |
Defined in Control.Lens.At | |
| Ord k => Ixed (Map k a) | |
Defined in Control.Lens.At | |
| Ixed (Style v n) | |
Defined in Diagrams.Core.Style | |
| Ixed (f a) => Ixed (Point f a) | |
Defined in Linear.Affine | |
| (Eq k, Hashable k) => Ixed (HashMap k a) | |
Defined in Control.Lens.At | |
| (a ~ a2, a ~ a3) => Ixed (a, a2, a3) | |
Defined in Control.Lens.At Methods ix :: Index (a, a2, a3) -> Traversal' (a, a2, a3) (IxValue (a, a2, a3)) # | |
| Ixed (V n a) | |
| (a ~ a2, a ~ a3, a ~ a4) => Ixed (a, a2, a3, a4) | |
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) | |
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) | |
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) | |
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) | |
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) | |
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)) # | |
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:
ixk ≡atk.traverse
Minimal complete definition
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
Instances
| (a ~ Word8, b ~ Word8) => Each ByteString ByteString a b |
|
Defined in Control.Lens.Each Methods each :: Traversal ByteString ByteString a b # | |
| (a ~ Word8, b ~ Word8) => Each ByteString ByteString a b |
|
Defined in Control.Lens.Each Methods each :: Traversal ByteString ByteString a b # | |
| Each Name Name AName AName | |
| (a ~ Char, b ~ Char) => Each Text Text a b |
|
| (a ~ Char, b ~ Char) => Each Text Text a b |
|
| Each [a] [b] a b |
|
Defined in Control.Lens.Each | |
| Each (Maybe a) (Maybe b) a b |
|
| (Storable a, Storable b) => Each (Vector a) (Vector b) a b |
|
| Each (Complex a) (Complex b) a b |
|
| Each (Identity a) (Identity b) a b |
|
| Each (NonEmpty a) (NonEmpty b) a b |
|
| Each (IntMap a) (IntMap b) a b |
|
| Each (Tree a) (Tree b) a b |
|
| Each (Seq a) (Seq b) a b |
|
| (Prim a, Prim b) => Each (Vector a) (Vector b) a b |
|
| (Unbox a, Unbox b) => Each (Vector a) (Vector b) a b |
|
| Each (Vector a) (Vector b) a b |
|
| Each (Plucker a) (Plucker b) a b | |
| Each (Quaternion a) (Quaternion b) a b | |
Defined in Linear.Quaternion Methods each :: Traversal (Quaternion a) (Quaternion b) a b # | |
| Each (V0 a) (V0 b) a b | |
| Each (V4 a) (V4 b) a b | |
| Each (V3 a) (V3 b) a b | |
| Each (V2 a) (V2 b) a b | |
| Each (V1 a) (V1 b) a b | |
| (a ~ a', b ~ b') => Each (Either a a') (Either b b') a b |
Since: lens-4.18 |
| (a ~ a', b ~ b') => Each (a, a') (b, b') a b |
|
Defined in Control.Lens.Each | |
| (Ix i, IArray UArray a, IArray UArray b, i ~ j) => Each (UArray i a) (UArray j b) a b |
|
| (Ix i, i ~ j) => Each (Array i a) (Array j b) a b |
|
| c ~ d => Each (Map c a) (Map d b) a b |
|
| Traversable f => Each (Point f a) (Point f b) a b | |
| c ~ d => Each (HashMap c a) (HashMap d b) a b |
|
| Each (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n')) Source # | |
| Each (Style v n) (Style v' n') (Attribute v n) (Attribute v' n') | |
| Each (FixedSegment v n) (FixedSegment v' n') (Point v n) (Point v' n') Source # | |
Defined in Diagrams.Segment Methods each :: Traversal (FixedSegment v n) (FixedSegment v' n') (Point v n) (Point v' n') # | |
| (Additive v', Foldable v', Ord n') => Each (BoundingBox v n) (BoundingBox v' n') (Point v n) (Point v' n') Source # | Only valid if the second point is not smaller than the first. |
Defined in Diagrams.BoundingBox Methods each :: Traversal (BoundingBox v n) (BoundingBox 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 |
|
Defined in Control.Lens.Each | |
| Each (V n a) (V n b) a b | |
| Each (Segment c v n) (Segment c v' n') (v n) (v' n') Source # | |
| Each (Offset c v n) (Offset c v' n') (v n) (v' n') Source # | |
| (a ~ a2, a ~ a3, a ~ a4, b ~ b2, b ~ b3, b ~ b4) => Each (a, a2, a3, a4) (b, b2, b3, b4) a b |
|
Defined in Control.Lens.Each | |
| (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 |
|
Defined in Control.Lens.Each | |
| (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 |
|
Defined in Control.Lens.Each | |
| (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 |
|
Defined in Control.Lens.Each | |
| (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 |
|
Defined in Control.Lens.Each | |
| (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 |
|
Defined in Control.Lens.Each | |
composOpFold :: Plated a => b -> (b -> b -> b) -> (a -> b) -> a -> b #
Fold the immediate children of a Plated container.
composOpFoldz c f =foldrOfplate(c.f) z
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.
holesOnOfb 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(Indexedi) a a s]holesOnOf::Traversal's a ->IndexedTraversal'i a a -> s -> [Pretext(Indexedi) a a s]
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(Indexedi) a a s]holesOn::IndexedTraversal'i s a -> s -> [Pretext(Indexedi) 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 =childrenl x==mappos(holesl x) propId x =all(==x) [extractw | w <-holesl x]
holes=holesOfplate
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 -> [Contexta a s]
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.
contextsOnb ≡contextsOnOfbplate
contextsOn::Plateda =>Traversal's a -> s -> [Contexta a s]
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 =universeOfl x==mappos(contextsOfl x) propId l x =all(==x) [extractw | w <-contextsOfl x]
contextsOf::Traversal'a a -> a -> [Contexta a 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::Monadm =>Traversal's a ->Traversal'a 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::Monadm =>Traversal'a 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 #
Transform every element in the tree in a region indicated by a supplied Traversal, in a bottom-up manner, monadically.
transformMOn:: (Monadm,Plateda) =>Traversal's a -> (a -> m a) -> s -> m s
transformM :: (Monad m, Plated a) => (a -> m a) -> a -> m a #
Transform every element in the tree, in a bottom-up manner, monadically.
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 -> stransformOnOf::Setter's a ->Setter'a 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 -> atransformOf::Setter'a a -> (a -> a) -> a -> 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::Plateda =>Traversal's a -> (a -> a) -> s -> stransformOn::Plateda =>Setter's a -> (a -> a) -> s -> s
cosmosOnOf :: (Applicative f, Contravariant f) => LensLike' f s a -> LensLike' f a a -> LensLike' f s a #
cosmosOn :: (Applicative f, Contravariant f, Plated a) => LensLike' f s a -> LensLike' f s a #
cosmosOf :: (Applicative f, Contravariant f) => LensLike' f a a -> LensLike' f a a #
cosmos :: Plated a => Fold a a #
Fold over all transitive descendants of a Plated container, including itself.
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.
toListOfl ≡universeOnOflignored
universeOn :: Plated a => Getting [a] s a -> s -> [a] #
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::Folda a -> a -> [a]
universe :: Plated a => a -> [a] #
Retrieve all of the transitive descendants of a Plated container, including itself.
rewriteMOnOf :: Monad m => LensLike (WrappedMonad m) s t a b -> LensLike (WrappedMonad m) a b a b -> (b -> m (Maybe a)) -> s -> m t #
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.
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.
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.
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 ->Maybea) -> s -> srewriteOnOf::Lens's a ->Lens'a a -> (a ->Maybea) -> s -> srewriteOnOf::Traversal's a ->Traversal'a a -> (a ->Maybea) -> s -> srewriteOnOf::Setter's a ->Setter'a a -> (a ->Maybea) -> s -> s
rewriteOn :: Plated a => ASetter s t a a -> (a -> Maybe a) -> s -> t #
Rewrite recursively over part of a larger structure.
rewriteOn::Plateda =>Iso's a -> (a ->Maybea) -> s -> srewriteOn::Plateda =>Lens's a -> (a ->Maybea) -> s -> srewriteOn::Plateda =>Traversal's a -> (a ->Maybea) -> s -> srewriteOn::Plateda =>ASetter's a -> (a ->Maybea) -> s -> s
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) (universeOfl (rewriteOfl 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 which performs both rewrites until a fixed point.<|> g a
rewriteOf::Iso'a a -> (a ->Maybea) -> a -> arewriteOf::Lens'a a -> (a ->Maybea) -> a -> arewriteOf::Traversal'a a -> (a ->Maybea) -> a -> arewriteOf::Setter'a a -> (a ->Maybea) -> a -> a
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(rewriter 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 which performs both rewrites until a fixed point.<|> g 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::Plateds =>Folds a ->Folds adeep::Plateds =>IndexedFolds a ->IndexedFolds adeep::Plateds =>Traversals s a b ->Traversals s a bdeep::Plateds =>IndexedTraversals s a b ->IndexedTraversals s a b
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 = ValInt| Neg Expr | Add Expr Expr deriving (Eq,Ord,Show,Read,Data,Typeable)
instancePlatedExpr whereplatef (Neg e) = Neg<$>f eplatef (Add a b) = Add<$>f a<*>f bplate_ a =purea
or
instancePlatedExpr whereplate=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)
instancePlated(Tree a) whereplatef (Bin l r) = Bin<$>f l<*>f rplate_ t =puret
or
instanceDataa =>Plated(Tree a) whereplate=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.
toListOfbiplate≡universeOnOfbiplateignored
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 #
Instances
class GPlated a (g :: k -> Type) #
Minimal complete definition
gplate'
Instances
| GPlated a (V1 :: k -> Type) | |
Defined in Control.Lens.Plated Methods gplate' :: Traversal' (V1 p) a | |
| GPlated a (U1 :: k -> Type) | |
Defined in Control.Lens.Plated Methods gplate' :: Traversal' (U1 p) a | |
| GPlated a (URec b :: k -> Type) | |
Defined in Control.Lens.Plated Methods gplate' :: Traversal' (URec b p) a | |
| GPlated a (K1 i a :: k -> Type) | |
Defined in Control.Lens.Plated Methods gplate' :: Traversal' (K1 i a p) a | |
| GPlated a (K1 i b :: k -> Type) | |
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) | |
Defined in Control.Lens.Plated Methods gplate' :: Traversal' ((f :+: g) p) a | |
| (GPlated a f, GPlated a g) => GPlated a (f :*: g :: k -> Type) | |
Defined in Control.Lens.Plated Methods gplate' :: Traversal' ((f :*: g) p) a | |
| GPlated a f => GPlated a (M1 i c f :: k -> Type) | |
Defined in Control.Lens.Plated Methods gplate' :: Traversal' (M1 i c f p) a | |
class GPlated1 (f :: k -> Type) (g :: k -> Type) #
Minimal complete definition
gplate1'
Instances
| GPlated1 (f :: k -> Type) (V1 :: k -> Type) | ignored |
Defined in Control.Lens.Plated Methods gplate1' :: Traversal' (V1 a) (f a) | |
| GPlated1 (f :: k -> Type) (U1 :: k -> Type) | ignored |
Defined in Control.Lens.Plated Methods gplate1' :: Traversal' (U1 a) (f a) | |
| GPlated1 (f :: k -> Type) (URec a :: k -> Type) | ignored |
Defined in Control.Lens.Plated Methods gplate1' :: Traversal' (URec a a0) (f a0) | |
| GPlated1 (f :: k -> Type) (Rec1 f :: k -> Type) | match |
Defined in Control.Lens.Plated Methods gplate1' :: Traversal' (Rec1 f a) (f a) | |
| GPlated1 (f :: k -> Type) (Rec1 g :: k -> Type) | ignored |
Defined in Control.Lens.Plated Methods gplate1' :: Traversal' (Rec1 g a) (f a) | |
| GPlated1 (f :: k -> Type) (K1 i a :: k -> Type) | ignored |
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 |
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 |
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 |
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 |
Defined in Control.Lens.Plated Methods gplate1' :: Traversal' ((t :.: g) a) (f a) | |
| GPlated1 (f :: Type -> Type) Par1 | ignored |
Defined in Control.Lens.Plated Methods gplate1' :: Traversal' (Par1 a) (f a) | |
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) | |
Defined in Control.Lens.Zoom | |
| type Zoomed (ListT m) | |
Defined in Control.Lens.Zoom | |
| type Zoomed (IdentityT m) | |
Defined in Control.Lens.Zoom | |
| type Zoomed (ExceptT e m) | |
Defined in Control.Lens.Zoom | |
| type Zoomed (FreeT f m) | |
Defined in Control.Lens.Zoom | |
| type Zoomed (ErrorT e m) | |
Defined in Control.Lens.Zoom | |
| type Zoomed (StateT s z) | |
Defined in Control.Lens.Zoom | |
| type Zoomed (WriterT w m) | |
Defined in Control.Lens.Zoom | |
| type Zoomed (StateT s z) | |
Defined in Control.Lens.Zoom | |
| type Zoomed (WriterT w m) | |
Defined in Control.Lens.Zoom | |
| type Zoomed (ReaderT e m) | |
Defined in Control.Lens.Zoom | |
| type Zoomed (RWST r w s z) | |
Defined in Control.Lens.Zoom | |
| type Zoomed (RWST r w s z) | |
Defined in Control.Lens.Zoom | |
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) | |
Defined in Control.Lens.Zoom | |
| type Magnified ((->) b :: Type -> Type) | |
| type Magnified (ReaderT b m) | |
Defined in Control.Lens.Zoom | |
| type Magnified (RWST a w s m) | |
Defined in Control.Lens.Zoom | |
| type Magnified (RWST a w s m) | |
Defined in Control.Lens.Zoom | |
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 ida
>>>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::Monadm =>Lens's t ->StateTt m a ->StateTs m azoom:: (Monadm,Monoidc) =>Traversal's t ->StateTt m c ->StateTs m czoom:: (Monadm,Monoidw) =>Lens's t ->RWSTr w t m c ->RWSTr w s m czoom:: (Monadm,Monoidw,Monoidc) =>Traversal's t ->RWSTr w t m c ->RWSTr w s m czoom:: (Monadm,Monoidw,Errore) =>Lens's t ->ErrorTe (RWSTr w t m) c ->ErrorTe (RWSTr w s m) czoom:: (Monadm,Monoidw,Monoidc,Errore) =>Traversal's t ->ErrorTe (RWSTr w t m) c ->ErrorTe (RWSTr w s m) c ...
Instances
| Zoom m n s t => Zoom (MaybeT m) (MaybeT n) s t | |
| Zoom m n s t => Zoom (ListT m) (ListT n) s t | |
| Zoom m n s t => Zoom (IdentityT m) (IdentityT n) s t | |
| Zoom m n s t => Zoom (ExceptT e m) (ExceptT e n) s t | |
| (Functor f, Zoom m n s t) => Zoom (FreeT f m) (FreeT f n) s t | |
| (Error e, Zoom m n s t) => Zoom (ErrorT e m) (ErrorT e n) s t | |
| Monad z => Zoom (StateT s z) (StateT t z) s t | |
| (Monoid w, Zoom m n s t) => Zoom (WriterT w m) (WriterT w n) s t | |
| Monad z => Zoom (StateT s z) (StateT t z) s t | |
| (Monoid w, Zoom m n s t) => Zoom (WriterT w m) (WriterT w n) s t | |
| Zoom m n s t => Zoom (ReaderT e m) (ReaderT e n) s t | |
| (Monoid w, Monad z) => Zoom (RWST r w s z) (RWST r w t z) s t | |
| (Monoid w, Monad z) => Zoom (RWST r w s z) (RWST r w t z) s t | |
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 :: (Functor (Magnified m c) -> Contravariant (Magnified m c) -> 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.ask1
>>>flip Reader.runReader (1,2,[10..20]) $ magnify (_3._tail) Reader.ask[11,12,13,14,15,16,17,18,19,20]
The type can be read as
magnify :: LensLike' (Magnified m c) a b -> m c -> n c
but the higher-rank constraints make it easier to apply magnify to a
Getter in highly-polymorphic code.
magnify::Getters a -> (a -> r) -> s -> rmagnify::Monoidr =>Folds a -> (a -> r) -> s -> r
magnify::Monoidw =>Getters t ->RWSt w st c ->RWSs w st cmagnify:: (Monoidw,Monoidc) =>Folds a ->RWSa w st c ->RWSs w st c ...
Instances
| Magnify m n b a => Magnify (IdentityT m) (IdentityT n) b a | |
| Magnify ((->) b :: Type -> Type) ((->) a :: Type -> Type) b a |
|
Defined in Control.Lens.Zoom | |
| Monad m => Magnify (ReaderT b m) (ReaderT a m) b a | |
| (Monad m, Monoid w) => Magnify (RWST b w s m) (RWST a w s m) b a | |
| (Monad m, Monoid w) => Magnify (RWST b w s m) (RWST a w s m) b a | |
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
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
_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.
_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' :: 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' :: 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.
_Unwrapped :: Rewrapping s t => Iso (Unwrapped t) (Unwrapped s) t s #
_Wrapped :: Rewrapping s t => Iso s t (Unwrapped s) (Unwrapped t) #
Work under a newtype wrapper.
>>>Const "hello" & _Wrapped %~ Prelude.length & getConst5
_Wrapped≡from_Unwrapped_Unwrapped≡from_Wrapped
_Unwrapped' :: Wrapped s => Iso' (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) #
Wrapped provides isomorphisms to wrap and unwrap newtypes or
data types with one constructor.
Minimal complete definition
Nothing
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
class Wrapped s => Rewrapped s t #
Instances
class (Rewrapped s t, Rewrapped t s) => Rewrapping s t #
Instances
| (Rewrapped s t, Rewrapped t s) => Rewrapping s t | |
Defined in Control.Lens.Wrapped | |
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
snoc :: Snoc s s a a => s -> a -> s infixl 5 #
snoc an element onto the end of a container.
>>>snoc (Seq.fromList []) afromList [a]
>>>snoc (Seq.fromList [b, c]) afromList [b,c,a]
>>>snoc (LazyT.pack "hello") '!'"hello!"
_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]^?!_lastc
>>>[]^?_lastNothing
>>>[a,b,c] & _last %~ f[a,b,f c]
>>>[1,2]^?_lastJust 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" ^? _lastJust 'e'
>>>Vector.empty ^? _lastNothing
>>>(Vector.fromList "abcde" & _last .~ 'Q') == Vector.fromList "abcdQ"True
_last::Traversal'[a] a_last::Traversal'(Seqa) a_last::Traversal'(Vectora) 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]^?_initJust [a,b,c]
>>>[]^?_initNothing
>>>[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]^?_initJust [1,2]
>>>[1,2,3,4]^?!_init[1,2,3]
>>>"hello"^._init"hell"
>>>""^._init""
_init::Traversal'[a] [a]_init::Traversal'(Seqa) (Seqa)_init::Traversal'(Vectora) (Vectora)
_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]^?_tailJust [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] ^? _tailJust (fromList [b,c])
>>>Seq.fromList [] ^? _tailNothing
_tail::Traversal'[a] [a]_tail::Traversal'(Seqa) (Seqa)_tail::Traversal'(Vectora) (Vectora)
_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]^? _headJust a
>>>[a,b,c] & _head .~ d[d,b,c]
>>>[a,b,c] & _head %~ f[f a,b,c]
>>>[] & _head %~ f[]
>>>[1,2,3]^?!_head1
>>>[]^?_headNothing
>>>[1,2]^?_headJust 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 %~ ffromList [f a,b,c,d]
>>>Seq.fromList [] ^? _headNothing
>>>Seq.fromList [a,b,c,d] ^? _headJust a
_head::Traversal'[a] a_head::Traversal'(Seqa) a_head::Traversal'(Vectora) a
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])
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]
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
Instances
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
Instances
Minimal complete definition
Nothing
Instances
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
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 ::Bifunctorp =>Isos t a b ->Iso(p x s) (p y t) (p x a) (p y b) seconding ::Bifunctorp =>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') #
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 ::Profunctorp =>Isos t a b ->Iso(p x s) (p y t) (p x a) (p y b) rmapping ::Profunctorp =>Iso's a ->Iso'(p x s) (p x 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 ::Profunctorp =>Isos t a b ->Iso(p a x) (p b y) (p s x) (p t y) lmapping ::Profunctorp =>Iso's a ->Iso'(p a x) (p s x)
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 ::Profunctorp =>Isos t a b ->Isos' t' a' b' ->Iso(p a s') (p b t') (p s a') (p t b') dimapping ::Profunctorp =>Iso's a ->Iso's' a' ->Iso'(p a s') (p s a')
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 ::Contravariantf =>Isos t a b ->Iso(f a) (f b) (f s) (f t) contramapping ::Contravariantf =>Iso's a ->Iso'(f a) (f s)
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.
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"
lazy :: Strict lazy strict => Iso' strict lazy #
An Iso between the strict variant of a structure and its lazy
counterpart.
lazy=fromstrict
See http://hackage.haskell.org/package/strict-base-types for an example use.
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)
anon :: a -> (a -> Bool) -> Iso' (Maybe a) a #
anon a pnon a
This function assumes that p a holds TrueMaybe (a | not (p a))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" .~ NothingfromList []
non' :: APrism' a () -> Iso' (Maybe a) a #
non' pnon (p # ())Prism
This function generates an isomorphism between Maybe (a | isn't p a)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" .~ NothingfromList []
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 vMaybe a'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 +~ 2fromList [("hello",3)]
>>>Map.fromList [("hello",1)] & at "hello" . non 0 -~ 1fromList []
>>>Map.fromList [("hello",1)] ^. at "hello" . non 01
>>>Map.fromList [] ^. at "hello" . non 00
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" .~ NothingfromList []
It can also be used in reverse to exclude a given value:
>>>non 0 # rem 10 4Just 2
>>>non 0 # rem 10 5Nothing
enum :: Enum a => Iso' Int a #
This isomorphism can be used to convert to or from an instance of Enum.
>>>LT^.from enum0
>>>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.
auf :: (Functor f, Functor g) => AnIso s t a b -> (f t -> g s) -> f b -> g a #
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 (_Wrapping 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::Isos t a b -> ((r -> t) -> e -> s) -> (r -> b) -> e -> a
but the signature is general.
Note: The direction of the Iso required for this function changed in lens 4.18 to match up
with the behavior of au. For the old behavior use xplatf or for a version that is compatible
across both old and new versions of lens you can just use coerce!
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
au = xplat . from
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.
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.
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.
class Bifunctor p => Swapped (p :: Type -> Type -> Type) where #
This class provides for symmetric bifunctors.
Methods
Instances
| Swapped Either | |
| Swapped (,) | |
Defined in Control.Lens.Iso | |
| Swapped ((,,) x) | |
Defined in Control.Lens.Iso | |
| Swapped ((,,,) x y) | |
Defined in Control.Lens.Iso | |
| Swapped ((,,,,) x y z) | |
Defined in Control.Lens.Iso | |
| Swapped p => Swapped (Flip p) | |
| Swapped ((,,,,,) x y z w) | |
Defined in Control.Lens.Iso | |
| (Swapped p, Swapped q) => Swapped (Sum p q) | |
| (Swapped f, Swapped g) => Swapped (Product f g) | |
| Swapped ((,,,,,,) x y z w v) | |
Defined in Control.Lens.Iso | |
| (Functor f, Swapped p) => Swapped (Tannen f p) | |
| (f ~ g, Functor f, Swapped p) => Swapped (Biff p f g) | |
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.
withEquality :: AnEquality s t a b -> ((s :~: a) -> (b :~: t) -> r) -> r #
A version of substEq that provides explicit, rather than implicit,
equality evidence.
fromLeibniz' :: ((s :~: s) -> s :~: a) -> Equality' s a #
fromLeibniz :: (Identical a b a b -> Identical a b s t) -> Equality s t a b #
Convert a "profunctor lens" form of equality to an equality. Reverses
overEquality.
The type should be understood as
fromLeibniz :: (forall p. p a b -> p s t) -> Equality s t a b
underEquality :: AnEquality s t a b -> p t s -> p b a #
The opposite of working overEquality is working underEquality.
overEquality :: AnEquality s t a b -> p a b -> p s t #
Recover a "profunctor lens" form of equality. Reverses fromLeibniz.
equality :: (s :~: a) -> (b :~: t) -> Equality s t a b #
Construct an Equality from explicit equality evidence.
cloneEquality :: AnEquality s t a b -> Equality s t a b #
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.
fromEq :: AnEquality s t a b -> Equality b a t s #
Equality is symmetric.
mapEq :: AnEquality s t a b -> f s -> f a #
We can use Equality to do substitution into anything.
substEq :: AnEquality s t a b -> ((s ~ a) -> (t ~ b) -> r) -> r #
Substituting types with Equality.
runEq :: AnEquality s t a b -> Identical s t a b #
Extract a witness of type 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.
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.
type AnEquality' (s :: k2) (a :: k2) = AnEquality s s a a #
A Simple AnEquality.
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 #
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) #
ifoldMapByOf :: IndexedFold i t a -> (r -> r -> r) -> r -> (i -> a -> r) -> t -> r #
ifoldMapBy :: FoldableWithIndex i t => (r -> r -> r) -> r -> (i -> a -> r) -> t a -> r #
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
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
iforM :: (TraversableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m (t b) #
imapM :: (TraversableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m (t b) #
ifor :: (TraversableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f (t b) #
itoList :: FoldableWithIndex i f => f a -> [(i, a)] #
ifoldlM :: (FoldableWithIndex i f, Monad m) => (i -> b -> a -> m b) -> b -> f a -> m b #
ifoldrM :: (FoldableWithIndex i f, Monad m) => (i -> a -> b -> m b) -> b -> f a -> m b #
ifind :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Maybe (i, a) #
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.consticoncatMap≡ifoldMap
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_≡flipimapM_
When you don't need access to the index then forMOf_ is more flexible in what it accepts.
forMOf_l a ≡iforMOfl 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
ifor_ :: (FoldableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f () #
itraverse_ :: (FoldableWithIndex i t, Applicative f) => (i -> a -> f b) -> t a -> f () #
inone :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool #
iall :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool #
iany :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool #
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 2Just "world"
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.
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::IndexedGettera 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")]
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:
imapf.imapg ≡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
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 . asIndexFoldableWithIndex.
>>>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
Instances
| FoldableWithIndex Int [] | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex Int ZipList | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex Int NonEmpty | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex Int IntMap | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex Int Seq | |
| FoldableWithIndex Int Vector | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex () Maybe | |
| FoldableWithIndex () Par1 | |
| FoldableWithIndex () Identity | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex k (Map k) | |
| FoldableWithIndex k (HashMap k) | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex k ((,) k) | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex i (Level i) | |
| Ix i => FoldableWithIndex i (Array i) | |
| FoldableWithIndex Void (V1 :: Type -> Type) | |
| FoldableWithIndex Void (U1 :: Type -> Type) | |
| FoldableWithIndex Void (Proxy :: Type -> Type) | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex Int (V n) | |
| FoldableWithIndex () (Tagged a) | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex i f => FoldableWithIndex i (Reverse f) | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex i f => FoldableWithIndex i (Rec1 f) | |
| FoldableWithIndex i m => FoldableWithIndex i (IdentityT m) | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex i f => FoldableWithIndex i (Backwards f) | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex i (Magma i t b) | |
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) | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex [Int] Tree | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex (E Plucker) Plucker | |
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 | |
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 | |
| FoldableWithIndex (E V4) V4 | |
| FoldableWithIndex (E V3) V3 | |
| FoldableWithIndex (E V2) V2 | |
| FoldableWithIndex (E V1) V1 | |
| FoldableWithIndex i f => FoldableWithIndex [i] (Free f) | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex i f => FoldableWithIndex [i] (Cofree f) | |
Defined in Control.Lens.Indexed | |
| (FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (Sum f g) | |
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) | |
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) | |
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) | |
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) | |
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) | |
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 (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(constIdentity) ≡Identityfmap(itraversef).itraverseg ≡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≡itraverseOfitraversed
itraversed :: IndexedTraversal i (t a) (t b) a b #
The IndexedTraversal of a TraversableWithIndex container.
Instances
newtype ReifiedLens s t a b #
Reify a ReifiedLens so it can be stored safely in a container.
type ReifiedLens' s a = ReifiedLens s s a a #
typeReifiedLens'=SimpleReifiedLens
newtype ReifiedIndexedLens i s t a b #
Reify an ReifiedIndexedLens so it can be stored safely in a container.
Constructors
| IndexedLens | |
Fields
| |
type ReifiedIndexedLens' i s a = ReifiedIndexedLens i s s a a #
typeReifiedIndexedLens'i =Simple(ReifiedIndexedLensi)
newtype ReifiedIndexedTraversal i s t a b #
Reify an ReifiedIndexedTraversal so it can be stored safely in a container.
Constructors
| IndexedTraversal | |
Fields
| |
type ReifiedIndexedTraversal' i s a = ReifiedIndexedTraversal i s s a a #
typeReifiedIndexedTraversal'i =Simple(ReifiedIndexedTraversali)
newtype ReifiedTraversal s t a b #
A form of ReifiedTraversal that can be stored monomorphically in a container.
Constructors
| Traversal | |
Fields
| |
type ReifiedTraversal' s a = ReifiedTraversal s s a a #
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 ((,) <$> Getter _2 <*> Getter (_1.to length))("world",5)
Instances
newtype ReifiedIndexedGetter i s a #
Reify an ReifiedIndexedGetter so it can be stored safely in a container.
Constructors
| IndexedGetter | |
Fields
| |
Instances
newtype ReifiedFold s a #
Reify a ReifiedFold so it can be stored safely in a container.
This can also be useful for creatively combining folds as
ReifiedFold sReaderT s [] and provides similar
instances.
>>>("hello","world")^..runFold ((,) <$> Fold _2 <*> Fold both)[("world","hello"),("world","world")]
Instances
newtype ReifiedIndexedFold i s a #
Constructors
| IndexedFold | |
Fields
| |
Instances
newtype ReifiedSetter s t a b #
Reify a ReifiedSetter so it can be stored safely in a container.
type ReifiedSetter' s a = ReifiedSetter s s a a #
typeReifiedSetter'=SimpleReifiedSetter
newtype ReifiedIndexedSetter i s t a b #
Reify an ReifiedIndexedSetter so it can be stored safely in a container.
Constructors
| IndexedSetter | |
Fields
| |
type ReifiedIndexedSetter' i s a = ReifiedIndexedSetter i s s a a #
typeReifiedIndexedSetter'i =Simple(ReifiedIndexedSetteri)
newtype ReifiedIso s t a b #
Reify an ReifiedIso so it can be stored safely in a container.
type ReifiedIso' s a = ReifiedIso s s a a #
typeReifiedIso'=SimpleReifiedIso
newtype ReifiedPrism s t a b #
Reify a ReifiedPrism so it can be stored safely in a container.
type ReifiedPrism' s a = ReifiedPrism s s a a #
typeReifiedPrism'=SimpleReifiedPrism
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::IndexedTraversali s t a b ->IndexedTraversalInts t (Leveli a) (Leveli b)ilevels::IndexedFoldi s a ->IndexedFoldInts (Leveli a)
Note: Internally this is implemented by using an illegal Applicative, as it extracts information
in an order that violates the Applicative laws.
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
sequenceByOftraverse≡sequenceBy
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
traverseByOftraverse≡traverseBy
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::Traversals t a b ->Traversals 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 #
Try the second traversal. If it returns no entries, try again with all entries from the first traversal, recursively.
deepOf::Folds s ->Folds a ->Folds adeepOf::Traversal's s ->Traversal's a ->Traversal's adeepOf::Traversals t s t ->Traversals t a b ->Traversals t a bdeepOf::Folds s ->IndexedFoldi s a ->IndexedFoldi s adeepOf::Traversals t s t ->IndexedTraversali s t a b ->IndexedTraversali s t a b
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::Traversals t a b ->Traversals t a b ->Traversals t a bfailing::Prisms t a b ->Prisms t a b ->Traversals t a bfailing::Folds a ->Folds a ->Folds a
These cases are also supported, trivially, but are boring, because the left hand side always succeeds.
failing::Lenss t a b ->Traversals t a b ->Traversals t a bfailing::Isos t a b ->Traversals t a b ->Traversals t a bfailing::Equalitys t a b ->Traversals t a b ->Traversals t a bfailing::Getters a ->Folds a ->Folds 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::IndexedTraversali s t a b ->IndexedTraversali s t a b ->IndexedTraversali s t a bfailing::IndexedFoldi s a ->IndexedFoldi s a ->IndexedFoldi s a
These cases are also supported, trivially, but are boring, because the left hand side always succeeds.
failing::IndexedLensi s t a b ->IndexedTraversali s t a b ->IndexedTraversali s t a bfailing::IndexedGetteri s a ->IndexedGetteri s a ->IndexedFoldi s a
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
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
elements :: Traversable t => (Int -> Bool) -> IndexedTraversal' Int (t a) a #
Traverse elements of a Traversable container where their ordinal positions match a predicate.
elements≡elementsOftraverse
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'Ints aelementsOf::Folds a -> (Int->Bool) ->IndexedFoldInts a
element :: Traversable t => Int -> IndexedTraversal' Int (t a) a #
Traverse the nth element of a Traversable container.
element≡elementOftraverse
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) 1Just 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'Ints aelementOf::Folds a ->Int->IndexedFoldInts a
ignored :: Applicative f => pafb -> s -> f s #
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.
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.
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.
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.
mapAccumLOfl ≡imapAccumLOfl.const
imapAccumLOf::IndexedLensi s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)imapAccumLOf::IndexedTraversali s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, 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.
mapAccumROfl ≡imapAccumROfl.const
imapAccumROf::IndexedLensi s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)imapAccumROf::IndexedTraversali s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, 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).
forMOfl a ≡iforMOfl a.constiforMOf≡flip.imapMOf
iforMOf::Monadm =>IndexedLensi s t a b -> s -> (i -> a -> m b) -> m tiforMOf::Monadm =>IndexedTraversali s t a b -> s -> (i -> a -> m b) -> m 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.
mapMOfl ≡imapMOfl.const
imapMOf::Monadm =>IndexedLensi s t a b -> (i -> a -> m b) -> s -> m timapMOf::Monadm =>IndexedTraversali s t a b -> (i -> a -> m b) -> s -> m timapMOf::Bindm =>IndexedTraversal1i s t a b -> (i -> a -> m b) -> s -> m 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).
forOfl a ≡iforOfl a.constiforOf≡flip.itraverseOf
iforOf::Functorf =>IndexedLensi s t a b -> s -> (i -> a -> f b) -> f tiforOf::Applicativef =>IndexedTraversali s t a b -> s -> (i -> a -> f b) -> f tiforOf::Applyf =>IndexedTraversal1i s t a b -> s -> (i -> a -> f b) -> f t
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≡withIndextraverseOfl =itraverseOfl.const=id
itraverseOf::Functorf =>IndexedLensi s t a b -> (i -> a -> f b) -> s -> f titraverseOf::Applicativef =>IndexedTraversali s t a b -> (i -> a -> f b) -> s -> f titraverseOf::Applyf =>IndexedTraversal1i s t a b -> (i -> a -> f b) -> s -> f t
cloneIndexedTraversal1 :: AnIndexedTraversal1 i s t a b -> IndexedTraversal1 i s t a b #
Clone an IndexedTraversal1 yielding an IndexedTraversal1 with the same index.
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.
cloneTraversal1 :: ATraversal1 s t a b -> Traversal1 s t a b #
A Traversal1 is completely characterized by its behavior on a Bazaar1.
cloneIndexedTraversal :: AnIndexedTraversal i s t a b -> IndexedTraversal i s t a b #
Clone an IndexedTraversal yielding an IndexedTraversal with the same index.
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.
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 ->Traversals t a b
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 bothJust "world"
Dropping works on infinite traversals as well:
>>>[1..] ^? dropping 1 foldedJust 2
dropping::Int->Traversal's a ->Traversal's adropping::Int->Lens's a ->Traversal's adropping::Int->Iso's a ->Traversal's adropping::Int->Prism's a ->Traversal's adropping::Int->Getters a ->Folds adropping::Int->Folds a ->Folds adropping::Int->IndexedTraversal'i s a ->IndexedTraversal'i s adropping::Int->IndexedLens'i s a ->IndexedTraversal'i s adropping::Int->IndexedGetteri s a ->IndexedFoldi s adropping::Int->IndexedFoldi s a ->IndexedFoldi s a
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 ataking::Int->Lens's a ->Traversal's ataking::Int->Iso's a ->Traversal's ataking::Int->Prism's a ->Traversal's ataking::Int->Getters a ->Folds ataking::Int->Folds a ->Folds ataking::Int->IndexedTraversal'i s a ->IndexedTraversal'i s ataking::Int->IndexedLens'i s a ->IndexedTraversal'i s ataking::Int->IndexedGetteri s a ->IndexedFoldi s ataking::Int->IndexedFoldi s a ->IndexedFoldi s a
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 bboth1::Traversal1(Eithera a) (Eitherb b) a b
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. Use each to traverse
the elements of arbitrary homogeneous tuples.
>>>(1,2) & both *~ 10(10,20)
>>>over both length ("hello","world")(5,5)
>>>("hello","world")^.both"helloworld"
both::Traversal(a, a) (b, b) a bboth::Traversal(Eithera a) (Eitherb b) a b
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'(Indexedi) a s)holes1Of::IndexedTraversal1'i s a -> s ->NonEmpty(Pretext'(Indexedi) a s)
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 =toListOfl x==mappos(holesOfl x) propId l x =all(==x) [extractw | w <-holesOfl 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'(Indexedi) a s]holesOf::IndexedTraversal'i s a -> s -> [Pretext'(Indexedi) a s]
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::Traversals t a b ->Lenss t a bunsafeSingular::Folds a ->Getters aunsafeSingular::IndexedTraversali s t a b ->IndexedLensi s t a bunsafeSingular::IndexedFoldi s a ->IndexedGetteri s a
iunsafePartsOf' :: Over (Indexed i) (Bazaar (Indexed i) a b) s t a b -> IndexedLens [i] s t [a] [b] #
unsafePartsOf' :: ATraversal s t a b -> Lens 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] #
An indexed version of unsafePartsOf that receives the entire list of indices as its index.
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::Isos t a b ->Lenss t [a] [b]unsafePartsOf::Lenss t a b ->Lenss t [a] [b]unsafePartsOf::Traversals t a b ->Lenss t [a] [b]unsafePartsOf::Folds a ->Getters [a]unsafePartsOf::Getters a ->Getters [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] #
A type-restricted version of ipartsOf that can only be used with an IndexedTraversal.
partsOf' :: ATraversal s t a a -> Lens 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] #
An indexed version of partsOf that receives the entire list of indices as its index.
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::Folds a ->Getters [a]partsOf::Getters a ->Getters [a]
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.
loci :: Traversal (Bazaar ((->) :: Type -> Type -> Type) a c s) (Bazaar ((->) :: Type -> Type -> Type) b c s) a b #
mapAccumLOf :: LensLike (State acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t) #
This generalizes mapAccumL to an arbitrary Traversal.
mapAccumL≡mapAccumLOftraverse
mapAccumLOf accumulates State from left to right.
mapAccumLOf::Isos t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)mapAccumLOf::Lenss t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)mapAccumLOf::Traversals t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumLOf::LensLike(Stateacc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)mapAccumLOfl f acc0 s =swap(runState(l (a ->state(acc ->swap(f acc a))) s) acc0)
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≡mapAccumROftraverse
mapAccumROf accumulates State from right to left.
mapAccumROf::Isos t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)mapAccumROf::Lenss t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)mapAccumROf::Traversals t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
mapAccumROf::LensLike(Backwards(Stateacc)) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, 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≡transposeOftraverse
Since every Lens is a Traversal, we can use this as a form of
monadic strength as well:
transposeOf_2:: (b, [a]) -> [(b, a)]
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≡sequenceOftraversesequenceOfl ≡mapMOflidsequenceOfl ≡unwrapMonad.lWrapMonad
sequenceOf::Monadm =>Isos t (m b) b -> s -> m tsequenceOf::Monadm =>Lenss t (m b) b -> s -> m tsequenceOf::Monadm =>Traversals t (m b) 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≡forMOftraverseforMOfl ≡flip(mapMOfl)iforMOfl s ≡forMl s.Indexed
forMOf::Monadm =>Isos t a b -> s -> (a -> m b) -> m tforMOf::Monadm =>Lenss t a b -> s -> (a -> m b) -> m tforMOf::Monadm =>Traversals t a b -> s -> (a -> m b) -> m 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≡mapMOftraverseimapMOfl ≡forMl.Indexed
mapMOf::Monadm =>Isos t a b -> (a -> m b) -> s -> m tmapMOf::Monadm =>Lenss t a b -> (a -> m b) -> s -> m tmapMOf::Monadm =>Traversals t a b -> (a -> m b) -> s -> m 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≡sequenceAOftraverse≡traverseidsequenceAOfl ≡traverseOflid≡ lid
sequenceAOf::Functorf =>Isos t (f b) b -> s -> f tsequenceAOf::Functorf =>Lenss t (f b) b -> s -> f tsequenceAOf::Applicativef =>Traversals t (f b) 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) print1 2 3 ((),(),())
This function is only provided for consistency, flip is strictly more general.
forOf≡flipforOf≡flip.traverseOf
for≡forOftraverseiforl s ≡forl s.Indexed
forOf::Functorf =>Isos t a b -> s -> (a -> f b) -> f tforOf::Functorf =>Lenss t a b -> s -> (a -> f b) -> f tforOf::Applicativef =>Traversals t a b -> s -> (a -> f b) -> f t
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≡iditraverseOfl ≡traverseOfl.IndexeditraverseOfitraversed≡itraverse
This yields the obvious law:
traverse≡traverseOftraverse
traverseOf::Functorf =>Isos t a b -> (a -> f b) -> s -> f ttraverseOf::Functorf =>Lenss t a b -> (a -> f b) -> s -> f ttraverseOf::Applyf =>Traversal1s t a b -> (a -> f b) -> s -> f ttraverseOf::Applicativef =>Traversals t a b -> (a -> f b) -> s -> f t
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.
type ATraversal' s a = ATraversal s s a a #
typeATraversal'=SimpleATraversal
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 ATraversal1' s a = ATraversal1 s s a a #
typeATraversal1'=SimpleATraversal1
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 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 a = AnIndexedTraversal i s s a a #
typeAnIndexedTraversal'=Simple(AnIndexedTraversali)
type AnIndexedTraversal1' i s a = AnIndexedTraversal1 i s s a a #
typeAnIndexedTraversal1'=Simple(AnIndexedTraversal1i)
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
pis an instance ofIndexedi, - to be unindexed if
pis(->), - a
TraversaliffisApplicative, - a
Getteriffis only aFunctorandContravariant, - a
Lensiffis only aFunctor, - a
FoldiffisApplicativeandContravariant.
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 a = Traversing p f s s a a #
typeTraversing'f =Simple(Traversingf)
type Traversing1' (p :: Type -> Type -> Type) (f :: Type -> Type) s a = Traversing1 p f s s a a #
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 | |
Defined in Control.Lens.Traversal Methods traverseMin :: IndexedTraversal' Int (IntMap v) v # | |
| Ord k => TraverseMin k (Map k) | |
Defined in Control.Lens.Traversal Methods traverseMin :: IndexedTraversal' k (Map k v) v # | |
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 | |
Defined in Control.Lens.Traversal Methods traverseMax :: IndexedTraversal' Int (IntMap v) v # | |
| Ord k => TraverseMax k (Map k) | |
Defined in Control.Lens.Traversal Methods traverseMax :: IndexedTraversal' k (Map k v) v # | |
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.
foldMapByOffolded≡foldMapBy
foldMapByOf::Getters a -> (r -> r -> r) -> r -> (a -> r) -> s -> rfoldMapByOf::Folds a -> (r -> r -> r) -> r -> (a -> r) -> s -> rfoldMapByOf::Traversal's a -> (r -> r -> r) -> r -> (a -> r) -> s -> rfoldMapByOf::Lens's a -> (r -> r -> r) -> r -> (a -> r) -> s -> rfoldMapByOf::Iso's a -> (r -> r -> r) -> r -> (a -> r) -> s -> r
>>>foldMapByOf both (+) 0 length ("hello","world")10
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.
foldByOffolded≡foldBy
foldByOf::Getters a -> (a -> a -> a) -> a -> s -> afoldByOf::Folds a -> (a -> a -> a) -> a -> s -> afoldByOf::Lens's a -> (a -> a -> a) -> a -> s -> afoldByOf::Traversal's a -> (a -> a -> a) -> a -> s -> afoldByOf::Iso's a -> (a -> a -> a) -> a -> s -> a
>>>foldByOf both (++) [] ("hello","world")"helloworld"
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) ->IndexedFoldi s a ->IndexedFoldi s aidroppingWhile:: (i -> a ->Bool) ->IndexedTraversal'i s a ->IndexedFoldi s a -- see notesidroppingWhile:: (i -> a ->Bool) ->IndexedLens'i s a ->IndexedFoldi s a -- see notesidroppingWhile:: (i -> a ->Bool) ->IndexedGetteri s a ->IndexedFoldi 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.
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) ->IndexedFoldi s a ->IndexedFoldi s aitakingWhile:: (i -> a ->Bool) ->IndexedTraversal'i s a ->IndexedFoldi s aitakingWhile:: (i -> a ->Bool) ->IndexedLens'i s a ->IndexedFoldi s aitakingWhile:: (i -> a ->Bool) ->IndexedGetteri s a ->IndexedFoldi 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.
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!
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≡findIndicesOffolded
findIndicesOf::IndexedFoldi s a -> (a ->Bool) -> s -> [i]findIndicesOf::IndexedTraversal'i s a -> (a ->Bool) -> 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≡findIndexOffolded
findIndexOf::IndexedFoldi s a -> (a ->Bool) -> s ->MaybeifindIndexOf::IndexedTraversal'i s a -> (a ->Bool) -> s ->Maybei
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≡elemIndicesOffolded
elemIndicesOf::Eqa =>IndexedFoldi s a -> a -> s -> [i]elemIndicesOf::Eqa =>IndexedTraversal'i s a -> a -> s -> [i]
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≡elemIndexOffolded
elemIndexOf::Eqa =>IndexedFoldi s a -> a -> s ->MaybeielemIndexOf::Eqa =>IndexedTraversal'i s a -> a -> s ->Maybei
(^@?!) :: 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 ->IndexedGetteri s a -> (i, a) (^@?!) :: s ->IndexedFoldi s a -> (i, a) (^@?!) :: s ->IndexedLens'i s a -> (i, a) (^@?!) :: s ->IndexedTraversal'i s a -> (i, a)
(^@?) :: 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 ->IndexedGetteri s a ->Maybe(i, a) (^@?) :: s ->IndexedFoldi s a ->Maybe(i, a) (^@?) :: s ->IndexedLens'i s a ->Maybe(i, a) (^@?) :: s ->IndexedTraversal'i s a ->Maybe(i, a)
(^@..) :: s -> IndexedGetting i (Endo [(i, a)]) s a -> [(i, a)] infixl 8 #
An infix version of itoListOf.
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.
toListOfl ≡mapsnd.itoListOfl
itoListOf::IndexedGetteri s a -> s -> [(i,a)]itoListOf::IndexedFoldi s a -> s -> [(i,a)]itoListOf::IndexedLens'i s a -> s -> [(i,a)]itoListOf::IndexedTraversal'i s a -> s -> [(i,a)]
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.
foldlMOfl ≡ifoldlMOfl.const
ifoldlMOf::Monadm =>IndexedGetteri s a -> (i -> r -> a -> m r) -> r -> s -> m rifoldlMOf::Monadm =>IndexedFoldi s a -> (i -> r -> a -> m r) -> r -> s -> m rifoldlMOf::Monadm =>IndexedLens'i s a -> (i -> r -> a -> m r) -> r -> s -> m rifoldlMOf::Monadm =>IndexedTraversal'i s a -> (i -> r -> a -> m r) -> r -> s -> m 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.
foldrMOfl ≡ifoldrMOfl.const
ifoldrMOf::Monadm =>IndexedGetteri s a -> (i -> a -> r -> m r) -> r -> s -> m rifoldrMOf::Monadm =>IndexedFoldi s a -> (i -> a -> r -> m r) -> r -> s -> m rifoldrMOf::Monadm =>IndexedLens'i s a -> (i -> a -> r -> m r) -> r -> s -> m rifoldrMOf::Monadm =>IndexedTraversal'i s a -> (i -> a -> r -> m r) -> r -> s -> m 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'::IndexedGetteri s a -> (i -> r -> a -> r) -> r -> s -> rifoldlOf'::IndexedFoldi s a -> (i -> r -> a -> r) -> r -> s -> rifoldlOf'::IndexedLens'i s a -> (i -> r -> a -> r) -> r -> s -> rifoldlOf'::IndexedTraversal'i s a -> (i -> r -> a -> r) -> r -> s -> r
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'::IndexedGetteri s a -> (i -> a -> r -> r) -> r -> s -> rifoldrOf'::IndexedFoldi s a -> (i -> a -> r -> r) -> r -> s -> rifoldrOf'::IndexedLens'i s a -> (i -> a -> r -> r) -> r -> s -> rifoldrOf'::IndexedTraversal'i s a -> (i -> a -> r -> r) -> r -> s -> r
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.
findMOfl ≡ifindMOfl.const
ifindMOf::Monadm =>IndexedGetteri s a -> (i -> a -> mBool) -> s -> m (Maybea)ifindMOf::Monadm =>IndexedFoldi s a -> (i -> a -> mBool) -> s -> m (Maybea)ifindMOf::Monadm =>IndexedLens'i s a -> (i -> a -> mBool) -> s -> m (Maybea)ifindMOf::Monadm =>IndexedTraversal'i s a -> (i -> a -> mBool) -> s -> m (Maybea)
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.
findOfl ≡ifindOfl.const
ifindOf::IndexedGetteri s a -> (i -> a ->Bool) -> s ->MaybeaifindOf::IndexedFoldi s a -> (i -> a ->Bool) -> s ->MaybeaifindOf::IndexedLens'i s a -> (i -> a ->Bool) -> s ->MaybeaifindOf::IndexedTraversal'i s a -> (i -> a ->Bool) -> s ->Maybea
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.
concatMapOfl ≡iconcatMapOfl.consticoncatMapOf≡ifoldMapOf
iconcatMapOf::IndexedGetteri s a -> (i -> a -> [r]) -> s -> [r]iconcatMapOf::IndexedFoldi 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]
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 ≡iforMOfl a.const
iforMOf_::Monadm =>IndexedGetteri s a -> s -> (i -> a -> m r) -> m ()iforMOf_::Monadm =>IndexedFoldi s a -> s -> (i -> a -> m r) -> m ()iforMOf_::Monadm =>IndexedLens'i s a -> s -> (i -> a -> m r) -> m ()iforMOf_::Monadm =>IndexedTraversal'i s a -> s -> (i -> a -> m r) -> m ()
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 ≡imapMOfl.const
imapMOf_::Monadm =>IndexedGetteri s a -> (i -> a -> m r) -> s -> m ()imapMOf_::Monadm =>IndexedFoldi s a -> (i -> a -> m r) -> s -> m ()imapMOf_::Monadm =>IndexedLens'i s a -> (i -> a -> m r) -> s -> m ()imapMOf_::Monadm =>IndexedTraversal'i s a -> (i -> a -> m r) -> s -> m ()
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_::Functorf =>IndexedGetteri s a -> s -> (i -> a -> f r) -> f ()iforOf_::Applicativef =>IndexedFoldi s a -> s -> (i -> a -> f r) -> f ()iforOf_::Functorf =>IndexedLens'i s a -> s -> (i -> a -> f r) -> f ()iforOf_::Applicativef =>IndexedTraversal'i s a -> s -> (i -> a -> f r) -> f ()
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 ≡itraverseOfl.const
itraverseOf_::Functorf =>IndexedGetteri s a -> (i -> a -> f r) -> s -> f ()itraverseOf_::Applicativef =>IndexedFoldi s a -> (i -> a -> f r) -> s -> f ()itraverseOf_::Functorf =>IndexedLens'i s a -> (i -> a -> f r) -> s -> f ()itraverseOf_::Applicativef =>IndexedTraversal'i s a -> (i -> a -> f r) -> s -> f ()
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.
noneOfl ≡inoneOfl.const
inoneOf::IndexedGetteri s a -> (i -> a ->Bool) -> s ->BoolinoneOf::IndexedFoldi s a -> (i -> a ->Bool) -> s ->BoolinoneOf::IndexedLens'i s a -> (i -> a ->Bool) -> s ->BoolinoneOf::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.
allOfl ≡iallOfl.const
iallOf::IndexedGetteri s a -> (i -> a ->Bool) -> s ->BooliallOf::IndexedFoldi s a -> (i -> a ->Bool) -> s ->BooliallOf::IndexedLens'i s a -> (i -> a ->Bool) -> s ->BooliallOf::IndexedTraversal'i s a -> (i -> a ->Bool) -> s ->Bool
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.
anyOfl ≡ianyOfl.const
ianyOf::IndexedGetteri s a -> (i -> a ->Bool) -> s ->BoolianyOf::IndexedFoldi s a -> (i -> a ->Bool) -> s ->BoolianyOf::IndexedLens'i s a -> (i -> a ->Bool) -> s ->BoolianyOf::IndexedTraversal'i s a -> (i -> a ->Bool) -> s ->Bool
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.
foldlOfl ≡ifoldlOfl.const
ifoldlOf::IndexedGetteri s a -> (i -> r -> a -> r) -> r -> s -> rifoldlOf::IndexedFoldi s a -> (i -> r -> a -> r) -> r -> s -> rifoldlOf::IndexedLens'i s a -> (i -> r -> a -> r) -> r -> s -> rifoldlOf::IndexedTraversal'i s a -> (i -> r -> a -> r) -> r -> s -> r
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.
foldrOfl ≡ifoldrOfl.const
ifoldrOf::IndexedGetteri s a -> (i -> a -> r -> r) -> r -> s -> rifoldrOf::IndexedFoldi s a -> (i -> a -> r -> r) -> r -> s -> rifoldrOf::IndexedLens'i s a -> (i -> a -> r -> r) -> r -> s -> rifoldrOf::IndexedTraversal'i s a -> (i -> a -> r -> r) -> r -> s -> 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.
foldMapOfl ≡ifoldMapOfl.const
ifoldMapOf::IndexedGetteri s a -> (i -> a -> m) -> s -> mifoldMapOf::Monoidm =>IndexedFoldi s a -> (i -> a -> m) -> s -> mifoldMapOf::IndexedLens'i s a -> (i -> a -> m) -> s -> mifoldMapOf::Monoidm =>IndexedTraversal'i s a -> (i -> a -> m) -> s -> m
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::MonadStates m =>IndexedGetteri s a -> (i -> a -> r) -> m (Mayber)ipreuses::MonadStates m =>IndexedFoldi s a -> (i -> a -> r) -> m (Mayber)ipreuses::MonadStates m =>IndexedLens'i s a -> (i -> a -> r) -> m (Mayber)ipreuses::MonadStates m =>IndexedTraversal'i s a -> (i -> a -> r) -> m (Mayber)
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::MonadStates m =>Getters a -> (a -> r) -> m (Mayber)preuses::MonadStates m =>Folds a -> (a -> r) -> m (Mayber)preuses::MonadStates m =>Lens's a -> (a -> r) -> m (Mayber)preuses::MonadStates m =>Iso's a -> (a -> r) -> m (Mayber)preuses::MonadStates m =>Traversal's a -> (a -> r) -> m (Mayber)
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::MonadStates m =>IndexedGetteri s a -> m (Maybe(i, a))ipreuse::MonadStates m =>IndexedFoldi s a -> m (Maybe(i, a))ipreuse::MonadStates m =>IndexedLens'i s a -> m (Maybe(i, a))ipreuse::MonadStates m =>IndexedTraversal'i s a -> m (Maybe(i, a))
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::MonadStates m =>Getters a -> m (Maybea)preuse::MonadStates m =>Folds a -> m (Maybea)preuse::MonadStates m =>Lens's a -> m (Maybea)preuse::MonadStates m =>Iso's a -> m (Maybea)preuse::MonadStates m =>Traversal's a -> m (Maybea)
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::IndexedGetteri s a -> (i -> a -> r) -> s ->Mayberipreviews::IndexedFoldi s a -> (i -> a -> r) -> s ->Mayberipreviews::IndexedLens'i s a -> (i -> a -> r) -> s ->Mayberipreviews::IndexedTraversal'i s a -> (i -> a -> r) -> s ->Mayber
However, it may be useful to think of its full generality when working with
a Monad transformer stack:
ipreviews::MonadReaders m =>IndexedGetteri s a -> (i -> a -> r) -> m (Mayber)ipreviews::MonadReaders m =>IndexedFoldi s a -> (i -> a -> r) -> m (Mayber)ipreviews::MonadReaders m =>IndexedLens'i s a -> (i -> a -> r) -> m (Mayber)ipreviews::MonadReaders m =>IndexedTraversal'i s a -> (i -> a -> r) -> m (Mayber)
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::IndexedGetteri s a -> s ->Maybe(i, a)ipreview::IndexedFoldi 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::MonadReaders m =>IndexedGetters a -> m (Maybe(i, a))ipreview::MonadReaders m =>IndexedFolds a -> m (Maybe(i, a))ipreview::MonadReaders m =>IndexedLens's a -> m (Maybe(i, a))ipreview::MonadReaders m =>IndexedTraversal's a -> m (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 firstOf and ^?, which are similar with
some subtle differences (explained below).
listToMaybe.toList≡previewfolded
preview=view.pre
Unlike ^?, this function uses a
MonadReader to read the value to be focused in on.
This allows one to pass the value as the last argument by using the
MonadReader instance for (->) s
However, it may also be used as part of some deeply nested transformer stack.
preview uses a monoidal value to obtain the result.
This means that it generally has good performance, but can occasionally cause space leaks
or even stack overflows on some data types.
There is another function, firstOf, which avoids these issues at the cost of
a slight constant performance cost and a little less flexibility.
It may be helpful to think of preview as having one of the following
more specialized types:
preview::Getters a -> s ->Maybeapreview::Folds a -> s ->Maybeapreview::Lens's a -> s ->Maybeapreview::Iso's a -> s ->Maybeapreview::Traversal's a -> s ->Maybea
preview::MonadReaders m =>Getters a -> m (Maybea)preview::MonadReaders m =>Folds a -> m (Maybea)preview::MonadReaders m =>Lens's a -> m (Maybea)preview::MonadReaders m =>Iso's a -> m (Maybea)preview::MonadReaders m =>Traversal's a -> m (Maybea)
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::IndexedGetteri s a ->IndexPreservingGetters (Maybe(i, a))ipre::IndexedFoldi s a ->IndexPreservingGetters (Maybe(i, a))ipre::IndexedTraversal'i s a ->IndexPreservingGetters (Maybe(i, a))ipre::IndexedLens'i s a ->IndexPreservingGetters (Maybe(i, a))
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::Getters a ->IndexPreservingGetters (Maybea)pre::Folds a ->IndexPreservingGetters (Maybea)pre::Traversal's a ->IndexPreservingGetters (Maybea)pre::Lens's a ->IndexPreservingGetters (Maybea)pre::Iso's a ->IndexPreservingGetters (Maybea)pre::Prism's a ->IndexPreservingGetters (Maybea)
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::Getters a -> s ->Boolhas::Folds a -> s ->Boolhas::Iso's a -> s ->Boolhas::Lens's a -> s ->Boolhas::Traversal's a -> s ->Bool
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≡foldlMOffolded
foldlMOf::Monadm =>Getters a -> (r -> a -> m r) -> r -> s -> m rfoldlMOf::Monadm =>Folds a -> (r -> a -> m r) -> r -> s -> m rfoldlMOf::Monadm =>Iso's a -> (r -> a -> m r) -> r -> s -> m rfoldlMOf::Monadm =>Lens's a -> (r -> a -> m r) -> r -> s -> m rfoldlMOf::Monadm =>Traversal's a -> (r -> a -> m r) -> r -> s -> m r
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≡foldrMOffolded
foldrMOf::Monadm =>Getters a -> (a -> r -> m r) -> r -> s -> m rfoldrMOf::Monadm =>Folds a -> (a -> r -> m r) -> r -> s -> m rfoldrMOf::Monadm =>Iso's a -> (a -> r -> m r) -> r -> s -> m rfoldrMOf::Monadm =>Lens's a -> (a -> r -> m r) -> r -> s -> m rfoldrMOf::Monadm =>Traversal's a -> (a -> r -> m r) -> r -> s -> m r
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.toListOfl
foldl1Of'::Getters a -> (a -> a -> a) -> s -> afoldl1Of'::Folds a -> (a -> a -> a) -> s -> afoldl1Of'::Iso's a -> (a -> a -> a) -> s -> afoldl1Of'::Lens's a -> (a -> a -> a) -> s -> afoldl1Of'::Traversal's a -> (a -> a -> a) -> s -> a
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.
foldr1Ofl f ≡foldr1f.toListOfl
foldr1Of'::Getters a -> (a -> a -> a) -> s -> afoldr1Of'::Folds a -> (a -> a -> a) -> s -> afoldr1Of'::Iso's a -> (a -> a -> a) -> s -> afoldr1Of'::Lens's a -> (a -> a -> a) -> s -> afoldr1Of'::Traversal's a -> (a -> a -> a) -> s -> a
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'::Getters a -> (r -> a -> r) -> r -> s -> rfoldlOf'::Folds a -> (r -> a -> r) -> r -> s -> rfoldlOf'::Iso's a -> (r -> a -> r) -> r -> s -> rfoldlOf'::Lens's a -> (r -> a -> r) -> r -> s -> rfoldlOf'::Traversal's a -> (r -> a -> r) -> r -> s -> r
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'::Getters a -> (a -> r -> r) -> r -> s -> rfoldrOf'::Folds a -> (a -> r -> r) -> r -> s -> rfoldrOf'::Iso's a -> (a -> r -> r) -> r -> s -> rfoldrOf'::Lens's a -> (a -> r -> r) -> r -> s -> rfoldrOf'::Traversal's a -> (a -> r -> r) -> r -> s -> r
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
foldl1Ofl f ≡foldl1f.toListOflfoldl1≡foldl1Offolded
foldl1Of::Getters a -> (a -> a -> a) -> s -> afoldl1Of::Folds a -> (a -> a -> a) -> s -> afoldl1Of::Iso's a -> (a -> a -> a) -> s -> afoldl1Of::Lens's a -> (a -> a -> a) -> s -> afoldl1Of::Traversal's a -> (a -> a -> a) -> s -> a
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
foldr1Ofl f ≡foldr1f.toListOflfoldr1≡foldr1Offolded
foldr1Of::Getters a -> (a -> a -> a) -> s -> afoldr1Of::Folds a -> (a -> a -> a) -> s -> afoldr1Of::Iso's a -> (a -> a -> a) -> s -> afoldr1Of::Lens's a -> (a -> a -> a) -> s -> afoldr1Of::Traversal's a -> (a -> a -> a) -> s -> a
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::Eqk =>Folds (k,v) -> k -> s ->Maybev
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:: (Monadm,Getters a) -> (a -> mBool) -> s -> m (Maybea)findMOf:: (Monadm,Folds a) -> (a -> mBool) -> s -> m (Maybea)findMOf:: (Monadm,Iso's a) -> (a -> mBool) -> s -> m (Maybea)findMOf:: (Monadm,Lens's a) -> (a -> mBool) -> s -> m (Maybea)findMOf:: (Monadm,Traversal's a) -> (a -> mBool) -> s -> m (Maybea)
findMOffolded:: (Monad m, Foldable f) => (a -> m Bool) -> f a -> m (Maybe a)ifindMOfl ≡findMOfl.Indexed
A simpler version that didn't permit indexing, would be:
findMOf:: Monad m =>Getting(Endo(m (Maybea))) s a -> (a -> mBool) -> s -> m (Maybea)findMOfl p =foldrOfl (a y -> p a >>= x -> if x then return (Justa) else y) $ returnNothing
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::Getters a -> (a ->Bool) -> s ->MaybeafindOf::Folds a -> (a ->Bool) -> s ->MaybeafindOf::Iso's a -> (a ->Bool) -> s ->MaybeafindOf::Lens's a -> (a ->Bool) -> s ->MaybeafindOf::Traversal's a -> (a ->Bool) -> s ->Maybea
find≡findOffoldedifindOfl ≡findOfl.Indexed
A simpler version that didn't permit indexing, would be:
findOf::Getting(Endo(Maybea)) s a -> (a ->Bool) -> s ->MaybeafindOfl p =foldrOfl (a y -> if p a thenJusta else y)Nothing
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"
minimumBycmp ≡fromMaybe(error"empty").minimumByOffoldedcmp
minimumByOf::Getters a -> (a -> a ->Ordering) -> s ->MaybeaminimumByOf::Folds a -> (a -> a ->Ordering) -> s ->MaybeaminimumByOf::Iso's a -> (a -> a ->Ordering) -> s ->MaybeaminimumByOf::Lens's a -> (a -> a ->Ordering) -> s ->MaybeaminimumByOf::Traversal's a -> (a -> a ->Ordering) -> s ->Maybea
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.
maximumBycmp ≡fromMaybe(error"empty").maximumByOffoldedcmp
maximumByOf::Getters a -> (a -> a ->Ordering) -> s ->MaybeamaximumByOf::Folds a -> (a -> a ->Ordering) -> s ->MaybeamaximumByOf::Iso's a -> (a -> a ->Ordering) -> s ->MaybeamaximumByOf::Lens's a -> (a -> a ->Ordering) -> s ->MaybeamaximumByOf::Traversal's a -> (a -> a ->Ordering) -> s ->Maybea
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::Orda =>Getters a -> s -> aminimum1Of::Orda =>Fold1s a -> s -> aminimum1Of::Orda =>Iso's a -> s -> aminimum1Of::Orda =>Lens's a -> s -> aminimum1Of::Orda =>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").minimumOffolded
In the interest of efficiency, This operation has semantics more strict than strictly necessary.
rmap getMin (foldMapOf l Min)
minimumOf::Orda =>Getters a -> s ->MaybeaminimumOf::Orda =>Folds a -> s ->MaybeaminimumOf::Orda =>Iso's a -> s ->MaybeaminimumOf::Orda =>Lens's a -> s ->MaybeaminimumOf::Orda =>Traversal's a -> s ->Maybea
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::Orda =>Getters a -> s -> amaximum1Of::Orda =>Fold1s a -> s -> amaximum1Of::Orda =>Iso's a -> s -> amaximum1Of::Orda =>Lens's a -> s -> amaximum1Of::Orda =>Traversal1's a -> s -> a
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").maximumOffolded
In the interest of efficiency, This operation has semantics more strict than strictly necessary.
rmap getMax (foldMapOf l Max)
maximumOf::Orda =>Getters a -> s ->MaybeamaximumOf::Orda =>Folds a -> s ->MaybeamaximumOf::Orda =>Iso's a -> s ->MaybeamaximumOf::Orda =>Lens's a -> s ->MaybeamaximumOf::Orda =>Traversal's a -> s ->Maybea
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≡notNullOffolded
This may be rather inefficient compared to the not . null
>>>notNullOf _1 (1,2)True
>>>notNullOf traverse [1..10]True
>>>notNullOf folded []False
>>>notNullOf (element 20) [1..10]False
notNullOf(folded._1.folded) :: (Foldablef,Foldableg) => f (g a, b) ->Bool
notNullOf::Getters a -> s ->BoolnotNullOf::Folds a -> s ->BoolnotNullOf::Iso's a -> s ->BoolnotNullOf::Lens's a -> s ->BoolnotNullOf::Traversal's a -> s ->Bool
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≡nullOffolded
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) :: (Foldablef,Foldableg) => f (g a, b) ->Bool
nullOf::Getters a -> s ->BoolnullOf::Folds a -> s ->BoolnullOf::Iso's a -> s ->BoolnullOf::Lens's a -> s ->BoolnullOf::Traversal's a -> s ->Bool
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::Getters a -> s ->Maybealast1Of::Fold1s a -> s ->Maybealast1Of::Lens's a -> s ->Maybealast1Of::Iso's a -> s ->Maybealast1Of::Traversal1's a -> s ->Maybea
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 . foldMapOfJust 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::Getters a -> s ->MaybealastOf::Folds a -> s ->MaybealastOf::Lens's a -> s ->MaybealastOf::Iso's a -> s ->MaybealastOf::Traversal's a -> s ->Maybea
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::Getters a -> s -> afirst1Of::Fold1s a -> s -> afirst1Of::Lens's a -> s -> afirst1Of::Iso's a -> s -> afirst1Of::Traversal1's a -> s -> 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 preview^?'
and gives you back access to the outermost Just constructor more quickly, but does so
in a way that builds an intermediate structure, and thus may have worse
constant factors. This also means that it can not be used in any MonadReader,
but must instead have s passed as its last argument, unlike preview.
Note: this could been named headOf.
>>>firstOf traverse [1..10]Just 1
>>>firstOf both (1,2)Just 1
>>>firstOf ignored ()Nothing
firstOf::Getters a -> s ->MaybeafirstOf::Folds a -> s ->MaybeafirstOf::Lens's a -> s ->MaybeafirstOf::Iso's a -> s ->MaybeafirstOf::Traversal's a -> s ->Maybea
(^?!) :: HasCallStack => s -> Getting (Endo a) s a -> a infixl 8 #
(^?) :: 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. This is because ^? works by using the
First monoid, which can occasionally cause space leaks.
>>>Left 4 ^?_LeftJust 4
>>>Right 4 ^?_LeftNothing
>>>"world" ^? ix 3Just 'l'
>>>"world" ^? ix 20Nothing
This operator works as an infix version of preview.
(^?) ≡flippreview
It may be helpful to think of ^? as having one of the following
more specialized types:
(^?) :: s ->Getters a ->Maybea (^?) :: s ->Folds a ->Maybea (^?) :: s ->Lens's a ->Maybea (^?) :: s ->Iso's a ->Maybea (^?) :: s ->Traversal's a ->Maybea
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≡lengthOffolded
>>>lengthOf _1 ("hello",())1
>>>lengthOf traverse [1..10]10
>>>lengthOf (traverse.traverse) [[1,2],[3,4],[5,6]]6
lengthOf(folded.folded) :: (Foldablef,Foldableg) => f (g a) ->Int
lengthOf::Getters a -> s ->IntlengthOf::Folds a -> s ->IntlengthOf::Lens's a -> s ->IntlengthOf::Iso's a -> s ->IntlengthOf::Traversal's a -> s ->Int
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≡concatOffoldedconcatOf≡view
concatOf::Getters [r] -> s -> [r]concatOf::Folds [r] -> s -> [r]concatOf::Iso's [r] -> s -> [r]concatOf::Lens's [r] -> s -> [r]concatOf::Traversal's [r] -> s -> [r]
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≡concatMapOffolded
concatMapOf::Getters a -> (a -> [r]) -> s -> [r]concatMapOf::Folds 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]
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≡notElemOffolded
notElemOf::Eqa =>Getters a -> a -> s ->BoolnotElemOf::Eqa =>Folds a -> a -> s ->BoolnotElemOf::Eqa =>Iso's a -> a -> s ->BoolnotElemOf::Eqa =>Lens's a -> a -> s ->BoolnotElemOf::Eqa =>Traversal's a -> a -> s ->BoolnotElemOf::Eqa =>Prism's a -> a -> s ->Bool
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≡elemOffolded
elemOf::Eqa =>Getters a -> a -> s ->BoolelemOf::Eqa =>Folds a -> a -> s ->BoolelemOf::Eqa =>Lens's a -> a -> s ->BoolelemOf::Eqa =>Iso's a -> a -> s ->BoolelemOf::Eqa =>Traversal's a -> a -> s ->BoolelemOf::Eqa =>Prism's a -> a -> s ->Bool
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≡msumOffolded
msumOf::MonadPlusm =>Getters (m a) -> s -> m amsumOf::MonadPlusm =>Folds (m a) -> s -> m amsumOf::MonadPlusm =>Lens's (m a) -> s -> m amsumOf::MonadPlusm =>Iso's (m a) -> s -> m amsumOf::MonadPlusm =>Traversal's (m a) -> s -> m amsumOf::MonadPlusm =>Prism's (m a) -> s -> m a
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≡asumOffolded
asumOf::Alternativef =>Getters (f a) -> s -> f aasumOf::Alternativef =>Folds (f a) -> s -> f aasumOf::Alternativef =>Lens's (f a) -> s -> f aasumOf::Alternativef =>Iso's (f a) -> s -> f aasumOf::Alternativef =>Traversal's (f a) -> s -> f aasumOf::Alternativef =>Prism's (f a) -> s -> f a
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_::Monadm =>Getters (m a) -> s -> m ()sequenceOf_::Monadm =>Folds (m a) -> s -> m ()sequenceOf_::Monadm =>Lens's (m a) -> s -> m ()sequenceOf_::Monadm =>Iso's (m a) -> s -> m ()sequenceOf_::Monadm =>Traversal's (m a) -> s -> m ()sequenceOf_::Monadm =>Prism's (m a) -> 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") putStrLnhello world
forM_≡forMOf_folded
forMOf_::Monadm =>Getters a -> s -> (a -> m r) -> m ()forMOf_::Monadm =>Folds a -> s -> (a -> m r) -> m ()forMOf_::Monadm =>Lens's a -> s -> (a -> m r) -> m ()forMOf_::Monadm =>Iso's a -> s -> (a -> m r) -> m ()forMOf_::Monadm =>Traversal's a -> s -> (a -> m r) -> m ()forMOf_::Monadm =>Prism's a -> s -> (a -> m r) -> m ()
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_::Monadm =>Getters a -> (a -> m r) -> s -> m ()mapMOf_::Monadm =>Folds a -> (a -> m r) -> s -> m ()mapMOf_::Monadm =>Lens's a -> (a -> m r) -> s -> m ()mapMOf_::Monadm =>Iso's a -> (a -> m r) -> s -> m ()mapMOf_::Monadm =>Traversal's a -> (a -> m r) -> s -> m ()mapMOf_::Monadm =>Prism's a -> (a -> m r) -> s -> m ()
sequence1Of_ :: Functor f => Getting (TraversedF a f) s (f a) -> s -> f () #
See sequenceAOf_ and traverse1Of_.
sequence1Of_::Applyf =>Fold1s (f a) -> 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_::Applyf =>Fold1s a -> s -> (a -> f r) -> f ()
Since: lens-4.16
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_::Applyf =>Fold1s a -> (a -> f r) -> s -> f ()
Since: lens-4.16
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_::Functorf =>Getters (f a) -> s -> f ()sequenceAOf_::Applicativef =>Folds (f a) -> s -> f ()sequenceAOf_::Functorf =>Lens's (f a) -> s -> f ()sequenceAOf_::Functorf =>Iso's (f a) -> s -> f ()sequenceAOf_::Applicativef =>Traversal's (f a) -> s -> f ()sequenceAOf_::Applicativef =>Prism's (f a) -> 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") putStrLnhello 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_::Functorf =>Getters a -> s -> (a -> f r) -> f ()forOf_::Applicativef =>Folds a -> s -> (a -> f r) -> f ()forOf_::Functorf =>Lens's a -> s -> (a -> f r) -> f ()forOf_::Functorf =>Iso's a -> s -> (a -> f r) -> f ()forOf_::Applicativef =>Traversal's a -> s -> (a -> f r) -> f ()forOf_::Applicativef =>Prism's a -> s -> (a -> f r) -> f ()
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::Functorf => (c -> f r) -> (d, c) -> f ()traverseOf__Left::Applicativef => (a -> f b) ->Eithera 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_::Functorf =>Getters a -> (a -> f r) -> s -> f ()traverseOf_::Applicativef =>Folds a -> (a -> f r) -> s -> f ()traverseOf_::Functorf =>Lens's a -> (a -> f r) -> s -> f ()traverseOf_::Functorf =>Iso's a -> (a -> f r) -> s -> f ()traverseOf_::Applicativef =>Traversal's a -> (a -> f r) -> s -> f ()traverseOf_::Applicativef =>Prism's a -> (a -> f r) -> s -> f ()
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)])] :: Int10
sum≡sumOffolded
This operation may be more strict than you would expect. If you
want a lazier version use ala Sum . foldMapOf
sumOf_1::Numa => (a, b) -> asumOf(folded._1) :: (Foldablef,Numa) => f (a, b) -> a
sumOf::Numa =>Getters a -> s -> asumOf::Numa =>Folds a -> s -> asumOf::Numa =>Lens's a -> s -> asumOf::Numa =>Iso's a -> s -> asumOf::Numa =>Traversal's a -> s -> asumOf::Numa =>Prism's a -> s -> a
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≡productOffolded
This operation may be more strict than you would expect. If you
want a lazier version use ala Product . foldMapOf
productOf::Numa =>Getters a -> s -> aproductOf::Numa =>Folds a -> s -> aproductOf::Numa =>Lens's a -> s -> aproductOf::Numa =>Iso's a -> s -> aproductOf::Numa =>Traversal's a -> s -> aproductOf::Numa =>Prism's a -> s -> a
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
inoneOfl =noneOfl.Indexed
noneOf::Getters a -> (a ->Bool) -> s ->BoolnoneOf::Folds a -> (a ->Bool) -> s ->BoolnoneOf::Lens's a -> (a ->Bool) -> s ->BoolnoneOf::Iso's a -> (a ->Bool) -> s ->BoolnoneOf::Traversal's a -> (a ->Bool) -> s ->BoolnoneOf::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≡allOffolded
iallOfl =allOfl.Indexed
allOf::Getters a -> (a ->Bool) -> s ->BoolallOf::Folds a -> (a ->Bool) -> s ->BoolallOf::Lens's a -> (a ->Bool) -> s ->BoolallOf::Iso's a -> (a ->Bool) -> s ->BoolallOf::Traversal's a -> (a ->Bool) -> s ->BoolallOf::Prism's a -> (a ->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≡anyOffolded
ianyOfl ≡anyOfl.Indexed
anyOf::Getters a -> (a ->Bool) -> s ->BoolanyOf::Folds a -> (a ->Bool) -> s ->BoolanyOf::Lens's a -> (a ->Bool) -> s ->BoolanyOf::Iso's a -> (a ->Bool) -> s ->BoolanyOf::Traversal's a -> (a ->Bool) -> s ->BoolanyOf::Prism's a -> (a ->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≡orOffolded
orOf::GettersBool-> s ->BoolorOf::FoldsBool-> s ->BoolorOf::Lens'sBool-> s ->BoolorOf::Iso'sBool-> s ->BoolorOf::Traversal'sBool-> s ->BoolorOf::Prism'sBool-> s ->Bool
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≡andOffolded
andOf::GettersBool-> s ->BoolandOf::FoldsBool-> s ->BoolandOf::Lens'sBool-> s ->BoolandOf::Iso'sBool-> s ->BoolandOf::Traversal'sBool-> s ->BoolandOf::Prism'sBool-> s ->Bool
(^..) :: 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]
toListxs ≡ xs^..folded(^..) ≡fliptoListOf
(^..) :: s ->Getters a -> a :: s ->Folds a -> a :: s ->Lens's a -> a :: s ->Iso's a -> a :: s ->Traversal's a -> a :: s ->Prism's a -> [a]
toNonEmptyOf :: Getting (NonEmptyDList a) s a -> s -> NonEmpty a #
Extract a NonEmpty of the targets of Fold1.
>>>toNonEmptyOf both1 ("hello", "world")"hello" :| ["world"]
toNonEmptyOf::Getters a -> s -> NonEmpty atoNonEmptyOf::Fold1s a -> s -> NonEmpty atoNonEmptyOf::Lens's a -> s -> NonEmpty atoNonEmptyOf::Iso's a -> s -> NonEmpty atoNonEmptyOf::Traversal1's a -> s -> NonEmpty atoNonEmptyOf::Prism's a -> s -> NonEmpty a
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≡foldlOffolded
foldlOf::Getters a -> (r -> a -> r) -> r -> s -> rfoldlOf::Folds a -> (r -> a -> r) -> r -> s -> rfoldlOf::Lens's a -> (r -> a -> r) -> r -> s -> rfoldlOf::Iso's a -> (r -> a -> r) -> r -> s -> rfoldlOf::Traversal's a -> (r -> a -> r) -> r -> s -> rfoldlOf::Prism's a -> (r -> a -> r) -> r -> s -> r
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≡foldrOffolded
foldrOf::Getters a -> (a -> r -> r) -> r -> s -> rfoldrOf::Folds a -> (a -> r -> r) -> r -> s -> rfoldrOf::Lens's a -> (a -> r -> r) -> r -> s -> rfoldrOf::Iso's a -> (a -> r -> r) -> r -> s -> rfoldrOf::Traversal's a -> (a -> r -> r) -> r -> s -> rfoldrOf::Prism's a -> (a -> r -> r) -> r -> s -> r
ifoldrOfl ≡foldrOfl.Indexed
foldrOf::Getting(Endor) s a -> (a -> r -> r) -> 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=foldOffolded
foldOf≡view
foldOf::Getters m -> s -> mfoldOf::Monoidm =>Folds m -> s -> mfoldOf::Lens's m -> s -> mfoldOf::Iso's m -> s -> mfoldOf::Monoidm =>Traversal's m -> s -> mfoldOf::Monoidm =>Prism's m -> s -> m
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=foldMapOffolded
foldMapOf≡viewsifoldMapOfl =foldMapOfl.Indexed
foldMapOf::Getters a -> (a -> r) -> s -> rfoldMapOf::Monoidr =>Folds a -> (a -> r) -> s -> rfoldMapOf::Semigroupr =>Fold1s a -> (a -> r) -> s -> rfoldMapOf::Lens's a -> (a -> r) -> s -> rfoldMapOf::Iso's a -> (a -> r) -> s -> rfoldMapOf::Monoidr =>Traversal's a -> (a -> r) -> s -> rfoldMapOf::Semigroupr =>Traversal1's a -> (a -> r) -> s -> rfoldMapOf::Monoidr =>Prism's a -> (a -> r) -> s -> r
foldMapOf::Gettingr s a -> (a -> r) -> s -> r
lined :: Applicative f => IndexedLensLike' Int f String String #
A Fold over the individual lines of a String.
lined::FoldStringStringlined::Traversal'StringString
lined::IndexedFoldIntStringStringlined::IndexedTraversal'IntStringString
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.
worded :: Applicative f => IndexedLensLike' Int f String String #
A Fold over the individual words of a String.
worded::FoldStringStringworded::Traversal'StringString
worded::IndexedFoldIntStringStringworded::IndexedTraversal'IntStringString
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).
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.
dropWhilep ≡toListOf(droppingWhilepfolded)
>>>toListOf (droppingWhile (<=3) folded) [1..6][4,5,6]
>>>toListOf (droppingWhile (<=3) folded) [1,6,1][6,1]
droppingWhile:: (a ->Bool) ->Folds a ->Folds adroppingWhile:: (a ->Bool) ->Getters a ->Folds adroppingWhile:: (a ->Bool) ->Traversal's a ->Folds a -- see notesdroppingWhile:: (a ->Bool) ->Lens's a ->Folds a -- see notesdroppingWhile:: (a ->Bool) ->Prism's a ->Folds a -- see notesdroppingWhile:: (a ->Bool) ->Iso's a ->Folds a -- see notes
droppingWhile:: (a ->Bool) ->IndexPreservingTraversal's a ->IndexPreservingFolds a -- see notesdroppingWhile:: (a ->Bool) ->IndexPreservingLens's a ->IndexPreservingFolds a -- see notesdroppingWhile:: (a ->Bool) ->IndexPreservingGetters a ->IndexPreservingFolds adroppingWhile:: (a ->Bool) ->IndexPreservingFolds a ->IndexPreservingFolds a
droppingWhile:: (a ->Bool) ->IndexedTraversal'i s a ->IndexedFoldi s a -- see notesdroppingWhile:: (a ->Bool) ->IndexedLens'i s a ->IndexedFoldi s a -- see notesdroppingWhile:: (a ->Bool) ->IndexedGetteri s a ->IndexedFoldi s adroppingWhile:: (a ->Bool) ->IndexedFoldi s a ->IndexedFoldi 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( is. For example:dropping 1 . droppingWhile p) t
>>>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]
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.
takeWhilep ≡toListOf(takingWhilepfolded)
>>>timingOut $ toListOf (takingWhile (<=3) folded) [1..][1,2,3]
takingWhile:: (a ->Bool) ->Folds a ->Folds atakingWhile:: (a ->Bool) ->Getters a ->Folds atakingWhile:: (a ->Bool) ->Traversal's a ->Folds a -- * See note belowtakingWhile:: (a ->Bool) ->Lens's a ->Folds a -- * See note belowtakingWhile:: (a ->Bool) ->Prism's a ->Folds a -- * See note belowtakingWhile:: (a ->Bool) ->Iso's a ->Folds a -- * See note belowtakingWhile:: (a ->Bool) ->IndexedTraversal'i s a ->IndexedFoldi s a -- * See note belowtakingWhile:: (a ->Bool) ->IndexedLens'i s a ->IndexedFoldi s a -- * See note belowtakingWhile:: (a ->Bool) ->IndexedFoldi s a ->IndexedFoldi s atakingWhile:: (a ->Bool) ->IndexedGetteri s a ->IndexedFoldi 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.
filteredBy :: (Indexable i p, Applicative f) => Getting (First i) a i -> p a (f a) -> a -> f a #
Obtain a potentially empty IndexedTraversal by taking the first element from another,
potentially empty Fold and using it as an index.
The resulting optic can be composed with to filter another Lens, Iso, Getter, Fold (or Traversal).
>>>[(Just 2, 3), (Nothing, 4)] & mapped . filteredBy (_1 . _Just) <. _2 %@~ (*) :: [(Maybe Int, Int)][(Just 2,6),(Nothing,4)]
filteredBy::Folda i ->IndexedTraversal'i a a
Note: As with filtered, this is not a legal IndexedTraversal, unless you are very careful not to invalidate the predicate on the target!
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 fails the predicate.
As a counter example, consider that given evens = the second filtered evenTraversal law is violated:
overevenssucc.overevenssucc/=overevens (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.
replicated :: Int -> Fold a a #
A Fold that replicates its input n times.
replicaten ≡toListOf(replicatedn)
>>>5^..replicated 20[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
folded64 :: Foldable f => IndexedFold Int64 (f a) a #
folded :: Foldable f => IndexedFold Int (f a) a #
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.
foldring :: (Contravariant f, Applicative f) => ((a -> f a -> f a) -> f a -> s -> f a) -> LensLike f s t a b #
ifolding :: (Foldable f, Indexable i p, Contravariant g, Applicative g) => (s -> f (i, a)) -> Over p g s t a b #
_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 OrderingJust EQ
_Show≡prism'showreadMaybe
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 [] nullNothing
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.
_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 # 5Just 5
>>>5^.re _JustJust 5
Interestingly,
m^?_Just≡ m
>>>Just x ^? _JustJust x
>>>Nothing ^? _JustNothing
_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 # 5Right 5
>>>5^.re _RightRight 5
_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 # 5Left 5
>>>5^.re _LeftLeft 5
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) IntLeft Nothing
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"]]
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.
without :: APrism s t a b -> APrism u v c d -> Prism (Either s u) (Either t v) (Either a c) (Either b d) #
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.
withPrism :: APrism s t a b -> ((b -> t) -> (s -> Either t a) -> r) -> r #
Convert APrism to the pair of functions that characterize it.
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.
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.rereuses(untof) g ≡gets(g.f)
>>>evalState (reuses _Left isLeft) (5 :: Int)True
reuses::MonadStatea m =>Prism's a -> (s -> r) -> m rreuses::MonadStatea m =>Iso'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.rereuse.unto≡gets
>>>evalState (reuse _Left) 5Left 5
>>>evalState (reuse (unto succ)) 56
reuse::MonadStatea m =>Prism's a -> m sreuse::MonadStatea m =>Iso'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.rereviews(untof) g ≡ g.f
>>>reviews _Left isRight "mustard"False
>>>reviews (unto succ) (*2) 38
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 -> rreviews::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::MonadReadera m =>Iso's a -> (s -> r) -> m rreviews::MonadReadera m =>Prism's a -> (s -> r) -> m r
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.rereview.unto≡id
>>>review _Left "mustard"Left "mustard"
>>>review (unto succ) 56
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 -> sreview::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::MonadReadera m =>Iso's a -> m sreview::MonadReadera m =>Prism's a -> m s
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 _LeftLeft 5
>>>6 ^.re (_Left.unto succ)Left 7
review≡view.rereviews≡views.rereuse≡use.rereuses≡uses.re
re::Prisms t a b ->Getterb tre::Isos t a b ->Getterb t
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::Traversals t a b ->Folds agetting::Lenss t a b ->Getters agetting::IndexedTraversali s t a b ->IndexedFoldi s agetting::IndexedLensi s t a b ->IndexedGetteri s a
(^@.) :: 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 ->IndexedGetteri s a -> (i, a) (^@.) :: s ->IndexedLens'i s a -> (i, a)
The result probably doesn't have much meaning when applied to an IndexedFold.
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.
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.
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
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.
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::MonadWriterw m =>IndexedGetterw u -> (i -> u -> v) -> m a -> m (a, v)ilistenings::MonadWriterw m =>IndexedLens'w u -> (i -> u -> v) -> m a -> m (a, v)ilistenings:: (MonadWriterw m,Monoidv) =>IndexedFoldw u -> (i -> u -> v) -> m a -> m (a, v)ilistenings:: (MonadWriterw m,Monoidv) =>IndexedTraversal'w u -> (i -> u -> v) -> m a -> m (a, v)
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::MonadWriterw m =>Getterw u -> (u -> v) -> m a -> m (a, v)listenings::MonadWriterw m =>Lens'w u -> (u -> v) -> m a -> m (a, v)listenings::MonadWriterw m =>Iso'w u -> (u -> v) -> m a -> m (a, v)listenings:: (MonadWriterw m,Monoidv) =>Foldw u -> (u -> v) -> m a -> m (a, v)listenings:: (MonadWriterw m,Monoidv) =>Traversal'w u -> (u -> v) -> m a -> m (a, v)listenings:: (MonadWriterw m,Monoidv) =>Prism'w u -> (u -> v) -> m a -> m (a, v)
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::MonadWriterw m =>IndexedGetteri w u -> m a -> m (a, (i, u))ilistening::MonadWriterw m =>IndexedLens'i w u -> m a -> m (a, (i, u))ilistening:: (MonadWriterw m,Monoidu) =>IndexedFoldi w u -> m a -> m (a, (i, u))ilistening:: (MonadWriterw m,Monoidu) =>IndexedTraversal'i w u -> m a -> m (a, (i, u))
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::MonadWriterw m =>Getterw u -> m a -> m (a, u)listening::MonadWriterw m =>Lens'w u -> m a -> m (a, u)listening::MonadWriterw m =>Iso'w u -> m a -> m (a, u)listening:: (MonadWriterw m,Monoidu) =>Foldw u -> m a -> m (a, u)listening:: (MonadWriterw m,Monoidu) =>Traversal'w u -> m a -> m (a, u)listening:: (MonadWriterw m,Monoidu) =>Prism'w u -> m a -> m (a, u)
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::MonadStates m =>Getters a -> (a -> r) -> m ruses:: (MonadStates m,Monoidr) =>Folds a -> (a -> r) -> m ruses::MonadStates m =>Lens's a -> (a -> r) -> m ruses::MonadStates m =>Iso's a -> (a -> r) -> m ruses:: (MonadStates m,Monoidr) =>Traversal's a -> (a -> r) -> m r
uses::MonadStates m =>Gettingr s t a b -> (a -> r) -> m r
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::MonadStates m =>Getters a -> m ause:: (MonadStates m,Monoidr) =>Folds r -> m ruse::MonadStates m =>Iso's a -> m ause::MonadStates m =>Lens's a -> m ause:: (MonadStates m,Monoidr) =>Traversal's 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)^._2b
>>>("hello","world")^._2"world"
>>>import Data.Complex>>>((0, 1 :+ 2), 3)^._1._2.to magnitude2.23606797749979
(^.) :: s ->Getters a -> a (^.) ::Monoidm => s ->Folds m -> m (^.) :: s ->Iso's a -> a (^.) :: s ->Lens's a -> a (^.) ::Monoidm => s ->Traversal's m -> m
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.
viewsl f ≡view(l.tof)
>>>views (to f) g ag (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::Getters a -> (a -> r) -> s -> rviews::Monoidm =>Folds a -> (a -> m) -> s -> mviews::Iso's a -> (a -> r) -> s -> rviews::Lens's a -> (a -> r) -> s -> rviews::Monoidm =>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::MonadReaders m =>Getters a -> (a -> r) -> m rviews:: (MonadReaders m,Monoidr) =>Folds a -> (a -> r) -> m rviews::MonadReaders m =>Iso's a -> (a -> r) -> m rviews::MonadReaders m =>Lens's a -> (a -> r) -> m rviews:: (MonadReaders m,Monoidr) =>Traversal's a -> (a -> r) -> m r
views::MonadReaders m =>Gettingr s a -> (a -> r) -> m r
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) af a
>>>view _2 (1,"hello")"hello"
>>>view (to succ) 56
>>>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::Getters a -> s -> aview::Monoidm =>Folds m -> s -> mview::Iso's a -> s -> aview::Lens's a -> s -> aview::Monoidm =>Traversal's m -> s -> m
In a more general setting, such as when working with a Monad transformer stack you can use:
view::MonadReaders m =>Getters a -> m aview:: (MonadReaders m,Monoida) =>Folds a -> m aview::MonadReaders m =>Iso's a -> m aview::MonadReaders m =>Lens's a -> m aview:: (MonadReaders m,Monoida) =>Traversal's a -> m a
ilike :: (Indexable i p, Contravariant f, Functor f) => i -> a -> Over' p f s a #
ilike:: i -> a ->IndexedGetteri s a
like :: (Profunctor p, Contravariant f, Functor f) => a -> Optic' p f s a #
ito :: (Indexable i p, Contravariant f) => (s -> (i, a)) -> Over' p f s a #
ito:: (s -> (i, a)) ->IndexedGetteri s a
to :: (Profunctor p, Contravariant f) => (s -> a) -> Optic' p f s a #
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 ar is a Monoid, then
you can pass a Fold (or
Traversal), otherwise you can only pass this a
Getter or Lens.
type IndexedGetting i m s a = Indexed i a (Const m a) -> s -> Const m s #
Used to consume an IndexedFold.
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.
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
Access the 1st field of a tuple (and possibly change its type).
>>>(1,2)^._11
>>>_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 | |
| Field1 (Plucker a) (Plucker a) a a | |
| Field1 (Quaternion a) (Quaternion a) a a | |
Defined in Linear.Quaternion Methods _1 :: Lens (Quaternion a) (Quaternion a) a a # | |
| Field1 (V4 a) (V4 a) a a | |
| Field1 (V3 a) (V3 a) a a | |
| Field1 (V2 a) (V2 a) a a | |
| Field1 (V1 a) (V1 b) a b | |
| Field1 (a, b) (a', b) a a' |
|
Defined in Control.Lens.Tuple | |
| Field1 (a, b, c) (a', b, c) a a' | |
Defined in Control.Lens.Tuple | |
| 1 <= n => Field1 (V n a) (V n a) a a | |
| Field1 (a, b, c, d) (a', b, c, d) a a' | |
Defined in Control.Lens.Tuple | |
| Field1 ((f :*: g) p) ((f' :*: g) p) (f p) (f' p) | |
| Field1 (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' | |
Defined in Control.Lens.Tuple | |
| Field1 (a, b, c, d, e, f) (a', b, c, d, e, f) a a' | |
Defined in Control.Lens.Tuple | |
| Field1 (a, b, c, d, e, f, g) (a', b, c, d, e, f, g) a a' | |
Defined in Control.Lens.Tuple | |
| Field1 (a, b, c, d, e, f, g, h) (a', b, c, d, e, f, g, h) a a' | |
Defined in Control.Lens.Tuple | |
| Field1 (a, b, c, d, e, f, g, h, i) (a', b, c, d, e, f, g, h, i) a a' | |
Defined in Control.Lens.Tuple | |
| Field1 (a, b, c, d, e, f, g, h, i, j) (a', b, c, d, e, f, g, h, i, j) a a' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
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) ->Booltraverse._2:: (Applicativef,Traversablet) => (a -> f b) -> t (s, a) -> f (t (s, b))foldMapOf(traverse._2) :: (Traversablet,Monoidm) => (s -> m) -> t (b, s) -> m
Instances
| Field2 (Plucker a) (Plucker a) a a | |
| Field2 (Quaternion a) (Quaternion a) a a | |
Defined in Linear.Quaternion Methods _2 :: Lens (Quaternion a) (Quaternion a) a a # | |
| Field2 (V4 a) (V4 a) a a | |
| Field2 (V3 a) (V3 a) a a | |
| Field2 (V2 a) (V2 a) a a | |
| Field2 (a, b) (a, b') b b' |
|
Defined in Control.Lens.Tuple | |
| Field2 (a, b, c) (a, b', c) b b' | |
Defined in Control.Lens.Tuple | |
| 2 <= n => Field2 (V n a) (V n a) a a | |
| Field2 (a, b, c, d) (a, b', c, d) b b' | |
Defined in Control.Lens.Tuple | |
| Field2 ((f :*: g) p) ((f :*: g') p) (g p) (g' p) | |
| Field2 (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' | |
Defined in Control.Lens.Tuple | |
| Field2 (a, b, c, d, e, f) (a, b', c, d, e, f) b b' | |
Defined in Control.Lens.Tuple | |
| Field2 (a, b, c, d, e, f, g) (a, b', c, d, e, f, g) b b' | |
Defined in Control.Lens.Tuple | |
| Field2 (a, b, c, d, e, f, g, h) (a, b', c, d, e, f, g, h) b b' | |
Defined in Control.Lens.Tuple | |
| Field2 (a, b, c, d, e, f, g, h, i) (a, b', c, d, e, f, g, h, i) b b' | |
Defined in Control.Lens.Tuple | |
| Field2 (a, b, c, d, e, f, g, h, i, j) (a, b', c, d, e, f, g, h, i, j) b b' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
Instances
| Field3 (Plucker a) (Plucker a) a a | |
| Field3 (Quaternion a) (Quaternion a) a a | |
Defined in Linear.Quaternion Methods _3 :: Lens (Quaternion a) (Quaternion a) a a # | |
| Field3 (V4 a) (V4 a) a a | |
| Field3 (V3 a) (V3 a) a a | |
| Field3 (a, b, c) (a, b, c') c c' | |
Defined in Control.Lens.Tuple | |
| 3 <= n => Field3 (V n a) (V n a) a a | |
| Field3 (a, b, c, d) (a, b, c', d) c c' | |
Defined in Control.Lens.Tuple | |
| Field3 (a, b, c, d, e) (a, b, c', d, e) c c' | |
Defined in Control.Lens.Tuple | |
| Field3 (a, b, c, d, e, f) (a, b, c', d, e, f) c c' | |
Defined in Control.Lens.Tuple | |
| Field3 (a, b, c, d, e, f, g) (a, b, c', d, e, f, g) c c' | |
Defined in Control.Lens.Tuple | |
| Field3 (a, b, c, d, e, f, g, h) (a, b, c', d, e, f, g, h) c c' | |
Defined in Control.Lens.Tuple | |
| Field3 (a, b, c, d, e, f, g, h, i) (a, b, c', d, e, f, g, h, i) c c' | |
Defined in Control.Lens.Tuple | |
| Field3 (a, b, c, d, e, f, g, h, i, j) (a, b, c', d, e, f, g, h, i, j) c c' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
Instances
| Field4 (Plucker a) (Plucker a) a a | |
| Field4 (Quaternion a) (Quaternion a) a a | |
Defined in Linear.Quaternion Methods _4 :: Lens (Quaternion a) (Quaternion a) a a # | |
| Field4 (V4 a) (V4 a) a a | |
| 4 <= n => Field4 (V n a) (V n a) a a | |
| Field4 (a, b, c, d) (a, b, c, d') d d' | |
Defined in Control.Lens.Tuple | |
| Field4 (a, b, c, d, e) (a, b, c, d', e) d d' | |
Defined in Control.Lens.Tuple | |
| Field4 (a, b, c, d, e, f) (a, b, c, d', e, f) d d' | |
Defined in Control.Lens.Tuple | |
| Field4 (a, b, c, d, e, f, g) (a, b, c, d', e, f, g) d d' | |
Defined in Control.Lens.Tuple | |
| Field4 (a, b, c, d, e, f, g, h) (a, b, c, d', e, f, g, h) d d' | |
Defined in Control.Lens.Tuple | |
| Field4 (a, b, c, d, e, f, g, h, i) (a, b, c, d', e, f, g, h, i) d d' | |
Defined in Control.Lens.Tuple | |
| Field4 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d', e, f, g, h, i, j) d d' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
Instances
| Field5 (Plucker a) (Plucker a) a a | |
| 5 <= n => Field5 (V n a) (V n a) a a | |
| Field5 (a, b, c, d, e) (a, b, c, d, e') e e' | |
Defined in Control.Lens.Tuple | |
| Field5 (a, b, c, d, e, f) (a, b, c, d, e', f) e e' | |
Defined in Control.Lens.Tuple | |
| Field5 (a, b, c, d, e, f, g) (a, b, c, d, e', f, g) e e' | |
Defined in Control.Lens.Tuple | |
| Field5 (a, b, c, d, e, f, g, h) (a, b, c, d, e', f, g, h) e e' | |
Defined in Control.Lens.Tuple | |
| Field5 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e', f, g, h, i) e e' | |
Defined in Control.Lens.Tuple | |
| Field5 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e', f, g, h, i, j) e e' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
Instances
| Field6 (Plucker a) (Plucker a) a a | |
| 6 <= n => Field6 (V n a) (V n a) a a | |
| Field6 (a, b, c, d, e, f) (a, b, c, d, e, f') f f' | |
Defined in Control.Lens.Tuple | |
| Field6 (a, b, c, d, e, f, g) (a, b, c, d, e, f', g) f f' | |
Defined in Control.Lens.Tuple | |
| Field6 (a, b, c, d, e, f, g, h) (a, b, c, d, e, f', g, h) f f' | |
Defined in Control.Lens.Tuple | |
| Field6 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f', g, h, i) f f' | |
Defined in Control.Lens.Tuple | |
| Field6 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f', g, h, i, j) f f' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
Instances
| 7 <= n => Field7 (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' | |
Defined in Control.Lens.Tuple | |
| Field7 (a, b, c, d, e, f, g, h) (a, b, c, d, e, f, g', h) g g' | |
Defined in Control.Lens.Tuple | |
| Field7 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g', h, i) g g' | |
Defined in Control.Lens.Tuple | |
| Field7 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g', h, i, j) g g' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
Instances
| 8 <= n => Field8 (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' | |
Defined in Control.Lens.Tuple | |
| Field8 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g, h', i) h h' | |
Defined in Control.Lens.Tuple | |
| Field8 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h', i, j) h h' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
Instances
| 9 <= n => Field9 (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' | |
Defined in Control.Lens.Tuple | |
| Field9 (a, b, c, d, e, f, g, h, i, j) (a, b, c, d, e, f, g, h, i', j) i i' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
Instances
| 10 <= n => Field10 (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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
Instances
| 11 <= n => Field11 (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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
Instances
| 12 <= n => Field12 (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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
Instances
| 13 <= n => Field13 (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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
Instances
| 14 <= n => Field14 (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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
Instances
| 15 <= n => Field15 (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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
Instances
| 16 <= n => Field16 (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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
Instances
| 17 <= n => Field17 (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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
Instances
| 18 <= n => Field18 (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' | |
Defined in Control.Lens.Tuple | |
| 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' | |
Defined in Control.Lens.Tuple | |
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
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::Lenss t a b ->Lenss t a b
last1 :: Traversable1 t => Lens' (t a) a #
A Lens focusing on the last element of a Traversable1 container.
>>>2 :| [3, 4] & last1 +~ 102 :| [3,14]
>>>Node 'a' [Node 'b' [], Node 'c' []] ^. last1'c'
head1 :: Traversable1 t => Lens' (t a) a #
A Lens focusing on the first element of a Traversable1 container.
>>>2 :| [3, 4] & head1 +~ 1012 :| [3,4]
>>>Identity True ^. head1True
We can always retrieve a () from any type.
>>>"hello"^.united()
>>>"hello" & united .~ ()"hello"
(<#=) :: MonadState s m => ALens s s a b -> b -> m b infix 4 #
(#%%=) :: MonadState s m => ALens s s a b -> (a -> (r, b)) -> m r infix 4 #
(<#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m b infix 4 #
(#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m () infix 4 #
(#=) :: MonadState s m => ALens s s a b -> b -> m () infix 4 #
(<<%@=) :: 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.
(<<%@=) ::MonadStates m =>IndexedLensi s s a b -> (i -> a -> b) -> m a (<<%@=) :: (MonadStates m,Monoidb) =>IndexedTraversali s s a b -> (i -> a -> b) -> m a
(<%@=) :: 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.
(<%@=) ::MonadStates m =>IndexedLensi s s a b -> (i -> a -> b) -> m b (<%@=) :: (MonadStates m,Monoidb) =>IndexedTraversali s s a b -> (i -> a -> b) -> m b
(%%@=) :: 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)
(%%@=) ::MonadStates m =>IndexedLensi s s a b -> (i -> a -> (r, b)) -> s -> m r (%%@=) :: (MonadStates m,Monoidr) =>IndexedTraversali s s a b -> (i -> a -> (r, b)) -> s -> m r
(%%@~) :: 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
(%%@~) ::Functorf =>IndexedLensi s t a b -> (i -> a -> f b) -> s -> f t (%%@~) ::Applicativef =>IndexedTraversali 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:
(%%@~) ::IndexedLensi s t a b -> (i -> a -> (r, b)) -> s -> (r, t) (%%@~) ::Monoidr =>IndexedTraversali s t a b -> (i -> a -> (r, b)) -> s -> (r, 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.
(<<%@~) ::IndexedLensi s t a b -> (i -> a -> b) -> s -> (a, t) (<<%@~) ::Monoida =>IndexedTraversali s t a b -> (i -> a -> b) -> s -> (a, 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<%@~constf
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 (%~).
(<%@~) ::IndexedLensi s t a b -> (i -> a -> b) -> s -> (b, t) (<%@~) ::Monoidb =>IndexedTraversali s t a b -> (i -> a -> b) -> s -> (b, t)
(<<~) :: 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.
(<<~) ::MonadStates m =>Isos s a b -> m b -> m b (<<~) ::MonadStates m =>Lenss 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.
(<<<>=) :: (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.
(<<<>=) :: (MonadStates m,Monoidr) =>Lens's r -> r -> m r (<<<>=) :: (MonadStates m,Monoidr) =>Iso's r -> r -> m r
(<<&&=) :: 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.
(<<&&=) ::MonadStates m =>Lens'sBool->Bool-> mBool(<<&&=) ::MonadStates m =>Iso'sBool->Bool-> mBool
(<<||=) :: 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.
(<<||=) ::MonadStates m =>Lens'sBool->Bool-> mBool(<<||=) ::MonadStates m =>Iso'sBool->Bool-> mBool
(<<**=) :: (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.
(<<**=) :: (MonadStates m,Floatinga) =>Lens's a -> a -> m a (<<**=) :: (MonadStates m,Floatinga) =>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.
(<<^^=) :: (MonadStates m,Fractionala,Integrale) =>Lens's a -> e -> m a (<<^^=) :: (MonadStates m,Fractionala,Integrale) =>Iso's a -> e -> 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.
(<<^=) :: (MonadStates m,Numa,Integrale) =>Lens's a -> e -> m a (<<^=) :: (MonadStates m,Numa,Integrale) =>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.
(<<//=) :: (MonadStates m,Fractionala) =>Lens's a -> a -> m a (<<//=) :: (MonadStates m,Fractionala) =>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.
(<<*=) :: (MonadStates m,Numa) =>Lens's a -> a -> m a (<<*=) :: (MonadStates m,Numa) =>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.
(<<-=) :: (MonadStates m,Numa) =>Lens's a -> a -> m a (<<-=) :: (MonadStates m,Numa) =>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 adding a value
and return the old value that was replaced.
When you do not need the result of the operation, (+=) is more flexible.
(<<+=) :: (MonadStates m,Numa) =>Lens's a -> a -> m a (<<+=) :: (MonadStates m,Numa) =>Iso'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.
(<<?=) ::MonadStates m =>Lenss t a (Maybe b) -> b -> m a (<<?=) ::MonadStates m =>Isos t a (Maybe b) -> b -> m a (<<?=) :: (MonadStates m,Monoida) =>Traversals t a (Maybe b) -> 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.
(<<.=) ::MonadStates m =>Lens's a -> a -> m a (<<.=) ::MonadStates m =>Iso's a -> a -> m a (<<.=) :: (MonadStates m,Monoida) =>Traversal's a -> a -> m a
(<<%=) :: (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.
(<<%=) ::MonadStates m =>Lens's a -> (a -> a) -> m a (<<%=) ::MonadStates m =>Iso's a -> (a -> a) -> m a (<<%=) :: (MonadStates m,Monoida) =>Traversal's a -> (a -> a) -> m a
(<<%=) ::MonadStates m =>LensLike((,)a) s s a b -> (a -> b) -> 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.
(<**=) :: (MonadStates m,Floatinga) =>Lens's a -> a -> m a (<**=) :: (MonadStates m,Floatinga) =>Iso's a -> a -> 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.
(<^^=) :: (MonadStates m,Fractionalb,Integrale) =>Lens's a -> e -> m a (<^^=) :: (MonadStates m,Fractionalb,Integrale) =>Iso's a -> e -> 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.
(<^=) :: (MonadStates m,Numa,Integrale) =>Lens's a -> e -> m a (<^=) :: (MonadStates m,Numa,Integrale) =>Iso's a -> e -> 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.
(<//=) :: (MonadStates m,Fractionala) =>Lens's a -> a -> m a (<//=) :: (MonadStates m,Fractionala) =>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.
(<*=) :: (MonadStates m,Numa) =>Lens's a -> a -> m a (<*=) :: (MonadStates m,Numa) =>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.
(<-=) :: (MonadStates m,Numa) =>Lens's a -> a -> m a (<-=) :: (MonadStates m,Numa) =>Iso's 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.
(<+=) :: (MonadStates m,Numa) =>Lens's a -> a -> m a (<+=) :: (MonadStates m,Numa) =>Iso's a -> a -> m a
(<%=) :: 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.
(<%=) ::MonadStates m =>Lens's a -> (a -> a) -> m a (<%=) ::MonadStates m =>Iso's a -> (a -> a) -> m a (<%=) :: (MonadStates m,Monoida) =>Traversal's a -> (a -> a) -> m a
(<<<>~) :: 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"))
(<<<>~) ::Monoidr =>Lens's r -> r -> s -> (r, s) (<<<>~) ::Monoidr =>Iso's r -> r -> s -> (r, 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)
(<<||~) :: 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'sBool->Bool-> s -> (Bool, s) (<<||~) ::Iso'sBool->Bool-> s -> (Bool, 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))
(<<**~) ::Floatinga =>Lens's a -> a -> s -> (a, s) (<<**~) ::Floatinga =>Iso's a -> a -> 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.
(<<^^~) :: (Fractionala,Integrale) =>Lens's a -> e -> s -> (a, s) (<<^^~) :: (Fractionala,Integrale) =>Iso's a -> e -> 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 => 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))
(<<*~) ::Numa =>Lens's a -> a -> s -> (a, s) (<<*~) ::Numa =>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))
(<<-~) ::Numa =>Lens's a -> a -> s -> (a, s) (<<-~) ::Numa =>Iso's a -> a -> s -> (a, s)
(<<+~) :: 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))
(<<+~) ::Numa =>Lens's a -> a -> s -> (a, s) (<<+~) ::Numa =>Iso's a -> a -> s -> (a, s)
(<<?~) :: 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")]))
(<<?~) ::Isos t a (Maybeb) -> b -> s -> (a, t) (<<?~) ::Lenss t a (Maybeb) -> b -> s -> (a, t) (<<?~) ::Traversals t a (Maybeb) -> b -> s -> (a, t)
(<^^~) :: (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.
(<^^~) :: (Fractionala,Integrale) =>Lens's a -> e -> s -> (a, s) (<^^~) :: (Fractionala,Integrale) =>Iso's a -> e -> 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.
(<//~) ::Fractionala =>Lens's a -> a -> s -> (a, s) (<//~) ::Fractionala =>Iso's a -> a -> s -> (a, s)
cloneIndexedLens :: AnIndexedLens i s t a b -> IndexedLens i s t a b #
Clone an IndexedLens as an IndexedLens with the same index.
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.
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")
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.
iposw ≡ w^.locusiseeks w ≡ w&locus.~siseeksf w ≡ w&locus%~f
locus::Lens'(Context'a s) alocus::Conjoinedp =>Lens'(Pretext'p a s) alocus::Conjoinedp =>Lens'(PretextT'p g a s) 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::Lenss t a b ->Lenss' t' a' b' ->Lens(s,s') (t,t') (a,a') (b,b')alongside::Getters a ->Getters' a' ->Getter(s,s') (a,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≡choosingidid
>>>Left a^.chosena
>>>Right a^.chosena
>>>Right "hello"^.chosen"hello"
>>>Right a & chosen *~ bRight (a * b)
chosen::Lens(Eithera a) (Eitherb b) a bchosenf (Lefta) =Left<$>f achosenf (Righta) =Right<$>f a
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≡choosingidid
choosing::Getters a ->Getters' a ->Getter(Eithers s') achoosing::Folds a ->Folds' a ->Fold(Eithers s') achoosing::Lens's a ->Lens's' a ->Lens'(Eithers s') achoosing::Traversal's a ->Traversal's' a ->Traversal'(Eithers s') achoosing::Setter's a ->Setter's' a ->Setter'(Eithers s') a
(??) :: 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) ah a x
>>>execState ?? [] $ modify (1:)[1]
>>>over _2 ?? ("hello","world") $ length("hello",5)
>>>over ?? length ?? ("hello","world") $ _2("hello",5)
(%%=) :: 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:
(%%=) ::MonadStates m =>Isos s a b -> (a -> (r, b)) -> m r (%%=) ::MonadStates m =>Lenss s a b -> (a -> (r, b)) -> m r (%%=) :: (MonadStates m,Monoidr) =>Traversals s a b -> (a -> (r, b)) -> m r
(%%~) :: 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:
(%%~) ::Functorf =>Isos t a b -> (a -> f b) -> s -> f t (%%~) ::Functorf =>Lenss t a b -> (a -> f b) -> s -> f t (%%~) ::Applicativef =>Traversals 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)
(%%~) ::Isos t a b -> (a -> (r, b)) -> s -> (r, t) (%%~) ::Lenss t a b -> (a -> (r, b)) -> s -> (r, t) (%%~) ::Monoidm =>Traversals t a b -> (a -> (m, b)) -> s -> (m, t)
(&~) :: 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)
ilens :: (s -> (i, a)) -> (s -> b -> t) -> IndexedLens i s t a b #
Build an IndexedLens from a Getter and
a Setter.
iplens :: (s -> a) -> (s -> b -> t) -> IndexPreservingLens s t a b #
withLens :: ALens s t a b -> ((s -> a) -> (s -> b -> t) -> r) -> r #
Obtain a getter and a setter from a lens, reversing lens.
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 AnIndexedLens' i s a = AnIndexedLens i s s a a #
typeAnIndexedLens'=Simple(AnIndexedLensi)
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.
mapOfl ≡imapOfl.const
imapOf::IndexedSetteri s t a b -> (i -> a -> b) -> s -> timapOf::IndexedLensi s t a b -> (i -> a -> b) -> s -> timapOf::IndexedTraversali s t a b -> (i -> a -> b) -> s -> t
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::Arrowp =>Isos t a b -> p s b -> p s tassignA::Arrowp =>Lenss t a b -> p s b -> p s tassignA::Arrowp =>Traversals t a b -> p s b -> p s tassignA::Arrowp =>Setters t a b -> p s b -> p s t
(.@=) :: 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.@=constb
(.@=) ::MonadStates m =>IndexedSetteri s s a b -> (i -> b) -> m () (.@=) ::MonadStates m =>IndexedLensi s s a b -> (i -> b) -> m () (.@=) ::MonadStates m =>IndexedTraversali s t a b -> (i -> 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 -> 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%@=constf
(%@=) ::MonadStates m =>IndexedSetteri s s a b -> (i -> a -> b) -> m () (%@=) ::MonadStates m =>IndexedLensi s s a b -> (i -> a -> b) -> m () (%@=) ::MonadStates m =>IndexedTraversali s t a b -> (i -> a -> b) -> m ()
(.@~) :: 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.@~constb
(.@~) ::IndexedSetteri s t a b -> (i -> b) -> s -> t (.@~) ::IndexedLensi s t a b -> (i -> b) -> s -> t (.@~) ::IndexedTraversali s t a b -> (i -> b) -> s -> t
(%@~) :: 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%@~constf
(%@~) ::IndexedSetteri s t a b -> (i -> a -> b) -> s -> t (%@~) ::IndexedLensi s t a b -> (i -> a -> b) -> s -> t (%@~) ::IndexedTraversali s t a b -> (i -> a -> 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:
fid≡idf g.f h ≡ f (g.h)
Equational reasoning:
isets.iover≡idiover.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.
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.
setl ≡isetl.const
iset::IndexedSetteri s t a b -> (i -> b) -> s -> tiset::IndexedLensi s t a b -> (i -> b) -> s -> tiset::IndexedTraversali s t a b -> (i -> b) -> s -> t
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.
overl ≡ioverl.constioverl ≡overl.Indexed
iover::IndexedSetteri s t a b -> (i -> a -> b) -> s -> tiover::IndexedLensi s t a b -> (i -> a -> b) -> s -> tiover::IndexedTraversali s t a b -> (i -> a -> b) -> s -> t
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.
locallyl f ≡ilocallyl f . constilocallyl f ≡locallyl f .Indexed
ilocally :: MonadReader s m =>IndexedLenss s a b -> (i -> a -> b) -> m r -> m r ilocally :: MonadReader s m =>IndexedTraversals s a b -> (i -> a -> b) -> m r -> m r ilocally :: MonadReader s m =>IndexedSetters s a b -> (i -> a -> b) -> m r -> m r
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.
locallylida ≡ alocallyl f.locally l g ≡locallyl (f.g)
>>>(1,1) & locally _1 (+1) (uncurry (+))3
>>>"," & locally ($) ("Hello" <>) (<> " world!")"Hello, world!"
locally :: MonadReader s m =>Isos s a b -> (a -> b) -> m r -> m r locally :: MonadReader s m =>Lenss s a b -> (a -> b) -> m r -> m r locally :: MonadReader s m =>Traversals s a b -> (a -> b) -> m r -> m r locally :: MonadReader s m =>Setters s a b -> (a -> b) -> m r -> m r
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.
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.
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.
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.
scribe :: (MonadWriter t m, Monoid s) => ASetter s t a b -> b -> m () #
Write to a fragment of a larger Writer format.
(<>=) :: (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!!!")
(<>=) :: (MonadStates m,Monoida) =>Setter's a -> a -> m () (<>=) :: (MonadStates m,Monoida) =>Iso's a -> a -> m () (<>=) :: (MonadStates m,Monoida) =>Lens's a -> a -> m () (<>=) :: (MonadStates m,Monoida) =>Traversal's a -> a -> m ()
(<>~) :: 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!!!")
(<>~) ::Monoida =>Setters t a a -> a -> s -> t (<>~) ::Monoida =>Isos t a a -> a -> s -> t (<>~) ::Monoida =>Lenss t a a -> a -> s -> t (<>~) ::Monoida =>Traversals t a a -> a -> s -> t
(<?=) :: 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 will avoid unused binding warnings.?= d
(<?=) ::MonadStates m =>Setters s a (Maybeb) -> b -> m b (<?=) ::MonadStates m =>Isos s a (Maybeb) -> b -> m b (<?=) ::MonadStates m =>Lenss s a (Maybeb) -> b -> m b (<?=) ::MonadStates m =>Traversals s a (Maybeb) -> b -> m b
(<.=) :: 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 will avoid unused binding warnings..= d
(<.=) ::MonadStates m =>Setters s a b -> b -> m b (<.=) ::MonadStates m =>Isos s a b -> b -> m b (<.=) ::MonadStates m =>Lenss s a b -> b -> m b (<.=) ::MonadStates m =>Traversals s a b -> b -> m b
(<~) :: 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.
(<~) ::MonadStates m =>Isos s a b -> m b -> m () (<~) ::MonadStates m =>Lenss s a b -> m b -> m () (<~) ::MonadStates m =>Traversals s a b -> m b -> m () (<~) ::MonadStates m =>Setters 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
...
(||=) :: 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)
(||=) ::MonadStates m =>Setter'sBool->Bool-> m () (||=) ::MonadStates m =>Iso'sBool->Bool-> m () (||=) ::MonadStates m =>Lens'sBool->Bool-> m () (||=) ::MonadStates m =>Traversal'sBool->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,False,False,False)
(&&=) ::MonadStates m =>Setter'sBool->Bool-> m () (&&=) ::MonadStates m =>Iso'sBool->Bool-> m () (&&=) ::MonadStates m =>Lens'sBool->Bool-> m () (&&=) ::MonadStates m =>Traversal'sBool->Bool-> 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)
(**=) :: (MonadStates m,Floatinga) =>Setter's a -> a -> m () (**=) :: (MonadStates m,Floatinga) =>Iso's a -> a -> m () (**=) :: (MonadStates m,Floatinga) =>Lens's a -> a -> m () (**=) :: (MonadStates m,Floatinga) =>Traversal's a -> a -> 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.
(^^=) :: (MonadStates m,Fractionala,Integrale) =>Setter's a -> e -> m () (^^=) :: (MonadStates m,Fractionala,Integrale) =>Iso's a -> e -> m () (^^=) :: (MonadStates m,Fractionala,Integrale) =>Lens's a -> e -> m () (^^=) :: (MonadStates m,Fractionala,Integrale) =>Traversal's a -> e -> 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.
(^=) :: (MonadStates m,Numa,Integrale) =>Setter's a -> e -> m () (^=) :: (MonadStates m,Numa,Integrale) =>Iso's a -> e -> m () (^=) :: (MonadStates m,Numa,Integrale) =>Lens's a -> e -> m () (^=) :: (MonadStates m,Numa,Integrale) =>Traversal's a -> e -> 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)
(//=) :: (MonadStates m,Fractionala) =>Setter's a -> a -> m () (//=) :: (MonadStates m,Fractionala) =>Iso's a -> a -> m () (//=) :: (MonadStates m,Fractionala) =>Lens's a -> a -> m () (//=) :: (MonadStates m,Fractionala) =>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)
(*=) :: (MonadStates m,Numa) =>Setter's a -> a -> m () (*=) :: (MonadStates m,Numa) =>Iso's a -> a -> m () (*=) :: (MonadStates m,Numa) =>Lens's a -> a -> m () (*=) :: (MonadStates m,Numa) =>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)
(-=) :: (MonadStates m,Numa) =>Setter's a -> a -> m () (-=) :: (MonadStates m,Numa) =>Iso's a -> a -> m () (-=) :: (MonadStates m,Numa) =>Lens's a -> a -> m () (-=) :: (MonadStates m,Numa) =>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 adding a value.
Example:
fresh::MonadStateIntm => mIntfresh= doid+=1useid
>>>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")
(+=) :: (MonadStates m,Numa) =>Setter's a -> a -> m () (+=) :: (MonadStates m,Numa) =>Iso's a -> a -> m () (+=) :: (MonadStates m,Numa) =>Lens's a -> a -> m () (+=) :: (MonadStates m,Numa) =>Traversal's a -> a -> m ()
(?=) :: 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.emptyfromList [(1,a),(2,b)]
>>>execState (do _1 ?= b; _2 ?= c) (Just a, Nothing)(Just b,Just c)
(?=) ::MonadStates m =>Iso's (Maybea) -> a -> m () (?=) ::MonadStates m =>Lens's (Maybea) -> a -> m () (?=) ::MonadStates m =>Traversal's (Maybea) -> a -> m () (?=) ::MonadStates m =>Setter's (Maybea) -> a -> 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 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)
(%=) ::MonadStates m =>Iso's a -> (a -> a) -> m () (%=) ::MonadStates m =>Lens's a -> (a -> a) -> m () (%=) ::MonadStates m =>Traversal's a -> (a -> a) -> m () (%=) ::MonadStates m =>Setter's a -> (a -> a) -> m ()
(%=) ::MonadStates m =>ASetters s a b -> (a -> b) -> 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)
(.=) ::MonadStates m =>Iso's a -> a -> m () (.=) ::MonadStates m =>Lens's a -> a -> m () (.=) ::MonadStates m =>Traversal's a -> a -> m () (.=) ::MonadStates m =>Setter's a -> a -> m ()
It puts the state in the monad or it gets the hose again.
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::MonadStates m =>Iso's a -> a -> m ()assign::MonadStates m =>Lens's a -> a -> m ()assign::MonadStates m =>Traversal's a -> a -> m ()assign::MonadStates m =>Setter's a -> a -> m ()
(&&~) :: 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'sBool->Bool-> s -> s (&&~) ::Iso'sBool->Bool-> s -> s (&&~) ::Lens'sBool->Bool-> s -> s (&&~) ::Traversal'sBool->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)(True,True)
>>>both ||~ False $ (False,True)(False,True)
(||~) ::Setter'sBool->Bool-> s -> s (||~) ::Iso'sBool->Bool-> s -> s (||~) ::Lens'sBool->Bool-> s -> s (||~) ::Traversal'sBool->Bool-> 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)
(**~) ::Floatinga =>Setter's a -> a -> s -> s (**~) ::Floatinga =>Iso's a -> a -> s -> s (**~) ::Floatinga =>Lens's a -> a -> s -> s (**~) ::Floatinga =>Traversal's a -> a -> 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)
(^^~) :: (Fractionala,Integrale) =>Setter's a -> e -> s -> s (^^~) :: (Fractionala,Integrale) =>Iso's a -> e -> s -> s (^^~) :: (Fractionala,Integrale) =>Lens's a -> e -> s -> s (^^~) :: (Fractionala,Integrale) =>Traversal's a -> e -> 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)
(^~) :: (Numa,Integrale) =>Setter's a -> e -> s -> s (^~) :: (Numa,Integrale) =>Iso's a -> e -> s -> s (^~) :: (Numa,Integrale) =>Lens's a -> e -> s -> s (^~) :: (Numa,Integrale) =>Traversal's a -> e -> 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)
(//~) ::Fractionala =>Setter's a -> a -> s -> s (//~) ::Fractionala =>Iso's a -> a -> s -> s (//~) ::Fractionala =>Lens's a -> a -> s -> s (//~) ::Fractionala =>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]]
(-~) ::Numa =>Setter's a -> a -> s -> s (-~) ::Numa =>Iso's a -> a -> s -> s (-~) ::Numa =>Lens's a -> a -> s -> s (-~) ::Numa =>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 *~ 2Just 48
(*~) ::Numa =>Setter's a -> a -> s -> s (*~) ::Numa =>Iso's a -> a -> s -> s (*~) ::Numa =>Lens's a -> a -> s -> s (*~) ::Numa =>Traversal's a -> a -> s -> s
(+~) :: 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)]
(+~) ::Numa =>Setter's a -> a -> s -> s (+~) ::Numa =>Iso's a -> a -> s -> s (+~) ::Numa =>Lens's a -> a -> s -> s (+~) ::Numa =>Traversal's a -> a -> s -> s
(<?~) :: 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 directly is a good idea.?~ d
>>>import Data.Map as Map>>>_2.at "hello" <?~ "world" $ (42,Map.fromList [("goodnight","gracie")])("world",(42,fromList [("goodnight","gracie"),("hello","world")]))
(<?~) ::Setters t a (Maybeb) -> b -> s -> (b, t) (<?~) ::Isos t a (Maybeb) -> b -> s -> (b, t) (<?~) ::Lenss t a (Maybeb) -> b -> s -> (b, t) (<?~) ::Traversals t a (Maybeb) -> b -> s -> (b, 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 directly is a good idea..~ t
>>>(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")]))
(<.~) ::Setters t a b -> b -> s -> (b, t) (<.~) ::Isos t a b -> b -> s -> (b, t) (<.~) ::Lenss t a b -> b -> s -> (b, t) (<.~) ::Traversals t a b -> b -> s -> (b, 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 ≡setl (Justt)
>>>Nothing & id ?~ aJust a
>>>Map.empty & at 3 ?~ xfromList [(3,x)]
?~ can be used type-changily:
>>>('a', ('b', 'c')) & _2.both ?~ 'x'('a',(Just 'x',Just 'x'))
(?~) ::Setters t a (Maybeb) -> b -> s -> t (?~) ::Isos t a (Maybeb) -> b -> s -> t (?~) ::Lenss t a (Maybeb) -> b -> s -> t (?~) ::Traversals t a (Maybeb) -> 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)
(.~) ::Setters t a b -> b -> s -> t (.~) ::Isos t a b -> b -> s -> t (.~) ::Lenss t a b -> b -> s -> t (.~) ::Traversals t a b -> b -> s -> t
(%~) :: 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.
fmapf ≡mapped%~ffmapDefaultf ≡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]]
(%~) ::Setters t a b -> (a -> b) -> s -> t (%~) ::Isos t a b -> (a -> b) -> s -> t (%~) ::Lenss t a b -> (a -> b) -> s -> t (%~) ::Traversals t a b -> (a -> 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 -> sset'::Iso's a -> a -> s -> sset'::Lens's a -> a -> s -> sset'::Traversal's a -> a -> s -> s
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.
(<$) ≡setmapped
>>>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::Setters t a b -> b -> s -> tset::Isos t a b -> b -> s -> tset::Lenss t a b -> b -> s -> tset::Traversals t a b -> b -> s -> t
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≡overmappedfmapDefault≡overtraversesets.over≡idover.sets≡id
Given any valid Setter l, you can also rely on the law:
overl f.overl g =overl (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::Setters t a b -> (a -> b) -> s -> tover::ASetters t a b -> (a -> b) -> s -> t
cloneIndexedSetter :: AnIndexedSetter i s t a b -> IndexedSetter i s t a b #
Clone an IndexedSetter.
cloneIndexPreservingSetter :: ASetter s t a b -> IndexPreservingSetter s t a b #
Build an IndexPreservingSetter from any Setter.
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) ->Setters t a b
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:
fid≡idf g.f h ≡ f (g.h)
Equational reasoning:
setting.over≡idover.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) ->Setters t a b
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≡overcontramapped
>>>getPredicate (over contramapped (*2) (Predicate even)) 5True
>>>getOp (over contramapped (*5) (Op show)) 100"500"
>>>Prelude.map ($ 1) $ over (mapped . _Unwrapping' Op . contramapped) (*12) [(*2),(+1),(^3)][24,13,1728]
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≡overlifted
>>>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
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≡overmappedfmapDefault≡overtraverse(<$) ≡setmapped
>>>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::Functorf =>Setter(f a) (f b) a b
If you want an IndexPreservingSetter use setting fmap
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.
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 AnIndexedSetter' i s a = AnIndexedSetter i s s a a #
typeAnIndexedSetter'i =Simple(AnIndexedSetteri)
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 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 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:
viewl (setl v s) ≡ v
2) Putting back what you got doesn't change anything:
setl (viewl s) s ≡ s
3) Setting twice is the same as setting once:
setl v' (setl v s) ≡setl 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 ss This is a consequence of law #1
2) set lv 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:
setl v (setl v s) ≡setl 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:
lpure≡purefmap(l f).l g ≡getCompose.l (Compose.fmapf.g)
typeLenss t a b = forall f.Functorf =>LensLikef s t a b
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 IndexedLens' i s a = IndexedLens i s s a a #
typeIndexedLens'i =Simple(IndexedLensi)
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 IndexPreservingLens' s a = IndexPreservingLens s s a a #
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::Traversablef =>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".
tpure≡purefmap(t f).t g ≡getCompose.t (Compose.fmapf.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 Traversal' s a = Traversal s s a a #
typeTraversal'=SimpleTraversal
type Traversal1 s t a b = forall (f :: Type -> Type). Apply f => (a -> f b) -> s -> f t #
type Traversal1' s a = Traversal1 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 #
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 IndexedTraversal' i s a = IndexedTraversal i s s a a #
typeIndexedTraversal'i =Simple(IndexedTraversali)
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 IndexedTraversal1' i s a = IndexedTraversal1 i 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) #
An IndexPreservingLens leaves any index it is composed with alone.
type IndexPreservingTraversal' s a = IndexPreservingTraversal 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 IndexPreservingTraversal1' s a = IndexPreservingTraversal1 s s a a #
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
setl y (setl x a) ≡setl 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:
overlid≡idoverl f.overl g ≡overl (f.g)
These can be stated more directly:
lpure≡purel 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 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 IndexedSetter' i s a = IndexedSetter i s s a a #
typeIndexedSetter'i =Simple(IndexedSetteri)
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 IndexPreservingSetter' s a = IndexPreservingSetter s s a a #
typeIndexedPreservingSetter'i =SimpleIndexedPreservingSetter
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 Review t b = forall (p :: Type -> Type -> Type) (f :: Type -> Type). (Choice p, Bifunctor p, Settable f) => Optic' p f t b #
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:
previewl (reviewl b) ≡Justb
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:
previewl s ≡Justa ⟹reviewl a ≡ s
Third, if you get non-match t, you can convert it result back to s:
matchingl s ≡Leftt ⟹matchingl t ≡Lefts
The first two laws imply that the Traversal laws hold for every Prism and that we traverse at most 1 element:
lengthOfl x<=1
It may help to think of this as an Iso that can be partial in one direction.
Every Prism is a valid Traversal.
For example, you might have a Prism' Integer NaturalNatural 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'IntegerNaturalnat=prismtoInteger$\ i -> if i<0 thenLefti elseRight(fromIntegeri)
Now we can ask if an Integer is a Natural.
>>>5^?natJust 5
>>>(-5)^?natNothing
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 -- :: Natural5
Similarly we can use a Prism to traverse the Left half of an Either:
>>>Left "hello" & _Left %~ lengthLeft 5
or to construct an Either:
>>>5^.re _LeftLeft 5
such that if you query it with the Prism, you will get your original input back.
>>>5^.re _Left ^? _LeftJust 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 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 As (a :: k2) = Equality' a a #
Composable asTypeOf. Useful for constraining excess
polymorphism, foo . (id :: As Int) . bar.
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 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 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 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 aFoldable
typeclass, see foldMapOf and the other Fold combinators.
By convention, if there exists a foo method that expects a Foldable (f a)fooOf method that takes a Fold s as.
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 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 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 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 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 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 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::SimpleLens(Complexa) atraversed::Simple(IndexedTraversalInt) [a] a
Note: To use this alias in your own code with LensLike fSetter, you may have to turn on LiberalTypeSynonyms.
This is commonly abbreviated as a "prime" marker, e.g. Lens' = Simple Lens.
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:
lpure≡purel (Procomposef 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.
typeLensLikef s t a b =Optic(->) f s t a b
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 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 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 bFunctor f,
then they may be passed a Lens.
Further, if f is an Applicative, they may also be passed a
Traversal.
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 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 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.
class (Applicative f, Distributive f, Traversable f) => Settable (f :: Type -> Type) #
Minimal complete definition
Instances
| Settable Identity | So you can pass our |
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) | |
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) | |
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) # | |
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 (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 | |
Defined in Control.Lens.Internal.Review | |
This provides a way to peek at the internal structure of a
Traversal or IndexedTraversal
Instances
| FunctorWithIndex i (Magma i t b) | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex i (Magma i t b) | |
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 # | |
| TraversableWithIndex i (Magma i t b) | |
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 # | |
| Functor (Magma i t b) | |
| Foldable (Magma i t b) | |
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 # | |
| Traversable (Magma i t b) | |
Defined in Control.Lens.Internal.Magma | |
| (Show i, Show a) => Show (Magma i t b 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
| FunctorWithIndex i (Level i) | |
Defined in Control.Lens.Indexed | |
| FoldableWithIndex i (Level i) | |
| TraversableWithIndex i (Level i) | |
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 # | |
| Functor (Level i) | |
| Foldable (Level i) | |
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 # elem :: Eq a => a -> Level i a -> Bool # maximum :: Ord a => Level i a -> a # minimum :: Ord a => Level i a -> a # | |
| Traversable (Level i) | |
| (Eq i, Eq a) => Eq (Level i a) | |
| (Ord i, Ord a) => Ord (Level i a) | |
| (Read i, Read a) => Read (Level i a) | |
| (Show i, Show a) => Show (Level i a) | |
This class provides a generalized notion of list reversal extended to other containers.
Instances
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 ta and a function from b to
t, a Bazaar a b tN 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
| |
Instances
| Profunctor p => Bizarre p (Bazaar p) | |
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) | |
Defined in Control.Lens.Internal.Bazaar | |
| IndexedFunctor (Bazaar p) | |
Defined in Control.Lens.Internal.Bazaar | |
| Conjoined p => IndexedComonad (Bazaar p) | |
| Functor (Bazaar p a b) | |
| Applicative (Bazaar p a b) | |
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) | |
Defined in Control.Lens.Internal.Bazaar | |
| (a ~ b, Conjoined p) => Comonad (Bazaar p a b) | |
| (a ~ b, Conjoined p) => ComonadApply (Bazaar p a b) | |
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 ta and a function from b to
t, a Bazaar1 a b tN 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
| |
Instances
| Profunctor p => Bizarre1 p (Bazaar1 p) | |
Defined in Control.Lens.Internal.Bazaar | |
| Corepresentable p => Sellable p (Bazaar1 p) | |
Defined in Control.Lens.Internal.Bazaar | |
| IndexedFunctor (Bazaar1 p) | |
Defined in Control.Lens.Internal.Bazaar | |
| Conjoined p => IndexedComonad (Bazaar1 p) | |
| Functor (Bazaar1 p a b) | |
| Apply (Bazaar1 p a b) | |
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) | |
| (a ~ b, Conjoined p) => ComonadApply (Bazaar1 p a b) | |
The indexed store can be used to characterize a Lens
and is used by cloneLens.
Context a b tnewtype ,
and to Context a b t = Context { runContext :: forall f. Functor f => (a -> f b) -> f t }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 | |
Defined in Control.Lens.Internal.Context | |
| IndexedComonad Context | |
| IndexedComonadStore Context | |
| a ~ b => ComonadStore a (Context a b) | |
Defined in Control.Lens.Internal.Context | |
| Functor (Context a b) | |
| a ~ b => Comonad (Context a b) | |
| Sellable ((->) :: Type -> Type -> Type) Context | |
Defined in Control.Lens.Internal.Context | |
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.
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")]
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::Traversals t a b ->IndexedTraversalInt64s t a bindexing64::Prisms t a b ->IndexedTraversalInt64s t a bindexing64::Lenss t a b ->IndexedLensInt64s t a bindexing64::Isos t a b ->IndexedLensInt64s t a bindexing64::Folds a ->IndexedFoldInt64s aindexing64::Getters a ->IndexedGetterInt64s a
indexing64::IndexableInt64p =>LensLike(Indexing64f) s t a b ->Overp f s t a b
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::Traversals t a b ->IndexedTraversalInts t a bindexing::Prisms t a b ->IndexedTraversalInts t a bindexing::Lenss t a b ->IndexedLensInts t a bindexing::Isos t a b ->IndexedLensInts t a bindexing::Folds a ->IndexedFoldInts aindexing::Getters a ->IndexedGetterInts a
indexing::IndexableIntp =>LensLike(Indexingf) s t a b ->Overp f s t 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 | |
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) | |
| Conjoined ((->) :: Type -> Type -> Type) | |
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
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
| |
Instances
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) | |
| Applicative f => Monoid (Traversed a f) | |
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 =>"?
class (Foldable1 t, Traversable t) => Traversable1 (t :: Type -> Type) where #
Instances
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.
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.
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.
Methods
left' :: p a b -> p (Either a c) (Either b c) #
Laws:
left'≡dimapswapE swapE.right'where swapE ::Eithera b ->Eitherb a swapE =eitherRightLeftrmapLeft≡lmapLeft.left'lmap(rightf).left'≡rmap(rightf).left'left'.left'≡dimapassocE unassocE.left'where assocE ::Either(Eithera b) c ->Eithera (Eitherb c) assocE (Left(Lefta)) =Lefta assocE (Left(Rightb)) =Right(Leftb) assocE (Rightc) =Right(Rightc) unassocE ::Eithera (Eitherb c) ->Either(Eithera b) c unassocE (Lefta) =Left(Lefta) unassocE (Right(Leftb)) =Left(Rightb) unassocE (Right(Rightc)) =Rightc
right' :: p a b -> p (Either c a) (Either c b) #
Laws:
right'≡dimapswapE swapE.left'where swapE ::Eithera b ->Eitherb a swapE =eitherRightLeftrmapRight≡lmapRight.right'lmap(leftf).right'≡rmap(leftf).right'right'.right'≡dimapunassocE assocE.right'where assocE ::Either(Eithera b) c ->Eithera (Eitherb c) assocE (Left(Lefta)) =Lefta assocE (Left(Rightb)) =Right(Leftb) assocE (Rightc) =Right(Rightc) unassocE ::Eithera (Eitherb c) ->Either(Eithera b) c unassocE (Lefta) =Left(Lefta) unassocE (Right(Leftb)) =Left(Rightb) unassocE (Right(Rightc)) =Rightc
Instances
class Functor f => Applicative (f :: Type -> Type) where #
A functor with application, providing operations to
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:
(<*>) =liftA2id
liftA2f x y = f<$>x<*>y
Further, any definition must satisfy the following:
- identity
pureid<*>v = v- composition
pure(.)<*>u<*>v<*>w = u<*>(v<*>w)- homomorphism
puref<*>purex =pure(f x)- interchange
u
<*>purey =pure($y)<*>u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the Functor instance for f will satisfy
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
liftA2p (liftA2q u v) =liftA2f u .liftA2g v
If f is also a Monad, it should satisfy
(which implies that pure and <*> satisfy the applicative functor laws).
Methods
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 f => f a -> f b -> f b infixl 4 #
Sequence actions, discarding the value of the first argument.
(<*) :: Applicative f => f a -> f b -> f a infixl 4 #
Sequence actions, discarding the value of the second argument.
(<$>) :: 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, <$> is function
application lifted over a Functor.
Examples
Convert from a Maybe IntMaybe Stringshow:
>>>show <$> NothingNothing>>>show <$> Just 3Just "3"
Convert from an Either Int IntEither IntString using show:
>>>show <$> Left 17Left 17>>>show <$> Right 17Right "17"
Double each element of a list:
>>>(*2) <$> [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>even <$> (2,2)(2,True)
liftA :: Applicative f => (a -> b) -> f a -> f b #
liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c #
liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d #
Lift a ternary function to actions.