Copyright | (c) 2016 Stephen Diehl (c) 20016-2018 Serokell (c) 2018 Kowainik |
---|---|
License | MIT |
Maintainer | Kowainik <xrom.xkov@gmail.com> |
Safe Haskell | Safe |
Language | Haskell2010 |
Synopsis
- (&&&) :: Arrow a => a b c -> a b c' -> a b (c, c')
- class Bifunctor (p :: * -> * -> *) where
- class Functor (f :: * -> *) where
- void :: Functor f => f a -> f ()
- ($>) :: Functor f => f a -> b -> f b
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- newtype Compose (f :: k -> *) (g :: k1 -> k) (a :: k1) :: forall k k1. (k -> *) -> (k1 -> k) -> k1 -> * = Compose {
- getCompose :: f (g a)
- newtype Identity a = Identity {
- runIdentity :: a
Documentation
(&&&) :: Arrow a => a b c -> a b c' -> a b (c, c') infixr 3 #
Fanout: send the input to both argument arrows and combine their output.
The default definition may be overridden with a more efficient version if desired.
class Bifunctor (p :: * -> * -> *) where #
A bifunctor is a type constructor that takes
two type arguments and is a functor in both arguments. That
is, unlike with Functor
, a type constructor such as Either
does not need to be partially applied for a Bifunctor
instance, and the methods in this class permit mapping
functions over the Left
value or the Right
value,
or both at the same time.
Formally, the class Bifunctor
represents a bifunctor
from Hask
-> Hask
.
Intuitively it is a bifunctor where both the first and second arguments are covariant.
You can define a Bifunctor
by either defining bimap
or by
defining both first
and second
.
If you supply bimap
, you should ensure that:
bimap
id
id
≡id
If you supply first
and second
, ensure:
first
id
≡id
second
id
≡id
If you supply both, you should also ensure:
bimap
f g ≡first
f.
second
g
These ensure by parametricity:
bimap
(f.
g) (h.
i) ≡bimap
f h.
bimap
g ifirst
(f.
g) ≡first
f.
first
gsecond
(f.
g) ≡second
f.
second
g
Since: base-4.8.0.0
bimap :: (a -> b) -> (c -> d) -> p a c -> p b d #
Map over both arguments at the same time.
bimap
f g ≡first
f.
second
g
Examples
>>>
bimap toUpper (+1) ('j', 3)
('J',4)
>>>
bimap toUpper (+1) (Left 'j')
Left 'J'
>>>
bimap toUpper (+1) (Right 3)
Right 4
Instances
Bifunctor Either | Since: base-4.8.0.0 |
Bifunctor (,) | Since: base-4.8.0.0 |
Bifunctor Arg | Since: base-4.9.0.0 |
Bifunctor ((,,) x1) | Since: base-4.8.0.0 |
Bifunctor (Const :: * -> * -> *) | Since: base-4.8.0.0 |
Bifunctor (K1 i :: * -> * -> *) | Since: base-4.9.0.0 |
Bifunctor ((,,,) x1 x2) | Since: base-4.8.0.0 |
Bifunctor ((,,,,) x1 x2 x3) | Since: base-4.8.0.0 |
Bifunctor ((,,,,,) x1 x2 x3 x4) | Since: base-4.8.0.0 |
Bifunctor ((,,,,,,) x1 x2 x3 x4 x5) | Since: base-4.8.0.0 |
class Functor (f :: * -> *) where #
The Functor
class is used for types that can be mapped over.
Instances of Functor
should satisfy the following laws:
fmap id == id fmap (f . g) == fmap f . fmap g
The instances of Functor
for lists, Maybe
and IO
satisfy these laws.
Instances
Functor [] | Since: base-2.1 |
Functor Maybe | Since: base-2.1 |
Functor IO | Since: base-2.1 |
Functor Par1 | |
Functor Complex | |
Functor Min | Since: base-4.9.0.0 |
Functor Max | Since: base-4.9.0.0 |
Functor First | Since: base-4.9.0.0 |
Functor Last | Since: base-4.9.0.0 |
Functor Option | Since: base-4.9.0.0 |
Functor ZipList | |
Functor Identity | Since: base-4.8.0.0 |
Functor Handler | Since: base-4.6.0.0 |
Functor STM | Since: base-4.3.0.0 |
Functor First | |
Functor Last | |
Functor Dual | Since: base-4.8.0.0 |
Functor Sum | Since: base-4.8.0.0 |
Functor Product | Since: base-4.8.0.0 |
Functor Down | Since: base-4.11.0.0 |
Functor ReadPrec | Since: base-2.1 |
Functor ReadP | Since: base-2.1 |
Functor NonEmpty | Since: base-4.9.0.0 |
Functor Put | |
Defined in Data.ByteString.Builder.Internal | |
Functor IntMap | |
Functor Tree | |
Functor Seq | |
Functor FingerTree | |
Defined in Data.Sequence.Internal fmap :: (a -> b) -> FingerTree a -> FingerTree b # (<$) :: a -> FingerTree b -> FingerTree a # | |
Functor Digit | |
Functor Node | |
Functor Elem | |
Functor ViewL | |
Functor ViewR | |
Functor P | |
Defined in Text.ParserCombinators.ReadP | |
Functor (Either a) | Since: base-3.0 |
Functor (V1 :: * -> *) | Since: base-4.9.0.0 |
Functor (U1 :: * -> *) | Since: base-4.9.0.0 |
Functor ((,) a) | Since: base-2.1 |
Functor (Array i) | Since: base-2.1 |
Functor (Arg a) | Since: base-4.9.0.0 |
Monad m => Functor (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a # | |
Arrow a => Functor (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in Control.Arrow fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 # | |
Functor (Proxy :: * -> *) | Since: base-4.7.0.0 |
Functor (Map k) | |
Functor m => Functor (MaybeT m) | |
Functor (HashMap k) | |
Functor f => Functor (Rec1 f) | |
Functor (URec Char :: * -> *) | |
Functor (URec Double :: * -> *) | |
Functor (URec Float :: * -> *) | |
Functor (URec Int :: * -> *) | |
Functor (URec Word :: * -> *) | |
Functor (URec (Ptr ()) :: * -> *) | |
Arrow a => Functor (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # | |
Functor (Const m :: * -> *) | Since: base-2.1 |
Functor f => Functor (Alt f) | |
(Applicative f, Monad f) => Functor (WhenMissing f x) | Since: containers-0.5.9 |
Defined in Data.IntMap.Internal fmap :: (a -> b) -> WhenMissing f x a -> WhenMissing f x b # (<$) :: a -> WhenMissing f x b -> WhenMissing f x a # | |
Functor m => Functor (IdentityT m) | |
Functor m => Functor (ErrorT e m) | |
Functor m => Functor (ExceptT e m) | |
Functor m => Functor (StateT s m) | |
Functor ((->) r :: * -> *) | Since: base-2.1 |
Functor (K1 i c :: * -> *) | |
(Functor f, Functor g) => Functor (f :+: g) | |
(Functor f, Functor g) => Functor (f :*: g) | |
(Functor f, Functor g) => Functor (Product f g) | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (Sum f g) | Since: base-4.9.0.0 |
Functor f => Functor (WhenMatched f x y) | Since: containers-0.5.9 |
Defined in Data.IntMap.Internal fmap :: (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b # (<$) :: a -> WhenMatched f x y b -> WhenMatched f x y a # | |
(Applicative f, Monad f) => Functor (WhenMissing f k x) | Since: containers-0.5.9 |
Defined in Data.Map.Internal fmap :: (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b # (<$) :: a -> WhenMissing f k x b -> WhenMissing f k x a # | |
Functor m => Functor (ReaderT r m) | |
Functor f => Functor (M1 i c f) | |
(Functor f, Functor g) => Functor (f :.: g) | |
(Functor f, Functor g) => Functor (Compose f g) | Since: base-4.9.0.0 |
Functor f => Functor (WhenMatched f k x y) | Since: containers-0.5.9 |
Defined in Data.Map.Internal fmap :: (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b # (<$) :: a -> WhenMatched f k x y b -> WhenMatched f k x y a # |
void :: Functor f => f a -> f () #
discards or ignores the result of evaluation, such
as the return value of an void
valueIO
action.
Examples
Replace the contents of a
with unit:Maybe
Int
>>>
void Nothing
Nothing>>>
void (Just 3)
Just ()
Replace the contents of an
with unit,
resulting in an Either
Int
Int
:Either
Int
'()'
>>>
void (Left 8675309)
Left 8675309>>>
void (Right 8675309)
Right ()
Replace every element of a list with unit:
>>>
void [1,2,3]
[(),(),()]
Replace the second element of a pair with unit:
>>>
void (1,2)
(1,())
Discard the result of an IO
action:
>>>
mapM print [1,2]
1 2 [(),()]>>>
void $ mapM print [1,2]
1 2
($>) :: Functor f => f a -> b -> f b infixl 4 #
Flipped version of <$
.
Examples
Replace the contents of a
with a constant Maybe
Int
String
:
>>>
Nothing $> "foo"
Nothing>>>
Just 90210 $> "foo"
Just "foo"
Replace the contents of an
with a constant
Either
Int
Int
String
, resulting in an
:Either
Int
String
>>>
Left 8675309 $> "foo"
Left 8675309>>>
Right 8675309 $> "foo"
Right "foo"
Replace each element of a list with a constant String
:
>>>
[1,2,3] $> "foo"
["foo","foo","foo"]
Replace the second element of a pair with a constant String
:
>>>
(1,2) $> "foo"
(1,"foo")
Since: base-4.7.0.0
(<$>) :: 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, <$>
is function
application lifted over a Functor
.
Examples
Convert from a
to a Maybe
Int
using Maybe
String
show
:
>>>
show <$> Nothing
Nothing>>>
show <$> Just 3
Just "3"
Convert from an
to an Either
Int
Int
Either
Int
String
using show
:
>>>
show <$> Left 17
Left 17>>>
show <$> Right 17
Right "17"
Double each element of a list:
>>>
(*2) <$> [1,2,3]
[2,4,6]
Apply even
to the second element of a pair:
>>>
even <$> (2,2)
(2,True)
newtype Compose (f :: k -> *) (g :: k1 -> k) (a :: k1) :: forall k k1. (k -> *) -> (k1 -> k) -> k1 -> * infixr 9 #
Right-to-left composition of functors. The composition of applicative functors is always applicative, but the composition of monads is not always a monad.
Compose infixr 9 | |
|
Instances
Functor f => Generic1 (Compose f g :: k -> *) | |
(Functor f, Functor g) => Functor (Compose f g) | Since: base-4.9.0.0 |
(Applicative f, Applicative g) => Applicative (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose | |
(Foldable f, Foldable g) => Foldable (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose fold :: Monoid m => Compose f g m -> m # foldMap :: Monoid m => (a -> m) -> Compose f g a -> m # foldr :: (a -> b -> b) -> b -> Compose f g a -> b # foldr' :: (a -> b -> b) -> b -> Compose f g a -> b # foldl :: (b -> a -> b) -> b -> Compose f g a -> b # foldl' :: (b -> a -> b) -> b -> Compose f g a -> b # foldr1 :: (a -> a -> a) -> Compose f g a -> a # foldl1 :: (a -> a -> a) -> Compose f g a -> a # toList :: Compose f g a -> [a] # null :: Compose f g a -> Bool # length :: Compose f g a -> Int # elem :: Eq a => a -> Compose f g a -> Bool # maximum :: Ord a => Compose f g a -> a # minimum :: Ord a => Compose f g a -> a # | |
(Traversable f, Traversable g) => Traversable (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose | |
(Eq1 f, Eq1 g) => Eq1 (Compose f g) | Since: base-4.9.0.0 |
(Ord1 f, Ord1 g) => Ord1 (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose | |
(Read1 f, Read1 g) => Read1 (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Compose f g a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Compose f g a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Compose f g a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Compose f g a] # | |
(Show1 f, Show1 g) => Show1 (Compose f g) | Since: base-4.9.0.0 |
(Alternative f, Applicative g) => Alternative (Compose f g) | Since: base-4.9.0.0 |
(NFData1 f, NFData1 g) => NFData1 (Compose f g) | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
(Hashable1 f, Hashable1 g) => Hashable1 (Compose f g) | |
Defined in Data.Hashable.Class | |
(Eq1 f, Eq1 g, Eq a) => Eq (Compose f g a) | Since: base-4.9.0.0 |
(Typeable a, Typeable f, Typeable g, Typeable k1, Typeable k2, Data (f (g a))) => Data (Compose f g a) | |
Defined in Data.Functor.Compose gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g0. g0 -> c g0) -> Compose f g a -> c (Compose f g a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Compose f g a) # toConstr :: Compose f g a -> Constr # dataTypeOf :: Compose f g a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Compose f g a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Compose f g a)) # gmapT :: (forall b. Data b => b -> b) -> Compose f g a -> Compose f g a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r # gmapQ :: (forall d. Data d => d -> u) -> Compose f g a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Compose f g a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) # | |
(Ord1 f, Ord1 g, Ord a) => Ord (Compose f g a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose compare :: Compose f g a -> Compose f g a -> Ordering # (<) :: Compose f g a -> Compose f g a -> Bool # (<=) :: Compose f g a -> Compose f g a -> Bool # (>) :: Compose f g a -> Compose f g a -> Bool # (>=) :: Compose f g a -> Compose f g a -> Bool # | |
(Read1 f, Read1 g, Read a) => Read (Compose f g a) | Since: base-4.9.0.0 |
(Show1 f, Show1 g, Show a) => Show (Compose f g a) | Since: base-4.9.0.0 |
Generic (Compose f g a) | |
(NFData1 f, NFData1 g, NFData a) => NFData (Compose f g a) | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
(Hashable1 f, Hashable1 g, Hashable a) => Hashable (Compose f g a) | In general, |
Defined in Data.Hashable.Class | |
type Rep1 (Compose f g :: k -> *) | |
Defined in Data.Functor.Compose | |
type Rep (Compose f g a) | |
Defined in Data.Functor.Compose |
Identity functor and monad. (a non-strict monad)
Since: base-4.8.0.0
Identity | |
|