Data.Functor

Functors: uniform action over a parameterized type, generalizing the map function on lists.

Documentation

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.

Minimal complete definition

fmap

Methods

fmap :: (a -> b) -> f a -> f b

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

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

Instances

Functor []

Since: 2.1

Methods

fmap :: (a -> b) -> [a] -> [b]

(<$) :: a -> [b] -> [a]

Functor Maybe

Since: 2.1

Methods

fmap :: (a -> b) -> Maybe a -> Maybe b

(<$) :: a -> Maybe b -> Maybe a

Functor IO

Since: 2.1

Methods

fmap :: (a -> b) -> IO a -> IO b

(<$) :: a -> IO b -> IO a

Functor Par1

Methods

fmap :: (a -> b) -> Par1 a -> Par1 b

(<$) :: a -> Par1 b -> Par1 a

Functor ReadP

Since: 2.1

Methods

fmap :: (a -> b) -> ReadP a -> ReadP b

(<$) :: a -> ReadP b -> ReadP a

Functor ReadPrec

Since: 2.1

Methods

fmap :: (a -> b) -> ReadPrec a -> ReadPrec b

(<$) :: a -> ReadPrec b -> ReadPrec a

Functor Last

Methods

fmap :: (a -> b) -> Last a -> Last b

(<$) :: a -> Last b -> Last a

Functor First

Methods

fmap :: (a -> b) -> First a -> First b

(<$) :: a -> First b -> First a

Functor Product

Since: 4.8.0.0

Methods

fmap :: (a -> b) -> Product a -> Product b

(<$) :: a -> Product b -> Product a

Functor Sum

Since: 4.8.0.0

Methods

fmap :: (a -> b) -> Sum a -> Sum b

(<$) :: a -> Sum b -> Sum a

Functor Dual

Since: 4.8.0.0

Methods

fmap :: (a -> b) -> Dual a -> Dual b

(<$) :: a -> Dual b -> Dual a

Functor STM

Since: 4.3.0.0

Methods

fmap :: (a -> b) -> STM a -> STM b

(<$) :: a -> STM b -> STM a

Functor Handler

Since: 4.6.0.0

Methods

fmap :: (a -> b) -> Handler a -> Handler b

(<$) :: a -> Handler b -> Handler a

Functor Identity

Since: 4.8.0.0

Methods

fmap :: (a -> b) -> Identity a -> Identity b

(<$) :: a -> Identity b -> Identity a

Functor ZipList

Methods

fmap :: (a -> b) -> ZipList a -> ZipList b

(<$) :: a -> ZipList b -> ZipList a

Functor ArgDescr

Since: 4.6.0.0

Methods

fmap :: (a -> b) -> ArgDescr a -> ArgDescr b

(<$) :: a -> ArgDescr b -> ArgDescr a

Functor OptDescr

Since: 4.6.0.0

Methods

fmap :: (a -> b) -> OptDescr a -> OptDescr b

(<$) :: a -> OptDescr b -> OptDescr a

Functor ArgOrder

Since: 4.6.0.0

Methods

fmap :: (a -> b) -> ArgOrder a -> ArgOrder b

(<$) :: a -> ArgOrder b -> ArgOrder a

Functor NonEmpty

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> NonEmpty a -> NonEmpty b

(<$) :: a -> NonEmpty b -> NonEmpty a

Functor Option

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Option a -> Option b

(<$) :: a -> Option b -> Option a

Functor Last

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Last a -> Last b

(<$) :: a -> Last b -> Last a

Functor First

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> First a -> First b

(<$) :: a -> First b -> First a

Functor Max

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Max a -> Max b

(<$) :: a -> Max b -> Max a

Functor Min

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Min a -> Min b

(<$) :: a -> Min b -> Min a

Functor Complex

Methods

fmap :: (a -> b) -> Complex a -> Complex b

(<$) :: a -> Complex b -> Complex a

Functor (Either a)

Since: 3.0

Methods

fmap :: (a -> b) -> Either a a -> Either a b

(<$) :: a -> Either a b -> Either a a

Functor (V1 *)

Methods

fmap :: (a -> b) -> V1 * a -> V1 * b

(<$) :: a -> V1 * b -> V1 * a

Functor (U1 *)

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> U1 * a -> U1 * b

(<$) :: a -> U1 * b -> U1 * a

Functor ((,) a)

Since: 2.1

Methods

fmap :: (a -> b) -> (a, a) -> (a, b)

(<$) :: a -> (a, b) -> (a, a)

Functor (ST s)

Since: 2.1

Methods

fmap :: (a -> b) -> ST s a -> ST s b

(<$) :: a -> ST s b -> ST s a

Functor (Proxy *)

Since: 4.7.0.0

Methods

fmap :: (a -> b) -> Proxy * a -> Proxy * b

(<$) :: a -> Proxy * b -> Proxy * a

Arrow a => Functor (ArrowMonad a)

Since: 4.6.0.0

Methods

fmap :: (a -> b) -> ArrowMonad a a -> ArrowMonad a b

(<$) :: a -> ArrowMonad a b -> ArrowMonad a a

Monad m => Functor (WrappedMonad m)

Since: 2.1

Methods

fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b

(<$) :: a -> WrappedMonad m b -> WrappedMonad m a

Functor (ST s)

Since: 2.1

Methods

fmap :: (a -> b) -> ST s a -> ST s b

(<$) :: a -> ST s b -> ST s a

Functor (Arg a)

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Arg a a -> Arg a b

(<$) :: a -> Arg a b -> Arg a a

Functor f => Functor (Rec1 * f)

Methods

fmap :: (a -> b) -> Rec1 * f a -> Rec1 * f b

(<$) :: a -> Rec1 * f b -> Rec1 * f a

Functor (URec * Char)

Methods

fmap :: (a -> b) -> URec * Char a -> URec * Char b

(<$) :: a -> URec * Char b -> URec * Char a

Functor (URec * Double)

Methods

fmap :: (a -> b) -> URec * Double a -> URec * Double b

(<$) :: a -> URec * Double b -> URec * Double a

Functor (URec * Float)

Methods

fmap :: (a -> b) -> URec * Float a -> URec * Float b

(<$) :: a -> URec * Float b -> URec * Float a

Functor (URec * Int)

Methods

fmap :: (a -> b) -> URec * Int a -> URec * Int b

(<$) :: a -> URec * Int b -> URec * Int a

Functor (URec * Word)

Methods

fmap :: (a -> b) -> URec * Word a -> URec * Word b

(<$) :: a -> URec * Word b -> URec * Word a

Functor (URec * (Ptr ()))

Methods

fmap :: (a -> b) -> URec * (Ptr ()) a -> URec * (Ptr ()) b

(<$) :: a -> URec * (Ptr ()) b -> URec * (Ptr ()) a

Functor f => Functor (Alt * f)

Methods

fmap :: (a -> b) -> Alt * f a -> Alt * f b

(<$) :: a -> Alt * f b -> Alt * f a

Functor (Const * m)

Since: 2.1

Methods

fmap :: (a -> b) -> Const * m a -> Const * m b

(<$) :: a -> Const * m b -> Const * m a

Arrow a => Functor (WrappedArrow a b)

Since: 2.1

Methods

fmap :: (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b

(<$) :: a -> WrappedArrow a b b -> WrappedArrow a b a

Functor ((->) LiftedRep LiftedRep r)

Since: 2.1

Methods

fmap :: (a -> b) -> (LiftedRep -> LiftedRep) r a -> (LiftedRep -> LiftedRep) r b

(<$) :: a -> (LiftedRep -> LiftedRep) r b -> (LiftedRep -> LiftedRep) r a

Functor (K1 * i c)

Methods

fmap :: (a -> b) -> K1 * i c a -> K1 * i c b

(<$) :: a -> K1 * i c b -> K1 * i c a

(Functor g, Functor f) => Functor ((:+:) * f g)

Methods

fmap :: (a -> b) -> (* :+: f) g a -> (* :+: f) g b

(<$) :: a -> (* :+: f) g b -> (* :+: f) g a

(Functor g, Functor f) => Functor ((:*:) * f g)

Methods

fmap :: (a -> b) -> (* :*: f) g a -> (* :*: f) g b

(<$) :: a -> (* :*: f) g b -> (* :*: f) g a

(Functor f, Functor g) => Functor (Sum * f g)

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Sum * f g a -> Sum * f g b

(<$) :: a -> Sum * f g b -> Sum * f g a

(Functor f, Functor g) => Functor (Product * f g)

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Product * f g a -> Product * f g b

(<$) :: a -> Product * f g b -> Product * f g a

Functor f => Functor (M1 * i c f)

Methods

fmap :: (a -> b) -> M1 * i c f a -> M1 * i c f b

(<$) :: a -> M1 * i c f b -> M1 * i c f a

(Functor g, Functor f) => Functor ((:.:) * * f g)

Methods

fmap :: (a -> b) -> (* :.: *) f g a -> (* :.: *) f g b

(<$) :: a -> (* :.: *) f g b -> (* :.: *) f g a

(Functor f, Functor g) => Functor (Compose * * f g)

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Compose * * f g a -> Compose * * f g b

(<$) :: a -> Compose * * f g b -> Compose * * f g a

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

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

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

Flipped version of <$.

Examples

Replace the contents of a Maybe Int with a constant String:

>>> Nothing $> "foo"
Nothing
>>> Just 90210 $> "foo"
Just "foo"

Replace the contents of an Either Int Int with a constant 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: 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 Maybe Int to a Maybe String using show:

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

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

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

Double each element of a list:

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

Apply even to the second element of a pair:

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

void :: Functor f => f a -> f ()

void value discards or ignores the result of evaluation, such as the return value of an IO action.

Examples

Replace the contents of a Maybe Int with unit:

>>> void Nothing
Nothing
>>> void (Just 3)
Just ()

Replace the contents of an Either Int Int with unit, resulting in an 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