base-4.10.1.0: Basic libraries

Copyright | (c) The University of Glasgow 2001
License | BSD-style (see the file libraries/base/LICENSE)
Maintainer | libraries@haskell.org
Stability | provisional
Portability | portable
Safe Haskell | Trustworthy
Language | Haskell2010

Data.Functor

Description

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

Synopsis

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

# 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