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 | Safe |
Language | Haskell2010 |
A type f
is a Functor if it provides a function fmap
which, given any types a
and b
,
lets you apply any function of type (a -> b)
to turn an f a
into an f b
, preserving the
structure of f
.
Examples
>>>
fmap show (Just 1) -- (a -> b) -> f a -> f b
Just "1" -- (Int -> String) -> Maybe Int -> Maybe String
>>>
fmap show Nothing -- (a -> b) -> f a -> f b
Nothing -- (Int -> String) -> Maybe Int -> Maybe String
>>>
fmap show [1,2,3] -- (a -> b) -> f a -> f b
["1","2","3"] -- (Int -> String) -> [Int] -> [String]
>>>
fmap show [] -- (a -> b) -> f a -> f b
[] -- (Int -> String) -> [Int] -> [String]
The fmap
function is also available as the infix operator <$>
:
>>>
fmap show (Just 1) -- (Int -> String) -> Maybe Int -> Maybe String
Just "1"
>>>
show <$> (Just 1) -- (Int -> String) -> Maybe Int -> Maybe String
Just "1"
Synopsis
Documentation
class Functor (f :: Type -> Type) where Source #
A type f
is a Functor if it provides a function fmap
which, given any types a
and b
lets you apply any function from (a -> b)
to turn an f a
into an f b
, preserving the
structure of f
. Furthermore f
needs to adhere to the following:
Note, that the second law follows from the free theorem of the type fmap
and
the first law, so you need only check that the former condition holds.
See these articles by School of Haskell or
David Luposchainsky
for an explanation.
fmap :: (a -> b) -> f a -> f b Source #
fmap
is used to apply a function of type (a -> b)
to a value of type f a
,
where f is a functor, to produce a value of type f b
.
Note that for any type constructor with more than one parameter (e.g., Either
),
only the last type parameter can be modified with fmap
(e.g., b
in `Either a b`).
Some type constructors with two parameters or more have a
instance that allows
both the last and the penultimate parameters to be mapped over.Bifunctor
Examples
Convert from a
to a Maybe
IntMaybe String
using show
:
>>>
fmap show Nothing
Nothing>>>
fmap show (Just 3)
Just "3"
Convert from an
to an
Either
Int IntEither Int String
using show
:
>>>
fmap show (Left 17)
Left 17>>>
fmap show (Right 17)
Right "17"
Double each element of a list:
>>>
fmap (*2) [1,2,3]
[2,4,6]
Apply even
to the second element of a pair:
>>>
fmap even (2,2)
(2,True)
It may seem surprising that the function is only applied to the last element of the tuple
compared to the list example above which applies it to every element in the list.
To understand, remember that tuples are type constructors with multiple type parameters:
a tuple of 3 elements (a,b,c)
can also be written (,,) a b c
and its Functor
instance
is defined for Functor ((,,) a b)
(i.e., only the third parameter is free to be mapped over
with fmap
).
It explains why fmap
can be used with tuples containing values of different types as in the
following example:
>>>
fmap even ("hello", 1.0, 4)
("hello",1.0,True)
Instances
Functor Complex Source # | Since: base-4.9.0.0 |
Functor First Source # | Since: base-4.9.0.0 |
Functor Last Source # | Since: base-4.9.0.0 |
Functor Max Source # | Since: base-4.9.0.0 |
Functor Min Source # | Since: base-4.9.0.0 |
Functor ArgDescr Source # | Since: base-4.7.0.0 |
Functor ArgOrder Source # | Since: base-4.7.0.0 |
Functor OptDescr Source # | Since: base-4.7.0.0 |
Functor NonEmpty | Since: base-4.9.0.0 |
Functor STM | Since: base-4.3.0.0 |
Functor Handler | Since: base-4.6.0.0 |
Functor Identity | Since: base-4.8.0.0 |
Functor First | Since: base-4.8.0.0 |
Functor Last | Since: base-4.8.0.0 |
Functor Down | Since: base-4.11.0.0 |
Functor Dual | Since: base-4.8.0.0 |
Functor Product | Since: base-4.8.0.0 |
Functor Sum | Since: base-4.8.0.0 |
Functor ZipList | Since: base-2.1 |
Functor NoIO | Since: base-4.8.0.0 |
Functor Par1 | Since: base-4.9.0.0 |
Functor P | Since: base-4.8.0.0 |
Functor ReadP | Since: base-2.1 |
Functor ReadPrec | Since: base-2.1 |
Functor IO | Since: base-2.1 |
Functor Maybe | Since: base-2.1 |
Functor Solo | Since: base-4.15 |
Functor [] | Since: base-2.1 |
Monad m => Functor (WrappedMonad m) Source # | Since: base-2.1 |
Defined in Control.Applicative fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source # | |
Functor (Arg a) Source # | Since: base-4.9.0.0 |
Functor (Array i) | Since: base-2.1 |
Arrow a => Functor (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in GHC.Internal.Control.Arrow fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # | |
Functor (ST s) | Since: base-2.1 |
Functor (Either a) | Since: base-3.0 |
Functor (StateL s) | Since: base-4.0 |
Functor (StateR s) | Since: base-4.0 |
Functor (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Functor (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Functor (V1 :: Type -> Type) | Since: base-4.9.0.0 |
Functor (ST s) | Since: base-2.1 |
Functor ((,) a) | Since: base-2.1 |
Arrow a => Functor (WrappedArrow a b) Source # | Since: base-2.1 |
Defined in Control.Applicative fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # | |
Functor m => Functor (Kleisli m a) | Since: base-4.14.0.0 |
Functor (Const m :: Type -> Type) | Since: base-2.1 |
Monad m => Functor (StateT s m) | Since: base-4.18.0.0 |
Functor f => Functor (Ap f) | Since: base-4.12.0.0 |
Functor f => Functor (Alt f) | Since: base-4.8.0.0 |
(Generic1 f, Functor (Rep1 f)) => Functor (Generically1 f) | Since: base-4.17.0.0 |
Defined in GHC.Internal.Generics fmap :: (a -> b) -> Generically1 f a -> Generically1 f b Source # (<$) :: a -> Generically1 f b -> Generically1 f a Source # | |
Functor f => Functor (Rec1 f) | Since: base-4.9.0.0 |
Functor (URec (Ptr ()) :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Char :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Double :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Float :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Int :: Type -> Type) | Since: base-4.9.0.0 |
Functor (URec Word :: Type -> Type) | Since: base-4.9.0.0 |
Functor ((,,) a b) | Since: base-4.14.0.0 |
(Functor f, Functor g) => Functor (Product f g) Source # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (Sum f g) Source # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :*: g) | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :+: g) | Since: base-4.9.0.0 |
Functor (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
Functor ((,,,) a b c) | Since: base-4.14.0.0 |
Functor ((->) r) | Since: base-2.1 |
(Functor f, Functor g) => Functor (Compose f g) Source # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :.: g) | Since: base-4.9.0.0 |
Functor f => Functor (M1 i c f) | Since: base-4.9.0.0 |
Functor ((,,,,) a b c d) | Since: base-4.18.0.0 |
Functor ((,,,,,) a b c d e) | Since: base-4.18.0.0 |
Functor ((,,,,,,) a b c d e f) | Since: base-4.18.0.0 |
($>) :: Functor f => f a -> b -> f b infixl 4 Source #
Flipped version of <$
.
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 Source #
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)
unzip :: Functor f => f (a, b) -> (f a, f b) Source #
Generalization of Data.List.
unzip
.
Examples
>>>
unzip (Just ("Hello", "World"))
(Just "Hello",Just "World")
>>>
unzip [("I", "love"), ("really", "haskell")]
(["I","really"],["love","haskell"])
Since: base-4.19.0.0
void :: Functor f => f a -> f () Source #
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