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Data.Functor
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 |
Description
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"
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 https://www.schoolofhaskell.com/user/edwardk/snippets/fmap or https://github.com/quchen/articles/blob/master/second_functor_law.md for an explanation.
Minimal complete definition
Methods
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 Bifunctor
instance that allows both the last and the penultimate parameters to be mapped over.
Examples
Convert from a Maybe Int
to a Maybe String
using show
:
>>> fmap show Nothing
Nothing
>>> fmap show (Just 3)
Just "3"
Convert from an Either Int Int
to an Either 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)
(<$) :: a -> f b -> f a infixl 4 Source
Replace all locations in the input with the same value. The default definition is fmap . const
, but this may be overridden with a more efficient version.
Instances
Functor ZipList Source | Since: base-2.1 |
Functor Handler Source | Since: base-4.6.0.0 |
Functor Complex Source | Since: base-4.9.0.0 |
Functor Identity Source | Since: base-4.8.0.0 |
Functor First Source | Since: base-4.8.0.0 |
Functor Last Source | Since: base-4.8.0.0 |
Functor Down Source | Since: base-4.11.0.0 |
Functor First Source | Since: base-4.9.0.0 |
Functor Last Source | Since: base-4.9.0.0 |
Functor Max Source | Since: base-4.9.0.0 |
Functor Min Source | Since: base-4.9.0.0 |
Functor Dual Source | Since: base-4.8.0.0 |
Functor Product Source | Since: base-4.8.0.0 |
Functor Sum Source | Since: base-4.8.0.0 |
Functor STM Source | Since: base-4.3.0.0 |
Functor NoIO Source | Since: base-4.8.0.0 |
Functor Par1 Source | Since: base-4.9.0.0 |
Functor ArgDescr Source | Since: base-4.7.0.0 |
Functor ArgOrder Source | Since: base-4.7.0.0 |
Functor OptDescr Source | Since: base-4.7.0.0 |
Functor ReadP Source | Since: base-2.1 |
Functor ReadPrec Source | Since: base-2.1 |
Functor IO Source | Since: base-2.1 |
Functor NonEmpty Source | Since: base-4.9.0.0 |
Functor Maybe Source | Since: base-2.1 |
Functor Solo Source | Since: base-4.15 |
Functor [] Source | Since: base-2.1 |
Monad m => Functor (WrappedMonad m) Source | Since: base-2.1 |
Defined in Control.Applicative Methodsfmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source |
|
Arrow a => Functor (ArrowMonad a) Source | Since: base-4.6.0.0 |
Defined in Control.Arrow Methodsfmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source |
|
Functor (ST s) Source | Since: base-2.1 |
Functor (Either a) Source | Since: base-3.0 |
Functor (Proxy :: Type -> Type) Source | Since: base-4.7.0.0 |
Functor (Arg a) Source | Since: base-4.9.0.0 |
Functor (Array i) Source | Since: base-2.1 |
Functor (U1 :: Type -> Type) Source | Since: base-4.9.0.0 |
Functor (V1 :: Type -> Type) Source | Since: base-4.9.0.0 |
Functor (ST s) Source | Since: base-2.1 |
Functor ((,) a) Source | Since: base-2.1 |
Arrow a => Functor (WrappedArrow a b) Source | Since: base-2.1 |
Defined in Control.Applicative Methodsfmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source |
|
Functor m => Functor (Kleisli m a) Source | Since: base-4.14.0.0 |
Functor (Const m :: Type -> Type) Source | Since: base-2.1 |
Functor f => Functor (Ap f) Source | Since: base-4.12.0.0 |
Functor f => Functor (Alt f) Source | Since: base-4.8.0.0 |
(Generic1 f, Functor (Rep1 f)) => Functor (Generically1 f) Source | Since: base-4.17.0.0 |
Defined in GHC.Generics Methodsfmap :: (a -> b) -> Generically1 f a -> Generically1 f b Source (<$) :: a -> Generically1 f b -> Generically1 f a Source |
|
Functor f => Functor (Rec1 f) Source | Since: base-4.9.0.0 |
Functor (URec (Ptr ()) :: Type -> Type) Source | Since: base-4.9.0.0 |
Functor (URec Char :: Type -> Type) Source | Since: base-4.9.0.0 |
Functor (URec Double :: Type -> Type) Source | Since: base-4.9.0.0 |
Functor (URec Float :: Type -> Type) Source | Since: base-4.9.0.0 |
Functor (URec Int :: Type -> Type) Source | Since: base-4.9.0.0 |
Functor (URec Word :: Type -> Type) Source | Since: base-4.9.0.0 |
Functor ((,,) a b) Source | Since: base-4.14.0.0 |
(Functor f, Functor g) => Functor (Product f g) Source | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (Sum f g) Source | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :*: g) Source | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :+: g) Source | Since: base-4.9.0.0 |
Functor (K1 i c :: Type -> Type) Source | Since: base-4.9.0.0 |
Functor ((,,,) a b c) Source | Since: base-4.14.0.0 |
Functor ((->) r) Source | Since: base-2.1 |
(Functor f, Functor g) => Functor (Compose f g) Source | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :.: g) Source | Since: base-4.9.0.0 |
Functor f => Functor (M1 i c f) Source | Since: base-4.9.0.0 |
($>) :: Functor f => f a -> b -> f b infixl 4 Source
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) $> "foo"
(1,"foo")
Since: base-4.7.0.0
(<$>) :: 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, <$>
is function application lifted over a Functor
.
Examples
Convert from a Maybe Int
to a Maybe String
using show
:
>>> show <$> 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 <$> (2,2)
(2,True)
(<&>) :: Functor f => f a -> (a -> b) -> f b infixl 1 Source
Flipped version of <$>
.
(<&>) = flip fmap
Examples
Apply (+1)
to a list, a Just
and a Right
:
>>> Just 2 <&> (+1)
Just 3
>>> [1,2,3] <&> (+1)
[2,3,4]
>>> Right 3 <&> (+1)
Right 4
Since: base-4.11.0.0
void :: Functor f => f a -> f () Source
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
© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/9.4.2/docs/libraries/base-4.17.0.0/Data-Functor.html