Copyright | (c) The University of Glasgow 2001 |
---|---|
License | BSD-style (see the file libraries/base/LICENSE) |
Maintainer | [email protected] |
Stability | provisional |
Portability | portable |
Safe Haskell | Trustworthy |
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
.
>>> 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.
Functor [] | Since: base-2.1 |
Functor Maybe | Since: base-2.1 |
Functor IO | Since: base-2.1 |
Functor Par1 | Since: base-4.9.0.0 |
Functor NonEmpty | Since: base-4.9.0.0 |
Functor NoIO | Since: base-4.8.0.0 |
Functor ReadP | Since: base-2.1 |
Functor ReadPrec | Since: base-2.1 |
Functor Down | Since: base-4.11.0.0 |
Functor Product | Since: base-4.8.0.0 |
Functor Sum | Since: base-4.8.0.0 |
Functor Dual | Since: base-4.8.0.0 |
Functor Last | Since: base-4.8.0.0 |
Functor First | Since: base-4.8.0.0 |
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 ZipList | Since: base-2.1 |
Functor ArgDescr | Since: base-4.6.0.0 |
Functor OptDescr | Since: base-4.6.0.0 |
Functor ArgOrder | Since: base-4.6.0.0 |
Functor Option | Since: base-4.9.0.0 |
Functor Last | Since: base-4.9.0.0 |
Functor First | Since: base-4.9.0.0 |
Functor Max | Since: base-4.9.0.0 |
Functor Min | Since: base-4.9.0.0 |
Functor Complex | Since: base-4.9.0.0 |
Functor (Either a) | Since: base-3.0 |
Functor (V1 :: Type -> Type) | Since: base-4.9.0.0 |
Functor (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Functor ((,) a) | Since: base-2.1 |
Functor (ST s) | Since: base-2.1 |
Functor (Array i) | Since: base-2.1 |
Functor (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Arrow a => Functor (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in Control.Arrow Methodsfmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source | |
Monad m => Functor (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative Methodsfmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source | |
Functor (ST s) | Since: base-2.1 |
Functor (Arg a) | Since: base-4.9.0.0 |
Functor f => Functor (Rec1 f) | 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 (URec (Ptr ()) :: Type -> Type) | Since: base-4.9.0.0 |
Functor f => Functor (Alt f) | Since: base-4.8.0.0 |
Functor f => Functor (Ap f) | Since: base-4.12.0.0 |
Functor (Const m :: Type -> Type) | Since: base-2.1 |
Arrow a => Functor (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methodsfmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source | |
Functor ((->) r :: Type -> Type) | Since: base-2.1 |
Functor (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :+: g) | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :*: g) | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (Sum f g) | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (Product f g) | Since: base-4.9.0.0 |
Functor f => Functor (M1 i c f) | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :.: g) | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (Compose f g) | Since: base-4.9.0.0 |
(<$) :: Functor f => 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.
($>) :: Functor f => f a -> b -> f b infixl 4 Source
Flipped version of <$
.
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, <$>
is function application lifted over a Functor
.
Convert from a Maybe Int
to a Maybe
String
using show
:
>>> show <$> 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
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.
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/8.8.3/docs/html/libraries/base-4.13.0.0/Data-Functor.html