| 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