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 bJust "1" -- (Int -> String) -> Maybe Int -> Maybe String

>>>fmap show Nothing -- (a -> b) -> f a -> f bNothing -- (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 StringJust "1" >>>show <$> (Just 1) -- (Int -> String) -> Maybe Int -> Maybe StringJust "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 <$> NothingNothing >>>show <$> Just 3Just "3"

Convert from an `Either Int Int`

to an `Either Int`

`String`

using `show`

:

>>>show <$> Left 17Left 17 >>>show <$> Right 17Right "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 NothingNothing >>>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