/Haskell 8

# Data.Functor

Copyright (c) The University of Glasgow 2001 BSD-style (see the file libraries/base/LICENSE) [email protected] provisional portable Trustworthy 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
Expand
```>>> 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"
```

class Functor f 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:

Identity
`fmap id == id`
Composition
`fmap (f . g) == fmap f . fmap g`

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.

#### Methods

fmap :: (a -> b) -> f a -> f b Source

##### Instances
Instances details
Functor []

Since: base-2.1

Instance details

Defined in GHC.Base

#### Methods

fmap :: (a -> b) -> [a] -> [b] Source

(<\$) :: a -> [b] -> [a] Source

Functor Maybe

Since: base-2.1

Instance details

Defined in GHC.Base

#### Methods

fmap :: (a -> b) -> Maybe a -> Maybe b Source

(<\$) :: a -> Maybe b -> Maybe a Source

Functor IO

Since: base-2.1

Instance details

Defined in GHC.Base

#### Methods

fmap :: (a -> b) -> IO a -> IO b Source

(<\$) :: a -> IO b -> IO a Source

Functor Par1

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

#### Methods

fmap :: (a -> b) -> Par1 a -> Par1 b Source

(<\$) :: a -> Par1 b -> Par1 a Source

Functor NonEmpty

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

#### Methods

fmap :: (a -> b) -> NonEmpty a -> NonEmpty b Source

(<\$) :: a -> NonEmpty b -> NonEmpty a Source

Functor NoIO

Since: base-4.8.0.0

Instance details

Defined in GHC.GHCi

#### Methods

fmap :: (a -> b) -> NoIO a -> NoIO b Source

(<\$) :: a -> NoIO b -> NoIO a Source

Functor ReadP

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadP

#### Methods

fmap :: (a -> b) -> ReadP a -> ReadP b Source

(<\$) :: a -> ReadP b -> ReadP a Source

Functor ReadPrec

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadPrec

#### Methods

fmap :: (a -> b) -> ReadPrec a -> ReadPrec b Source

(<\$) :: a -> ReadPrec b -> ReadPrec a Source

Functor Down

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

#### Methods

fmap :: (a -> b) -> Down a -> Down b Source

(<\$) :: a -> Down b -> Down a Source

Functor Product

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

#### Methods

fmap :: (a -> b) -> Product a -> Product b Source

(<\$) :: a -> Product b -> Product a Source

Functor Sum

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

#### Methods

fmap :: (a -> b) -> Sum a -> Sum b Source

(<\$) :: a -> Sum b -> Sum a Source

Functor Dual

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

#### Methods

fmap :: (a -> b) -> Dual a -> Dual b Source

(<\$) :: a -> Dual b -> Dual a Source

Functor Last

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

#### Methods

fmap :: (a -> b) -> Last a -> Last b Source

(<\$) :: a -> Last b -> Last a Source

Functor First

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

#### Methods

fmap :: (a -> b) -> First a -> First b Source

(<\$) :: a -> First b -> First a Source

Functor STM

Since: base-4.3.0.0

Instance details

Defined in GHC.Conc.Sync

#### Methods

fmap :: (a -> b) -> STM a -> STM b Source

(<\$) :: a -> STM b -> STM a Source

Functor Handler

Since: base-4.6.0.0

Instance details

Defined in Control.Exception

#### Methods

fmap :: (a -> b) -> Handler a -> Handler b Source

(<\$) :: a -> Handler b -> Handler a Source

Functor Identity

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

#### Methods

fmap :: (a -> b) -> Identity a -> Identity b Source

(<\$) :: a -> Identity b -> Identity a Source

Functor ZipList

Since: base-2.1

Instance details

Defined in Control.Applicative

#### Methods

fmap :: (a -> b) -> ZipList a -> ZipList b Source

(<\$) :: a -> ZipList b -> ZipList a Source

Functor ArgDescr

Since: base-4.6.0.0

Instance details

Defined in System.Console.GetOpt

#### Methods

fmap :: (a -> b) -> ArgDescr a -> ArgDescr b Source

(<\$) :: a -> ArgDescr b -> ArgDescr a Source

Functor OptDescr

Since: base-4.6.0.0

Instance details

Defined in System.Console.GetOpt

#### Methods

fmap :: (a -> b) -> OptDescr a -> OptDescr b Source

(<\$) :: a -> OptDescr b -> OptDescr a Source

Functor ArgOrder

Since: base-4.6.0.0

Instance details

Defined in System.Console.GetOpt

#### Methods

fmap :: (a -> b) -> ArgOrder a -> ArgOrder b Source

(<\$) :: a -> ArgOrder b -> ArgOrder a Source

Functor Option

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

#### Methods

fmap :: (a -> b) -> Option a -> Option b Source

(<\$) :: a -> Option b -> Option a Source

Functor Last

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

#### Methods

fmap :: (a -> b) -> Last a -> Last b Source

(<\$) :: a -> Last b -> Last a Source

Functor First

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

#### Methods

fmap :: (a -> b) -> First a -> First b Source

(<\$) :: a -> First b -> First a Source

Functor Max

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

#### Methods

fmap :: (a -> b) -> Max a -> Max b Source

(<\$) :: a -> Max b -> Max a Source

Functor Min

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

#### Methods

fmap :: (a -> b) -> Min a -> Min b Source

(<\$) :: a -> Min b -> Min a Source

Functor Complex

Since: base-4.9.0.0

Instance details

Defined in Data.Complex

#### Methods

fmap :: (a -> b) -> Complex a -> Complex b Source

(<\$) :: a -> Complex b -> Complex a Source

Functor (Either a)

Since: base-3.0

Instance details

Defined in Data.Either

#### Methods

fmap :: (a0 -> b) -> Either a a0 -> Either a b Source

(<\$) :: a0 -> Either a b -> Either a a0 Source

Functor (V1 :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

#### Methods

fmap :: (a -> b) -> V1 a -> V1 b Source

(<\$) :: a -> V1 b -> V1 a Source

Functor (U1 :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

#### Methods

fmap :: (a -> b) -> U1 a -> U1 b Source

(<\$) :: a -> U1 b -> U1 a Source

Functor ((,) a)

Since: base-2.1

Instance details

Defined in GHC.Base

#### Methods

fmap :: (a0 -> b) -> (a, a0) -> (a, b) Source

(<\$) :: a0 -> (a, b) -> (a, a0) Source

Functor (ST s)

Since: base-2.1

Instance details

Defined in GHC.ST

#### Methods

fmap :: (a -> b) -> ST s a -> ST s b Source

(<\$) :: a -> ST s b -> ST s a Source

Functor (Array i)

Since: base-2.1

Instance details

Defined in GHC.Arr

#### Methods

fmap :: (a -> b) -> Array i a -> Array i b Source

(<\$) :: a -> Array i b -> Array i a Source

Functor (Proxy :: Type -> Type)

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

#### Methods

fmap :: (a -> b) -> Proxy a -> Proxy b Source

(<\$) :: a -> Proxy b -> Proxy a Source

Arrow a => Functor (ArrowMonad a)

Since: base-4.6.0.0

Instance details

Defined in Control.Arrow

#### Methods

fmap :: (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

Instance details

Defined in Control.Applicative

#### Methods

fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source

(<\$) :: a -> WrappedMonad m b -> WrappedMonad m a Source

Functor (ST s)

Since: base-2.1

Instance details

Defined in Control.Monad.ST.Lazy.Imp

#### Methods

fmap :: (a -> b) -> ST s a -> ST s b Source

(<\$) :: a -> ST s b -> ST s a Source

Functor (Arg a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

#### Methods

fmap :: (a0 -> b) -> Arg a a0 -> Arg a b Source

(<\$) :: a0 -> Arg a b -> Arg a a0 Source

Functor f => Functor (Rec1 f)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

#### Methods

fmap :: (a -> b) -> Rec1 f a -> Rec1 f b Source

(<\$) :: a -> Rec1 f b -> Rec1 f a Source

Functor (URec Char :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

#### Methods

fmap :: (a -> b) -> URec Char a -> URec Char b Source

(<\$) :: a -> URec Char b -> URec Char a Source

Functor (URec Double :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

#### Methods

fmap :: (a -> b) -> URec Double a -> URec Double b Source

(<\$) :: a -> URec Double b -> URec Double a Source

Functor (URec Float :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

#### Methods

fmap :: (a -> b) -> URec Float a -> URec Float b Source

(<\$) :: a -> URec Float b -> URec Float a Source

Functor (URec Int :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

#### Methods

fmap :: (a -> b) -> URec Int a -> URec Int b Source

(<\$) :: a -> URec Int b -> URec Int a Source

Functor (URec Word :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

#### Methods

fmap :: (a -> b) -> URec Word a -> URec Word b Source

(<\$) :: a -> URec Word b -> URec Word a Source

Functor (URec (Ptr ()) :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

#### Methods

fmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b Source

(<\$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a Source

Functor f => Functor (Alt f)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

#### Methods

fmap :: (a -> b) -> Alt f a -> Alt f b Source

(<\$) :: a -> Alt f b -> Alt f a Source

Functor f => Functor (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

#### Methods

fmap :: (a -> b) -> Ap f a -> Ap f b Source

(<\$) :: a -> Ap f b -> Ap f a Source

Functor (Const m :: Type -> Type)

Since: base-2.1

Instance details

Defined in Data.Functor.Const

#### Methods

fmap :: (a -> b) -> Const m a -> Const m b Source

(<\$) :: a -> Const m b -> Const m a Source

Arrow a => Functor (WrappedArrow a b)

Since: base-2.1

Instance details

Defined in Control.Applicative

#### Methods

fmap :: (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

Instance details

Defined in GHC.Base

#### Methods

fmap :: (a -> b) -> (r -> a) -> r -> b Source

(<\$) :: a -> (r -> b) -> r -> a Source

Functor (K1 i c :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

#### Methods

fmap :: (a -> b) -> K1 i c a -> K1 i c b Source

(<\$) :: a -> K1 i c b -> K1 i c a Source

(Functor f, Functor g) => Functor (f :+: g)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

#### Methods

fmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b Source

(<\$) :: a -> (f :+: g) b -> (f :+: g) a Source

(Functor f, Functor g) => Functor (f :*: g)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

#### Methods

fmap :: (a -> b) -> (f :*: g) a -> (f :*: g) b Source

(<\$) :: a -> (f :*: g) b -> (f :*: g) a Source

(Functor f, Functor g) => Functor (Sum f g)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Sum

#### Methods

fmap :: (a -> b) -> Sum f g a -> Sum f g b Source

(<\$) :: a -> Sum f g b -> Sum f g a Source

(Functor f, Functor g) => Functor (Product f g)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

#### Methods

fmap :: (a -> b) -> Product f g a -> Product f g b Source

(<\$) :: a -> Product f g b -> Product f g a Source

Functor f => Functor (M1 i c f)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

#### Methods

fmap :: (a -> b) -> M1 i c f a -> M1 i c f b Source

(<\$) :: a -> M1 i c f b -> M1 i c f a Source

(Functor f, Functor g) => Functor (f :.: g)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

#### Methods

fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b Source

(<\$) :: a -> (f :.: g) b -> (f :.: g) a Source

(Functor f, Functor g) => Functor (Compose f g)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Compose

#### Methods

fmap :: (a -> b) -> Compose f g a -> Compose f g b Source

(<\$) :: a -> Compose f g b -> Compose f g a Source

(<\$) :: 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 `<\$`.

##### Examples
Expand

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
Expand

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
Expand

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
Expand

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