# Functor

### From HaskellWiki

(Difference between revisions)

(→Description) |
(→Functor Laws) |
||

Line 37: | Line 37: | ||

;Functors preserve composition of morphisms | ;Functors preserve composition of morphisms | ||

:<pre>fmap (f . g) == fmap f . fmap g</pre> | :<pre>fmap (f . g) == fmap f . fmap g</pre> | ||

− | :If two sequential mapping operations are performed one after the other using two functions, the result should be the same as a single mapping operation with one function that is equivalent to applying the first function to the result of the second | + | :If two sequential mapping operations are performed one after the other using two functions, the result should be the same as a single mapping operation with one function that is equivalent to applying the first function to the result of the second. |

− | These two laws ensure that functors behave the way they were intended. The values of the functor are only modified by the function provided to the mapping operation. The mapping operation | + | These two laws ensure that functors behave the way they were intended. The values of the functor are only modified by the function provided to the mapping operation. The mapping operation by itself does not modify the values in the functor, only the function. The structure of the functor remains unchanged and only the values are modified. <hask>fmap</hask> returns an identical functor as the original, with it's values swapped to the result of calling a given function with the original value as an argument. |

== Methods == | == Methods == |

## Revision as of 01:38, 15 November 2017

The**typeclass represents the mathematical functor: a mapping between categories in the context of category theory. In practice a**

Functor

functor

Functor f

## Contents |

## 1 Packages

- (base) Prelude
- (base) Data.Functor
- (base) Control.Monad

## 2 Syntax

class Functor f where fmap :: (a -> b) -> f a -> f b (<$) :: a -> f b -> f a

### 2.1 Minimal Complete Definition

fmap

## 3 Description

An abstract datatypef a

Functor

Functor

f b

f a

f

f

Functor

f a

a

Functor

fmap

### 3.1 Functor Laws

- Functors must preserve identity morphisms
fmap id = id

- When performing the mapping operation, if the values in the functor are mapped to themselves, the result will be an unmodified functor.
- Functors preserve composition of morphisms
fmap (f . g) == fmap f . fmap g

- If two sequential mapping operations are performed one after the other using two functions, the result should be the same as a single mapping operation with one function that is equivalent to applying the first function to the result of the second.

fmap

## 4 Methods

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

- Create a new , from anf busing the results of calling a function on every value in thef a.f a

(<$) :: a -> f b -> f a

- Create a new , from anf bby replacing all of the values in thef aby a given value.f a

## 5 Related Functions

($>) :: a -> f b -> f a

- Create a new , from anf aby replacing all of the values in thef bby a given value.f b

(<$>) :: a -> f b -> f a

- An infix synonym for Data.Functor.fmap

void :: Functor f => f a -> f ()

- create a new from anf ()by replacing all of the values in thef abyf a()