Copyright | (C) 2008-2014 Edward Kmett, |
---|---|

License | BSD-style (see the file LICENSE) |

Maintainer | [email protected] |

Stability | provisional |

Portability | portable |

Safe Haskell | Safe |

Language | Haskell2010 |

Since: 4.8.0.0

class Bifunctor p where Source

Formally, the class `Bifunctor`

represents a bifunctor from `Hask`

-> `Hask`

.

Intuitively it is a bifunctor where both the first and second arguments are covariant.

You can define a `Bifunctor`

by either defining `bimap`

or by defining both `first`

and `second`

.

If you supply `bimap`

, you should ensure that:

`bimap`

`id`

`id`

≡`id`

If you supply `first`

and `second`

, ensure:

`first`

`id`

≡`id`

`second`

`id`

≡`id`

If you supply both, you should also ensure:

`bimap`

f g ≡`first`

f`.`

`second`

g

These ensure by parametricity:

`bimap`

(f`.`

g) (h`.`

i) ≡`bimap`

f h`.`

`bimap`

g i`first`

(f`.`

g) ≡`first`

f`.`

`first`

g`second`

(f`.`

g) ≡`second`

f`.`

`second`

g

Since: 4.8.0.0

bimap :: (a -> b) -> (c -> d) -> p a c -> p b d Source

Map over both arguments at the same time.

`bimap`

f g ≡`first`

f`.`

`second`

g

first :: (a -> b) -> p a c -> p b c Source

Map covariantly over the first argument.

`first`

f ≡`bimap`

f`id`

second :: (b -> c) -> p a b -> p a c Source

Map covariantly over the second argument.

`second`

≡`bimap`

`id`

© The University of Glasgow and others

Licensed under a BSD-style license (see top of the page).

https://downloads.haskell.org/~ghc/7.10.3/docs/html/libraries/base-4.8.2.0/Data-Bifunctor.html