License | BSD-style |
---|---|

Maintainer | Vincent Hanquez <vincent@snarc.org> |

Stability | experimental |

Portability | portable |

Safe Haskell | Safe |

Language | Haskell2010 |

A bifunctor is a type constructor that takes
two type arguments and is a functor in *both* arguments. That
is, unlike with `Functor`

, a type constructor such as `Either`

does not need to be partially applied for a `Bifunctor`

instance, and the methods in this class permit mapping
functions over the `Left`

value or the `Right`

value,
or both at the same time.

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`

.

- class Bifunctor p where

# Documentation

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*