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: base-4.8.0.0

class Bifunctor p where Source

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`

.

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: base-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

>>>bimap toUpper (+1) ('j', 3)('J',4)

>>>bimap toUpper (+1) (Left 'j')Left 'J'

>>>bimap toUpper (+1) (Right 3)Right 4

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

Map covariantly over the first argument.

first f ≡ bimap f id

>>>first toUpper ('j', 3)('J',3)

>>>first toUpper (Left 'j')Left 'J'

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

Map covariantly over the second argument.

second ≡ bimap id

>>>second (+1) ('j', 3)('j',4)

>>>second (+1) (Right 3)Right 4

Bifunctor Either | Since: base-4.8.0.0 |

Bifunctor (,) | Since: base-4.8.0.0 |

Bifunctor Arg | Since: base-4.9.0.0 |

Bifunctor ((,,) x1) | Since: base-4.8.0.0 |

Bifunctor (Const :: Type -> Type -> Type) | Since: base-4.8.0.0 |

Bifunctor (K1 i :: Type -> Type -> Type) | Since: base-4.9.0.0 |

Bifunctor ((,,,) x1 x2) | Since: base-4.8.0.0 |

Bifunctor ((,,,,) x1 x2 x3) | Since: base-4.8.0.0 |

Bifunctor ((,,,,,) x1 x2 x3 x4) | Since: base-4.8.0.0 |

Bifunctor ((,,,,,,) x1 x2 x3 x4 x5) | Since: base-4.8.0.0 |

Defined in Data.Bifunctor |

© The University of Glasgow and others

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

https://downloads.haskell.org/~ghc/8.6.1/docs/html/libraries/base-4.12.0.0/Data-Bifunctor.html