bifunctors-5: Bifunctors

Copyright (C) 2008-2015 Edward Kmett BSD-style (see the file LICENSE) Edward Kmett provisional portable Safe-Inferred Haskell98

Data.Bifunctor

Description

Synopsis

• class Bifunctor p where
• bimap :: (a -> b) -> (c -> d) -> p a c -> p b d
• first :: (a -> b) -> p a c -> p b c
• second :: (b -> c) -> p a b -> p a c

# Documentation

class Bifunctor p where Source

Minimal definition either `bimap` or `first` and `second`

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
```

Minimal complete definition

Methods

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``

Instances

 Bifunctor Either Bifunctor (,) Bifunctor Const Bifunctor Arg Bifunctor ((,,) x) Bifunctor (Tagged *) Functor f => Bifunctor (Clown f) Bifunctor p => Bifunctor (Flip p) Functor g => Bifunctor (Joker g) Bifunctor p => Bifunctor (WrappedBifunctor p) Bifunctor ((,,,) x y) (Bifunctor f, Bifunctor g) => Bifunctor (Product f g) (Functor f, Bifunctor p) => Bifunctor (Tannen f p) Bifunctor ((,,,,) x y z) (Bifunctor p, Functor f, Functor g) => Bifunctor (Biff p f g) Bifunctor ((,,,,,) x y z w) Bifunctor ((,,,,,,) x y z w v)