base-4.8.1.0: Basic libraries

Data.Bifunctor

Description

Since: 4.8.0.0

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

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

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

 Source Methodsbimap :: (a -> b) -> (c -> d) -> Either a c -> Either b d Sourcefirst :: (a -> b) -> Either a c -> Either b c Sourcesecond :: (b -> c) -> Either a b -> Either a c Source Source Methodsbimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d) Sourcefirst :: (a -> b) -> (a, c) -> (b, c) Sourcesecond :: (b -> c) -> (a, b) -> (a, c) Source Source Methodsbimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d Sourcefirst :: (a -> b) -> Const a c -> Const b c Sourcesecond :: (b -> c) -> Const a b -> Const a c Source Bifunctor ((,,) x1) Source Methodsbimap :: (a -> b) -> (c -> d) -> (x1, a, c) -> (x1, b, d) Sourcefirst :: (a -> b) -> (x1, a, c) -> (x1, b, c) Sourcesecond :: (b -> c) -> (x1, a, b) -> (x1, a, c) Source Bifunctor ((,,,) x1 x2) Source Methodsbimap :: (a -> b) -> (c -> d) -> (x1, x2, a, c) -> (x1, x2, b, d) Sourcefirst :: (a -> b) -> (x1, x2, a, c) -> (x1, x2, b, c) Sourcesecond :: (b -> c) -> (x1, x2, a, b) -> (x1, x2, a, c) Source Bifunctor ((,,,,) x1 x2 x3) Source Methodsbimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, d) Sourcefirst :: (a -> b) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, c) Sourcesecond :: (b -> c) -> (x1, x2, x3, a, b) -> (x1, x2, x3, a, c) Source Bifunctor ((,,,,,) x1 x2 x3 x4) Source Methodsbimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, d) Sourcefirst :: (a -> b) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, c) Sourcesecond :: (b -> c) -> (x1, x2, x3, x4, a, b) -> (x1, x2, x3, x4, a, c) Source Bifunctor ((,,,,,,) x1 x2 x3 x4 x5) Source Methodsbimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, d) Sourcefirst :: (a -> b) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, c) Sourcesecond :: (b -> c) -> (x1, x2, x3, x4, x5, a, b) -> (x1, x2, x3, x4, x5, a, c) Source