Module DA.Bifunctor

Typeclasses

class Bifunctor p where

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.

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' 'identity' 'identity' ≡ 'identity'@

If you supply ‘first’ and ‘second’, ensure:

@
'first' 'identity' ≡ 'identity'
'second' 'identity' ≡ 'identity'
@

If you supply both, you should also ensure:

@'bimap' f g ≡ 'first' f '.' 'second' g@
```

By parametricity, these will ensure that:

```
@
'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
@
```

bimap

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

Map over both arguments at the same time.

@'bimap' f g ≡ 'first' f '.' 'second' g@

Examples:

>>> bimap not (+1) (True, 3)
(False,4)

>>> bimap not (+1) (Left True)
Left False

>>> bimap not (+1) (Right 3)
Right 4

first

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

Map covariantly over the first argument.

@'first' f ≡ 'bimap' f 'identity'@
```

Examples:

```
>>> first not (True, 3)
(False,3)

>>> first not (Left True : Either Bool Int)
Left False
```

second

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

Map covariantly over the second argument.

@'second' ≡ 'bimap' 'identity'@

Examples:

>>> second (+1) (True, 3)
(True,4)

>>> second (+1) (Right 3 : Either Bool Int)
Right 4

instance Bifunctor Either

instance Bifunctor ()

instance Bifunctor x1

instance Bifunctor (x1, x2)

instance Bifunctor (x1, x2, x3)

instance Bifunctor (x1, x2, x3, x4)

instance Bifunctor (x1, x2, x3, x4, x5)