Data.Bifunctor

Documentation

class Bifunctor p where

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

Methods

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

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

Map covariantly over the first argument.

first f ≡ bimap f id

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

Map covariantly over the second argument.

second ≡ bimap id

Instances

Bifunctor Either

Bifunctor (,)

Bifunctor Const

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 ((,,,,) x y z)