Documentation

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

bimap | first, second

Methods

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

bimap  f g ≡ first  f .  second  g

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

first  f ≡ bimap  f id 

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

second  ≡ bimap  id 

Instances