bifunctors-4.1.1.1: Bifunctors

Portability portable provisional Edward Kmett Safe-Inferred

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 whereSource

Minimal definition either bimap or first and second

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 idid

If you supply first and second, ensure:

first idid
second idid

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 dSource

Map over both arguments at the same time.

bimap f g ≡ first f . second g

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

Map covariantly over the first argument.

first f ≡ bimap f id

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

Map covariantly over the second argument.

secondbimap 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 f, Bifunctor g) => Bifunctor (Product f g) Bifunctor ((,,,,) x y z)