bifunctors-5: Bifunctors

Copyright(C) 2008-2015 Edward Kmett
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <>
Safe HaskellSafe-Inferred






class Bifunctor p where Source

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 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

Minimal complete definition

bimap | first, second


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.

secondbimap id