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DA.Bifunctor

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Module Snapshot

Lifecycle

Stable.

Notices

Status: active Introduced in: 3.4.9 Removed in: - Warnings: 0 Deprecations: 0 Deprecated since: -

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Typeclasses

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class Bifunctor p

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
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
    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
Instances:
  • 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)