base-4.16.0.0: Basic libraries
Copyright(C) 2008-2014 Edward Kmett
LicenseBSD-style (see the file LICENSE)
Maintainerlibraries@haskell.org
Stabilityprovisional
Portabilityportable
Safe HaskellSafe
LanguageHaskell2010

Data.Bifunctor

Description

Since: base-4.8.0.0

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 where Source #

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.

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

Since: base-4.8.0.0

Minimal complete definition

bimap | first, second

Methods

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

Examples

Expand
>>> bimap toUpper (+1) ('j', 3)
('J',4)
>>> bimap toUpper (+1) (Left 'j')
Left 'J'
>>> bimap toUpper (+1) (Right 3)
Right 4

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

Map covariantly over the first argument.

first f ≡ bimap f id

Examples

Expand
>>> first toUpper ('j', 3)
('J',3)
>>> first toUpper (Left 'j')
Left 'J'

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

Map covariantly over the second argument.

secondbimap id

Examples

Expand
>>> second (+1) ('j', 3)
('j',4)
>>> second (+1) (Right 3)
Right 4

Instances

Instances details
Bifunctor Either #

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> Either a c -> Either b d Source #

first :: (a -> b) -> Either a c -> Either b c Source #

second :: (b -> c) -> Either a b -> Either a c Source #

Bifunctor (,) #

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d) Source #

first :: (a -> b) -> (a, c) -> (b, c) Source #

second :: (b -> c) -> (a, b) -> (a, c) Source #

Bifunctor Arg #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d Source #

first :: (a -> b) -> Arg a c -> Arg b c Source #

second :: (b -> c) -> Arg a b -> Arg a c Source #

Bifunctor ((,,) x1) #

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, a, c) -> (x1, b, d) Source #

first :: (a -> b) -> (x1, a, c) -> (x1, b, c) Source #

second :: (b -> c) -> (x1, a, b) -> (x1, a, c) Source #

Bifunctor (Const :: Type -> Type -> Type) #

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d Source #

first :: (a -> b) -> Const a c -> Const b c Source #

second :: (b -> c) -> Const a b -> Const a c Source #

Bifunctor (K1 i :: Type -> Type -> Type) #

Since: base-4.9.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> K1 i a c -> K1 i b d Source #

first :: (a -> b) -> K1 i a c -> K1 i b c Source #

second :: (b -> c) -> K1 i a b -> K1 i a c Source #

Bifunctor ((,,,) x1 x2) #

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, a, c) -> (x1, x2, b, d) Source #

first :: (a -> b) -> (x1, x2, a, c) -> (x1, x2, b, c) Source #

second :: (b -> c) -> (x1, x2, a, b) -> (x1, x2, a, c) Source #

Bifunctor ((,,,,) x1 x2 x3) #

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, d) Source #

first :: (a -> b) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, c) Source #

second :: (b -> c) -> (x1, x2, x3, a, b) -> (x1, x2, x3, a, c) Source #

Bifunctor ((,,,,,) x1 x2 x3 x4) #

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, d) Source #

first :: (a -> b) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, c) Source #

second :: (b -> c) -> (x1, x2, x3, x4, a, b) -> (x1, x2, x3, x4, a, c) Source #

Bifunctor ((,,,,,,) x1 x2 x3 x4 x5) #

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, d) Source #

first :: (a -> b) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, c) Source #

second :: (b -> c) -> (x1, x2, x3, x4, x5, a, b) -> (x1, x2, x3, x4, x5, a, c) Source #