License	BSD-style
Maintainer	Vincent Hanquez <vincent@snarc.org>
Stability	experimental
Portability	portable
Safe Haskell	Safe
Language	Haskell2010

Basement.Compat.Bifunctor

Description

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.

Synopsis

Documentation

class Bifunctor (p :: * -> * -> *) where #

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 #

Map over both arguments at the same time.

bimap f g ≡ first f . second g

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

Map covariantly over the first argument.

first f ≡ bimap f id

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

Map covariantly over the second argument.

second ≡ bimap id

Instances

Bifunctor Either	Since: 4.8.0.0
Methods bimap :: (a -> b) -> (c -> d) -> Either a c -> Either b d # first :: (a -> b) -> Either a c -> Either b c # second :: (b -> c) -> Either a b -> Either a c #
Bifunctor (,)	Since: 4.8.0.0
Methods bimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d) # first :: (a -> b) -> (a, c) -> (b, c) # second :: (b -> c) -> (a, b) -> (a, c) #
Bifunctor Arg	Since: 4.9.0.0
Methods bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d # first :: (a -> b) -> Arg a c -> Arg b c # second :: (b -> c) -> Arg a b -> Arg a c #
Bifunctor These #
Methods bimap :: (a -> b) -> (c -> d) -> These a c -> These b d # first :: (a -> b) -> These a c -> These b c # second :: (b -> c) -> These a b -> These a c #
Bifunctor ((,,) x1)	Since: 4.8.0.0
Methods bimap :: (a -> b) -> (c -> d) -> (x1, a, c) -> (x1, b, d) # first :: (a -> b) -> (x1, a, c) -> (x1, b, c) # second :: (b -> c) -> (x1, a, b) -> (x1, a, c) #
Bifunctor (Const *)	Since: 4.8.0.0
Methods bimap :: (a -> b) -> (c -> d) -> Const * a c -> Const * b d # first :: (a -> b) -> Const * a c -> Const * b c # second :: (b -> c) -> Const * a b -> Const * a c #
Bifunctor (K1 * i)	Since: 4.9.0.0
Methods bimap :: (a -> b) -> (c -> d) -> K1 * i a c -> K1 * i b d # first :: (a -> b) -> K1 * i a c -> K1 * i b c # second :: (b -> c) -> K1 * i a b -> K1 * i a c #
Bifunctor ((,,,) x1 x2)	Since: 4.8.0.0
Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, a, c) -> (x1, x2, b, d) # first :: (a -> b) -> (x1, x2, a, c) -> (x1, x2, b, c) # second :: (b -> c) -> (x1, x2, a, b) -> (x1, x2, a, c) #
Bifunctor ((,,,,) x1 x2 x3)	Since: 4.8.0.0
Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, d) # first :: (a -> b) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, c) # second :: (b -> c) -> (x1, x2, x3, a, b) -> (x1, x2, x3, a, c) #
Bifunctor ((,,,,,) x1 x2 x3 x4)	Since: 4.8.0.0
Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, d) # first :: (a -> b) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, c) # second :: (b -> c) -> (x1, x2, x3, x4, a, b) -> (x1, x2, x3, x4, a, c) #
Bifunctor ((,,,,,,) x1 x2 x3 x4 x5)	Since: 4.8.0.0
Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, d) # first :: (a -> b) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, c) # second :: (b -> c) -> (x1, x2, x3, x4, x5, a, b) -> (x1, x2, x3, x4, x5, a, c) #