Copyright	(C) 2008-2014 Edward Kmett,
License	BSD-style (see the file LICENSE)
Maintainer	libraries@haskell.org
Stability	provisional
Portability	portable
Safe Haskell	Safe
Language	Haskell2010

Data.Bifunctor

Description

Since: 4.8.0.0

Synopsis

Documentation

class Bifunctor p where Source

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 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.

second ≡ bimap id

Instances

Bifunctor Either
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 (,)
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
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)
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 Lifted))
Methods bimap :: (a -> b) -> (c -> d) -> Const (TYPE Lifted) a c -> Const (TYPE Lifted) b d Source first :: (a -> b) -> Const (TYPE Lifted) a c -> Const (TYPE Lifted) b c Source second :: (b -> c) -> Const (TYPE Lifted) a b -> Const (TYPE Lifted) a c Source
Bifunctor ((,,,) x1 x2)
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)
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)
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)
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