base-4.9.1.0: Basic libraries

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

- class Bifunctor p where

# 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 (K1 i) # |
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) # |
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 *) # |
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 ((,,,) 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 #