base-4.18.1.0: 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: base-4.8.0.0

Synopsis

- class (forall a. Functor (p a)) => 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 (forall a. Functor (p a)) => 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`. A partially applied `Bifunctor` must be a `Functor` and the `second` method must agree with `fmap`. From this it follows that:

    second id = id

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 4.18.0.0 `Functor` is a superclass of 'Bifunctor.

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.

    second ≡ bimap id

#### Examples

Expand

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

    >>> second (+1) (Right 3)
    Right 4

#### Instances

Instances details

Bifunctor Either Source # | 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 Arg Source # | 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 (,) Source #

Class laws for tuples hold only up to laziness. Both `first` `id` and `second` `id` are lazier than `id` (and `fmap` `id`):

    >>> first id (undefined :: (Int, Word)) `seq` ()
    ()
    >>> second id (undefined :: (Int, Word)) `seq` ()
    ()
    >>> id (undefined :: (Int, Word)) `seq` ()
    *** Exception: Prelude.undefined

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 (Const :: Type -> Type -> Type) Source # | 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 ((,,) x1) Source # | 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 (K1 i :: Type -> Type -> Type) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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 #