bifunctors-5.1: Bifunctors

Copyright | (C) 2011-2015 Edward Kmett
License | BSD-style (see the file LICENSE)
Maintainer | Edward Kmett <ekmett@gmail.com>
Stability | provisional
Portability | portable
Safe Haskell | Safe
Language | Haskell98

Data.Bifoldable

Description

Synopsis

- class Bifoldable p where
  - bifold :: Monoid m => p m m -> m
  - bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> p a b -> m
  - bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> p a b -> c
  - bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> p a b -> c
- bifoldr' :: Bifoldable t => (a -> c -> c) -> (b -> c -> c) -> c -> t a b -> c
- bifoldrM :: (Bifoldable t, Monad m) => (a -> c -> m c) -> (b -> c -> m c) -> c -> t a b -> m c
- bifoldl' :: Bifoldable t => (a -> b -> a) -> (a -> c -> a) -> a -> t b c -> a
- bifoldlM :: (Bifoldable t, Monad m) => (a -> b -> m a) -> (a -> c -> m a) -> a -> t b c -> m a
- bitraverse_ :: (Bifoldable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f ()
- bifor_ :: (Bifoldable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f ()
- bimapM_ :: (Bifoldable t, Monad m) => (a -> m c) -> (b -> m d) -> t a b -> m ()
- biforM_ :: (Bifoldable t, Monad m) => t a b -> (a -> m c) -> (b -> m d) -> m ()
- bisequenceA_ :: (Bifoldable t, Applicative f) => t (f a) (f b) -> f ()
- bisequence_ :: (Bifoldable t, Monad m) => t (m a) (m b) -> m ()
- biList :: Bifoldable t => t a a -> [a]
- biconcat :: Bifoldable t => t [a] [a] -> [a]
- biconcatMap :: Bifoldable t => (a -> [c]) -> (b -> [c]) -> t a b -> [c]
- biany :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool
- biall :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool

# Documentation

class Bifoldable p where Source

Minimal definition either `bifoldr` or `bifoldMap`

`Bifoldable` identifies foldable structures with two different varieties of elements. Common examples are `Either` and '(,)':

    instance Bifoldable Either where
      bifoldMap f _ (Left  a) = f a
      bifoldMap _ g (Right b) = g b

    instance Bifoldable (,) where
      bifoldr f g z (a, b) = f a (g b z)

When defining more than the minimal set of definitions, one should ensure that the following identities hold:

    bifold ≡ bifoldMap id id
    bifoldMap f g ≡ bifoldr (mappend . f) (mappend . g) mempty
    bifoldr f g z t ≡ appEndo (bifoldMap (Endo . f) (Endo . g) t) z

Minimal complete definition

bifoldr | bifoldMap

Methods

bifold :: Monoid m => p m m -> m Source

Combines the elements of a structure using a monoid.

    bifold ≡ bifoldMap id id

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> p a b -> m Source

Combines the elements of a structure, given ways of mapping them to a common monoid.

    bifoldMap f g ≡ bifoldr (mappend . f) (mappend . g) mempty

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> p a b -> c Source

Combines the elements of a structure in a right associative manner. Given a hypothetical function `toEitherList :: p a b -> [Either a b]` yielding a list of all elements of a structure in order, the following would hold:

    bifoldr f g z ≡ foldr (either f g) z . toEitherList

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> p a b -> c Source

Combines the elments of a structure in a left associative manner. Given a hypothetical function `toEitherList :: p a b -> [Either a b]` yielding a list of all elements of a structure in order, the following would hold:

    bifoldl f g z ≡ foldl (acc -> either (f acc) (g acc)) z .  toEitherList

Instances

Bifoldable Either Source |
Bifoldable (,) Source |
Bifoldable Const Source |
Bifoldable Arg Source |
Bifoldable ((,,) x) Source |
Bifoldable (Tagged *) Source |
Foldable f => Bifoldable (Clown f) Source |
Bifoldable p => Bifoldable (Flip p) Source |
Foldable g => Bifoldable (Joker g) Source |
Bifoldable p => Bifoldable (WrappedBifunctor p) Source |
Bifoldable ((,,,) x y) Source |
(Bifoldable f, Bifoldable g) => Bifoldable (Product f g) Source |
(Foldable f, Bifoldable p) => Bifoldable (Tannen f p) Source |
Bifoldable ((,,,,) x y z) Source |
(Bifoldable p, Foldable f, Foldable g) => Bifoldable (Biff p f g) Source |
Bifoldable ((,,,,,) x y z w) Source |
Bifoldable ((,,,,,,) x y z w v) Source |

bifoldr' :: Bifoldable t => (a -> c -> c) -> (b -> c -> c) -> c -> t a b -> c Source

As `bifoldr`, but strict in the result of the reduction functions at each step.

bifoldrM :: (Bifoldable t, Monad m) => (a -> c -> m c) -> (b -> c -> m c) -> c -> t a b -> m c Source

Right associative monadic bifold over a structure.

bifoldl' :: Bifoldable t => (a -> b -> a) -> (a -> c -> a) -> a -> t b c -> a Source

As `bifoldl`, but strict in the result of the reductionf unctions at each step.

bifoldlM :: (Bifoldable t, Monad m) => (a -> b -> m a) -> (a -> c -> m a) -> a -> t b c -> m a Source

Left associative monadic bifold over a structure.

bitraverse_ :: (Bifoldable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f () Source

As `bitraverse`, but ignores the results of the functions, merely performing the "actions".

bifor_ :: (Bifoldable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f () Source

As `bitraverse_`, but with the structure as the primary argument.

bimapM_ :: (Bifoldable t, Monad m) => (a -> m c) -> (b -> m d) -> t a b -> m () Source

As `bimapM`, but ignores the results of the functions, merely performing the "actions".

biforM_ :: (Bifoldable t, Monad m) => t a b -> (a -> m c) -> (b -> m d) -> m () Source

As `bimapM_`, but with the structure as the primary argument.

bisequenceA_ :: (Bifoldable t, Applicative f) => t (f a) (f b) -> f () Source

As `bisequenceA`, but ignores the results of the actions.

bisequence_ :: (Bifoldable t, Monad m) => t (m a) (m b) -> m () Source

As `bisequence`, but ignores the results of the actions.

biList :: Bifoldable t => t a a -> [a] Source

Collects the list of elements of a structure in order.

biconcat :: Bifoldable t => t [a] [a] -> [a] Source

Reduces a structure of lists to the concatenation of those lists.

biconcatMap :: Bifoldable t => (a -> [c]) -> (b -> [c]) -> t a b -> [c] Source

Given a means of mapping the elements of a structure to lists, computes the concatenation of all such lists in order.

biany :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool Source

Determines whether any element of the structure satisfies the appropriate predicate.

biall :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool Source

Determines whether all elements of the structure satisfy the appropriate predicate.