bifunctors-5: Bifunctors

Copyright(C) 2011-2015 Edward Kmett
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <ekmett@gmail.com>
Stabilityprovisional
Portabilityportable
Safe HaskellSafe
LanguageHaskell98

Data.Bifoldable

Description

 

Synopsis

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:

bifoldbifoldMap 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.

bifoldbifoldMap 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 

Methods

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

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

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

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

Bifoldable (,) Source 

Methods

bifold :: Monoid m => (m, m) -> m Source

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

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

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

Bifoldable Const Source 

Methods

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

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

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

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

Bifoldable Arg Source 

Methods

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

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

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

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

Bifoldable ((,,) x) Source 

Methods

bifold :: Monoid m => (x, m, m) -> m Source

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

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> (x, a, b) -> c Source

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> (x, a, b) -> c Source

Bifoldable (Tagged *) Source 

Methods

bifold :: Monoid m => Tagged * m m -> m Source

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

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Tagged * a b -> c Source

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Tagged * a b -> c Source

Foldable f => Bifoldable (Clown f) Source 

Methods

bifold :: Monoid m => Clown f m m -> m Source

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

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Clown f a b -> c Source

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Clown f a b -> c Source

Bifoldable p => Bifoldable (Flip p) Source 

Methods

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

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

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

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

Foldable g => Bifoldable (Joker g) Source 

Methods

bifold :: Monoid m => Joker g m m -> m Source

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

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Joker g a b -> c Source

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Joker g a b -> c Source

Bifoldable p => Bifoldable (WrappedBifunctor p) Source 

Methods

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

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

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

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

Bifoldable ((,,,) x y) Source 

Methods

bifold :: Monoid m => (x, y, m, m) -> m Source

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> (x, y, a, b) -> m Source

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> (x, y, a, b) -> c Source

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> (x, y, a, b) -> c Source

(Bifoldable f, Bifoldable g) => Bifoldable (Product f g) Source 

Methods

bifold :: Monoid m => Product f g m m -> m Source

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Product f g a b -> m Source

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Product f g a b -> c Source

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Product f g a b -> c Source

(Foldable f, Bifoldable p) => Bifoldable (Tannen f p) Source 

Methods

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

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

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

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

Bifoldable ((,,,,) x y z) Source 

Methods

bifold :: Monoid m => (x, y, z, m, m) -> m Source

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> (x, y, z, a, b) -> m Source

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> (x, y, z, a, b) -> c Source

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> (x, y, z, a, b) -> c Source

(Bifoldable p, Foldable f, Foldable g) => Bifoldable (Biff p f g) Source 

Methods

bifold :: Monoid m => Biff p f g m m -> m Source

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

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Biff p f g a b -> c Source

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Biff p f g a b -> c Source

Bifoldable ((,,,,,) x y z w) Source 

Methods

bifold :: Monoid m => (x, y, z, w, m, m) -> m Source

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> (x, y, z, w, a, b) -> m Source

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> (x, y, z, w, a, b) -> c Source

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> (x, y, z, w, a, b) -> c Source

Bifoldable ((,,,,,,) x y z w v) Source 

Methods

bifold :: Monoid m => (x, y, z, w, v, m, m) -> m Source

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> (x, y, z, w, v, a, b) -> m Source

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> (x, y, z, w, v, a, b) -> c Source

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> (x, y, z, w, v, a, b) -> c 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.