class Bifoldable p where Source

Bifoldable identifies foldable structures with two different varieties of elements (as opposed to Foldable, which has one variety of element). 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)

A minimal Bifoldable definition consists of either bifoldMap or bifoldr. When defining more than this minimal set, 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

If the type is also a Bifunctor instance, it should satisfy:

'bifoldMap' f g ≡ 'bifold' . 'bimap' f g

which implies that

'bifoldMap' f g . 'bimap' h i ≡ 'bifoldMap' (f . h) (g . i)

Since: base-4.10.0.0

bifold ≡ bifoldMap id id

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

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

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

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.

Since: base-4.10.0.0

bifoldr1 :: Bifoldable t => (a -> a -> a) -> t a a -> a Source

A variant of bifoldr that has no base case, and thus may only be applied to non-empty structures.

Since: base-4.10.0.0

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.

Since: base-4.10.0.0

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

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

This ensures that each step of the bifold is forced to weak head normal form before being applied, avoiding the collection of thunks that would otherwise occur. This is often what you want to strictly reduce a finite structure to a single, monolithic result (e.g., bilength).

Since: base-4.10.0.0

bifoldl1 :: Bifoldable t => (a -> a -> a) -> t a a -> a Source

A variant of bifoldl that has no base case, and thus may only be applied to non-empty structures.

Since: base-4.10.0.0

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.

Since: base-4.10.0.0

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

Map each element of a structure using one of two actions, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results, see bitraverse.

Since: base-4.10.0.0

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. For a version that doesn't ignore the results, see bifor.

>>> > bifor_ ('a', "bc") print (print . reverse)
'a'
"cb"

Since: base-4.10.0.0

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

Alias for bitraverse_.

Since: base-4.10.0.0

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

Alias for bifor_.

Since: base-4.10.0.0

bimsum :: (Bifoldable t, Alternative f) => t (f a) (f a) -> f a Source

Alias for biasum.

Since: base-4.10.0.0

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

Alias for bisequence_.

Since: base-4.10.0.0

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

Evaluate each action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results, see bisequence.

Since: base-4.10.0.0

biasum :: (Bifoldable t, Alternative f) => t (f a) (f a) -> f a Source

The sum of a collection of actions, generalizing biconcat.

Since: base-4.10.0.0

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

Collects the list of elements of a structure, from left to right.

Since: base-4.10.0.0

binull :: Bifoldable t => t a b -> Bool Source

Test whether the structure is empty.

Since: base-4.10.0.0

bilength :: Bifoldable t => t a b -> Int Source

Returns the size/length of a finite structure as an Int.

Since: base-4.10.0.0

bielem :: (Bifoldable t, Eq a) => a -> t a a -> Bool Source

Does the element occur in the structure?

Since: base-4.10.0.0

bimaximum :: forall t a. (Bifoldable t, Ord a) => t a a -> a Source

The largest element of a non-empty structure.

Since: base-4.10.0.0

biminimum :: forall t a. (Bifoldable t, Ord a) => t a a -> a Source

The least element of a non-empty structure.

Since: base-4.10.0.0

bisum :: (Bifoldable t, Num a) => t a a -> a Source

The bisum function computes the sum of the numbers of a structure.

Since: base-4.10.0.0

biproduct :: (Bifoldable t, Num a) => t a a -> a Source

The biproduct function computes the product of the numbers of a structure.

Since: base-4.10.0.0

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

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

Since: base-4.10.0.0

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.

Since: base-4.10.0.0

biand :: Bifoldable t => t Bool Bool -> Bool Source

biand returns the conjunction of a container of Bools. For the result to be True, the container must be finite; False, however, results from a False value finitely far from the left end.

Since: base-4.10.0.0

bior :: Bifoldable t => t Bool Bool -> Bool Source

bior returns the disjunction of a container of Bools. For the result to be False, the container must be finite; True, however, results from a True value finitely far from the left end.

Since: base-4.10.0.0

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

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

Since: base-4.10.0.0

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

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

Since: base-4.10.0.0

bimaximumBy :: Bifoldable t => (a -> a -> Ordering) -> t a a -> a Source

The largest element of a non-empty structure with respect to the given comparison function.

Since: base-4.10.0.0

biminimumBy :: Bifoldable t => (a -> a -> Ordering) -> t a a -> a Source

The least element of a non-empty structure with respect to the given comparison function.

Since: base-4.10.0.0

binotElem :: (Bifoldable t, Eq a) => a -> t a a -> Bool Source

binotElem is the negation of bielem.

Since: base-4.10.0.0

bifind :: Bifoldable t => (a -> Bool) -> t a a -> Maybe a Source

The bifind function takes a predicate and a structure and returns the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

Since: base-4.10.0.0