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Language	Haskell2010

Bifoldable

Contents

Bifoldable
Bifoldable1

Synopsis

class Bifoldable (p :: * -> * -> *) where
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 ()
bisequence_ :: (Bifoldable t, Applicative f) => t (f a) (f b) -> f ()
biasum :: (Bifoldable t, Alternative f) => t (f a) (f a) -> f a
biList :: Bifoldable t => t a a -> [a]
binull :: Bifoldable t => t a b -> Bool
bilength :: Bifoldable t => t a b -> Int
bielem :: (Bifoldable t, Eq a) => a -> t a a -> Bool
bisum :: (Bifoldable t, Num a) => t a a -> a
biproduct :: (Bifoldable t, Num a) => t a a -> a
biconcatMap :: Bifoldable t => (a -> [c]) -> (b -> [c]) -> t a b -> [c]
biand :: Bifoldable t => t Bool Bool -> Bool
bior :: Bifoldable t => t Bool Bool -> Bool
biany :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool
biall :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool
binotElem :: (Bifoldable t, Eq a) => a -> t a a -> Bool
bifind :: Bifoldable t => (a -> Bool) -> t a a -> Maybe a
class Bifoldable t => Bifoldable1 (t :: * -> * -> *) where
bitraverse1_ :: (Bifoldable1 t, Apply f) => (a -> f b) -> (c -> f d) -> t a c -> f ()
bifor1_ :: (Bifoldable1 t, Apply f) => t a c -> (a -> f b) -> (c -> f d) -> f ()
bisequenceA1_ :: (Bifoldable1 t, Apply f) => t (f a) (f b) -> f ()

Bifoldable

class Bifoldable (p :: * -> * -> *) where #

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

Minimal complete definition

bifoldr | bifoldMap

Methods

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

Combines the elements of a structure using a monoid.

bifold ≡ bifoldMap id id

Since: base-4.10.0.0

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

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

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

Since: base-4.10.0.0

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

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

Since: base-4.10.0.0

Instances

Bifoldable Either	Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => Either m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Either a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Either a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Either a b -> c #
Bifoldable (,)	Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => (m, m) -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> (a, b) -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> (a, b) -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> (a, b) -> c #
Bifoldable Arg	Since: base-4.10.0.0
Instance details Defined in Data.Semigroup Methods bifold :: Monoid m => Arg m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Arg a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Arg a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Arg a b -> c #
Bifoldable ((,,) x)	Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => (x, m, m) -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> (x, a, b) -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> (x, a, b) -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> (x, a, b) -> c #
Bifoldable (Const :: * -> * -> *)	Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => Const m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Const a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Const a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Const a b -> c #
Foldable f => Bifoldable (FreeF f)
Instance details Defined in Control.Monad.Trans.Free Methods bifold :: Monoid m => FreeF f m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> FreeF f a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> FreeF f a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> FreeF f a b -> c #
Foldable f => Bifoldable (CofreeF f)
Instance details Defined in Control.Comonad.Trans.Cofree Methods bifold :: Monoid m => CofreeF f m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> CofreeF f a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> CofreeF f a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> CofreeF f a b -> c #
Bifoldable (Tagged :: * -> * -> *)
Instance details Defined in Data.Tagged Methods bifold :: Monoid m => Tagged m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Tagged a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Tagged a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Tagged a b -> c #
Bifoldable (K1 i :: * -> * -> *)	Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => K1 i m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> K1 i a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> K1 i a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> K1 i a b -> c #
Bifoldable ((,,,) x y)	Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => (x, y, m, m) -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> (x, y, a, b) -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> (x, y, a, b) -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> (x, y, a, b) -> c #
Bifoldable ((,,,,) x y z)	Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => (x, y, z, m, m) -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> (x, y, z, a, b) -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> (x, y, z, a, b) -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> (x, y, z, a, b) -> c #
Bifoldable p => Bifoldable (WrappedBifunctor p)
Instance details Defined in Data.Bifunctor.Wrapped Methods bifold :: Monoid m => WrappedBifunctor p m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> WrappedBifunctor p a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> WrappedBifunctor p a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> WrappedBifunctor p a b -> c #
Foldable g => Bifoldable (Joker g :: * -> * -> *)
Instance details Defined in Data.Bifunctor.Joker Methods bifold :: Monoid m => Joker g m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Joker g a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Joker g a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Joker g a b -> c #
Bifoldable p => Bifoldable (Flip p)
Instance details Defined in Data.Bifunctor.Flip Methods bifold :: Monoid m => Flip p m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Flip p a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Flip p a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Flip p a b -> c #
Foldable f => Bifoldable (Clown f :: * -> * -> *)
Instance details Defined in Data.Bifunctor.Clown Methods bifold :: Monoid m => Clown f m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Clown f a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Clown f a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Clown f a b -> c #
Bifoldable ((,,,,,) x y z w)	Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => (x, y, z, w, m, m) -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> (x, y, z, w, a, b) -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> (x, y, z, w, a, b) -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> (x, y, z, w, a, b) -> c #
(Bifoldable p, Bifoldable q) => Bifoldable (Sum p q)
Instance details Defined in Data.Bifunctor.Sum Methods bifold :: Monoid m => Sum p q m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Sum p q a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Sum p q a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Sum p q a b -> c #
(Bifoldable f, Bifoldable g) => Bifoldable (Product f g)
Instance details Defined in Data.Bifunctor.Product Methods bifold :: Monoid m => Product f g m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Product f g a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Product f g a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Product f g a b -> c #
Bifoldable ((,,,,,,) x y z w v)	Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => (x, y, z, w, v, m, m) -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> (x, y, z, w, v, a, b) -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> (x, y, z, w, v, a, b) -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> (x, y, z, w, v, a, b) -> c #
(Foldable f, Bifoldable p) => Bifoldable (Tannen f p)
Instance details Defined in Data.Bifunctor.Tannen Methods bifold :: Monoid m => Tannen f p m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Tannen f p a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Tannen f p a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Tannen f p a b -> c #
(Bifoldable p, Foldable f, Foldable g) => Bifoldable (Biff p f g)
Instance details Defined in Data.Bifunctor.Biff Methods bifold :: Monoid m => Biff p f g m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Biff p f g a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Biff p f g a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Biff p f g a b -> c #

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

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

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 #

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 #

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

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

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 () #

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 () #

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

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

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 #

The sum of a collection of actions, generalizing biconcat.

Since: base-4.10.0.0

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

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 #

Test whether the structure is empty.

Since: base-4.10.0.0

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

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 #

Does the element occur in the structure?

Since: base-4.10.0.0

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

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 #

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

Since: base-4.10.0.0

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

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 #

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 #

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 #

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 #

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

Since: base-4.10.0.0

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

binotElem is the negation of bielem.

Since: base-4.10.0.0

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

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

Bifoldable1

class Bifoldable t => Bifoldable1 (t :: * -> * -> *) where #

Methods

bifold1 :: Semigroup m => t m m -> m #

bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> t a b -> m #

Instances

Bifoldable1 Either
Instance details Defined in Data.Semigroup.Foldable.Class Methods bifold1 :: Semigroup m => Either m m -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Either a b -> m #
Bifoldable1 (,)
Instance details Defined in Data.Semigroup.Foldable.Class Methods bifold1 :: Semigroup m => (m, m) -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> (a, b) -> m #
Bifoldable1 Arg
Instance details Defined in Data.Semigroup.Foldable.Class Methods bifold1 :: Semigroup m => Arg m m -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Arg a b -> m #
Bifoldable1 ((,,) x)
Instance details Defined in Data.Semigroup.Foldable.Class Methods bifold1 :: Semigroup m => (x, m, m) -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> (x, a, b) -> m #
Bifoldable1 (Const :: * -> * -> *)
Instance details Defined in Data.Semigroup.Foldable.Class Methods bifold1 :: Semigroup m => Const m m -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Const a b -> m #
Bifoldable1 (Tagged :: * -> * -> *)
Instance details Defined in Data.Semigroup.Foldable.Class Methods bifold1 :: Semigroup m => Tagged m m -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Tagged a b -> m #
Bifoldable1 ((,,,) x y)
Instance details Defined in Data.Semigroup.Foldable.Class Methods bifold1 :: Semigroup m => (x, y, m, m) -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> (x, y, a, b) -> m #
Bifoldable1 ((,,,,) x y z)
Instance details Defined in Data.Semigroup.Foldable.Class Methods bifold1 :: Semigroup m => (x, y, z, m, m) -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> (x, y, z, a, b) -> m #
Bifoldable1 p => Bifoldable1 (WrappedBifunctor p)
Instance details Defined in Data.Semigroup.Foldable.Class Methods bifold1 :: Semigroup m => WrappedBifunctor p m m -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> WrappedBifunctor p a b -> m #
Foldable1 g => Bifoldable1 (Joker g :: * -> * -> *)
Instance details Defined in Data.Semigroup.Foldable.Class Methods bifold1 :: Semigroup m => Joker g m m -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Joker g a b -> m #
Bifoldable1 p => Bifoldable1 (Flip p)
Instance details Defined in Data.Semigroup.Foldable.Class Methods bifold1 :: Semigroup m => Flip p m m -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Flip p a b -> m #
Foldable1 f => Bifoldable1 (Clown f :: * -> * -> *)
Instance details Defined in Data.Semigroup.Foldable.Class Methods bifold1 :: Semigroup m => Clown f m m -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Clown f a b -> m #
(Bifoldable1 f, Bifoldable1 g) => Bifoldable1 (Product f g)
Instance details Defined in Data.Semigroup.Foldable.Class Methods bifold1 :: Semigroup m => Product f g m m -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Product f g a b -> m #
(Foldable1 f, Bifoldable1 p) => Bifoldable1 (Tannen f p)
Instance details Defined in Data.Semigroup.Foldable.Class Methods bifold1 :: Semigroup m => Tannen f p m m -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Tannen f p a b -> m #
(Bifoldable1 p, Foldable1 f, Foldable1 g) => Bifoldable1 (Biff p f g)
Instance details Defined in Data.Semigroup.Foldable.Class Methods bifold1 :: Semigroup m => Biff p f g m m -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Biff p f g a b -> m #

bitraverse1_ :: (Bifoldable1 t, Apply f) => (a -> f b) -> (c -> f d) -> t a c -> f () #

bifor1_ :: (Bifoldable1 t, Apply f) => t a c -> (a -> f b) -> (c -> f d) -> f () #

bisequenceA1_ :: (Bifoldable1 t, Apply f) => t (f a) (f b) -> f () #