Data.Bifoldable

bifunctors-5.3: 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
- bifoldr1 :: Bifoldable t => (a -> a -> a) -> t a a -> a
- 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
- bifoldl1 :: Bifoldable t => (a -> a -> a) -> t a a -> 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 ()
- bimsum :: (Bifoldable t, MonadPlus m) => t (m a) (m a) -> m a
- bisequenceA_ :: (Bifoldable t, Applicative f) => t (f a) (f b) -> f ()
- bisequence_ :: (Bifoldable t, Monad m) => t (m a) (m b) -> m ()
- 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
- bimaximum :: forall t a. (Bifoldable t, Ord a) => t a a -> a
- biminimum :: forall t a. (Bifoldable t, Ord a) => t a a -> a
- bisum :: (Bifoldable t, Num a) => t a a -> a
- biproduct :: (Bifoldable t, Num a) => t a a -> a
- biconcat :: Bifoldable t => 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
- bimaximumBy :: Bifoldable t => (a -> a -> Ordering) -> t a a -> a
- biminimumBy :: Bifoldable t => (a -> a -> Ordering) -> t a a -> a
- binotElem :: (Bifoldable t, Eq a) => a -> t a a -> Bool
- bifind :: Bifoldable t => (a -> Bool) -> t a a -> Maybe a

# Documentation

class Bifoldable p where

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

Combines the elements of a structure using a monoid.

    bifold ≡ bifoldMap id id

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

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

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

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 |
Bifoldable (,) |
Bifoldable Const |
Bifoldable Arg |
Bifoldable Constant |
Bifoldable (K1 i) |
Bifoldable ((,,) x) |
Bifoldable (Tagged *) |
Bifoldable ((,,,) x y) |
Bifoldable ((,,,,) x y z) |
Foldable f => Bifoldable (Clown * * f) |
Bifoldable p => Bifoldable (Flip * * p) |
Foldable g => Bifoldable (Joker * * g) |
Bifoldable p => Bifoldable (WrappedBifunctor * * p) |
Bifoldable ((,,,,,) x y z w) |
(Bifoldable p, Bifoldable q) => Bifoldable (Sum * * p q) |
(Bifoldable f, Bifoldable g) => Bifoldable (Product * * f g) |
Bifoldable ((,,,,,,) x y z w v) |
(Foldable f, Bifoldable p) => Bifoldable (Tannen * * * f p) |
(Bifoldable p, Foldable f, Foldable g) => Bifoldable (Biff * * * * p f g) |

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.

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

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

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.

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

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

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

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

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.

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

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 ()

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 ()

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 ()

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

bimsum :: (Bifoldable t, MonadPlus m) => t (m a) (m a) -> m a

The sum of a collection of actions, generalizing `biconcat`.

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

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

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

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

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

The sum of a collection of actions, generalizing `biconcat`.

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

Collects the list of elements of a structure in order.

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

Test whether the structure is empty.

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

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

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

Does the element occur in the structure?

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

The largest element of a non-empty structure.

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

The least element of a non-empty structure.

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

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

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

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

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

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

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.

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.

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.

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

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

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

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

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

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

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

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

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

`binotElem` is the negation of `bielem`.

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.