Copyright | (C) 2011-2016 Edward Kmett |
---|---|
License | BSD-style (see the file LICENSE) |
Maintainer | [email protected] |
Stability | provisional |
Portability | portable |
Safe Haskell | Safe |
Language | Haskell2010 |
Since: 4.10.0.0
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: 4.10.0.0
bifold :: Monoid m => p m m -> m Source
Combines the elements of a structure using a monoid.
bifold
≡bifoldMap
id
id
Since: 4.10.0.0
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
Since: 4.10.0.0
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
Since: 4.10.0.0
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
Note that if you want an efficient left-fold, you probably want to use bifoldl'
instead of bifoldl
. The reason is that the latter does not force the "inner" results, resulting in a thunk chain which then must be evaluated from the outside-in.
Since: 4.10.0.0
Bifoldable Either | Since: 4.10.0.0 |
Bifoldable (,) | Since: 4.10.0.0 |
Bifoldable Arg | Since: 4.10.0.0 |
Bifoldable ((,,) x) | Since: 4.10.0.0 |
Bifoldable (Const *) | Since: 4.10.0.0 |
Bifoldable (K1 * i) | Since: 4.10.0.0 |
Bifoldable ((,,,) x y) | Since: 4.10.0.0 |
Bifoldable ((,,,,) x y z) | Since: 4.10.0.0 |
Bifoldable ((,,,,,) x y z w) | Since: 4.10.0.0 |
Bifoldable ((,,,,,,) x y z w v) | Since: 4.10.0.0 |
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: 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: 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: 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: 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: 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: 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: 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: 4.10.0.0
bimapM_ :: (Bifoldable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f () Source
Alias for bitraverse_
.
Since: 4.10.0.0
biforM_ :: (Bifoldable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f () Source
Alias for bifor_
.
Since: 4.10.0.0
bimsum :: (Bifoldable t, Alternative f) => t (f a) (f a) -> f a Source
Alias for biasum
.
Since: 4.10.0.0
bisequenceA_ :: (Bifoldable t, Applicative f) => t (f a) (f b) -> f () Source
Alias for bisequence_
.
Since: 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: 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: 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: 4.10.0.0
binull :: Bifoldable t => t a b -> Bool Source
Test whether the structure is empty.
Since: 4.10.0.0
bilength :: Bifoldable t => t a b -> Int Source
Returns the size/length of a finite structure as an Int
.
Since: 4.10.0.0
bielem :: (Bifoldable t, Eq a) => a -> t a a -> Bool Source
Does the element occur in the structure?
Since: 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: 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: 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: 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: 4.10.0.0
biconcat :: Bifoldable t => t [a] [a] -> [a] Source
Reduces a structure of lists to the concatenation of those lists.
Since: 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: 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: 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: 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: 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: 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: 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: 4.10.0.0
binotElem :: (Bifoldable t, Eq a) => a -> t a a -> Bool Source
binotElem
is the negation of bielem
.
Since: 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: 4.10.0.0
© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.2.1/docs/html/libraries/base-4.10.0.0/Data-Bifoldable.html