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 |
- 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 ()
- 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 ()
- bisequenceA_ :: (Bifoldable t, Applicative f) => t (f a) (f b) -> f ()
- bisequence_ :: (Bifoldable t, Monad m) => t (m a) (m b) -> m ()
- biList :: Bifoldable t => t a a -> [a]
- biconcat :: Bifoldable t => t [a] [a] -> [a]
- biconcatMap :: Bifoldable t => (a -> [c]) -> (b -> [c]) -> t a b -> [c]
- biany :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool
- biall :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool
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:
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
bifold :: Monoid m => p m m -> m Source
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
Bifoldable Either Source | |
Bifoldable (,) Source | |
Bifoldable Const Source | |
Bifoldable Arg Source | |
Bifoldable ((,,) x) Source | |
Bifoldable (Tagged *) Source | |
Bifoldable ((,,,) x y) Source | |
Bifoldable ((,,,,) x y z) Source | |
Foldable f => Bifoldable (Clown * * f) Source | |
Bifoldable p => Bifoldable (Flip * * p) Source | |
Foldable g => Bifoldable (Joker * * g) Source | |
Bifoldable p => Bifoldable (WrappedBifunctor * * p) Source | |
Bifoldable ((,,,,,) x y z w) Source | |
(Bifoldable p, Bifoldable q) => Bifoldable (Sum * * p q) Source | |
(Bifoldable f, Bifoldable g) => Bifoldable (Product * * f g) Source | |
Bifoldable ((,,,,,,) x y z w v) Source | |
(Foldable f, Bifoldable p) => Bifoldable (Tannen * * * f p) Source | |
(Bifoldable p, Foldable f, Foldable g) => Bifoldable (Biff * * * * p f g) 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.