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 | Trustworthy |

Language | Haskell98 |

- class Bifoldable p where
- 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 #

`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)

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

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

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.

Bifoldable Either # | |

Bifoldable (,) # | |

Bifoldable Arg # | |

Bifoldable (K1 i) # | |

Bifoldable ((,,) x) # | |

Bifoldable (Const *) # | |

Bifoldable (Tagged *) # | |

Bifoldable (Constant *) # | |

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 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`

).

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 () #

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`

.

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`

.

`>>>`

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

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 () #

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`

.

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, from left to right.

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.

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.