Data.Bifoldable

base-4.15.0.0: Basic libraries

Copyright | (C) 2011-2016 Edward Kmett
License | BSD-style (see the file LICENSE)
Maintainer | libraries@haskell.org
Stability | provisional
Portability | portable
Safe Haskell | Safe
Language | Haskell2010

Data.Bifoldable

Description

Since: base-4.10.0.0

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, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f ()
- biforM_ :: (Bifoldable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f ()
- bimsum :: (Bifoldable t, Alternative f) => t (f a) (f a) -> f a
- bisequenceA_ :: (Bifoldable t, Applicative f) => t (f a) (f b) -> 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
- 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 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)

Some examples below also use the following BiList to showcase empty Bifoldable behaviors when relevant (`Either` and '(,)' containing always exactly resp. 1 and 2 elements):

    data BiList a b = BiList [a] [b]

    instance Bifoldable BiList where
      bifoldr f g z (BiList as bs) = foldr f (foldr g z bs) as

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 Source #

Combines the elements of a structure using a monoid.

    bifold ≡ bifoldMap id id

#### Examples

Expand

Basic usage:

    >>> bifold (Right [1, 2, 3])
    [1,2,3]

    >>> bifold (Left [5, 6])
    [5,6]

    >>> bifold ([1, 2, 3], [4, 5])
    [1,2,3,4,5]

    >>> bifold (Product 6, Product 7)
    Product {getProduct = 42}

    >>> bifold (Sum 6, Sum 7)
    Sum {getSum = 13}

Since: base-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

#### Examples

Expand

Basic usage:

    >>> bifoldMap (take 3) (fmap digitToInt) ([1..], "89")
    [1,2,3,8,9]

    >>> bifoldMap (take 3) (fmap digitToInt) (Left [1..])
    [1,2,3]

    >>> bifoldMap (take 3) (fmap digitToInt) (Right "89")
    [8,9]

Since: base-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

#### Examples

Expand

Basic usage:

    > bifoldr (+) (*) 3 (5, 7)
    26 -- 5 + (7 * 3)

    > bifoldr (+) (*) 3 (7, 5)
    22 -- 7 + (5 * 3)

    > bifoldr (+) (*) 3 (Right 5)
    15 -- 5 * 3

    > bifoldr (+) (*) 3 (Left 5)
    8 -- 5 + 3

Since: base-4.10.0.0

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

Combines the elements 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.

#### Examples

Expand

Basic usage:

    > bifoldl (+) (*) 3 (5, 7)
    56 -- (5 + 3) * 7

    > bifoldl (+) (*) 3 (7, 5)
    50 -- (7 + 3) * 5

    > bifoldl (+) (*) 3 (Right 5)
    15 -- 5 * 3

    > bifoldl (+) (*) 3 (Left 5)
    8 -- 5 + 3

Since: base-4.10.0.0

#### Instances

Instances details

Bifoldable Either # | Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => Either m m -> m Source # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Either a b -> m Source # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Either a b -> c Source # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Either a b -> c Source #
Bifoldable (,) # | Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => (m, m) -> m Source # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> (a, b) -> m Source # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> (a, b) -> c Source # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> (a, b) -> c Source #
Bifoldable Arg # | Since: base-4.10.0.0
Instance details Defined in Data.Semigroup Methods bifold :: Monoid m => Arg m m -> m Source # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Arg a b -> m Source # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Arg a b -> c Source # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Arg a b -> c Source #
Bifoldable ((,,) x) # | Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => (x, m, m) -> m Source # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> (x, a, b) -> m Source # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> (x, a, b) -> c Source # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> (x, a, b) -> c Source #
Bifoldable (Const :: Type -> Type -> Type) # | Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => Const m m -> m Source # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Const a b -> m Source # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Const a b -> c Source # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Const a b -> c Source #
Bifoldable (K1 i :: Type -> Type -> Type) # | Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => K1 i m m -> m Source # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> K1 i a b -> m Source # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> K1 i a b -> c Source # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> K1 i a b -> c Source #
Bifoldable ((,,,) x y) # | Since: base-4.10.0.0
Instance details Defined in Data.Bifoldable Methods bifold :: Monoid m => (x, y, m, m) -> m Source # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> (x, y, a, b) -> m Source # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> (x, y, a, b) -> c Source # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> (x, y, a, b) -> c Source #
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 Source # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> (x, y, z, a, b) -> m Source # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> (x, y, z, a, b) -> c Source # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> (x, y, z, a, b) -> c Source #
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 Source # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> (x, y, z, w, a, b) -> m Source # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> (x, y, z, w, a, b) -> c Source # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> (x, y, z, w, a, b) -> c Source #
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 Source # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> (x, y, z, w, v, a, b) -> m Source # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> (x, y, z, w, v, a, b) -> c Source # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> (x, y, z, w, v, a, b) -> c 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.

Since: base-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.

#### Examples

Expand

Basic usage:

    >>> bifoldr1 (+) (5, 7)
    12

    >>> bifoldr1 (+) (Right 7)
    7

    >>> bifoldr1 (+) (Left 5)
    5

    > bifoldr1 (+) (BiList [1, 2] [3, 4])
    10 -- 1 + (2 + (3 + 4))

    >>> bifoldr1 (+) (BiList [1, 2] [])
    3

On empty structures, this function throws an exception:

    >>> bifoldr1 (+) (BiList [] [])
    *** Exception: bifoldr1: empty structure

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 Source #

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 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: base-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.

#### Examples

Expand

Basic usage:

    >>> bifoldl1 (+) (5, 7)
    12

    >>> bifoldl1 (+) (Right 7)
    7

    >>> bifoldl1 (+) (Left 5)
    5

    > bifoldl1 (+) (BiList [1, 2] [3, 4])
    10 -- ((1 + 2) + 3) + 4

    >>> bifoldl1 (+) (BiList [1, 2] [])
    3

On empty structures, this function throws an exception:

    >>> bifoldl1 (+) (BiList [] [])
    *** Exception: bifoldl1: empty structure

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 Source #

Left associative monadic bifold over a structure.

#### Examples

Expand

Basic usage:

    >>> bifoldlM (\a b -> print b >> pure a) (\a c -> print (show c) >> pure a) 42 ("Hello", True)
    "Hello"
    "True"
    42

    >>> bifoldlM (\a b -> print b >> pure a) (\a c -> print (show c) >> pure a) 42 (Right True)
    "True"
    42

    >>> bifoldlM (\a b -> print b >> pure a) (\a c -> print (show c) >> pure a) 42 (Left "Hello")
    "Hello"
    42

Since: base-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`.

#### Examples

Expand

Basic usage:

    >>> bitraverse_ print (print . show) ("Hello", True)
    "Hello"
    "True"

    >>> bitraverse_ print (print . show) (Right True)
    "True"

    >>> bitraverse_ print (print . show) (Left "Hello")
    "Hello"

Since: base-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`.

#### Examples

Expand

Basic usage:

    >>> bifor_ ("Hello", True) print (print . show)
    "Hello"
    "True"

    >>> bifor_ (Right True) print (print . show)
    "True"

    >>> bifor_ (Left "Hello") print (print . show)
    "Hello"

Since: base-4.10.0.0

bimapM_ :: (Bifoldable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f () Source #

Alias for `bitraverse_`.

Since: base-4.10.0.0

biforM_ :: (Bifoldable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f () Source #

Alias for `bifor_`.

Since: base-4.10.0.0

bimsum :: (Bifoldable t, Alternative f) => t (f a) (f a) -> f a Source #

Alias for `biasum`.

Since: base-4.10.0.0

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

Alias for `bisequence_`.

Since: base-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`.

#### Examples

Expand

Basic usage:

    >>> bisequence_ (print "Hello", print "World")
    "Hello"
    "World"

    >>> bisequence_ (Left (print "Hello"))
    "Hello"

    >>> bisequence_ (Right (print "World"))
    "World"

Since: base-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`.

#### Examples

Expand

Basic usage:

    >>> biasum (Nothing, Nothing)
    Nothing

    >>> biasum (Nothing, Just 42)
    Just 42

    >>> biasum (Just 18, Nothing)
    Just 18

    >>> biasum (Just 18, Just 42)
    Just 18

Since: base-4.10.0.0

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

Collects the list of elements of a structure, from left to right.

#### Examples

Expand

Basic usage:

    >>> biList (18, 42)
    [18,42]

    >>> biList (Left 18)
    [18]

Since: base-4.10.0.0

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

Test whether the structure is empty.

#### Examples

Expand

Basic usage:

    >>> binull (18, 42)
    False

    >>> binull (Right 42)
    False

    >>> binull (BiList [] [])
    True

Since: base-4.10.0.0

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

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

#### Examples

Expand

Basic usage:

    >>> bilength (True, 42)
    2

    >>> bilength (Right 42)
    1

    >>> bilength (BiList [1,2,3] [4,5])
    5

    >>> bilength (BiList [] [])
    0

On infinite structures, this function hangs:

    > bilength (BiList [1..] [])
    * Hangs forever *

Since: base-4.10.0.0

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

Does the element occur in the structure?

#### Examples

Expand

Basic usage:

    >>> bielem 42 (17, 42)
    True

    >>> bielem 42 (17, 43)
    False

    >>> bielem 42 (Left 42)
    True

    >>> bielem 42 (Right 13)
    False

    >>> bielem 42 (BiList [1..5] [1..100])
    True

    >>> bielem 42 (BiList [1..5] [1..41])
    False

Since: base-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.

#### Examples

Expand

Basic usage:

    >>> bimaximum (42, 17)
    42

    >>> bimaximum (Right 42)
    42

    >>> bimaximum (BiList [13, 29, 4] [18, 1, 7])
    29

    >>> bimaximum (BiList [13, 29, 4] [])
    29

On empty structures, this function throws an exception:

    >>> bimaximum (BiList [] [])
    *** Exception: bimaximum: empty structure

Since: base-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.

#### Examples

Expand

Basic usage:

    >>> biminimum (42, 17)
    17

    >>> biminimum (Right 42)
    42

    >>> biminimum (BiList [13, 29, 4] [18, 1, 7])
    1

    >>> biminimum (BiList [13, 29, 4] [])
    4

On empty structures, this function throws an exception:

    >>> biminimum (BiList [] [])
    *** Exception: biminimum: empty structure

Since: base-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.

#### Examples

Expand

Basic usage:

    >>> bisum (42, 17)
    59

    >>> bisum (Right 42)
    42

    >>> bisum (BiList [13, 29, 4] [18, 1, 7])
    72

    >>> bisum (BiList [13, 29, 4] [])
    46

    >>> bisum (BiList [] [])
    0

Since: base-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.

#### Examples

Expand

Basic usage:

    >>> biproduct (42, 17)
    714

    >>> biproduct (Right 42)
    42

    >>> biproduct (BiList [13, 29, 4] [18, 1, 7])
    190008

    >>> biproduct (BiList [13, 29, 4] [])
    1508

    >>> biproduct (BiList [] [])
    1

Since: base-4.10.0.0

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

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

#### Examples

Expand

Basic usage:

    >>> biconcat ([1, 2, 3], [4, 5])
    [1,2,3,4,5]

    >>> biconcat (Left [1, 2, 3])
    [1,2,3]

    >>> biconcat (BiList [[1, 2, 3, 4, 5], [6, 7, 8]] [[9]])
    [1,2,3,4,5,6,7,8,9]

Since: base-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.

#### Examples

Expand

Basic usage:

    >>> biconcatMap (take 3) (fmap digitToInt) ([1..], "89")
    [1,2,3,8,9]

    >>> biconcatMap (take 3) (fmap digitToInt) (Left [1..])
    [1,2,3]

    >>> biconcatMap (take 3) (fmap digitToInt) (Right "89")
    [8,9]

Since: base-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.

#### Examples

Expand

Basic usage:

    >>> biand (True, False)
    False

    >>> biand (True, True)
    True

    >>> biand (Left True)
    True

Empty structures yield `True`:

    >>> biand (BiList [] [])
    True

A `False` value finitely far from the left end yields `False` (short circuit):

    >>> biand (BiList [True, True, False, True] (repeat True))
    False

A `False` value infinitely far from the left end hangs:

    > biand (BiList (repeat True) [False])
    * Hangs forever *

An infinitely `True` value hangs:

    > biand (BiList (repeat True) [])
    * Hangs forever *

Since: base-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.

#### Examples

Expand

Basic usage:

    >>> bior (True, False)
    True

    >>> bior (False, False)
    False

    >>> bior (Left True)
    True

Empty structures yield `False`:

    >>> bior (BiList [] [])
    False

A `True` value finitely far from the left end yields `True` (short circuit):

    >>> bior (BiList [False, False, True, False] (repeat False))
    True

A `True` value infinitely far from the left end hangs:

    > bior (BiList (repeat False) [True])
    * Hangs forever *

An infinitely `False` value hangs:

    > bior (BiList (repeat False) [])
    * Hangs forever *

Since: base-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. Empty structures yield `False`.

#### Examples

Expand

Basic usage:

    >>> biany even isDigit (27, 't')
    False

    >>> biany even isDigit (27, '8')
    True

    >>> biany even isDigit (26, 't')
    True

    >>> biany even isDigit (Left 27)
    False

    >>> biany even isDigit (Left 26)
    True

    >>> biany even isDigit (BiList [27, 53] ['t', '8'])
    True

Empty structures yield `False`:

    >>> biany even isDigit (BiList [] [])
    False

Since: base-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. Empty structures yield `True`.

#### Examples

Expand

Basic usage:

    >>> biall even isDigit (27, 't')
    False

    >>> biall even isDigit (26, '8')
    True

    >>> biall even isDigit (Left 27)
    False

    >>> biall even isDigit (Left 26)
    True

    >>> biall even isDigit (BiList [26, 52] ['3', '8'])
    True

Empty structures yield `True`:

    >>> biall even isDigit (BiList [] [])
    True

Since: base-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.

#### Examples

Expand

Basic usage:

    >>> bimaximumBy compare (42, 17)
    42

    >>> bimaximumBy compare (Left 17)
    17

    >>> bimaximumBy compare (BiList [42, 17, 23] [-5, 18])
    42

On empty structures, this function throws an exception:

    >>> bimaximumBy compare (BiList [] [])
    *** Exception: bifoldr1: empty structure

Since: base-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.

#### Examples

Expand

Basic usage:

    >>> biminimumBy compare (42, 17)
    17

    >>> biminimumBy compare (Left 17)
    17

    >>> biminimumBy compare (BiList [42, 17, 23] [-5, 18])
    -5

On empty structures, this function throws an exception:

    >>> biminimumBy compare (BiList [] [])
    *** Exception: bifoldr1: empty structure

Since: base-4.10.0.0

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

`binotElem` is the negation of `bielem`.

#### Examples

Expand

Basic usage:

    >>> binotElem 42 (17, 42)
    False

    >>> binotElem 42 (17, 43)
    True

    >>> binotElem 42 (Left 42)
    False

    >>> binotElem 42 (Right 13)
    True

    >>> binotElem 42 (BiList [1..5] [1..100])
    False

    >>> binotElem 42 (BiList [1..5] [1..41])
    True

Since: base-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.

#### Examples

Expand

Basic usage:

    >>> bifind even (27, 53)
    Nothing

    >>> bifind even (27, 52)
    Just 52

    >>> bifind even (26, 52)
    Just 26

Empty structures always yield `Nothing`:

    >>> bifind even (BiList [] [])
    Nothing

Since: base-4.10.0.0