ref: f1650040b7185326951972b827e64acd655628cb
dir: /lib/Data/Bifoldable.hs/
{-# LANGUAGE Safe #-}
{-# LANGUAGE ScopedTypeVariables #-}
-----------------------------------------------------------------------------
-- |
-- Module : Data.Bifoldable
-- Copyright : (C) 2011-2016 Edward Kmett
-- License : BSD-style (see the file LICENSE)
--
-- Maintainer : libraries@haskell.org
-- Stability : provisional
-- Portability : portable
--
-- @since 4.10.0.0
----------------------------------------------------------------------------
module Data.Bifoldable
( Bifoldable(..)
, bifoldr'
, bifoldr1
, bifoldrM
, bifoldl'
, bifoldl1
, bifoldlM
, bitraverse_
, bifor_
, bimapM_
, biforM_
, bimsum
, bisequenceA_
, bisequence_
, biasum
, biList
, binull
, bilength
, bielem
, bimaximum
, biminimum
, bisum
, biproduct
, biconcat
, biconcatMap
, biand
, bior
, biany
, biall
, bimaximumBy
, biminimumBy
, binotElem
, bifind
) where
import Control.Applicative
import Data.Foldable.Internal
import Data.Functor.Const
import Data.Maybe(fromMaybe)
import Data.Monoid
import Data.Monoid.Internal hiding (Max(..), Min(..))
-- $setup
-- >>> import Prelude
-- >>> import Data.Char
-- >>> import GHC.Internal.Data.Monoid (Product (..), Sum (..))
-- >>> 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
-- | '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 an instance of 'Foldable', then
-- it must satisfy (up to laziness):
--
-- @
-- 'bifoldl' 'const' ≡ 'foldl'
-- 'bifoldr' ('flip' 'const') ≡ 'foldr'
-- 'bifoldMap' ('const' 'mempty') ≡ 'foldMap'
-- @
--
-- If the type is also a 'Data.Bifunctor.Bifunctor' instance, it should satisfy:
--
-- @
-- 'bifoldMap' f g ≡ 'bifold' . 'Data.Bifunctor.bimap' f g
-- @
--
-- which implies that
--
-- @
-- 'bifoldMap' f g . 'Data.Bifunctor.bimap' h i ≡ 'bifoldMap' (f . h) (g . i)
-- @
--
-- @since 4.10.0.0
class Bifoldable p where
{-# MINIMAL bifoldr | bifoldMap #-}
-- | Combines the elements of a structure using a monoid.
--
-- @'bifold' ≡ 'bifoldMap' 'id' 'id'@
--
-- ==== __Examples__
--
-- 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 4.10.0.0
bifold :: Monoid m => p m m -> m
bifold = bifoldMap id id
-- | 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__
--
-- 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 4.10.0.0
bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> p a b -> m
bifoldMap f g = bifoldr (mappend . f) (mappend . g) mempty
-- | 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__
--
-- 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 4.10.0.0
bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> p a b -> c
bifoldr f g z t = appEndo (bifoldMap (Endo . f) (Endo . g) t) z
-- | 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__
--
-- 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 4.10.0.0
bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> p a b -> c
bifoldl f g z t = appEndo (getDual (bifoldMap (Dual . Endo . flip f)
(Dual . Endo . flip g) t)) z
-- | Class laws for tuples hold only up to laziness. The
-- Bifoldable methods are lazier than their Foldable counterparts.
-- For example the law @'bifoldr' ('flip' 'const') ≡ 'foldr'@ does
-- not hold for tuples if laziness is exploited:
--
-- >>> bifoldr (flip const) (:) [] (undefined :: (Int, Word)) `seq` ()
-- ()
-- >>> foldr (:) [] (undefined :: (Int, Word)) `seq` ()
-- *** Exception: Prelude.undefined
--
-- @since 4.10.0.0
instance Bifoldable (,) where
bifoldMap f g ~(a, b) = f a `mappend` g b
-- | @since 4.10.0.0
instance Bifoldable Const where
bifoldMap f _ (Const a) = f a
{-
-- | @since 4.10.0.0
instance Bifoldable (K1 i) where
bifoldMap f _ (K1 c) = f c
-}
-- | @since 4.10.0.0
instance Bifoldable ((,,) x) where
bifoldMap f g ~(_,a,b) = f a `mappend` g b
-- | @since 4.10.0.0
instance Bifoldable ((,,,) x y) where
bifoldMap f g ~(_,_,a,b) = f a `mappend` g b
-- | @since 4.10.0.0
instance Bifoldable ((,,,,) x y z) where
bifoldMap f g ~(_,_,_,a,b) = f a `mappend` g b
-- | @since 4.10.0.0
instance Bifoldable ((,,,,,) x y z w) where
bifoldMap f g ~(_,_,_,_,a,b) = f a `mappend` g b
-- | @since 4.10.0.0
instance Bifoldable ((,,,,,,) x y z w v) where
bifoldMap f g ~(_,_,_,_,_,a,b) = f a `mappend` g b
-- | @since 4.10.0.0
instance Bifoldable Either where
bifoldMap f _ (Left a) = f a
bifoldMap _ g (Right b) = g b
-- | As 'bifoldr', but strict in the result of the reduction functions at each
-- step.
--
-- @since 4.10.0.0
bifoldr' :: Bifoldable t => (a -> c -> c) -> (b -> c -> c) -> c -> t a b -> c
bifoldr' f g z0 xs = bifoldl f' g' id xs z0 where
f' k x z = k $! f x z
g' k x z = k $! g x z
-- | A variant of 'bifoldr' that has no base case,
-- and thus may only be applied to non-empty structures.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
bifoldr1 :: Bifoldable t => (a -> a -> a) -> t a a -> a
bifoldr1 f xs = fromMaybe (error "bifoldr1: empty structure")
(bifoldr mbf mbf Nothing xs)
where
mbf x m = Just (case m of
Nothing -> x
Just y -> f x y)
-- | Right associative monadic bifold over a structure.
--
-- @since 4.10.0.0
bifoldrM :: (Bifoldable t, Monad m)
=> (a -> c -> m c) -> (b -> c -> m c) -> c -> t a b -> m c
bifoldrM f g z0 xs = bifoldl f' g' return xs z0 where
f' k x z = f x z >>= k
g' k x z = g x z >>= k
-- | 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
bifoldl':: Bifoldable t => (a -> b -> a) -> (a -> c -> a) -> a -> t b c -> a
bifoldl' f g z0 xs = bifoldr f' g' id xs z0 where
f' x k z = k $! f z x
g' x k z = k $! g z x
-- | A variant of 'bifoldl' that has no base case,
-- and thus may only be applied to non-empty structures.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
bifoldl1 :: Bifoldable t => (a -> a -> a) -> t a a -> a
bifoldl1 f xs = fromMaybe (error "bifoldl1: empty structure")
(bifoldl mbf mbf Nothing xs)
where
mbf m y = Just (case m of
Nothing -> y
Just x -> f x y)
-- | Left associative monadic bifold over a structure.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
bifoldlM :: (Bifoldable t, Monad m)
=> (a -> b -> m a) -> (a -> c -> m a) -> a -> t b c -> m a
bifoldlM f g z0 xs = bifoldr f' g' return xs z0 where
f' x k z = f z x >>= k
g' x k z = g z x >>= k
-- | 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 'Data.Bitraversable.bitraverse'.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
bitraverse_ :: (Bifoldable t, Applicative f)
=> (a -> f c) -> (b -> f d) -> t a b -> f ()
bitraverse_ f g = bifoldr ((*>) . f) ((*>) . g) (pure ())
-- | As 'bitraverse_', but with the structure as the primary argument. For a
-- version that doesn't ignore the results, see 'Data.Bitraversable.bifor'.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
bifor_ :: (Bifoldable t, Applicative f)
=> t a b -> (a -> f c) -> (b -> f d) -> f ()
bifor_ t f g = bitraverse_ f g t
-- | Alias for 'bitraverse_'.
--
-- @since 4.10.0.0
bimapM_ :: (Bifoldable t, Applicative f)
=> (a -> f c) -> (b -> f d) -> t a b -> f ()
bimapM_ = bitraverse_
-- | Alias for 'bifor_'.
--
-- @since 4.10.0.0
biforM_ :: (Bifoldable t, Applicative f)
=> t a b -> (a -> f c) -> (b -> f d) -> f ()
biforM_ = bifor_
-- | Alias for 'bisequence_'.
--
-- @since 4.10.0.0
bisequenceA_ :: (Bifoldable t, Applicative f) => t (f a) (f b) -> f ()
bisequenceA_ = bisequence_
-- | Evaluate each action in the structure from left to right, and ignore the
-- results. For a version that doesn't ignore the results, see
-- 'Data.Bitraversable.bisequence'.
--
-- ==== __Examples__
--
-- Basic usage:
--
-- >>> bisequence_ (print "Hello", print "World")
-- "Hello"
-- "World"
--
-- >>> bisequence_ (Left (print "Hello"))
-- "Hello"
--
-- >>> bisequence_ (Right (print "World"))
-- "World"
--
-- @since 4.10.0.0
bisequence_ :: (Bifoldable t, Applicative f) => t (f a) (f b) -> f ()
bisequence_ = bifoldr (*>) (*>) (pure ())
-- | The sum of a collection of actions, generalizing 'biconcat'.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
biasum :: (Bifoldable t, Alternative f) => t (f a) (f a) -> f a
biasum = bifoldr (<|>) (<|>) empty
-- | Alias for 'biasum'.
--
-- @since 4.10.0.0
bimsum :: (Bifoldable t, Alternative f) => t (f a) (f a) -> f a
bimsum = biasum
-- | Collects the list of elements of a structure, from left to right.
--
-- ==== __Examples__
--
-- Basic usage:
--
-- >>> biList (18, 42)
-- [18,42]
--
-- >>> biList (Left 18)
-- [18]
--
-- @since 4.10.0.0
biList :: Bifoldable t => t a a -> [a]
biList = bifoldr (:) (:) []
-- | Test whether the structure is empty.
--
-- ==== __Examples__
--
-- Basic usage:
--
-- >>> binull (18, 42)
-- False
--
-- >>> binull (Right 42)
-- False
--
-- >>> binull (BiList [] [])
-- True
--
-- @since 4.10.0.0
binull :: Bifoldable t => t a b -> Bool
binull = bifoldr (\_ _ -> False) (\_ _ -> False) True
-- | Returns the size/length of a finite structure as an 'Int'.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
bilength :: Bifoldable t => t a b -> Int
bilength = bifoldl' (\c _ -> c+1) (\c _ -> c+1) 0
-- | Does the element occur in the structure?
--
-- ==== __Examples__
--
-- 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 4.10.0.0
bielem :: (Bifoldable t, Eq a) => a -> t a a -> Bool
bielem x = biany (== x) (== x)
-- | Reduces a structure of lists to the concatenation of those lists.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
biconcat :: Bifoldable t => t [a] [a] -> [a]
biconcat = bifold
-- | The largest element of a non-empty structure.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
bimaximum :: forall t a. (Bifoldable t, Ord a) => t a a -> a
bimaximum = fromMaybe (error "bimaximum: empty structure") .
getMax . bifoldMap (Max . Just) (Max . Just)
-- | The least element of a non-empty structure.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
biminimum :: forall t a. (Bifoldable t, Ord a) => t a a -> a
biminimum = fromMaybe (error "biminimum: empty structure") .
getMin . bifoldMap (Min . Just) (Min . Just)
-- | The 'bisum' function computes the sum of the numbers of a structure.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
bisum :: (Bifoldable t, Num a) => t a a -> a
bisum = getSum . bifoldMap Sum Sum
-- | The 'biproduct' function computes the product of the numbers of a
-- structure.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
biproduct :: (Bifoldable t, Num a) => t a a -> a
biproduct = getProduct . bifoldMap Product Product
-- | Given a means of mapping the elements of a structure to lists, computes the
-- concatenation of all such lists in order.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
biconcatMap :: Bifoldable t => (a -> [c]) -> (b -> [c]) -> t a b -> [c]
biconcatMap = bifoldMap
-- | '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__
--
-- 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 4.10.0.0
biand :: Bifoldable t => t Bool Bool -> Bool
biand = getAll . bifoldMap All All
-- | '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__
--
-- 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 4.10.0.0
bior :: Bifoldable t => t Bool Bool -> Bool
bior = getAny . bifoldMap Any Any
-- | Determines whether any element of the structure satisfies its appropriate
-- predicate argument. Empty structures yield 'False'.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
biany :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool
biany p q = getAny . bifoldMap (Any . p) (Any . q)
-- | Determines whether all elements of the structure satisfy their appropriate
-- predicate argument. Empty structures yield 'True'.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
biall :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool
biall p q = getAll . bifoldMap (All . p) (All . q)
-- | The largest element of a non-empty structure with respect to the
-- given comparison function.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
bimaximumBy :: Bifoldable t => (a -> a -> Ordering) -> t a a -> a
bimaximumBy cmp = bifoldr1 max'
where max' x y = case cmp x y of
GT -> x
_ -> y
-- | The least element of a non-empty structure with respect to the
-- given comparison function.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
biminimumBy :: Bifoldable t => (a -> a -> Ordering) -> t a a -> a
biminimumBy cmp = bifoldr1 min'
where min' x y = case cmp x y of
GT -> y
_ -> x
-- | 'binotElem' is the negation of 'bielem'.
--
-- ==== __Examples__
--
-- 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 4.10.0.0
binotElem :: (Bifoldable t, Eq a) => a -> t a a-> Bool
binotElem x = not . bielem x
-- | 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__
--
-- 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 4.10.0.0
bifind :: Bifoldable t => (a -> Bool) -> t a a -> Maybe a
bifind p = getFirst . bifoldMap finder finder
where finder x = First (if p x then Just x else Nothing)