{-# 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.Functor.Utils (Max(..), Min(..), (#.)) import Data.Maybe (fromMaybe) import Data.Monoid import GHC.Generics (K1(..)) -- $setup -- >>> import Prelude -- >>> import Data.Char -- >>> import 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 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 -- | @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 mj mj where mj = Max #. (Just :: a -> Maybe a) -- | 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 mj mj where mj = Min #. (Just :: a -> Maybe a) -- | 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)