{-# LANGUAGE Trustworthy #-} ----------------------------------------------------------------------------- -- | -- Module : Data.Foldable -- Copyright : Ross Paterson 2005 -- License : BSD-style (see the LICENSE file in the distribution) -- -- Maintainer : libraries@haskell.org -- Stability : experimental -- Portability : portable -- -- Class of data structures that can be folded to a summary value. -- -- Many of these functions generalize "Prelude", "Control.Monad" and -- "Data.List" functions of the same names from lists to any 'Foldable' -- functor. To avoid ambiguity, either import those modules hiding -- these names or qualify uses of these function names with an alias -- for this module. -- ----------------------------------------------------------------------------- module Data.Foldable ( -- * Folds Foldable(..), -- ** Special biased folds foldrM, foldlM, -- ** Folding actions -- *** Applicative actions traverse_, for_, sequenceA_, asum, -- *** Monadic actions mapM_, forM_, sequence_, msum, -- ** Specialized folds toList, concat, concatMap, and, or, any, all, sum, product, maximum, maximumBy, minimum, minimumBy, -- ** Searches elem, notElem, find ) where import Prelude hiding (foldl, foldr, foldl1, foldr1, mapM_, sequence_, elem, notElem, concat, concatMap, and, or, any, all, sum, product, maximum, minimum) import qualified Prelude (foldl, foldr, foldl1, foldr1) import qualified Data.List as List (foldl') import Control.Applicative import Control.Monad (MonadPlus(..)) import Data.Maybe (fromMaybe, listToMaybe) import Data.Monoid import Data.Proxy import GHC.Exts (build) import GHC.Arr -- | Data structures that can be folded. -- -- Minimal complete definition: 'foldMap' or 'foldr'. -- -- For example, given a data type -- -- > data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a) -- -- a suitable instance would be -- -- > instance Foldable Tree where -- > foldMap f Empty = mempty -- > foldMap f (Leaf x) = f x -- > foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r -- -- This is suitable even for abstract types, as the monoid is assumed -- to satisfy the monoid laws. Alternatively, one could define @foldr@: -- -- > instance Foldable Tree where -- > foldr f z Empty = z -- > foldr f z (Leaf x) = f x z -- > foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l -- class Foldable t where -- | Combine the elements of a structure using a monoid. fold :: Monoid m => t m -> m fold = foldMap id -- | Map each element of the structure to a monoid, -- and combine the results. foldMap :: Monoid m => (a -> m) -> t a -> m foldMap f = foldr (mappend . f) mempty -- | Right-associative fold of a structure. -- -- @'foldr' f z = 'Prelude.foldr' f z . 'toList'@ foldr :: (a -> b -> b) -> b -> t a -> b foldr f z t = appEndo (foldMap (Endo . f) t) z -- | Right-associative fold of a structure, -- but with strict application of the operator. foldr' :: (a -> b -> b) -> b -> t a -> b foldr' f z0 xs = foldl f' id xs z0 where f' k x z = k $! f x z -- | Left-associative fold of a structure. -- -- @'foldl' f z = 'Prelude.foldl' f z . 'toList'@ foldl :: (b -> a -> b) -> b -> t a -> b foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z -- | Left-associative fold of a structure. -- but with strict application of the operator. -- -- @'foldl' f z = 'List.foldl'' f z . 'toList'@ foldl' :: (b -> a -> b) -> b -> t a -> b foldl' f z0 xs = foldr f' id xs z0 where f' x k z = k $! f z x -- | A variant of 'foldr' that has no base case, -- and thus may only be applied to non-empty structures. -- -- @'foldr1' f = 'Prelude.foldr1' f . 'toList'@ foldr1 :: (a -> a -> a) -> t a -> a foldr1 f xs = fromMaybe (error "foldr1: empty structure") (foldr mf Nothing xs) where mf x Nothing = Just x mf x (Just y) = Just (f x y) -- | A variant of 'foldl' that has no base case, -- and thus may only be applied to non-empty structures. -- -- @'foldl1' f = 'Prelude.foldl1' f . 'toList'@ foldl1 :: (a -> a -> a) -> t a -> a foldl1 f xs = fromMaybe (error "foldl1: empty structure") (foldl mf Nothing xs) where mf Nothing y = Just y mf (Just x) y = Just (f x y) {-# MINIMAL foldMap | foldr #-} -- instances for Prelude types instance Foldable Maybe where foldr _ z Nothing = z foldr f z (Just x) = f x z foldl _ z Nothing = z foldl f z (Just x) = f z x instance Foldable [] where foldr = Prelude.foldr foldl = Prelude.foldl foldl' = List.foldl' foldr1 = Prelude.foldr1 foldl1 = Prelude.foldl1 instance Foldable (Either a) where foldMap _ (Left _) = mempty foldMap f (Right y) = f y foldr _ z (Left _) = z foldr f z (Right y) = f y z instance Foldable ((,) a) where foldMap f (_, y) = f y foldr f z (_, y) = f y z instance Ix i => Foldable (Array i) where foldr f z = Prelude.foldr f z . elems foldl f z = Prelude.foldl f z . elems foldr1 f = Prelude.foldr1 f . elems foldl1 f = Prelude.foldl1 f . elems instance Foldable Proxy where foldMap _ _ = mempty {-# INLINE foldMap #-} fold _ = mempty {-# INLINE fold #-} foldr _ z _ = z {-# INLINE foldr #-} foldl _ z _ = z {-# INLINE foldl #-} foldl1 _ _ = error "foldl1: Proxy" {-# INLINE foldl1 #-} foldr1 _ _ = error "foldr1: Proxy" {-# INLINE foldr1 #-} instance Foldable (Const m) where foldMap _ _ = mempty -- | Monadic fold over the elements of a structure, -- associating to the right, i.e. from right to left. foldrM :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m b foldrM f z0 xs = foldl f' return xs z0 where f' k x z = f x z >>= k -- | Monadic fold over the elements of a structure, -- associating to the left, i.e. from left to right. foldlM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b foldlM f z0 xs = foldr f' return xs z0 where f' x k z = f z x >>= k -- | Map each element of a structure to an action, evaluate -- these actions from left to right, and ignore the results. traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f () traverse_ f = foldr ((*>) . f) (pure ()) -- | 'for_' is 'traverse_' with its arguments flipped. for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f () {-# INLINE for_ #-} for_ = flip traverse_ -- | Map each element of a structure to a monadic action, evaluate -- these actions from left to right, and ignore the results. mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m () mapM_ f = foldr ((>>) . f) (return ()) -- | 'forM_' is 'mapM_' with its arguments flipped. forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m () {-# INLINE forM_ #-} forM_ = flip mapM_ -- | Evaluate each action in the structure from left to right, -- and ignore the results. sequenceA_ :: (Foldable t, Applicative f) => t (f a) -> f () sequenceA_ = foldr (*>) (pure ()) -- | Evaluate each monadic action in the structure from left to right, -- and ignore the results. sequence_ :: (Foldable t, Monad m) => t (m a) -> m () sequence_ = foldr (>>) (return ()) -- | The sum of a collection of actions, generalizing 'concat'. asum :: (Foldable t, Alternative f) => t (f a) -> f a {-# INLINE asum #-} asum = foldr (<|>) empty -- | The sum of a collection of actions, generalizing 'concat'. msum :: (Foldable t, MonadPlus m) => t (m a) -> m a {-# INLINE msum #-} msum = foldr mplus mzero -- These use foldr rather than foldMap to avoid repeated concatenation. -- | List of elements of a structure. toList :: Foldable t => t a -> [a] {-# INLINE toList #-} toList t = build (\ c n -> foldr c n t) -- | The concatenation of all the elements of a container of lists. concat :: Foldable t => t [a] -> [a] concat = fold -- | Map a function over all the elements of a container and concatenate -- the resulting lists. concatMap :: Foldable t => (a -> [b]) -> t a -> [b] concatMap = foldMap -- | 'and' 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. and :: Foldable t => t Bool -> Bool and = getAll . foldMap All -- | 'or' 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. or :: Foldable t => t Bool -> Bool or = getAny . foldMap Any -- | Determines whether any element of the structure satisfies the predicate. any :: Foldable t => (a -> Bool) -> t a -> Bool any p = getAny . foldMap (Any . p) -- | Determines whether all elements of the structure satisfy the predicate. all :: Foldable t => (a -> Bool) -> t a -> Bool all p = getAll . foldMap (All . p) -- | The 'sum' function computes the sum of the numbers of a structure. sum :: (Foldable t, Num a) => t a -> a sum = getSum . foldMap Sum -- | The 'product' function computes the product of the numbers of a structure. product :: (Foldable t, Num a) => t a -> a product = getProduct . foldMap Product -- | The largest element of a non-empty structure. maximum :: (Foldable t, Ord a) => t a -> a maximum = foldr1 max -- | The largest element of a non-empty structure with respect to the -- given comparison function. maximumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a maximumBy cmp = foldr1 max' where max' x y = case cmp x y of GT -> x _ -> y -- | The least element of a non-empty structure. minimum :: (Foldable t, Ord a) => t a -> a minimum = foldr1 min -- | The least element of a non-empty structure with respect to the -- given comparison function. minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a minimumBy cmp = foldr1 min' where min' x y = case cmp x y of GT -> y _ -> x -- | Does the element occur in the structure? elem :: (Foldable t, Eq a) => a -> t a -> Bool elem = any . (==) -- | 'notElem' is the negation of 'elem'. notElem :: (Foldable t, Eq a) => a -> t a -> Bool notElem x = not . elem x -- | The 'find' 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. find :: Foldable t => (a -> Bool) -> t a -> Maybe a find p = listToMaybe . concatMap (\ x -> if p x then [x] else [])