--- /dev/null
+-----------------------------------------------------------------------------
+-- |
+-- Module : Data.Foldable
+-- Copyright : Ross Paterson 2005
+-- License : BSD-style (see the LICENSE file in the distribution)
+--
+-- Maintainer : ross@soi.city.ac.uk
+-- 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
+ foldr',
+ foldl',
+ 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 Control.Applicative
+import Control.Monad (MonadPlus(..))
+import Data.Maybe (fromMaybe, listToMaybe)
+import Data.Monoid
+
+#ifdef __NHC__
+import Control.Arrow (ArrowZero(..)) -- work around nhc98 typechecker problem
+#endif
+
+#ifdef __GLASGOW_HASKELL__
+import GHC.Exts (build)
+#endif
+
+-- | 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
+-- > 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.
+--
+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
+
+ -- | Left-associative fold of a structure.
+ --
+ -- @'foldl' f z = 'Prelude.foldl' f z . 'toList'@
+ foldl :: (a -> b -> a) -> a -> t b -> a
+ foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
+
+ -- | 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)
+
+-- instances for Prelude types
+
+instance Foldable Maybe where
+ foldr f z Nothing = z
+ foldr f z (Just x) = f x z
+
+ foldl f z Nothing = z
+ foldl f z (Just x) = f z x
+
+instance Foldable [] where
+ foldr = Prelude.foldr
+ foldl = Prelude.foldl
+ foldr1 = Prelude.foldr1
+ foldl1 = Prelude.foldl1
+
+-- | Fold over the elements of a structure,
+-- associating to the right, but strictly.
+foldr' :: Foldable t => (a -> b -> b) -> b -> t a -> b
+foldr' f z xs = foldl f' id xs z
+ where f' k x z = k $! f x z
+
+-- | 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 z xs = foldl f' return xs z
+ where f' k x z = f x z >>= k
+
+-- | Fold over the elements of a structure,
+-- associating to the left, but strictly.
+foldl' :: Foldable t => (a -> b -> a) -> a -> t b -> a
+foldl' f z xs = foldr f' id xs z
+ where f' x k z = k $! f z x
+
+-- | Monadic fold over the elements of a structure,
+-- associating to the left, i.e. from left to right.
+foldlM :: (Foldable t, Monad m) => (a -> b -> m a) -> a -> t b -> m a
+foldlM f z xs = foldr f' return xs z
+ 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]
+#ifdef __GLASGOW_HASKELL__
+toList t = build (\ c n -> foldr c n t)
+#else
+toList = foldr (:) []
+#endif
+
+-- | 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 [])
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