+{-# LANGUAGE CPP #-}
+
-----------------------------------------------------------------------------
-- |
-- Module : Data.Foldable
-- Copyright : Ross Paterson 2005
-- License : BSD-style (see the LICENSE file in the distribution)
--
--- Maintainer : ross@soi.city.ac.uk
+-- 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
- foldr',
- foldl',
- foldrM,
- foldlM,
- -- ** Folding actions
- traverse_,
- mapM_,
- sequenceA_,
- sequence_,
- -- ** Specialized folds
- toList,
- concat,
- concatMap,
- and,
- or,
- any,
- all,
- sum,
- product,
- maximum,
- maximumBy,
- minimum,
- minimumBy,
- -- ** Searches
- elem,
- notElem,
- find
- ) where
+ -- * 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)
+ 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
-import Data.Array
+
+#ifdef __NHC__
+import Control.Arrow (ArrowZero(..)) -- work around nhc98 typechecker problem
+#endif
#ifdef __GLASGOW_HASKELL__
import GHC.Exts (build)
#endif
+#if defined(__GLASGOW_HASKELL__)
+import GHC.Arr
+#elif defined(__HUGS__)
+import Hugs.Array
+#elif defined(__NHC__)
+import Array
+#endif
+
-- | Data structures that can be folded.
--
-- Minimal complete definition: 'foldMap' or 'foldr'.
--
-- a suitable instance would be
--
--- > instance Foldable Tree
+-- > 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
+-- > 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.
+-- 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
-
- -- | 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)
+ -- | 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
+ foldr _ z Nothing = z
+ foldr f z (Just x) = f x z
- foldl f z Nothing = z
- foldl f z (Just x) = f z x
+ foldl _ 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
+ foldr = Prelude.foldr
+ foldl = Prelude.foldl
+ foldr1 = Prelude.foldr1
+ foldl1 = Prelude.foldl1
instance Ix i => Foldable (Array i) where
- foldr f z = Prelude.foldr f z . elems
+ 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
-- | 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
+foldr' f z0 xs = foldl f' id xs z0
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
+foldrM f z0 xs = foldl f' return xs z0
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
+foldl' f z0 xs = foldr f' id xs z0
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
+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
traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f ()
traverse_ f = foldr ((*>) . f) (pure ())
--- | Map each element of a structure to an monadic action, evaluate
+-- | '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 ()
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 #-}
#ifdef __GLASGOW_HASKELL__
toList t = build (\ c n -> foldr c n t)
#else
-- | The concatenation of all the elements of a container of lists.
concat :: Foldable t => t [a] -> [a]
-concat = foldr (++) []
+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 f = foldr ((++) . f) []
+concatMap = foldMap
-- | 'and' returns the conjunction of a container of Bools. For the
-- result to be 'True', the container must be finite; 'False', however,
product :: (Foldable t, Num a) => t a -> a
product = getProduct . foldMap Product
--- | The largest element of the structure.
+-- | 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
+ GT -> x
+ _ -> y
--- | The least element of the structure.
+-- | 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
+ 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
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