-- 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
+ -- * 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,
-- > 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 _ z Nothing = z
- foldr f z (Just x) = f x z
+ foldr _ z Nothing = z
+ foldr f z (Just x) = f x z
- foldl _ 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
- foldl f z = Prelude.foldl f z . elems
- foldr1 f = Prelude.foldr1 f . elems
- foldl1 f = Prelude.foldl1 f . 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.
projects / ghc-base.git / blobdiff