-----------------------------------------------------------------------------
-- |
-- 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
import Data.Array
#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
instance Ix i => Foldable (Array i) where
foldr f z = Prelude.foldr f z . 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
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 an 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 [])