1 -----------------------------------------------------------------------------
3 -- Module : Data.Foldable
4 -- Copyright : Ross Paterson 2005
5 -- License : BSD-style (see the LICENSE file in the distribution)
7 -- Maintainer : ross@soi.city.ac.uk
8 -- Stability : experimental
9 -- Portability : portable
11 -- Class of data structures that can be folded to a summary value.
13 -- Many of these functions generalize "Prelude", "Control.Monad" and
14 -- "Data.List" functions of the same names from lists to any 'Foldable'
15 -- functor. To avoid ambiguity, either import those modules hiding
16 -- these names or qualify uses of these function names with an alias
19 module Data.Foldable (
22 -- ** Special biased folds
28 -- *** Applicative actions
33 -- *** Monadic actions
38 -- ** Specialized folds
58 import Prelude hiding (foldl, foldr, foldl1, foldr1, mapM_, sequence_,
59 elem, notElem, concat, concatMap, and, or, any, all,
60 sum, product, maximum, minimum)
61 import qualified Prelude (foldl, foldr, foldl1, foldr1)
62 import Control.Applicative
63 import Control.Monad (MonadPlus(..))
64 import Data.Maybe (fromMaybe, listToMaybe)
69 import Control.Arrow (ArrowZero(..)) -- work around nhc98 typechecker problem
72 #ifdef __GLASGOW_HASKELL__
73 import GHC.Exts (build)
76 -- | Data structures that can be folded.
78 -- Minimal complete definition: 'foldMap' or 'foldr'.
80 -- For example, given a data type
82 -- > data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
84 -- a suitable instance would be
86 -- > instance Foldable Tree
87 -- > foldMap f Empty = mempty
88 -- > foldMap f (Leaf x) = f x
89 -- > foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r
91 -- This is suitable even for abstract types, as the monoid is assumed
92 -- to satisfy the monoid laws.
94 class Foldable t where
95 -- | Combine the elements of a structure using a monoid.
96 fold :: Monoid m => t m -> m
99 -- | Map each element of the structure to a monoid,
100 -- and combine the results.
101 foldMap :: Monoid m => (a -> m) -> t a -> m
102 foldMap f = foldr (mappend . f) mempty
104 -- | Right-associative fold of a structure.
106 -- @'foldr' f z = 'Prelude.foldr' f z . 'toList'@
107 foldr :: (a -> b -> b) -> b -> t a -> b
108 foldr f z t = appEndo (foldMap (Endo . f) t) z
110 -- | Left-associative fold of a structure.
112 -- @'foldl' f z = 'Prelude.foldl' f z . 'toList'@
113 foldl :: (a -> b -> a) -> a -> t b -> a
114 foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
116 -- | A variant of 'foldr' that has no base case,
117 -- and thus may only be applied to non-empty structures.
119 -- @'foldr1' f = 'Prelude.foldr1' f . 'toList'@
120 foldr1 :: (a -> a -> a) -> t a -> a
121 foldr1 f xs = fromMaybe (error "foldr1: empty structure")
122 (foldr mf Nothing xs)
123 where mf x Nothing = Just x
124 mf x (Just y) = Just (f x y)
126 -- | A variant of 'foldl' that has no base case,
127 -- and thus may only be applied to non-empty structures.
129 -- @'foldl1' f = 'Prelude.foldl1' f . 'toList'@
130 foldl1 :: (a -> a -> a) -> t a -> a
131 foldl1 f xs = fromMaybe (error "foldl1: empty structure")
132 (foldl mf Nothing xs)
133 where mf Nothing y = Just y
134 mf (Just x) y = Just (f x y)
136 -- instances for Prelude types
138 instance Foldable Maybe where
139 foldr f z Nothing = z
140 foldr f z (Just x) = f x z
142 foldl f z Nothing = z
143 foldl f z (Just x) = f z x
145 instance Foldable [] where
146 foldr = Prelude.foldr
147 foldl = Prelude.foldl
148 foldr1 = Prelude.foldr1
149 foldl1 = Prelude.foldl1
151 instance Ix i => Foldable (Array i) where
152 foldr f z = Prelude.foldr f z . elems
154 -- | Fold over the elements of a structure,
155 -- associating to the right, but strictly.
156 foldr' :: Foldable t => (a -> b -> b) -> b -> t a -> b
157 foldr' f z xs = foldl f' id xs z
158 where f' k x z = k $! f x z
160 -- | Monadic fold over the elements of a structure,
161 -- associating to the right, i.e. from right to left.
162 foldrM :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m b
163 foldrM f z xs = foldl f' return xs z
164 where f' k x z = f x z >>= k
166 -- | Fold over the elements of a structure,
167 -- associating to the left, but strictly.
168 foldl' :: Foldable t => (a -> b -> a) -> a -> t b -> a
169 foldl' f z xs = foldr f' id xs z
170 where f' x k z = k $! f z x
172 -- | Monadic fold over the elements of a structure,
173 -- associating to the left, i.e. from left to right.
174 foldlM :: (Foldable t, Monad m) => (a -> b -> m a) -> a -> t b -> m a
175 foldlM f z xs = foldr f' return xs z
176 where f' x k z = f z x >>= k
178 -- | Map each element of a structure to an action, evaluate
179 -- these actions from left to right, and ignore the results.
180 traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f ()
181 traverse_ f = foldr ((*>) . f) (pure ())
183 -- | 'for_' is 'traverse_' with its arguments flipped.
184 for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f ()
186 for_ = flip traverse_
188 -- | Map each element of a structure to an monadic action, evaluate
189 -- these actions from left to right, and ignore the results.
190 mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
191 mapM_ f = foldr ((>>) . f) (return ())
193 -- | 'forM_' is 'mapM_' with its arguments flipped.
194 forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m ()
198 -- | Evaluate each action in the structure from left to right,
199 -- and ignore the results.
200 sequenceA_ :: (Foldable t, Applicative f) => t (f a) -> f ()
201 sequenceA_ = foldr (*>) (pure ())
203 -- | Evaluate each monadic action in the structure from left to right,
204 -- and ignore the results.
205 sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
206 sequence_ = foldr (>>) (return ())
208 -- | The sum of a collection of actions, generalizing 'concat'.
209 asum :: (Foldable t, Alternative f) => t (f a) -> f a
211 asum = foldr (<|>) empty
213 -- | The sum of a collection of actions, generalizing 'concat'.
214 msum :: (Foldable t, MonadPlus m) => t (m a) -> m a
216 msum = foldr mplus mzero
218 -- These use foldr rather than foldMap to avoid repeated concatenation.
220 -- | List of elements of a structure.
221 toList :: Foldable t => t a -> [a]
222 #ifdef __GLASGOW_HASKELL__
223 toList t = build (\ c n -> foldr c n t)
225 toList = foldr (:) []
228 -- | The concatenation of all the elements of a container of lists.
229 concat :: Foldable t => t [a] -> [a]
232 -- | Map a function over all the elements of a container and concatenate
233 -- the resulting lists.
234 concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
237 -- | 'and' returns the conjunction of a container of Bools. For the
238 -- result to be 'True', the container must be finite; 'False', however,
239 -- results from a 'False' value finitely far from the left end.
240 and :: Foldable t => t Bool -> Bool
241 and = getAll . foldMap All
243 -- | 'or' returns the disjunction of a container of Bools. For the
244 -- result to be 'False', the container must be finite; 'True', however,
245 -- results from a 'True' value finitely far from the left end.
246 or :: Foldable t => t Bool -> Bool
247 or = getAny . foldMap Any
249 -- | Determines whether any element of the structure satisfies the predicate.
250 any :: Foldable t => (a -> Bool) -> t a -> Bool
251 any p = getAny . foldMap (Any . p)
253 -- | Determines whether all elements of the structure satisfy the predicate.
254 all :: Foldable t => (a -> Bool) -> t a -> Bool
255 all p = getAll . foldMap (All . p)
257 -- | The 'sum' function computes the sum of the numbers of a structure.
258 sum :: (Foldable t, Num a) => t a -> a
259 sum = getSum . foldMap Sum
261 -- | The 'product' function computes the product of the numbers of a structure.
262 product :: (Foldable t, Num a) => t a -> a
263 product = getProduct . foldMap Product
265 -- | The largest element of a non-empty structure.
266 maximum :: (Foldable t, Ord a) => t a -> a
269 -- | The largest element of a non-empty structure with respect to the
270 -- given comparison function.
271 maximumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
272 maximumBy cmp = foldr1 max'
273 where max' x y = case cmp x y of
277 -- | The least element of a non-empty structure.
278 minimum :: (Foldable t, Ord a) => t a -> a
281 -- | The least element of a non-empty structure with respect to the
282 -- given comparison function.
283 minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
284 minimumBy cmp = foldr1 min'
285 where min' x y = case cmp x y of
289 -- | Does the element occur in the structure?
290 elem :: (Foldable t, Eq a) => a -> t a -> Bool
293 -- | 'notElem' is the negation of 'elem'.
294 notElem :: (Foldable t, Eq a) => a -> t a -> Bool
295 notElem x = not . elem x
297 -- | The 'find' function takes a predicate and a structure and returns
298 -- the leftmost element of the structure matching the predicate, or
299 -- 'Nothing' if there is no such element.
300 find :: Foldable t => (a -> Bool) -> t a -> Maybe a
301 find p = listToMaybe . concatMap (\ x -> if p x then [x] else [])