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)
68 import Control.Arrow (ArrowZero(..)) -- work around nhc98 typechecker problem
71 #ifdef __GLASGOW_HASKELL__
72 import GHC.Exts (build)
75 -- | Data structures that can be folded.
77 -- Minimal complete definition: 'foldMap' or 'foldr'.
79 -- For example, given a data type
81 -- > data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
83 -- a suitable instance would be
85 -- > instance Foldable Tree
86 -- > foldMap f Empty = mempty
87 -- > foldMap f (Leaf x) = f x
88 -- > foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r
90 -- This is suitable even for abstract types, as the monoid is assumed
91 -- to satisfy the monoid laws.
93 class Foldable t where
94 -- | Combine the elements of a structure using a monoid.
95 fold :: Monoid m => t m -> m
98 -- | Map each element of the structure to a monoid,
99 -- and combine the results.
100 foldMap :: Monoid m => (a -> m) -> t a -> m
101 foldMap f = foldr (mappend . f) mempty
103 -- | Right-associative fold of a structure.
105 -- @'foldr' f z = 'Prelude.foldr' f z . 'toList'@
106 foldr :: (a -> b -> b) -> b -> t a -> b
107 foldr f z t = appEndo (foldMap (Endo . f) t) z
109 -- | Left-associative fold of a structure.
111 -- @'foldl' f z = 'Prelude.foldl' f z . 'toList'@
112 foldl :: (a -> b -> a) -> a -> t b -> a
113 foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
115 -- | A variant of 'foldr' that has no base case,
116 -- and thus may only be applied to non-empty structures.
118 -- @'foldr1' f = 'Prelude.foldr1' f . 'toList'@
119 foldr1 :: (a -> a -> a) -> t a -> a
120 foldr1 f xs = fromMaybe (error "foldr1: empty structure")
121 (foldr mf Nothing xs)
122 where mf x Nothing = Just x
123 mf x (Just y) = Just (f x y)
125 -- | A variant of 'foldl' that has no base case,
126 -- and thus may only be applied to non-empty structures.
128 -- @'foldl1' f = 'Prelude.foldl1' f . 'toList'@
129 foldl1 :: (a -> a -> a) -> t a -> a
130 foldl1 f xs = fromMaybe (error "foldl1: empty structure")
131 (foldl mf Nothing xs)
132 where mf Nothing y = Just y
133 mf (Just x) y = Just (f x y)
135 -- instances for Prelude types
137 instance Foldable Maybe where
138 foldr f z Nothing = z
139 foldr f z (Just x) = f x z
141 foldl f z Nothing = z
142 foldl f z (Just x) = f z x
144 instance Foldable [] where
145 foldr = Prelude.foldr
146 foldl = Prelude.foldl
147 foldr1 = Prelude.foldr1
148 foldl1 = Prelude.foldl1
150 -- | Fold over the elements of a structure,
151 -- associating to the right, but strictly.
152 foldr' :: Foldable t => (a -> b -> b) -> b -> t a -> b
153 foldr' f z xs = foldl f' id xs z
154 where f' k x z = k $! f x z
156 -- | Monadic fold over the elements of a structure,
157 -- associating to the right, i.e. from right to left.
158 foldrM :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m b
159 foldrM f z xs = foldl f' return xs z
160 where f' k x z = f x z >>= k
162 -- | Fold over the elements of a structure,
163 -- associating to the left, but strictly.
164 foldl' :: Foldable t => (a -> b -> a) -> a -> t b -> a
165 foldl' f z xs = foldr f' id xs z
166 where f' x k z = k $! f z x
168 -- | Monadic fold over the elements of a structure,
169 -- associating to the left, i.e. from left to right.
170 foldlM :: (Foldable t, Monad m) => (a -> b -> m a) -> a -> t b -> m a
171 foldlM f z xs = foldr f' return xs z
172 where f' x k z = f z x >>= k
174 -- | Map each element of a structure to an action, evaluate
175 -- these actions from left to right, and ignore the results.
176 traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f ()
177 traverse_ f = foldr ((*>) . f) (pure ())
179 -- | 'for_' is 'traverse_' with its arguments flipped.
180 for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f ()
182 for_ = flip traverse_
184 -- | Map each element of a structure to a monadic action, evaluate
185 -- these actions from left to right, and ignore the results.
186 mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
187 mapM_ f = foldr ((>>) . f) (return ())
189 -- | 'forM_' is 'mapM_' with its arguments flipped.
190 forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m ()
194 -- | Evaluate each action in the structure from left to right,
195 -- and ignore the results.
196 sequenceA_ :: (Foldable t, Applicative f) => t (f a) -> f ()
197 sequenceA_ = foldr (*>) (pure ())
199 -- | Evaluate each monadic action in the structure from left to right,
200 -- and ignore the results.
201 sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
202 sequence_ = foldr (>>) (return ())
204 -- | The sum of a collection of actions, generalizing 'concat'.
205 asum :: (Foldable t, Alternative f) => t (f a) -> f a
207 asum = foldr (<|>) empty
209 -- | The sum of a collection of actions, generalizing 'concat'.
210 msum :: (Foldable t, MonadPlus m) => t (m a) -> m a
212 msum = foldr mplus mzero
214 -- These use foldr rather than foldMap to avoid repeated concatenation.
216 -- | List of elements of a structure.
217 toList :: Foldable t => t a -> [a]
218 #ifdef __GLASGOW_HASKELL__
219 toList t = build (\ c n -> foldr c n t)
221 toList = foldr (:) []
224 -- | The concatenation of all the elements of a container of lists.
225 concat :: Foldable t => t [a] -> [a]
228 -- | Map a function over all the elements of a container and concatenate
229 -- the resulting lists.
230 concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
233 -- | 'and' returns the conjunction of a container of Bools. For the
234 -- result to be 'True', the container must be finite; 'False', however,
235 -- results from a 'False' value finitely far from the left end.
236 and :: Foldable t => t Bool -> Bool
237 and = getAll . foldMap All
239 -- | 'or' returns the disjunction of a container of Bools. For the
240 -- result to be 'False', the container must be finite; 'True', however,
241 -- results from a 'True' value finitely far from the left end.
242 or :: Foldable t => t Bool -> Bool
243 or = getAny . foldMap Any
245 -- | Determines whether any element of the structure satisfies the predicate.
246 any :: Foldable t => (a -> Bool) -> t a -> Bool
247 any p = getAny . foldMap (Any . p)
249 -- | Determines whether all elements of the structure satisfy the predicate.
250 all :: Foldable t => (a -> Bool) -> t a -> Bool
251 all p = getAll . foldMap (All . p)
253 -- | The 'sum' function computes the sum of the numbers of a structure.
254 sum :: (Foldable t, Num a) => t a -> a
255 sum = getSum . foldMap Sum
257 -- | The 'product' function computes the product of the numbers of a structure.
258 product :: (Foldable t, Num a) => t a -> a
259 product = getProduct . foldMap Product
261 -- | The largest element of a non-empty structure.
262 maximum :: (Foldable t, Ord a) => t a -> a
265 -- | The largest element of a non-empty structure with respect to the
266 -- given comparison function.
267 maximumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
268 maximumBy cmp = foldr1 max'
269 where max' x y = case cmp x y of
273 -- | The least element of a non-empty structure.
274 minimum :: (Foldable t, Ord a) => t a -> a
277 -- | The least element of a non-empty structure with respect to the
278 -- given comparison function.
279 minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
280 minimumBy cmp = foldr1 min'
281 where min' x y = case cmp x y of
285 -- | Does the element occur in the structure?
286 elem :: (Foldable t, Eq a) => a -> t a -> Bool
289 -- | 'notElem' is the negation of 'elem'.
290 notElem :: (Foldable t, Eq a) => a -> t a -> Bool
291 notElem x = not . elem x
293 -- | The 'find' function takes a predicate and a structure and returns
294 -- the leftmost element of the structure matching the predicate, or
295 -- 'Nothing' if there is no such element.
296 find :: Foldable t => (a -> Bool) -> t a -> Maybe a
297 find p = listToMaybe . concatMap (\ x -> if p x then [x] else [])