1 {-# OPTIONS_GHC -XNoImplicitPrelude #-}
2 -----------------------------------------------------------------------------
5 -- Copyright : (c) The University of Glasgow 2001
6 -- License : BSD-style (see the file libraries/base/LICENSE)
8 -- Maintainer : libraries@haskell.org
10 -- Portability : portable
12 -- Operations on lists.
14 -----------------------------------------------------------------------------
25 (++) -- :: [a] -> [a] -> [a]
28 , tail -- :: [a] -> [a]
29 , init -- :: [a] -> [a]
30 , null -- :: [a] -> Bool
31 , length -- :: [a] -> Int
33 -- * List transformations
34 , map -- :: (a -> b) -> [a] -> [b]
35 , reverse -- :: [a] -> [a]
37 , intersperse -- :: a -> [a] -> [a]
38 , intercalate -- :: [a] -> [[a]] -> [a]
39 , transpose -- :: [[a]] -> [[a]]
41 , subsequences -- :: [a] -> [[a]]
42 , permutations -- :: [a] -> [[a]]
44 -- * Reducing lists (folds)
46 , foldl -- :: (a -> b -> a) -> a -> [b] -> a
47 , foldl' -- :: (a -> b -> a) -> a -> [b] -> a
48 , foldl1 -- :: (a -> a -> a) -> [a] -> a
49 , foldl1' -- :: (a -> a -> a) -> [a] -> a
50 , foldr -- :: (a -> b -> b) -> b -> [a] -> b
51 , foldr1 -- :: (a -> a -> a) -> [a] -> a
55 , concat -- :: [[a]] -> [a]
56 , concatMap -- :: (a -> [b]) -> [a] -> [b]
57 , and -- :: [Bool] -> Bool
58 , or -- :: [Bool] -> Bool
59 , any -- :: (a -> Bool) -> [a] -> Bool
60 , all -- :: (a -> Bool) -> [a] -> Bool
61 , sum -- :: (Num a) => [a] -> a
62 , product -- :: (Num a) => [a] -> a
63 , maximum -- :: (Ord a) => [a] -> a
64 , minimum -- :: (Ord a) => [a] -> a
69 , scanl -- :: (a -> b -> a) -> a -> [b] -> [a]
70 , scanl1 -- :: (a -> a -> a) -> [a] -> [a]
71 , scanr -- :: (a -> b -> b) -> b -> [a] -> [b]
72 , scanr1 -- :: (a -> a -> a) -> [a] -> [a]
74 -- ** Accumulating maps
75 , mapAccumL -- :: (a -> b -> (a,c)) -> a -> [b] -> (a,[c])
76 , mapAccumR -- :: (a -> b -> (a,c)) -> a -> [b] -> (a,[c])
79 , iterate -- :: (a -> a) -> a -> [a]
80 , repeat -- :: a -> [a]
81 , replicate -- :: Int -> a -> [a]
82 , cycle -- :: [a] -> [a]
85 , unfoldr -- :: (b -> Maybe (a, b)) -> b -> [a]
89 -- ** Extracting sublists
90 , take -- :: Int -> [a] -> [a]
91 , drop -- :: Int -> [a] -> [a]
92 , splitAt -- :: Int -> [a] -> ([a], [a])
94 , takeWhile -- :: (a -> Bool) -> [a] -> [a]
95 , dropWhile -- :: (a -> Bool) -> [a] -> [a]
96 , span -- :: (a -> Bool) -> [a] -> ([a], [a])
97 , break -- :: (a -> Bool) -> [a] -> ([a], [a])
99 , stripPrefix -- :: Eq a => [a] -> [a] -> Maybe [a]
101 , group -- :: Eq a => [a] -> [[a]]
103 , inits -- :: [a] -> [[a]]
104 , tails -- :: [a] -> [[a]]
107 , isPrefixOf -- :: (Eq a) => [a] -> [a] -> Bool
108 , isSuffixOf -- :: (Eq a) => [a] -> [a] -> Bool
109 , isInfixOf -- :: (Eq a) => [a] -> [a] -> Bool
113 -- ** Searching by equality
114 , elem -- :: a -> [a] -> Bool
115 , notElem -- :: a -> [a] -> Bool
116 , lookup -- :: (Eq a) => a -> [(a,b)] -> Maybe b
118 -- ** Searching with a predicate
119 , find -- :: (a -> Bool) -> [a] -> Maybe a
120 , filter -- :: (a -> Bool) -> [a] -> [a]
121 , partition -- :: (a -> Bool) -> [a] -> ([a], [a])
124 -- | These functions treat a list @xs@ as a indexed collection,
125 -- with indices ranging from 0 to @'length' xs - 1@.
127 , (!!) -- :: [a] -> Int -> a
129 , elemIndex -- :: (Eq a) => a -> [a] -> Maybe Int
130 , elemIndices -- :: (Eq a) => a -> [a] -> [Int]
132 , findIndex -- :: (a -> Bool) -> [a] -> Maybe Int
133 , findIndices -- :: (a -> Bool) -> [a] -> [Int]
135 -- * Zipping and unzipping lists
137 , zip -- :: [a] -> [b] -> [(a,b)]
139 , zip4, zip5, zip6, zip7
141 , zipWith -- :: (a -> b -> c) -> [a] -> [b] -> [c]
143 , zipWith4, zipWith5, zipWith6, zipWith7
145 , unzip -- :: [(a,b)] -> ([a],[b])
147 , unzip4, unzip5, unzip6, unzip7
151 -- ** Functions on strings
152 , lines -- :: String -> [String]
153 , words -- :: String -> [String]
154 , unlines -- :: [String] -> String
155 , unwords -- :: [String] -> String
157 -- ** \"Set\" operations
159 , nub -- :: (Eq a) => [a] -> [a]
161 , delete -- :: (Eq a) => a -> [a] -> [a]
162 , (\\) -- :: (Eq a) => [a] -> [a] -> [a]
164 , union -- :: (Eq a) => [a] -> [a] -> [a]
165 , intersect -- :: (Eq a) => [a] -> [a] -> [a]
168 , sort -- :: (Ord a) => [a] -> [a]
169 , insert -- :: (Ord a) => a -> [a] -> [a]
171 -- * Generalized functions
173 -- ** The \"@By@\" operations
174 -- | By convention, overloaded functions have a non-overloaded
175 -- counterpart whose name is suffixed with \`@By@\'.
177 -- It is often convenient to use these functions together with
178 -- 'Data.Function.on', for instance @'sortBy' ('compare'
181 -- *** User-supplied equality (replacing an @Eq@ context)
182 -- | The predicate is assumed to define an equivalence.
183 , nubBy -- :: (a -> a -> Bool) -> [a] -> [a]
184 , deleteBy -- :: (a -> a -> Bool) -> a -> [a] -> [a]
185 , deleteFirstsBy -- :: (a -> a -> Bool) -> [a] -> [a] -> [a]
186 , unionBy -- :: (a -> a -> Bool) -> [a] -> [a] -> [a]
187 , intersectBy -- :: (a -> a -> Bool) -> [a] -> [a] -> [a]
188 , groupBy -- :: (a -> a -> Bool) -> [a] -> [[a]]
190 -- *** User-supplied comparison (replacing an @Ord@ context)
191 -- | The function is assumed to define a total ordering.
192 , sortBy -- :: (a -> a -> Ordering) -> [a] -> [a]
193 , insertBy -- :: (a -> a -> Ordering) -> a -> [a] -> [a]
194 , maximumBy -- :: (a -> a -> Ordering) -> [a] -> a
195 , minimumBy -- :: (a -> a -> Ordering) -> [a] -> a
197 -- ** The \"@generic@\" operations
198 -- | The prefix \`@generic@\' indicates an overloaded function that
199 -- is a generalized version of a "Prelude" function.
201 , genericLength -- :: (Integral a) => [b] -> a
202 , genericTake -- :: (Integral a) => a -> [b] -> [b]
203 , genericDrop -- :: (Integral a) => a -> [b] -> [b]
204 , genericSplitAt -- :: (Integral a) => a -> [b] -> ([b], [b])
205 , genericIndex -- :: (Integral a) => [b] -> a -> b
206 , genericReplicate -- :: (Integral a) => a -> b -> [b]
215 import Data.Char ( isSpace )
217 #ifdef __GLASGOW_HASKELL__
224 infix 5 \\ -- comment to fool cpp
226 -- -----------------------------------------------------------------------------
229 -- | The 'stripPrefix' function drops the given prefix from a list.
230 -- It returns 'Nothing' if the list did not start with the prefix
231 -- given, or 'Just' the list after the prefix, if it does.
233 -- > stripPrefix "foo" "foobar" -> Just "bar"
234 -- > stripPrefix "foo" "foo" -> Just ""
235 -- > stripPrefix "foo" "barfoo" -> Nothing
236 -- > stripPrefix "foo" "barfoobaz" -> Nothing
237 stripPrefix :: Eq a => [a] -> [a] -> Maybe [a]
238 stripPrefix [] ys = Just ys
239 stripPrefix (x:xs) (y:ys)
240 | x == y = stripPrefix xs ys
241 stripPrefix _ _ = Nothing
243 -- | The 'elemIndex' function returns the index of the first element
244 -- in the given list which is equal (by '==') to the query element,
245 -- or 'Nothing' if there is no such element.
246 elemIndex :: Eq a => a -> [a] -> Maybe Int
247 elemIndex x = findIndex (x==)
249 -- | The 'elemIndices' function extends 'elemIndex', by returning the
250 -- indices of all elements equal to the query element, in ascending order.
251 elemIndices :: Eq a => a -> [a] -> [Int]
252 elemIndices x = findIndices (x==)
254 -- | The 'find' function takes a predicate and a list and returns the
255 -- first element in the list matching the predicate, or 'Nothing' if
256 -- there is no such element.
257 find :: (a -> Bool) -> [a] -> Maybe a
258 find p = listToMaybe . filter p
260 -- | The 'findIndex' function takes a predicate and a list and returns
261 -- the index of the first element in the list satisfying the predicate,
262 -- or 'Nothing' if there is no such element.
263 findIndex :: (a -> Bool) -> [a] -> Maybe Int
264 findIndex p = listToMaybe . findIndices p
266 -- | The 'findIndices' function extends 'findIndex', by returning the
267 -- indices of all elements satisfying the predicate, in ascending order.
268 findIndices :: (a -> Bool) -> [a] -> [Int]
270 #if defined(USE_REPORT_PRELUDE) || !defined(__GLASGOW_HASKELL__)
271 findIndices p xs = [ i | (x,i) <- zip xs [0..], p x]
273 -- Efficient definition
274 findIndices p ls = loop 0# ls
277 loop n (x:xs) | p x = I# n : loop (n +# 1#) xs
278 | otherwise = loop (n +# 1#) xs
279 #endif /* USE_REPORT_PRELUDE */
281 -- | The 'isPrefixOf' function takes two lists and returns 'True'
282 -- iff the first list is a prefix of the second.
283 isPrefixOf :: (Eq a) => [a] -> [a] -> Bool
284 isPrefixOf [] _ = True
285 isPrefixOf _ [] = False
286 isPrefixOf (x:xs) (y:ys)= x == y && isPrefixOf xs ys
288 -- | The 'isSuffixOf' function takes two lists and returns 'True'
289 -- iff the first list is a suffix of the second.
290 -- Both lists must be finite.
291 isSuffixOf :: (Eq a) => [a] -> [a] -> Bool
292 isSuffixOf x y = reverse x `isPrefixOf` reverse y
294 -- | The 'isInfixOf' function takes two lists and returns 'True'
295 -- iff the first list is contained, wholly and intact,
296 -- anywhere within the second.
300 -- >isInfixOf "Haskell" "I really like Haskell." -> True
301 -- >isInfixOf "Ial" "I really like Haskell." -> False
302 isInfixOf :: (Eq a) => [a] -> [a] -> Bool
303 isInfixOf needle haystack = any (isPrefixOf needle) (tails haystack)
305 -- | The 'nub' function removes duplicate elements from a list.
306 -- In particular, it keeps only the first occurrence of each element.
307 -- (The name 'nub' means \`essence\'.)
308 -- It is a special case of 'nubBy', which allows the programmer to supply
309 -- their own equality test.
310 nub :: (Eq a) => [a] -> [a]
311 #ifdef USE_REPORT_PRELUDE
315 nub l = nub' l [] -- '
319 | x `elem` ls = nub' xs ls -- '
320 | otherwise = x : nub' xs (x:ls) -- '
323 -- | The 'nubBy' function behaves just like 'nub', except it uses a
324 -- user-supplied equality predicate instead of the overloaded '=='
326 nubBy :: (a -> a -> Bool) -> [a] -> [a]
327 #ifdef USE_REPORT_PRELUDE
329 nubBy eq (x:xs) = x : nubBy eq (filter (\ y -> not (eq x y)) xs)
331 nubBy eq l = nubBy' l []
335 | elem_by eq y xs = nubBy' ys xs
336 | otherwise = y : nubBy' ys (y:xs)
339 -- Note that we keep the call to `eq` with arguments in the
340 -- same order as in the reference implementation
341 -- 'xs' is the list of things we've seen so far,
342 -- 'y' is the potential new element
343 elem_by :: (a -> a -> Bool) -> a -> [a] -> Bool
344 elem_by _ _ [] = False
345 elem_by eq y (x:xs) = x `eq` y || elem_by eq y xs
349 -- | 'delete' @x@ removes the first occurrence of @x@ from its list argument.
352 -- > delete 'a' "banana" == "bnana"
354 -- It is a special case of 'deleteBy', which allows the programmer to
355 -- supply their own equality test.
357 delete :: (Eq a) => a -> [a] -> [a]
358 delete = deleteBy (==)
360 -- | The 'deleteBy' function behaves like 'delete', but takes a
361 -- user-supplied equality predicate.
362 deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
364 deleteBy eq x (y:ys) = if x `eq` y then ys else y : deleteBy eq x ys
366 -- | The '\\' function is list difference ((non-associative).
367 -- In the result of @xs@ '\\' @ys@, the first occurrence of each element of
368 -- @ys@ in turn (if any) has been removed from @xs@. Thus
370 -- > (xs ++ ys) \\ xs == ys.
372 -- It is a special case of 'deleteFirstsBy', which allows the programmer
373 -- to supply their own equality test.
375 (\\) :: (Eq a) => [a] -> [a] -> [a]
376 (\\) = foldl (flip delete)
378 -- | The 'union' function returns the list union of the two lists.
381 -- > "dog" `union` "cow" == "dogcw"
383 -- Duplicates, and elements of the first list, are removed from the
384 -- the second list, but if the first list contains duplicates, so will
386 -- It is a special case of 'unionBy', which allows the programmer to supply
387 -- their own equality test.
389 union :: (Eq a) => [a] -> [a] -> [a]
392 -- | The 'unionBy' function is the non-overloaded version of 'union'.
393 unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
394 unionBy eq xs ys = xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs
396 -- | The 'intersect' function takes the list intersection of two lists.
399 -- > [1,2,3,4] `intersect` [2,4,6,8] == [2,4]
401 -- If the first list contains duplicates, so will the result.
402 -- It is a special case of 'intersectBy', which allows the programmer to
403 -- supply their own equality test.
405 intersect :: (Eq a) => [a] -> [a] -> [a]
406 intersect = intersectBy (==)
408 -- | The 'intersectBy' function is the non-overloaded version of 'intersect'.
409 intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
410 intersectBy eq xs ys = [x | x <- xs, any (eq x) ys]
412 -- | The 'intersperse' function takes an element and a list and
413 -- \`intersperses\' that element between the elements of the list.
416 -- > intersperse ',' "abcde" == "a,b,c,d,e"
418 intersperse :: a -> [a] -> [a]
419 intersperse _ [] = []
420 intersperse _ [x] = [x]
421 intersperse sep (x:xs) = x : sep : intersperse sep xs
423 -- | 'intercalate' @xs xss@ is equivalent to @('concat' ('intersperse' xs xss))@.
424 -- It inserts the list @xs@ in between the lists in @xss@ and concatenates the
426 intercalate :: [a] -> [[a]] -> [a]
427 intercalate xs xss = concat (intersperse xs xss)
429 -- | The 'transpose' function transposes the rows and columns of its argument.
432 -- > transpose [[1,2,3],[4,5,6]] == [[1,4],[2,5],[3,6]]
434 transpose :: [[a]] -> [[a]]
436 transpose ([] : xss) = transpose xss
437 transpose ((x:xs) : xss) = (x : [h | (h:_) <- xss]) : transpose (xs : [ t | (_:t) <- xss])
440 -- | The 'partition' function takes a predicate a list and returns
441 -- the pair of lists of elements which do and do not satisfy the
442 -- predicate, respectively; i.e.,
444 -- > partition p xs == (filter p xs, filter (not . p) xs)
446 partition :: (a -> Bool) -> [a] -> ([a],[a])
447 {-# INLINE partition #-}
448 partition p xs = foldr (select p) ([],[]) xs
450 select :: (a -> Bool) -> a -> ([a], [a]) -> ([a], [a])
451 select p x ~(ts,fs) | p x = (x:ts,fs)
452 | otherwise = (ts, x:fs)
454 -- | The 'mapAccumL' function behaves like a combination of 'map' and
455 -- 'foldl'; it applies a function to each element of a list, passing
456 -- an accumulating parameter from left to right, and returning a final
457 -- value of this accumulator together with the new list.
458 mapAccumL :: (acc -> x -> (acc, y)) -- Function of elt of input list
459 -- and accumulator, returning new
460 -- accumulator and elt of result list
461 -> acc -- Initial accumulator
463 -> (acc, [y]) -- Final accumulator and result list
464 mapAccumL _ s [] = (s, [])
465 mapAccumL f s (x:xs) = (s'',y:ys)
466 where (s', y ) = f s x
467 (s'',ys) = mapAccumL f s' xs
469 -- | The 'mapAccumR' function behaves like a combination of 'map' and
470 -- 'foldr'; it applies a function to each element of a list, passing
471 -- an accumulating parameter from right to left, and returning a final
472 -- value of this accumulator together with the new list.
473 mapAccumR :: (acc -> x -> (acc, y)) -- Function of elt of input list
474 -- and accumulator, returning new
475 -- accumulator and elt of result list
476 -> acc -- Initial accumulator
478 -> (acc, [y]) -- Final accumulator and result list
479 mapAccumR _ s [] = (s, [])
480 mapAccumR f s (x:xs) = (s'', y:ys)
481 where (s'',y ) = f s' x
482 (s', ys) = mapAccumR f s xs
484 -- | The 'insert' function takes an element and a list and inserts the
485 -- element into the list at the last position where it is still less
486 -- than or equal to the next element. In particular, if the list
487 -- is sorted before the call, the result will also be sorted.
488 -- It is a special case of 'insertBy', which allows the programmer to
489 -- supply their own comparison function.
490 insert :: Ord a => a -> [a] -> [a]
491 insert e ls = insertBy (compare) e ls
493 -- | The non-overloaded version of 'insert'.
494 insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a]
495 insertBy _ x [] = [x]
496 insertBy cmp x ys@(y:ys')
498 GT -> y : insertBy cmp x ys'
501 #ifdef __GLASGOW_HASKELL__
503 -- | 'maximum' returns the maximum value from a list,
504 -- which must be non-empty, finite, and of an ordered type.
505 -- It is a special case of 'Data.List.maximumBy', which allows the
506 -- programmer to supply their own comparison function.
507 maximum :: (Ord a) => [a] -> a
508 maximum [] = errorEmptyList "maximum"
509 maximum xs = foldl1 max xs
512 "maximumInt" maximum = (strictMaximum :: [Int] -> Int);
513 "maximumInteger" maximum = (strictMaximum :: [Integer] -> Integer)
516 -- We can't make the overloaded version of maximum strict without
517 -- changing its semantics (max might not be strict), but we can for
518 -- the version specialised to 'Int'.
519 strictMaximum :: (Ord a) => [a] -> a
520 strictMaximum [] = errorEmptyList "maximum"
521 strictMaximum xs = foldl1' max xs
523 -- | 'minimum' returns the minimum value from a list,
524 -- which must be non-empty, finite, and of an ordered type.
525 -- It is a special case of 'Data.List.minimumBy', which allows the
526 -- programmer to supply their own comparison function.
527 minimum :: (Ord a) => [a] -> a
528 minimum [] = errorEmptyList "minimum"
529 minimum xs = foldl1 min xs
532 "minimumInt" minimum = (strictMinimum :: [Int] -> Int);
533 "minimumInteger" minimum = (strictMinimum :: [Integer] -> Integer)
536 strictMinimum :: (Ord a) => [a] -> a
537 strictMinimum [] = errorEmptyList "minimum"
538 strictMinimum xs = foldl1' min xs
540 #endif /* __GLASGOW_HASKELL__ */
542 -- | The 'maximumBy' function takes a comparison function and a list
543 -- and returns the greatest element of the list by the comparison function.
544 -- The list must be finite and non-empty.
545 maximumBy :: (a -> a -> Ordering) -> [a] -> a
546 maximumBy _ [] = error "List.maximumBy: empty list"
547 maximumBy cmp xs = foldl1 maxBy xs
549 maxBy x y = case cmp x y of
553 -- | The 'minimumBy' function takes a comparison function and a list
554 -- and returns the least element of the list by the comparison function.
555 -- The list must be finite and non-empty.
556 minimumBy :: (a -> a -> Ordering) -> [a] -> a
557 minimumBy _ [] = error "List.minimumBy: empty list"
558 minimumBy cmp xs = foldl1 minBy xs
560 minBy x y = case cmp x y of
564 -- | The 'genericLength' function is an overloaded version of 'length'. In
565 -- particular, instead of returning an 'Int', it returns any type which is
566 -- an instance of 'Num'. It is, however, less efficient than 'length'.
567 genericLength :: (Num i) => [b] -> i
569 genericLength (_:l) = 1 + genericLength l
571 -- | The 'genericTake' function is an overloaded version of 'take', which
572 -- accepts any 'Integral' value as the number of elements to take.
573 genericTake :: (Integral i) => i -> [a] -> [a]
575 genericTake _ [] = []
576 genericTake n (x:xs) | n > 0 = x : genericTake (n-1) xs
577 genericTake _ _ = error "List.genericTake: negative argument"
579 -- | The 'genericDrop' function is an overloaded version of 'drop', which
580 -- accepts any 'Integral' value as the number of elements to drop.
581 genericDrop :: (Integral i) => i -> [a] -> [a]
582 genericDrop 0 xs = xs
583 genericDrop _ [] = []
584 genericDrop n (_:xs) | n > 0 = genericDrop (n-1) xs
585 genericDrop _ _ = error "List.genericDrop: negative argument"
587 -- | The 'genericSplitAt' function is an overloaded version of 'splitAt', which
588 -- accepts any 'Integral' value as the position at which to split.
589 genericSplitAt :: (Integral i) => i -> [b] -> ([b],[b])
590 genericSplitAt 0 xs = ([],xs)
591 genericSplitAt _ [] = ([],[])
592 genericSplitAt n (x:xs) | n > 0 = (x:xs',xs'') where
593 (xs',xs'') = genericSplitAt (n-1) xs
594 genericSplitAt _ _ = error "List.genericSplitAt: negative argument"
596 -- | The 'genericIndex' function is an overloaded version of '!!', which
597 -- accepts any 'Integral' value as the index.
598 genericIndex :: (Integral a) => [b] -> a -> b
599 genericIndex (x:_) 0 = x
600 genericIndex (_:xs) n
601 | n > 0 = genericIndex xs (n-1)
602 | otherwise = error "List.genericIndex: negative argument."
603 genericIndex _ _ = error "List.genericIndex: index too large."
605 -- | The 'genericReplicate' function is an overloaded version of 'replicate',
606 -- which accepts any 'Integral' value as the number of repetitions to make.
607 genericReplicate :: (Integral i) => i -> a -> [a]
608 genericReplicate n x = genericTake n (repeat x)
610 -- | The 'zip4' function takes four lists and returns a list of
611 -- quadruples, analogous to 'zip'.
612 zip4 :: [a] -> [b] -> [c] -> [d] -> [(a,b,c,d)]
613 zip4 = zipWith4 (,,,)
615 -- | The 'zip5' function takes five lists and returns a list of
616 -- five-tuples, analogous to 'zip'.
617 zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a,b,c,d,e)]
618 zip5 = zipWith5 (,,,,)
620 -- | The 'zip6' function takes six lists and returns a list of six-tuples,
621 -- analogous to 'zip'.
622 zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] ->
624 zip6 = zipWith6 (,,,,,)
626 -- | The 'zip7' function takes seven lists and returns a list of
627 -- seven-tuples, analogous to 'zip'.
628 zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] ->
629 [g] -> [(a,b,c,d,e,f,g)]
630 zip7 = zipWith7 (,,,,,,)
632 -- | The 'zipWith4' function takes a function which combines four
633 -- elements, as well as four lists and returns a list of their point-wise
634 -- combination, analogous to 'zipWith'.
635 zipWith4 :: (a->b->c->d->e) -> [a]->[b]->[c]->[d]->[e]
636 zipWith4 z (a:as) (b:bs) (c:cs) (d:ds)
637 = z a b c d : zipWith4 z as bs cs ds
638 zipWith4 _ _ _ _ _ = []
640 -- | The 'zipWith5' function takes a function which combines five
641 -- elements, as well as five lists and returns a list of their point-wise
642 -- combination, analogous to 'zipWith'.
643 zipWith5 :: (a->b->c->d->e->f) ->
644 [a]->[b]->[c]->[d]->[e]->[f]
645 zipWith5 z (a:as) (b:bs) (c:cs) (d:ds) (e:es)
646 = z a b c d e : zipWith5 z as bs cs ds es
647 zipWith5 _ _ _ _ _ _ = []
649 -- | The 'zipWith6' function takes a function which combines six
650 -- elements, as well as six lists and returns a list of their point-wise
651 -- combination, analogous to 'zipWith'.
652 zipWith6 :: (a->b->c->d->e->f->g) ->
653 [a]->[b]->[c]->[d]->[e]->[f]->[g]
654 zipWith6 z (a:as) (b:bs) (c:cs) (d:ds) (e:es) (f:fs)
655 = z a b c d e f : zipWith6 z as bs cs ds es fs
656 zipWith6 _ _ _ _ _ _ _ = []
658 -- | The 'zipWith7' function takes a function which combines seven
659 -- elements, as well as seven lists and returns a list of their point-wise
660 -- combination, analogous to 'zipWith'.
661 zipWith7 :: (a->b->c->d->e->f->g->h) ->
662 [a]->[b]->[c]->[d]->[e]->[f]->[g]->[h]
663 zipWith7 z (a:as) (b:bs) (c:cs) (d:ds) (e:es) (f:fs) (g:gs)
664 = z a b c d e f g : zipWith7 z as bs cs ds es fs gs
665 zipWith7 _ _ _ _ _ _ _ _ = []
667 -- | The 'unzip4' function takes a list of quadruples and returns four
668 -- lists, analogous to 'unzip'.
669 unzip4 :: [(a,b,c,d)] -> ([a],[b],[c],[d])
670 unzip4 = foldr (\(a,b,c,d) ~(as,bs,cs,ds) ->
671 (a:as,b:bs,c:cs,d:ds))
674 -- | The 'unzip5' function takes a list of five-tuples and returns five
675 -- lists, analogous to 'unzip'.
676 unzip5 :: [(a,b,c,d,e)] -> ([a],[b],[c],[d],[e])
677 unzip5 = foldr (\(a,b,c,d,e) ~(as,bs,cs,ds,es) ->
678 (a:as,b:bs,c:cs,d:ds,e:es))
681 -- | The 'unzip6' function takes a list of six-tuples and returns six
682 -- lists, analogous to 'unzip'.
683 unzip6 :: [(a,b,c,d,e,f)] -> ([a],[b],[c],[d],[e],[f])
684 unzip6 = foldr (\(a,b,c,d,e,f) ~(as,bs,cs,ds,es,fs) ->
685 (a:as,b:bs,c:cs,d:ds,e:es,f:fs))
688 -- | The 'unzip7' function takes a list of seven-tuples and returns
689 -- seven lists, analogous to 'unzip'.
690 unzip7 :: [(a,b,c,d,e,f,g)] -> ([a],[b],[c],[d],[e],[f],[g])
691 unzip7 = foldr (\(a,b,c,d,e,f,g) ~(as,bs,cs,ds,es,fs,gs) ->
692 (a:as,b:bs,c:cs,d:ds,e:es,f:fs,g:gs))
693 ([],[],[],[],[],[],[])
696 -- | The 'deleteFirstsBy' function takes a predicate and two lists and
697 -- returns the first list with the first occurrence of each element of
698 -- the second list removed.
699 deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
700 deleteFirstsBy eq = foldl (flip (deleteBy eq))
702 -- | The 'group' function takes a list and returns a list of lists such
703 -- that the concatenation of the result is equal to the argument. Moreover,
704 -- each sublist in the result contains only equal elements. For example,
706 -- > group "Mississippi" = ["M","i","ss","i","ss","i","pp","i"]
708 -- It is a special case of 'groupBy', which allows the programmer to supply
709 -- their own equality test.
710 group :: Eq a => [a] -> [[a]]
713 -- | The 'groupBy' function is the non-overloaded version of 'group'.
714 groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
716 groupBy eq (x:xs) = (x:ys) : groupBy eq zs
717 where (ys,zs) = span (eq x) xs
719 -- | The 'inits' function returns all initial segments of the argument,
720 -- shortest first. For example,
722 -- > inits "abc" == ["","a","ab","abc"]
724 inits :: [a] -> [[a]]
726 inits (x:xs) = [[]] ++ map (x:) (inits xs)
728 -- | The 'tails' function returns all final segments of the argument,
729 -- longest first. For example,
731 -- > tails "abc" == ["abc", "bc", "c",""]
733 tails :: [a] -> [[a]]
735 tails xxs@(_:xs) = xxs : tails xs
738 -- | The 'subsequences' function returns the list of all subsequences of the argument.
740 -- > subsequences "abc" == ["","a","b","ab","c","ac","bc","abc"]
741 subsequences :: [a] -> [[a]]
742 subsequences xs = [] : nonEmptySubsequences xs
744 -- | The 'nonEmptySubsequences' function returns the list of all subsequences of the argument,
745 -- except for the empty list.
747 -- > nonEmptySubsequences "abc" == ["a","b","ab","c","ac","bc","abc"]
748 nonEmptySubsequences :: [a] -> [[a]]
749 nonEmptySubsequences [] = []
750 nonEmptySubsequences (x:xs) = [x] : foldr f [] (nonEmptySubsequences xs)
751 where f ys r = ys : (x : ys) : r
754 -- | The 'permutations' function returns the list of all permutations of the argument.
756 -- > permutations "abc" == ["abc","bac","cba","bca","cab","acb"]
757 permutations :: [a] -> [[a]]
758 permutations xs0 = xs0 : perms xs0 []
761 perms (t:ts) is = foldr interleave (perms ts (t:is)) (permutations is)
762 where interleave xs r = let (_,zs) = interleave' id xs r in zs
763 interleave' _ [] r = (ts, r)
764 interleave' f (y:ys) r = let (us,zs) = interleave' (f . (y:)) ys r
765 in (y:us, f (t:y:us) : zs)
768 ------------------------------------------------------------------------------
769 -- Quick Sort algorithm taken from HBC's QSort library.
771 -- | The 'sort' function implements a stable sorting algorithm.
772 -- It is a special case of 'sortBy', which allows the programmer to supply
773 -- their own comparison function.
774 sort :: (Ord a) => [a] -> [a]
776 -- | The 'sortBy' function is the non-overloaded version of 'sort'.
777 sortBy :: (a -> a -> Ordering) -> [a] -> [a]
779 #ifdef USE_REPORT_PRELUDE
780 sort = sortBy compare
781 sortBy cmp = foldr (insertBy cmp) []
784 sortBy cmp l = mergesort cmp l
785 sort l = mergesort compare l
788 Quicksort replaced by mergesort, 14/5/2002.
790 From: Ian Lynagh <igloo@earth.li>
792 I am curious as to why the List.sort implementation in GHC is a
793 quicksort algorithm rather than an algorithm that guarantees n log n
794 time in the worst case? I have attached a mergesort implementation along
795 with a few scripts to time it's performance, the results of which are
796 shown below (* means it didn't finish successfully - in all cases this
797 was due to a stack overflow).
799 If I heap profile the random_list case with only 10000 then I see
800 random_list peaks at using about 2.5M of memory, whereas in the same
801 program using List.sort it uses only 100k.
803 Input style Input length Sort data Sort alg User time
804 stdin 10000 random_list sort 2.82
805 stdin 10000 random_list mergesort 2.96
806 stdin 10000 sorted sort 31.37
807 stdin 10000 sorted mergesort 1.90
808 stdin 10000 revsorted sort 31.21
809 stdin 10000 revsorted mergesort 1.88
810 stdin 100000 random_list sort *
811 stdin 100000 random_list mergesort *
812 stdin 100000 sorted sort *
813 stdin 100000 sorted mergesort *
814 stdin 100000 revsorted sort *
815 stdin 100000 revsorted mergesort *
816 func 10000 random_list sort 0.31
817 func 10000 random_list mergesort 0.91
818 func 10000 sorted sort 19.09
819 func 10000 sorted mergesort 0.15
820 func 10000 revsorted sort 19.17
821 func 10000 revsorted mergesort 0.16
822 func 100000 random_list sort 3.85
823 func 100000 random_list mergesort *
824 func 100000 sorted sort 5831.47
825 func 100000 sorted mergesort 2.23
826 func 100000 revsorted sort 5872.34
827 func 100000 revsorted mergesort 2.24
830 mergesort :: (a -> a -> Ordering) -> [a] -> [a]
831 mergesort cmp = mergesort' cmp . map wrap
833 mergesort' :: (a -> a -> Ordering) -> [[a]] -> [a]
835 mergesort' _ [xs] = xs
836 mergesort' cmp xss = mergesort' cmp (merge_pairs cmp xss)
838 merge_pairs :: (a -> a -> Ordering) -> [[a]] -> [[a]]
839 merge_pairs _ [] = []
840 merge_pairs _ [xs] = [xs]
841 merge_pairs cmp (xs:ys:xss) = merge cmp xs ys : merge_pairs cmp xss
843 merge :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
846 merge cmp (x:xs) (y:ys)
848 GT -> y : merge cmp (x:xs) ys
849 _ -> x : merge cmp xs (y:ys)
857 -- qsort is stable and does not concatenate.
858 qsort :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
861 qsort cmp (x:xs) r = qpart cmp x xs [] [] r
863 -- qpart partitions and sorts the sublists
864 qpart :: (a -> a -> Ordering) -> a -> [a] -> [a] -> [a] -> [a] -> [a]
865 qpart cmp x [] rlt rge r =
866 -- rlt and rge are in reverse order and must be sorted with an
867 -- anti-stable sorting
868 rqsort cmp rlt (x:rqsort cmp rge r)
869 qpart cmp x (y:ys) rlt rge r =
871 GT -> qpart cmp x ys (y:rlt) rge r
872 _ -> qpart cmp x ys rlt (y:rge) r
874 -- rqsort is as qsort but anti-stable, i.e. reverses equal elements
875 rqsort :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
878 rqsort cmp (x:xs) r = rqpart cmp x xs [] [] r
880 rqpart :: (a -> a -> Ordering) -> a -> [a] -> [a] -> [a] -> [a] -> [a]
881 rqpart cmp x [] rle rgt r =
882 qsort cmp rle (x:qsort cmp rgt r)
883 rqpart cmp x (y:ys) rle rgt r =
885 GT -> rqpart cmp x ys rle (y:rgt) r
886 _ -> rqpart cmp x ys (y:rle) rgt r
889 #endif /* USE_REPORT_PRELUDE */
891 -- | The 'unfoldr' function is a \`dual\' to 'foldr': while 'foldr'
892 -- reduces a list to a summary value, 'unfoldr' builds a list from
893 -- a seed value. The function takes the element and returns 'Nothing'
894 -- if it is done producing the list or returns 'Just' @(a,b)@, in which
895 -- case, @a@ is a prepended to the list and @b@ is used as the next
896 -- element in a recursive call. For example,
898 -- > iterate f == unfoldr (\x -> Just (x, f x))
900 -- In some cases, 'unfoldr' can undo a 'foldr' operation:
902 -- > unfoldr f' (foldr f z xs) == xs
904 -- if the following holds:
906 -- > f' (f x y) = Just (x,y)
909 -- A simple use of unfoldr:
911 -- > unfoldr (\b -> if b == 0 then Nothing else Just (b, b-1)) 10
912 -- > [10,9,8,7,6,5,4,3,2,1]
914 unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
917 Just (a,new_b) -> a : unfoldr f new_b
920 -- -----------------------------------------------------------------------------
922 -- | A strict version of 'foldl'.
923 foldl' :: (a -> b -> a) -> a -> [b] -> a
924 #ifdef __GLASGOW_HASKELL__
925 foldl' f z0 xs0 = lgo z0 xs0
927 lgo z (x:xs) = let z' = f z x in z' `seq` lgo z' xs
930 foldl' f a (x:xs) = let a' = f a x in a' `seq` foldl' f a' xs
933 #ifdef __GLASGOW_HASKELL__
934 -- | 'foldl1' is a variant of 'foldl' that has no starting value argument,
935 -- and thus must be applied to non-empty lists.
936 foldl1 :: (a -> a -> a) -> [a] -> a
937 foldl1 f (x:xs) = foldl f x xs
938 foldl1 _ [] = errorEmptyList "foldl1"
939 #endif /* __GLASGOW_HASKELL__ */
941 -- | A strict version of 'foldl1'
942 foldl1' :: (a -> a -> a) -> [a] -> a
943 foldl1' f (x:xs) = foldl' f x xs
944 foldl1' _ [] = errorEmptyList "foldl1'"
946 #ifdef __GLASGOW_HASKELL__
947 -- -----------------------------------------------------------------------------
948 -- List sum and product
950 {-# SPECIALISE sum :: [Int] -> Int #-}
951 {-# SPECIALISE sum :: [Integer] -> Integer #-}
952 {-# SPECIALISE product :: [Int] -> Int #-}
953 {-# SPECIALISE product :: [Integer] -> Integer #-}
954 -- | The 'sum' function computes the sum of a finite list of numbers.
955 sum :: (Num a) => [a] -> a
956 -- | The 'product' function computes the product of a finite list of numbers.
957 product :: (Num a) => [a] -> a
958 #ifdef USE_REPORT_PRELUDE
960 product = foldl (*) 1
965 sum' (x:xs) a = sum' xs (a+x)
969 prod (x:xs) a = prod xs (a*x)
972 -- -----------------------------------------------------------------------------
973 -- Functions on strings
975 -- | 'lines' breaks a string up into a list of strings at newline
976 -- characters. The resulting strings do not contain newlines.
977 lines :: String -> [String]
979 lines s = let (l, s') = break (== '\n') s
984 -- | 'unlines' is an inverse operation to 'lines'.
985 -- It joins lines, after appending a terminating newline to each.
986 unlines :: [String] -> String
987 #ifdef USE_REPORT_PRELUDE
988 unlines = concatMap (++ "\n")
990 -- HBC version (stolen)
991 -- here's a more efficient version
993 unlines (l:ls) = l ++ '\n' : unlines ls
996 -- | 'words' breaks a string up into a list of words, which were delimited
998 words :: String -> [String]
999 words s = case dropWhile {-partain:Char.-}isSpace s of
1003 break {-partain:Char.-}isSpace s'
1005 -- | 'unwords' is an inverse operation to 'words'.
1006 -- It joins words with separating spaces.
1007 unwords :: [String] -> String
1008 #ifdef USE_REPORT_PRELUDE
1010 unwords ws = foldr1 (\w s -> w ++ ' ':s) ws
1012 -- HBC version (stolen)
1013 -- here's a more efficient version
1016 unwords (w:ws) = w ++ ' ' : unwords ws
1019 #else /* !__GLASGOW_HASKELL__ */
1021 errorEmptyList :: String -> a
1022 errorEmptyList fun =
1023 error ("Prelude." ++ fun ++ ": empty list")
1025 #endif /* !__GLASGOW_HASKELL__ */