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) = y `eq` x || 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.
403 -- > [1,2,2,3,4] `intersect` [6,4,4,2] == [2,2,4]
405 -- It is a special case of 'intersectBy', which allows the programmer to
406 -- supply their own equality test.
408 intersect :: (Eq a) => [a] -> [a] -> [a]
409 intersect = intersectBy (==)
411 -- | The 'intersectBy' function is the non-overloaded version of 'intersect'.
412 intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
413 intersectBy eq xs ys = [x | x <- xs, any (eq x) ys]
415 -- | The 'intersperse' function takes an element and a list and
416 -- \`intersperses\' that element between the elements of the list.
419 -- > intersperse ',' "abcde" == "a,b,c,d,e"
421 intersperse :: a -> [a] -> [a]
422 intersperse _ [] = []
423 intersperse _ [x] = [x]
424 intersperse sep (x:xs) = x : sep : intersperse sep xs
426 -- | 'intercalate' @xs xss@ is equivalent to @('concat' ('intersperse' xs xss))@.
427 -- It inserts the list @xs@ in between the lists in @xss@ and concatenates the
429 intercalate :: [a] -> [[a]] -> [a]
430 intercalate xs xss = concat (intersperse xs xss)
432 -- | The 'transpose' function transposes the rows and columns of its argument.
435 -- > transpose [[1,2,3],[4,5,6]] == [[1,4],[2,5],[3,6]]
437 transpose :: [[a]] -> [[a]]
439 transpose ([] : xss) = transpose xss
440 transpose ((x:xs) : xss) = (x : [h | (h:_) <- xss]) : transpose (xs : [ t | (_:t) <- xss])
443 -- | The 'partition' function takes a predicate a list and returns
444 -- the pair of lists of elements which do and do not satisfy the
445 -- predicate, respectively; i.e.,
447 -- > partition p xs == (filter p xs, filter (not . p) xs)
449 partition :: (a -> Bool) -> [a] -> ([a],[a])
450 {-# INLINE partition #-}
451 partition p xs = foldr (select p) ([],[]) xs
453 select :: (a -> Bool) -> a -> ([a], [a]) -> ([a], [a])
454 select p x ~(ts,fs) | p x = (x:ts,fs)
455 | otherwise = (ts, x:fs)
457 -- | The 'mapAccumL' function behaves like a combination of 'map' and
458 -- 'foldl'; it applies a function to each element of a list, passing
459 -- an accumulating parameter from left to right, and returning a final
460 -- value of this accumulator together with the new list.
461 mapAccumL :: (acc -> x -> (acc, y)) -- Function of elt of input list
462 -- and accumulator, returning new
463 -- accumulator and elt of result list
464 -> acc -- Initial accumulator
466 -> (acc, [y]) -- Final accumulator and result list
467 mapAccumL _ s [] = (s, [])
468 mapAccumL f s (x:xs) = (s'',y:ys)
469 where (s', y ) = f s x
470 (s'',ys) = mapAccumL f s' xs
472 -- | The 'mapAccumR' function behaves like a combination of 'map' and
473 -- 'foldr'; it applies a function to each element of a list, passing
474 -- an accumulating parameter from right to left, and returning a final
475 -- value of this accumulator together with the new list.
476 mapAccumR :: (acc -> x -> (acc, y)) -- Function of elt of input list
477 -- and accumulator, returning new
478 -- accumulator and elt of result list
479 -> acc -- Initial accumulator
481 -> (acc, [y]) -- Final accumulator and result list
482 mapAccumR _ s [] = (s, [])
483 mapAccumR f s (x:xs) = (s'', y:ys)
484 where (s'',y ) = f s' x
485 (s', ys) = mapAccumR f s xs
487 -- | The 'insert' function takes an element and a list and inserts the
488 -- element into the list at the last position where it is still less
489 -- than or equal to the next element. In particular, if the list
490 -- is sorted before the call, the result will also be sorted.
491 -- It is a special case of 'insertBy', which allows the programmer to
492 -- supply their own comparison function.
493 insert :: Ord a => a -> [a] -> [a]
494 insert e ls = insertBy (compare) e ls
496 -- | The non-overloaded version of 'insert'.
497 insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a]
498 insertBy _ x [] = [x]
499 insertBy cmp x ys@(y:ys')
501 GT -> y : insertBy cmp x ys'
504 #ifdef __GLASGOW_HASKELL__
506 -- | 'maximum' returns the maximum value from a list,
507 -- which must be non-empty, finite, and of an ordered type.
508 -- It is a special case of 'Data.List.maximumBy', which allows the
509 -- programmer to supply their own comparison function.
510 maximum :: (Ord a) => [a] -> a
511 maximum [] = errorEmptyList "maximum"
512 maximum xs = foldl1 max xs
515 "maximumInt" maximum = (strictMaximum :: [Int] -> Int);
516 "maximumInteger" maximum = (strictMaximum :: [Integer] -> Integer)
519 -- We can't make the overloaded version of maximum strict without
520 -- changing its semantics (max might not be strict), but we can for
521 -- the version specialised to 'Int'.
522 strictMaximum :: (Ord a) => [a] -> a
523 strictMaximum [] = errorEmptyList "maximum"
524 strictMaximum xs = foldl1' max xs
526 -- | 'minimum' returns the minimum value from a list,
527 -- which must be non-empty, finite, and of an ordered type.
528 -- It is a special case of 'Data.List.minimumBy', which allows the
529 -- programmer to supply their own comparison function.
530 minimum :: (Ord a) => [a] -> a
531 minimum [] = errorEmptyList "minimum"
532 minimum xs = foldl1 min xs
535 "minimumInt" minimum = (strictMinimum :: [Int] -> Int);
536 "minimumInteger" minimum = (strictMinimum :: [Integer] -> Integer)
539 strictMinimum :: (Ord a) => [a] -> a
540 strictMinimum [] = errorEmptyList "minimum"
541 strictMinimum xs = foldl1' min xs
543 #endif /* __GLASGOW_HASKELL__ */
545 -- | The 'maximumBy' function takes a comparison function and a list
546 -- and returns the greatest element of the list by the comparison function.
547 -- The list must be finite and non-empty.
548 maximumBy :: (a -> a -> Ordering) -> [a] -> a
549 maximumBy _ [] = error "List.maximumBy: empty list"
550 maximumBy cmp xs = foldl1 maxBy xs
552 maxBy x y = case cmp x y of
556 -- | The 'minimumBy' function takes a comparison function and a list
557 -- and returns the least element of the list by the comparison function.
558 -- The list must be finite and non-empty.
559 minimumBy :: (a -> a -> Ordering) -> [a] -> a
560 minimumBy _ [] = error "List.minimumBy: empty list"
561 minimumBy cmp xs = foldl1 minBy xs
563 minBy x y = case cmp x y of
567 -- | The 'genericLength' function is an overloaded version of 'length'. In
568 -- particular, instead of returning an 'Int', it returns any type which is
569 -- an instance of 'Num'. It is, however, less efficient than 'length'.
570 genericLength :: (Num i) => [b] -> i
572 genericLength (_:l) = 1 + genericLength l
575 "genericLengthInt" genericLength = (strictGenericLength :: [a] -> Int);
576 "genericLengthInteger" genericLength = (strictGenericLength :: [a] -> Integer);
579 strictGenericLength :: (Num i) => [b] -> i
580 strictGenericLength l = gl l 0
583 gl (_:xs) a = let a' = a + 1 in a' `seq` gl xs a'
585 -- | The 'genericTake' function is an overloaded version of 'take', which
586 -- accepts any 'Integral' value as the number of elements to take.
587 genericTake :: (Integral i) => i -> [a] -> [a]
588 genericTake n _ | n <= 0 = []
589 genericTake _ [] = []
590 genericTake n (x:xs) = x : genericTake (n-1) xs
592 -- | The 'genericDrop' function is an overloaded version of 'drop', which
593 -- accepts any 'Integral' value as the number of elements to drop.
594 genericDrop :: (Integral i) => i -> [a] -> [a]
595 genericDrop n xs | n <= 0 = xs
596 genericDrop _ [] = []
597 genericDrop n (_:xs) = genericDrop (n-1) xs
600 -- | The 'genericSplitAt' function is an overloaded version of 'splitAt', which
601 -- accepts any 'Integral' value as the position at which to split.
602 genericSplitAt :: (Integral i) => i -> [b] -> ([b],[b])
603 genericSplitAt n xs | n <= 0 = ([],xs)
604 genericSplitAt _ [] = ([],[])
605 genericSplitAt n (x:xs) = (x:xs',xs'') where
606 (xs',xs'') = genericSplitAt (n-1) xs
608 -- | The 'genericIndex' function is an overloaded version of '!!', which
609 -- accepts any 'Integral' value as the index.
610 genericIndex :: (Integral a) => [b] -> a -> b
611 genericIndex (x:_) 0 = x
612 genericIndex (_:xs) n
613 | n > 0 = genericIndex xs (n-1)
614 | otherwise = error "List.genericIndex: negative argument."
615 genericIndex _ _ = error "List.genericIndex: index too large."
617 -- | The 'genericReplicate' function is an overloaded version of 'replicate',
618 -- which accepts any 'Integral' value as the number of repetitions to make.
619 genericReplicate :: (Integral i) => i -> a -> [a]
620 genericReplicate n x = genericTake n (repeat x)
622 -- | The 'zip4' function takes four lists and returns a list of
623 -- quadruples, analogous to 'zip'.
624 zip4 :: [a] -> [b] -> [c] -> [d] -> [(a,b,c,d)]
625 zip4 = zipWith4 (,,,)
627 -- | The 'zip5' function takes five lists and returns a list of
628 -- five-tuples, analogous to 'zip'.
629 zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a,b,c,d,e)]
630 zip5 = zipWith5 (,,,,)
632 -- | The 'zip6' function takes six lists and returns a list of six-tuples,
633 -- analogous to 'zip'.
634 zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] ->
636 zip6 = zipWith6 (,,,,,)
638 -- | The 'zip7' function takes seven lists and returns a list of
639 -- seven-tuples, analogous to 'zip'.
640 zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] ->
641 [g] -> [(a,b,c,d,e,f,g)]
642 zip7 = zipWith7 (,,,,,,)
644 -- | The 'zipWith4' function takes a function which combines four
645 -- elements, as well as four lists and returns a list of their point-wise
646 -- combination, analogous to 'zipWith'.
647 zipWith4 :: (a->b->c->d->e) -> [a]->[b]->[c]->[d]->[e]
648 zipWith4 z (a:as) (b:bs) (c:cs) (d:ds)
649 = z a b c d : zipWith4 z as bs cs ds
650 zipWith4 _ _ _ _ _ = []
652 -- | The 'zipWith5' function takes a function which combines five
653 -- elements, as well as five lists and returns a list of their point-wise
654 -- combination, analogous to 'zipWith'.
655 zipWith5 :: (a->b->c->d->e->f) ->
656 [a]->[b]->[c]->[d]->[e]->[f]
657 zipWith5 z (a:as) (b:bs) (c:cs) (d:ds) (e:es)
658 = z a b c d e : zipWith5 z as bs cs ds es
659 zipWith5 _ _ _ _ _ _ = []
661 -- | The 'zipWith6' function takes a function which combines six
662 -- elements, as well as six lists and returns a list of their point-wise
663 -- combination, analogous to 'zipWith'.
664 zipWith6 :: (a->b->c->d->e->f->g) ->
665 [a]->[b]->[c]->[d]->[e]->[f]->[g]
666 zipWith6 z (a:as) (b:bs) (c:cs) (d:ds) (e:es) (f:fs)
667 = z a b c d e f : zipWith6 z as bs cs ds es fs
668 zipWith6 _ _ _ _ _ _ _ = []
670 -- | The 'zipWith7' function takes a function which combines seven
671 -- elements, as well as seven lists and returns a list of their point-wise
672 -- combination, analogous to 'zipWith'.
673 zipWith7 :: (a->b->c->d->e->f->g->h) ->
674 [a]->[b]->[c]->[d]->[e]->[f]->[g]->[h]
675 zipWith7 z (a:as) (b:bs) (c:cs) (d:ds) (e:es) (f:fs) (g:gs)
676 = z a b c d e f g : zipWith7 z as bs cs ds es fs gs
677 zipWith7 _ _ _ _ _ _ _ _ = []
679 -- | The 'unzip4' function takes a list of quadruples and returns four
680 -- lists, analogous to 'unzip'.
681 unzip4 :: [(a,b,c,d)] -> ([a],[b],[c],[d])
682 unzip4 = foldr (\(a,b,c,d) ~(as,bs,cs,ds) ->
683 (a:as,b:bs,c:cs,d:ds))
686 -- | The 'unzip5' function takes a list of five-tuples and returns five
687 -- lists, analogous to 'unzip'.
688 unzip5 :: [(a,b,c,d,e)] -> ([a],[b],[c],[d],[e])
689 unzip5 = foldr (\(a,b,c,d,e) ~(as,bs,cs,ds,es) ->
690 (a:as,b:bs,c:cs,d:ds,e:es))
693 -- | The 'unzip6' function takes a list of six-tuples and returns six
694 -- lists, analogous to 'unzip'.
695 unzip6 :: [(a,b,c,d,e,f)] -> ([a],[b],[c],[d],[e],[f])
696 unzip6 = foldr (\(a,b,c,d,e,f) ~(as,bs,cs,ds,es,fs) ->
697 (a:as,b:bs,c:cs,d:ds,e:es,f:fs))
700 -- | The 'unzip7' function takes a list of seven-tuples and returns
701 -- seven lists, analogous to 'unzip'.
702 unzip7 :: [(a,b,c,d,e,f,g)] -> ([a],[b],[c],[d],[e],[f],[g])
703 unzip7 = foldr (\(a,b,c,d,e,f,g) ~(as,bs,cs,ds,es,fs,gs) ->
704 (a:as,b:bs,c:cs,d:ds,e:es,f:fs,g:gs))
705 ([],[],[],[],[],[],[])
708 -- | The 'deleteFirstsBy' function takes a predicate and two lists and
709 -- returns the first list with the first occurrence of each element of
710 -- the second list removed.
711 deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
712 deleteFirstsBy eq = foldl (flip (deleteBy eq))
714 -- | The 'group' function takes a list and returns a list of lists such
715 -- that the concatenation of the result is equal to the argument. Moreover,
716 -- each sublist in the result contains only equal elements. For example,
718 -- > group "Mississippi" = ["M","i","ss","i","ss","i","pp","i"]
720 -- It is a special case of 'groupBy', which allows the programmer to supply
721 -- their own equality test.
722 group :: Eq a => [a] -> [[a]]
725 -- | The 'groupBy' function is the non-overloaded version of 'group'.
726 groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
728 groupBy eq (x:xs) = (x:ys) : groupBy eq zs
729 where (ys,zs) = span (eq x) xs
731 -- | The 'inits' function returns all initial segments of the argument,
732 -- shortest first. For example,
734 -- > inits "abc" == ["","a","ab","abc"]
736 inits :: [a] -> [[a]]
738 inits (x:xs) = [[]] ++ map (x:) (inits xs)
740 -- | The 'tails' function returns all final segments of the argument,
741 -- longest first. For example,
743 -- > tails "abc" == ["abc", "bc", "c",""]
745 tails :: [a] -> [[a]]
747 tails xxs@(_:xs) = xxs : tails xs
750 -- | The 'subsequences' function returns the list of all subsequences of the argument.
752 -- > subsequences "abc" == ["","a","b","ab","c","ac","bc","abc"]
753 subsequences :: [a] -> [[a]]
754 subsequences xs = [] : nonEmptySubsequences xs
756 -- | The 'nonEmptySubsequences' function returns the list of all subsequences of the argument,
757 -- except for the empty list.
759 -- > nonEmptySubsequences "abc" == ["a","b","ab","c","ac","bc","abc"]
760 nonEmptySubsequences :: [a] -> [[a]]
761 nonEmptySubsequences [] = []
762 nonEmptySubsequences (x:xs) = [x] : foldr f [] (nonEmptySubsequences xs)
763 where f ys r = ys : (x : ys) : r
766 -- | The 'permutations' function returns the list of all permutations of the argument.
768 -- > permutations "abc" == ["abc","bac","cba","bca","cab","acb"]
769 permutations :: [a] -> [[a]]
770 permutations xs0 = xs0 : perms xs0 []
773 perms (t:ts) is = foldr interleave (perms ts (t:is)) (permutations is)
774 where interleave xs r = let (_,zs) = interleave' id xs r in zs
775 interleave' _ [] r = (ts, r)
776 interleave' f (y:ys) r = let (us,zs) = interleave' (f . (y:)) ys r
777 in (y:us, f (t:y:us) : zs)
780 ------------------------------------------------------------------------------
781 -- Quick Sort algorithm taken from HBC's QSort library.
783 -- | The 'sort' function implements a stable sorting algorithm.
784 -- It is a special case of 'sortBy', which allows the programmer to supply
785 -- their own comparison function.
786 sort :: (Ord a) => [a] -> [a]
788 -- | The 'sortBy' function is the non-overloaded version of 'sort'.
789 sortBy :: (a -> a -> Ordering) -> [a] -> [a]
791 #ifdef USE_REPORT_PRELUDE
792 sort = sortBy compare
793 sortBy cmp = foldr (insertBy cmp) []
797 GHC's mergesort replaced by a better implementation, 24/12/2009.
798 This code originally contributed to the nhc12 compiler by Thomas Nordin
799 in 2002. Rumoured to have been based on code by Lennart Augustsson, e.g.
800 http://www.mail-archive.com/haskell@haskell.org/msg01822.html
801 and possibly to bear similarities to a 1982 paper by Richard O'Keefe:
802 "A smooth applicative merge sort".
804 Benchmarks show it to be often 2x the speed of the previous implementation.
805 Fixes ticket http://hackage.haskell.org/trac/ghc/ticket/2143
808 sort = sortBy compare
809 sortBy cmp = mergeAll . sequences
812 | a `cmp` b == GT = descending b [a] xs
813 | otherwise = ascending b (a:) xs
816 descending a as (b:bs)
817 | a `cmp` b == GT = descending b (a:as) bs
818 descending a as bs = (a:as): sequences bs
820 ascending a as (b:bs)
821 | a `cmp` b /= GT = ascending b (\ys -> as (a:ys)) bs
822 ascending a as bs = as [a]: sequences bs
825 mergeAll xs = mergeAll (mergePairs xs)
827 mergePairs (a:b:xs) = merge a b: mergePairs xs
830 merge as@(a:as') bs@(b:bs')
831 | a `cmp` b == GT = b:merge as bs'
832 | otherwise = a:merge as' bs
837 sortBy cmp l = mergesort cmp l
838 sort l = mergesort compare l
840 Quicksort replaced by mergesort, 14/5/2002.
842 From: Ian Lynagh <igloo@earth.li>
844 I am curious as to why the List.sort implementation in GHC is a
845 quicksort algorithm rather than an algorithm that guarantees n log n
846 time in the worst case? I have attached a mergesort implementation along
847 with a few scripts to time it's performance, the results of which are
848 shown below (* means it didn't finish successfully - in all cases this
849 was due to a stack overflow).
851 If I heap profile the random_list case with only 10000 then I see
852 random_list peaks at using about 2.5M of memory, whereas in the same
853 program using List.sort it uses only 100k.
855 Input style Input length Sort data Sort alg User time
856 stdin 10000 random_list sort 2.82
857 stdin 10000 random_list mergesort 2.96
858 stdin 10000 sorted sort 31.37
859 stdin 10000 sorted mergesort 1.90
860 stdin 10000 revsorted sort 31.21
861 stdin 10000 revsorted mergesort 1.88
862 stdin 100000 random_list sort *
863 stdin 100000 random_list mergesort *
864 stdin 100000 sorted sort *
865 stdin 100000 sorted mergesort *
866 stdin 100000 revsorted sort *
867 stdin 100000 revsorted mergesort *
868 func 10000 random_list sort 0.31
869 func 10000 random_list mergesort 0.91
870 func 10000 sorted sort 19.09
871 func 10000 sorted mergesort 0.15
872 func 10000 revsorted sort 19.17
873 func 10000 revsorted mergesort 0.16
874 func 100000 random_list sort 3.85
875 func 100000 random_list mergesort *
876 func 100000 sorted sort 5831.47
877 func 100000 sorted mergesort 2.23
878 func 100000 revsorted sort 5872.34
879 func 100000 revsorted mergesort 2.24
881 mergesort :: (a -> a -> Ordering) -> [a] -> [a]
882 mergesort cmp = mergesort' cmp . map wrap
884 mergesort' :: (a -> a -> Ordering) -> [[a]] -> [a]
886 mergesort' _ [xs] = xs
887 mergesort' cmp xss = mergesort' cmp (merge_pairs cmp xss)
889 merge_pairs :: (a -> a -> Ordering) -> [[a]] -> [[a]]
890 merge_pairs _ [] = []
891 merge_pairs _ [xs] = [xs]
892 merge_pairs cmp (xs:ys:xss) = merge cmp xs ys : merge_pairs cmp xss
894 merge :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
897 merge cmp (x:xs) (y:ys)
899 GT -> y : merge cmp (x:xs) ys
900 _ -> x : merge cmp xs (y:ys)
909 -- qsort is stable and does not concatenate.
910 qsort :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
913 qsort cmp (x:xs) r = qpart cmp x xs [] [] r
915 -- qpart partitions and sorts the sublists
916 qpart :: (a -> a -> Ordering) -> a -> [a] -> [a] -> [a] -> [a] -> [a]
917 qpart cmp x [] rlt rge r =
918 -- rlt and rge are in reverse order and must be sorted with an
919 -- anti-stable sorting
920 rqsort cmp rlt (x:rqsort cmp rge r)
921 qpart cmp x (y:ys) rlt rge r =
923 GT -> qpart cmp x ys (y:rlt) rge r
924 _ -> qpart cmp x ys rlt (y:rge) r
926 -- rqsort is as qsort but anti-stable, i.e. reverses equal elements
927 rqsort :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
930 rqsort cmp (x:xs) r = rqpart cmp x xs [] [] r
932 rqpart :: (a -> a -> Ordering) -> a -> [a] -> [a] -> [a] -> [a] -> [a]
933 rqpart cmp x [] rle rgt r =
934 qsort cmp rle (x:qsort cmp rgt r)
935 rqpart cmp x (y:ys) rle rgt r =
937 GT -> rqpart cmp x ys rle (y:rgt) r
938 _ -> rqpart cmp x ys (y:rle) rgt r
941 #endif /* USE_REPORT_PRELUDE */
943 -- | The 'unfoldr' function is a \`dual\' to 'foldr': while 'foldr'
944 -- reduces a list to a summary value, 'unfoldr' builds a list from
945 -- a seed value. The function takes the element and returns 'Nothing'
946 -- if it is done producing the list or returns 'Just' @(a,b)@, in which
947 -- case, @a@ is a prepended to the list and @b@ is used as the next
948 -- element in a recursive call. For example,
950 -- > iterate f == unfoldr (\x -> Just (x, f x))
952 -- In some cases, 'unfoldr' can undo a 'foldr' operation:
954 -- > unfoldr f' (foldr f z xs) == xs
956 -- if the following holds:
958 -- > f' (f x y) = Just (x,y)
961 -- A simple use of unfoldr:
963 -- > unfoldr (\b -> if b == 0 then Nothing else Just (b, b-1)) 10
964 -- > [10,9,8,7,6,5,4,3,2,1]
966 unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
969 Just (a,new_b) -> a : unfoldr f new_b
972 -- -----------------------------------------------------------------------------
974 -- | A strict version of 'foldl'.
975 foldl' :: (a -> b -> a) -> a -> [b] -> a
976 #ifdef __GLASGOW_HASKELL__
977 foldl' f z0 xs0 = lgo z0 xs0
979 lgo z (x:xs) = let z' = f z x in z' `seq` lgo z' xs
982 foldl' f a (x:xs) = let a' = f a x in a' `seq` foldl' f a' xs
985 #ifdef __GLASGOW_HASKELL__
986 -- | 'foldl1' is a variant of 'foldl' that has no starting value argument,
987 -- and thus must be applied to non-empty lists.
988 foldl1 :: (a -> a -> a) -> [a] -> a
989 foldl1 f (x:xs) = foldl f x xs
990 foldl1 _ [] = errorEmptyList "foldl1"
991 #endif /* __GLASGOW_HASKELL__ */
993 -- | A strict version of 'foldl1'
994 foldl1' :: (a -> a -> a) -> [a] -> a
995 foldl1' f (x:xs) = foldl' f x xs
996 foldl1' _ [] = errorEmptyList "foldl1'"
998 #ifdef __GLASGOW_HASKELL__
999 -- -----------------------------------------------------------------------------
1000 -- List sum and product
1002 {-# SPECIALISE sum :: [Int] -> Int #-}
1003 {-# SPECIALISE sum :: [Integer] -> Integer #-}
1004 {-# SPECIALISE product :: [Int] -> Int #-}
1005 {-# SPECIALISE product :: [Integer] -> Integer #-}
1006 -- | The 'sum' function computes the sum of a finite list of numbers.
1007 sum :: (Num a) => [a] -> a
1008 -- | The 'product' function computes the product of a finite list of numbers.
1009 product :: (Num a) => [a] -> a
1010 #ifdef USE_REPORT_PRELUDE
1012 product = foldl (*) 1
1017 sum' (x:xs) a = sum' xs (a+x)
1018 product l = prod l 1
1021 prod (x:xs) a = prod xs (a*x)
1024 -- -----------------------------------------------------------------------------
1025 -- Functions on strings
1027 -- | 'lines' breaks a string up into a list of strings at newline
1028 -- characters. The resulting strings do not contain newlines.
1029 lines :: String -> [String]
1031 lines s = let (l, s') = break (== '\n') s
1034 (_:s'') -> lines s''
1036 -- | 'unlines' is an inverse operation to 'lines'.
1037 -- It joins lines, after appending a terminating newline to each.
1038 unlines :: [String] -> String
1039 #ifdef USE_REPORT_PRELUDE
1040 unlines = concatMap (++ "\n")
1042 -- HBC version (stolen)
1043 -- here's a more efficient version
1045 unlines (l:ls) = l ++ '\n' : unlines ls
1048 -- | 'words' breaks a string up into a list of words, which were delimited
1050 words :: String -> [String]
1051 words s = case dropWhile {-partain:Char.-}isSpace s of
1055 break {-partain:Char.-}isSpace s'
1057 -- | 'unwords' is an inverse operation to 'words'.
1058 -- It joins words with separating spaces.
1059 unwords :: [String] -> String
1060 #ifdef USE_REPORT_PRELUDE
1062 unwords ws = foldr1 (\w s -> w ++ ' ':s) ws
1064 -- HBC version (stolen)
1065 -- here's a more efficient version
1068 unwords (w:ws) = w ++ ' ' : unwords ws
1071 #else /* !__GLASGOW_HASKELL__ */
1073 errorEmptyList :: String -> a
1074 errorEmptyList fun =
1075 error ("Prelude." ++ fun ++ ": empty list")
1077 #endif /* !__GLASGOW_HASKELL__ */