Generic functions that take integral arguments should work the same way as their...
[packages/base.git] / Data / List.hs
1 {-# OPTIONS_GHC -XNoImplicitPrelude #-}
2 -----------------------------------------------------------------------------
3 -- |
4 -- Module : Data.List
5 -- Copyright : (c) The University of Glasgow 2001
6 -- License : BSD-style (see the file libraries/base/LICENSE)
7 --
8 -- Maintainer : libraries@haskell.org
9 -- Stability : stable
10 -- Portability : portable
11 --
12 -- Operations on lists.
13 --
14 -----------------------------------------------------------------------------
15
16 module Data.List
17 (
18 #ifdef __NHC__
19 [] (..)
20 ,
21 #endif
22
23 -- * Basic functions
24
25 (++) -- :: [a] -> [a] -> [a]
26 , head -- :: [a] -> a
27 , last -- :: [a] -> a
28 , tail -- :: [a] -> [a]
29 , init -- :: [a] -> [a]
30 , null -- :: [a] -> Bool
31 , length -- :: [a] -> Int
32
33 -- * List transformations
34 , map -- :: (a -> b) -> [a] -> [b]
35 , reverse -- :: [a] -> [a]
36
37 , intersperse -- :: a -> [a] -> [a]
38 , intercalate -- :: [a] -> [[a]] -> [a]
39 , transpose -- :: [[a]] -> [[a]]
40
41 , subsequences -- :: [a] -> [[a]]
42 , permutations -- :: [a] -> [[a]]
43
44 -- * Reducing lists (folds)
45
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
52
53 -- ** Special folds
54
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
65
66 -- * Building lists
67
68 -- ** Scans
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]
73
74 -- ** Accumulating maps
75 , mapAccumL -- :: (a -> b -> (a,c)) -> a -> [b] -> (a,[c])
76 , mapAccumR -- :: (a -> b -> (a,c)) -> a -> [b] -> (a,[c])
77
78 -- ** Infinite lists
79 , iterate -- :: (a -> a) -> a -> [a]
80 , repeat -- :: a -> [a]
81 , replicate -- :: Int -> a -> [a]
82 , cycle -- :: [a] -> [a]
83
84 -- ** Unfolding
85 , unfoldr -- :: (b -> Maybe (a, b)) -> b -> [a]
86
87 -- * Sublists
88
89 -- ** Extracting sublists
90 , take -- :: Int -> [a] -> [a]
91 , drop -- :: Int -> [a] -> [a]
92 , splitAt -- :: Int -> [a] -> ([a], [a])
93
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])
98
99 , stripPrefix -- :: Eq a => [a] -> [a] -> Maybe [a]
100
101 , group -- :: Eq a => [a] -> [[a]]
102
103 , inits -- :: [a] -> [[a]]
104 , tails -- :: [a] -> [[a]]
105
106 -- ** Predicates
107 , isPrefixOf -- :: (Eq a) => [a] -> [a] -> Bool
108 , isSuffixOf -- :: (Eq a) => [a] -> [a] -> Bool
109 , isInfixOf -- :: (Eq a) => [a] -> [a] -> Bool
110
111 -- * Searching lists
112
113 -- ** Searching by equality
114 , elem -- :: a -> [a] -> Bool
115 , notElem -- :: a -> [a] -> Bool
116 , lookup -- :: (Eq a) => a -> [(a,b)] -> Maybe b
117
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])
122
123 -- * Indexing lists
124 -- | These functions treat a list @xs@ as a indexed collection,
125 -- with indices ranging from 0 to @'length' xs - 1@.
126
127 , (!!) -- :: [a] -> Int -> a
128
129 , elemIndex -- :: (Eq a) => a -> [a] -> Maybe Int
130 , elemIndices -- :: (Eq a) => a -> [a] -> [Int]
131
132 , findIndex -- :: (a -> Bool) -> [a] -> Maybe Int
133 , findIndices -- :: (a -> Bool) -> [a] -> [Int]
134
135 -- * Zipping and unzipping lists
136
137 , zip -- :: [a] -> [b] -> [(a,b)]
138 , zip3
139 , zip4, zip5, zip6, zip7
140
141 , zipWith -- :: (a -> b -> c) -> [a] -> [b] -> [c]
142 , zipWith3
143 , zipWith4, zipWith5, zipWith6, zipWith7
144
145 , unzip -- :: [(a,b)] -> ([a],[b])
146 , unzip3
147 , unzip4, unzip5, unzip6, unzip7
148
149 -- * Special lists
150
151 -- ** Functions on strings
152 , lines -- :: String -> [String]
153 , words -- :: String -> [String]
154 , unlines -- :: [String] -> String
155 , unwords -- :: [String] -> String
156
157 -- ** \"Set\" operations
158
159 , nub -- :: (Eq a) => [a] -> [a]
160
161 , delete -- :: (Eq a) => a -> [a] -> [a]
162 , (\\) -- :: (Eq a) => [a] -> [a] -> [a]
163
164 , union -- :: (Eq a) => [a] -> [a] -> [a]
165 , intersect -- :: (Eq a) => [a] -> [a] -> [a]
166
167 -- ** Ordered lists
168 , sort -- :: (Ord a) => [a] -> [a]
169 , insert -- :: (Ord a) => a -> [a] -> [a]
170
171 -- * Generalized functions
172
173 -- ** The \"@By@\" operations
174 -- | By convention, overloaded functions have a non-overloaded
175 -- counterpart whose name is suffixed with \`@By@\'.
176 --
177 -- It is often convenient to use these functions together with
178 -- 'Data.Function.on', for instance @'sortBy' ('compare'
179 -- \`on\` 'fst')@.
180
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]]
189
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
196
197 -- ** The \"@generic@\" operations
198 -- | The prefix \`@generic@\' indicates an overloaded function that
199 -- is a generalized version of a "Prelude" function.
200
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]
207
208 ) where
209
210 #ifdef __NHC__
211 import Prelude
212 #endif
213
214 import Data.Maybe
215 import Data.Char ( isSpace )
216
217 #ifdef __GLASGOW_HASKELL__
218 import GHC.Num
219 import GHC.Real
220 import GHC.List
221 import GHC.Base
222 #endif
223
224 infix 5 \\ -- comment to fool cpp
225
226 -- -----------------------------------------------------------------------------
227 -- List functions
228
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.
232 --
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
242
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==)
248
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==)
253
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
259
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
265
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]
269
270 #if defined(USE_REPORT_PRELUDE) || !defined(__GLASGOW_HASKELL__)
271 findIndices p xs = [ i | (x,i) <- zip xs [0..], p x]
272 #else
273 -- Efficient definition
274 findIndices p ls = loop 0# ls
275 where
276 loop _ [] = []
277 loop n (x:xs) | p x = I# n : loop (n +# 1#) xs
278 | otherwise = loop (n +# 1#) xs
279 #endif /* USE_REPORT_PRELUDE */
280
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
287
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
293
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.
297 --
298 -- Example:
299 --
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)
304
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
312 nub = nubBy (==)
313 #else
314 -- stolen from HBC
315 nub l = nub' l [] -- '
316 where
317 nub' [] _ = [] -- '
318 nub' (x:xs) ls -- '
319 | x `elem` ls = nub' xs ls -- '
320 | otherwise = x : nub' xs (x:ls) -- '
321 #endif
322
323 -- | The 'nubBy' function behaves just like 'nub', except it uses a
324 -- user-supplied equality predicate instead of the overloaded '=='
325 -- function.
326 nubBy :: (a -> a -> Bool) -> [a] -> [a]
327 #ifdef USE_REPORT_PRELUDE
328 nubBy eq [] = []
329 nubBy eq (x:xs) = x : nubBy eq (filter (\ y -> not (eq x y)) xs)
330 #else
331 nubBy eq l = nubBy' l []
332 where
333 nubBy' [] _ = []
334 nubBy' (y:ys) xs
335 | elem_by eq y xs = nubBy' ys xs
336 | otherwise = y : nubBy' ys (y:xs)
337
338 -- Not exported:
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
346 #endif
347
348
349 -- | 'delete' @x@ removes the first occurrence of @x@ from its list argument.
350 -- For example,
351 --
352 -- > delete 'a' "banana" == "bnana"
353 --
354 -- It is a special case of 'deleteBy', which allows the programmer to
355 -- supply their own equality test.
356
357 delete :: (Eq a) => a -> [a] -> [a]
358 delete = deleteBy (==)
359
360 -- | The 'deleteBy' function behaves like 'delete', but takes a
361 -- user-supplied equality predicate.
362 deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
363 deleteBy _ _ [] = []
364 deleteBy eq x (y:ys) = if x `eq` y then ys else y : deleteBy eq x ys
365
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
369 --
370 -- > (xs ++ ys) \\ xs == ys.
371 --
372 -- It is a special case of 'deleteFirstsBy', which allows the programmer
373 -- to supply their own equality test.
374
375 (\\) :: (Eq a) => [a] -> [a] -> [a]
376 (\\) = foldl (flip delete)
377
378 -- | The 'union' function returns the list union of the two lists.
379 -- For example,
380 --
381 -- > "dog" `union` "cow" == "dogcw"
382 --
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
385 -- the result.
386 -- It is a special case of 'unionBy', which allows the programmer to supply
387 -- their own equality test.
388
389 union :: (Eq a) => [a] -> [a] -> [a]
390 union = unionBy (==)
391
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
395
396 -- | The 'intersect' function takes the list intersection of two lists.
397 -- For example,
398 --
399 -- > [1,2,3,4] `intersect` [2,4,6,8] == [2,4]
400 --
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.
404
405 intersect :: (Eq a) => [a] -> [a] -> [a]
406 intersect = intersectBy (==)
407
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]
411
412 -- | The 'intersperse' function takes an element and a list and
413 -- \`intersperses\' that element between the elements of the list.
414 -- For example,
415 --
416 -- > intersperse ',' "abcde" == "a,b,c,d,e"
417
418 intersperse :: a -> [a] -> [a]
419 intersperse _ [] = []
420 intersperse _ [x] = [x]
421 intersperse sep (x:xs) = x : sep : intersperse sep xs
422
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
425 -- result.
426 intercalate :: [a] -> [[a]] -> [a]
427 intercalate xs xss = concat (intersperse xs xss)
428
429 -- | The 'transpose' function transposes the rows and columns of its argument.
430 -- For example,
431 --
432 -- > transpose [[1,2,3],[4,5,6]] == [[1,4],[2,5],[3,6]]
433
434 transpose :: [[a]] -> [[a]]
435 transpose [] = []
436 transpose ([] : xss) = transpose xss
437 transpose ((x:xs) : xss) = (x : [h | (h:_) <- xss]) : transpose (xs : [ t | (_:t) <- xss])
438
439
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.,
443 --
444 -- > partition p xs == (filter p xs, filter (not . p) xs)
445
446 partition :: (a -> Bool) -> [a] -> ([a],[a])
447 {-# INLINE partition #-}
448 partition p xs = foldr (select p) ([],[]) xs
449
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)
453
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
462 -> [x] -- Input list
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
468
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
477 -> [x] -- Input list
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
483
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
492
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')
497 = case cmp x y of
498 GT -> y : insertBy cmp x ys'
499 _ -> x : ys
500
501 #ifdef __GLASGOW_HASKELL__
502
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
510
511 {-# RULES
512 "maximumInt" maximum = (strictMaximum :: [Int] -> Int);
513 "maximumInteger" maximum = (strictMaximum :: [Integer] -> Integer)
514 #-}
515
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
522
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
530
531 {-# RULES
532 "minimumInt" minimum = (strictMinimum :: [Int] -> Int);
533 "minimumInteger" minimum = (strictMinimum :: [Integer] -> Integer)
534 #-}
535
536 strictMinimum :: (Ord a) => [a] -> a
537 strictMinimum [] = errorEmptyList "minimum"
538 strictMinimum xs = foldl1' min xs
539
540 #endif /* __GLASGOW_HASKELL__ */
541
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
548 where
549 maxBy x y = case cmp x y of
550 GT -> x
551 _ -> y
552
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
559 where
560 minBy x y = case cmp x y of
561 GT -> y
562 _ -> x
563
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
568 genericLength [] = 0
569 genericLength (_:l) = 1 + genericLength l
570
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]
574 genericTake n _ | n <= 0 = []
575 genericTake _ [] = []
576 genericTake n (x:xs) = x : genericTake (n-1) xs
577
578 -- | The 'genericDrop' function is an overloaded version of 'drop', which
579 -- accepts any 'Integral' value as the number of elements to drop.
580 genericDrop :: (Integral i) => i -> [a] -> [a]
581 genericDrop n xs | n <= 0 = xs
582 genericDrop _ [] = []
583 genericDrop n (_:xs) = genericDrop (n-1) xs
584
585
586 -- | The 'genericSplitAt' function is an overloaded version of 'splitAt', which
587 -- accepts any 'Integral' value as the position at which to split.
588 genericSplitAt :: (Integral i) => i -> [b] -> ([b],[b])
589 genericSplitAt n xs | n <= 0 = ([],xs)
590 genericSplitAt _ [] = ([],[])
591 genericSplitAt n (x:xs) = (x:xs',xs'') where
592 (xs',xs'') = genericSplitAt (n-1) xs
593
594 -- | The 'genericIndex' function is an overloaded version of '!!', which
595 -- accepts any 'Integral' value as the index.
596 genericIndex :: (Integral a) => [b] -> a -> b
597 genericIndex (x:_) 0 = x
598 genericIndex (_:xs) n
599 | n > 0 = genericIndex xs (n-1)
600 | otherwise = error "List.genericIndex: negative argument."
601 genericIndex _ _ = error "List.genericIndex: index too large."
602
603 -- | The 'genericReplicate' function is an overloaded version of 'replicate',
604 -- which accepts any 'Integral' value as the number of repetitions to make.
605 genericReplicate :: (Integral i) => i -> a -> [a]
606 genericReplicate n x = genericTake n (repeat x)
607
608 -- | The 'zip4' function takes four lists and returns a list of
609 -- quadruples, analogous to 'zip'.
610 zip4 :: [a] -> [b] -> [c] -> [d] -> [(a,b,c,d)]
611 zip4 = zipWith4 (,,,)
612
613 -- | The 'zip5' function takes five lists and returns a list of
614 -- five-tuples, analogous to 'zip'.
615 zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a,b,c,d,e)]
616 zip5 = zipWith5 (,,,,)
617
618 -- | The 'zip6' function takes six lists and returns a list of six-tuples,
619 -- analogous to 'zip'.
620 zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] ->
621 [(a,b,c,d,e,f)]
622 zip6 = zipWith6 (,,,,,)
623
624 -- | The 'zip7' function takes seven lists and returns a list of
625 -- seven-tuples, analogous to 'zip'.
626 zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] ->
627 [g] -> [(a,b,c,d,e,f,g)]
628 zip7 = zipWith7 (,,,,,,)
629
630 -- | The 'zipWith4' function takes a function which combines four
631 -- elements, as well as four lists and returns a list of their point-wise
632 -- combination, analogous to 'zipWith'.
633 zipWith4 :: (a->b->c->d->e) -> [a]->[b]->[c]->[d]->[e]
634 zipWith4 z (a:as) (b:bs) (c:cs) (d:ds)
635 = z a b c d : zipWith4 z as bs cs ds
636 zipWith4 _ _ _ _ _ = []
637
638 -- | The 'zipWith5' function takes a function which combines five
639 -- elements, as well as five lists and returns a list of their point-wise
640 -- combination, analogous to 'zipWith'.
641 zipWith5 :: (a->b->c->d->e->f) ->
642 [a]->[b]->[c]->[d]->[e]->[f]
643 zipWith5 z (a:as) (b:bs) (c:cs) (d:ds) (e:es)
644 = z a b c d e : zipWith5 z as bs cs ds es
645 zipWith5 _ _ _ _ _ _ = []
646
647 -- | The 'zipWith6' function takes a function which combines six
648 -- elements, as well as six lists and returns a list of their point-wise
649 -- combination, analogous to 'zipWith'.
650 zipWith6 :: (a->b->c->d->e->f->g) ->
651 [a]->[b]->[c]->[d]->[e]->[f]->[g]
652 zipWith6 z (a:as) (b:bs) (c:cs) (d:ds) (e:es) (f:fs)
653 = z a b c d e f : zipWith6 z as bs cs ds es fs
654 zipWith6 _ _ _ _ _ _ _ = []
655
656 -- | The 'zipWith7' function takes a function which combines seven
657 -- elements, as well as seven lists and returns a list of their point-wise
658 -- combination, analogous to 'zipWith'.
659 zipWith7 :: (a->b->c->d->e->f->g->h) ->
660 [a]->[b]->[c]->[d]->[e]->[f]->[g]->[h]
661 zipWith7 z (a:as) (b:bs) (c:cs) (d:ds) (e:es) (f:fs) (g:gs)
662 = z a b c d e f g : zipWith7 z as bs cs ds es fs gs
663 zipWith7 _ _ _ _ _ _ _ _ = []
664
665 -- | The 'unzip4' function takes a list of quadruples and returns four
666 -- lists, analogous to 'unzip'.
667 unzip4 :: [(a,b,c,d)] -> ([a],[b],[c],[d])
668 unzip4 = foldr (\(a,b,c,d) ~(as,bs,cs,ds) ->
669 (a:as,b:bs,c:cs,d:ds))
670 ([],[],[],[])
671
672 -- | The 'unzip5' function takes a list of five-tuples and returns five
673 -- lists, analogous to 'unzip'.
674 unzip5 :: [(a,b,c,d,e)] -> ([a],[b],[c],[d],[e])
675 unzip5 = foldr (\(a,b,c,d,e) ~(as,bs,cs,ds,es) ->
676 (a:as,b:bs,c:cs,d:ds,e:es))
677 ([],[],[],[],[])
678
679 -- | The 'unzip6' function takes a list of six-tuples and returns six
680 -- lists, analogous to 'unzip'.
681 unzip6 :: [(a,b,c,d,e,f)] -> ([a],[b],[c],[d],[e],[f])
682 unzip6 = foldr (\(a,b,c,d,e,f) ~(as,bs,cs,ds,es,fs) ->
683 (a:as,b:bs,c:cs,d:ds,e:es,f:fs))
684 ([],[],[],[],[],[])
685
686 -- | The 'unzip7' function takes a list of seven-tuples and returns
687 -- seven lists, analogous to 'unzip'.
688 unzip7 :: [(a,b,c,d,e,f,g)] -> ([a],[b],[c],[d],[e],[f],[g])
689 unzip7 = foldr (\(a,b,c,d,e,f,g) ~(as,bs,cs,ds,es,fs,gs) ->
690 (a:as,b:bs,c:cs,d:ds,e:es,f:fs,g:gs))
691 ([],[],[],[],[],[],[])
692
693
694 -- | The 'deleteFirstsBy' function takes a predicate and two lists and
695 -- returns the first list with the first occurrence of each element of
696 -- the second list removed.
697 deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
698 deleteFirstsBy eq = foldl (flip (deleteBy eq))
699
700 -- | The 'group' function takes a list and returns a list of lists such
701 -- that the concatenation of the result is equal to the argument. Moreover,
702 -- each sublist in the result contains only equal elements. For example,
703 --
704 -- > group "Mississippi" = ["M","i","ss","i","ss","i","pp","i"]
705 --
706 -- It is a special case of 'groupBy', which allows the programmer to supply
707 -- their own equality test.
708 group :: Eq a => [a] -> [[a]]
709 group = groupBy (==)
710
711 -- | The 'groupBy' function is the non-overloaded version of 'group'.
712 groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
713 groupBy _ [] = []
714 groupBy eq (x:xs) = (x:ys) : groupBy eq zs
715 where (ys,zs) = span (eq x) xs
716
717 -- | The 'inits' function returns all initial segments of the argument,
718 -- shortest first. For example,
719 --
720 -- > inits "abc" == ["","a","ab","abc"]
721 --
722 inits :: [a] -> [[a]]
723 inits [] = [[]]
724 inits (x:xs) = [[]] ++ map (x:) (inits xs)
725
726 -- | The 'tails' function returns all final segments of the argument,
727 -- longest first. For example,
728 --
729 -- > tails "abc" == ["abc", "bc", "c",""]
730 --
731 tails :: [a] -> [[a]]
732 tails [] = [[]]
733 tails xxs@(_:xs) = xxs : tails xs
734
735
736 -- | The 'subsequences' function returns the list of all subsequences of the argument.
737 --
738 -- > subsequences "abc" == ["","a","b","ab","c","ac","bc","abc"]
739 subsequences :: [a] -> [[a]]
740 subsequences xs = [] : nonEmptySubsequences xs
741
742 -- | The 'nonEmptySubsequences' function returns the list of all subsequences of the argument,
743 -- except for the empty list.
744 --
745 -- > nonEmptySubsequences "abc" == ["a","b","ab","c","ac","bc","abc"]
746 nonEmptySubsequences :: [a] -> [[a]]
747 nonEmptySubsequences [] = []
748 nonEmptySubsequences (x:xs) = [x] : foldr f [] (nonEmptySubsequences xs)
749 where f ys r = ys : (x : ys) : r
750
751
752 -- | The 'permutations' function returns the list of all permutations of the argument.
753 --
754 -- > permutations "abc" == ["abc","bac","cba","bca","cab","acb"]
755 permutations :: [a] -> [[a]]
756 permutations xs0 = xs0 : perms xs0 []
757 where
758 perms [] _ = []
759 perms (t:ts) is = foldr interleave (perms ts (t:is)) (permutations is)
760 where interleave xs r = let (_,zs) = interleave' id xs r in zs
761 interleave' _ [] r = (ts, r)
762 interleave' f (y:ys) r = let (us,zs) = interleave' (f . (y:)) ys r
763 in (y:us, f (t:y:us) : zs)
764
765
766 ------------------------------------------------------------------------------
767 -- Quick Sort algorithm taken from HBC's QSort library.
768
769 -- | The 'sort' function implements a stable sorting algorithm.
770 -- It is a special case of 'sortBy', which allows the programmer to supply
771 -- their own comparison function.
772 sort :: (Ord a) => [a] -> [a]
773
774 -- | The 'sortBy' function is the non-overloaded version of 'sort'.
775 sortBy :: (a -> a -> Ordering) -> [a] -> [a]
776
777 #ifdef USE_REPORT_PRELUDE
778 sort = sortBy compare
779 sortBy cmp = foldr (insertBy cmp) []
780 #else
781
782 sortBy cmp l = mergesort cmp l
783 sort l = mergesort compare l
784
785 {-
786 Quicksort replaced by mergesort, 14/5/2002.
787
788 From: Ian Lynagh <igloo@earth.li>
789
790 I am curious as to why the List.sort implementation in GHC is a
791 quicksort algorithm rather than an algorithm that guarantees n log n
792 time in the worst case? I have attached a mergesort implementation along
793 with a few scripts to time it's performance, the results of which are
794 shown below (* means it didn't finish successfully - in all cases this
795 was due to a stack overflow).
796
797 If I heap profile the random_list case with only 10000 then I see
798 random_list peaks at using about 2.5M of memory, whereas in the same
799 program using List.sort it uses only 100k.
800
801 Input style Input length Sort data Sort alg User time
802 stdin 10000 random_list sort 2.82
803 stdin 10000 random_list mergesort 2.96
804 stdin 10000 sorted sort 31.37
805 stdin 10000 sorted mergesort 1.90
806 stdin 10000 revsorted sort 31.21
807 stdin 10000 revsorted mergesort 1.88
808 stdin 100000 random_list sort *
809 stdin 100000 random_list mergesort *
810 stdin 100000 sorted sort *
811 stdin 100000 sorted mergesort *
812 stdin 100000 revsorted sort *
813 stdin 100000 revsorted mergesort *
814 func 10000 random_list sort 0.31
815 func 10000 random_list mergesort 0.91
816 func 10000 sorted sort 19.09
817 func 10000 sorted mergesort 0.15
818 func 10000 revsorted sort 19.17
819 func 10000 revsorted mergesort 0.16
820 func 100000 random_list sort 3.85
821 func 100000 random_list mergesort *
822 func 100000 sorted sort 5831.47
823 func 100000 sorted mergesort 2.23
824 func 100000 revsorted sort 5872.34
825 func 100000 revsorted mergesort 2.24
826 -}
827
828 mergesort :: (a -> a -> Ordering) -> [a] -> [a]
829 mergesort cmp = mergesort' cmp . map wrap
830
831 mergesort' :: (a -> a -> Ordering) -> [[a]] -> [a]
832 mergesort' _ [] = []
833 mergesort' _ [xs] = xs
834 mergesort' cmp xss = mergesort' cmp (merge_pairs cmp xss)
835
836 merge_pairs :: (a -> a -> Ordering) -> [[a]] -> [[a]]
837 merge_pairs _ [] = []
838 merge_pairs _ [xs] = [xs]
839 merge_pairs cmp (xs:ys:xss) = merge cmp xs ys : merge_pairs cmp xss
840
841 merge :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
842 merge _ [] ys = ys
843 merge _ xs [] = xs
844 merge cmp (x:xs) (y:ys)
845 = case x `cmp` y of
846 GT -> y : merge cmp (x:xs) ys
847 _ -> x : merge cmp xs (y:ys)
848
849 wrap :: a -> [a]
850 wrap x = [x]
851
852 {-
853 OLD: qsort version
854
855 -- qsort is stable and does not concatenate.
856 qsort :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
857 qsort _ [] r = r
858 qsort _ [x] r = x:r
859 qsort cmp (x:xs) r = qpart cmp x xs [] [] r
860
861 -- qpart partitions and sorts the sublists
862 qpart :: (a -> a -> Ordering) -> a -> [a] -> [a] -> [a] -> [a] -> [a]
863 qpart cmp x [] rlt rge r =
864 -- rlt and rge are in reverse order and must be sorted with an
865 -- anti-stable sorting
866 rqsort cmp rlt (x:rqsort cmp rge r)
867 qpart cmp x (y:ys) rlt rge r =
868 case cmp x y of
869 GT -> qpart cmp x ys (y:rlt) rge r
870 _ -> qpart cmp x ys rlt (y:rge) r
871
872 -- rqsort is as qsort but anti-stable, i.e. reverses equal elements
873 rqsort :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
874 rqsort _ [] r = r
875 rqsort _ [x] r = x:r
876 rqsort cmp (x:xs) r = rqpart cmp x xs [] [] r
877
878 rqpart :: (a -> a -> Ordering) -> a -> [a] -> [a] -> [a] -> [a] -> [a]
879 rqpart cmp x [] rle rgt r =
880 qsort cmp rle (x:qsort cmp rgt r)
881 rqpart cmp x (y:ys) rle rgt r =
882 case cmp y x of
883 GT -> rqpart cmp x ys rle (y:rgt) r
884 _ -> rqpart cmp x ys (y:rle) rgt r
885 -}
886
887 #endif /* USE_REPORT_PRELUDE */
888
889 -- | The 'unfoldr' function is a \`dual\' to 'foldr': while 'foldr'
890 -- reduces a list to a summary value, 'unfoldr' builds a list from
891 -- a seed value. The function takes the element and returns 'Nothing'
892 -- if it is done producing the list or returns 'Just' @(a,b)@, in which
893 -- case, @a@ is a prepended to the list and @b@ is used as the next
894 -- element in a recursive call. For example,
895 --
896 -- > iterate f == unfoldr (\x -> Just (x, f x))
897 --
898 -- In some cases, 'unfoldr' can undo a 'foldr' operation:
899 --
900 -- > unfoldr f' (foldr f z xs) == xs
901 --
902 -- if the following holds:
903 --
904 -- > f' (f x y) = Just (x,y)
905 -- > f' z = Nothing
906 --
907 -- A simple use of unfoldr:
908 --
909 -- > unfoldr (\b -> if b == 0 then Nothing else Just (b, b-1)) 10
910 -- > [10,9,8,7,6,5,4,3,2,1]
911 --
912 unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
913 unfoldr f b =
914 case f b of
915 Just (a,new_b) -> a : unfoldr f new_b
916 Nothing -> []
917
918 -- -----------------------------------------------------------------------------
919
920 -- | A strict version of 'foldl'.
921 foldl' :: (a -> b -> a) -> a -> [b] -> a
922 #ifdef __GLASGOW_HASKELL__
923 foldl' f z0 xs0 = lgo z0 xs0
924 where lgo z [] = z
925 lgo z (x:xs) = let z' = f z x in z' `seq` lgo z' xs
926 #else
927 foldl' f a [] = a
928 foldl' f a (x:xs) = let a' = f a x in a' `seq` foldl' f a' xs
929 #endif
930
931 #ifdef __GLASGOW_HASKELL__
932 -- | 'foldl1' is a variant of 'foldl' that has no starting value argument,
933 -- and thus must be applied to non-empty lists.
934 foldl1 :: (a -> a -> a) -> [a] -> a
935 foldl1 f (x:xs) = foldl f x xs
936 foldl1 _ [] = errorEmptyList "foldl1"
937 #endif /* __GLASGOW_HASKELL__ */
938
939 -- | A strict version of 'foldl1'
940 foldl1' :: (a -> a -> a) -> [a] -> a
941 foldl1' f (x:xs) = foldl' f x xs
942 foldl1' _ [] = errorEmptyList "foldl1'"
943
944 #ifdef __GLASGOW_HASKELL__
945 -- -----------------------------------------------------------------------------
946 -- List sum and product
947
948 {-# SPECIALISE sum :: [Int] -> Int #-}
949 {-# SPECIALISE sum :: [Integer] -> Integer #-}
950 {-# SPECIALISE product :: [Int] -> Int #-}
951 {-# SPECIALISE product :: [Integer] -> Integer #-}
952 -- | The 'sum' function computes the sum of a finite list of numbers.
953 sum :: (Num a) => [a] -> a
954 -- | The 'product' function computes the product of a finite list of numbers.
955 product :: (Num a) => [a] -> a
956 #ifdef USE_REPORT_PRELUDE
957 sum = foldl (+) 0
958 product = foldl (*) 1
959 #else
960 sum l = sum' l 0
961 where
962 sum' [] a = a
963 sum' (x:xs) a = sum' xs (a+x)
964 product l = prod l 1
965 where
966 prod [] a = a
967 prod (x:xs) a = prod xs (a*x)
968 #endif
969
970 -- -----------------------------------------------------------------------------
971 -- Functions on strings
972
973 -- | 'lines' breaks a string up into a list of strings at newline
974 -- characters. The resulting strings do not contain newlines.
975 lines :: String -> [String]
976 lines "" = []
977 lines s = let (l, s') = break (== '\n') s
978 in l : case s' of
979 [] -> []
980 (_:s'') -> lines s''
981
982 -- | 'unlines' is an inverse operation to 'lines'.
983 -- It joins lines, after appending a terminating newline to each.
984 unlines :: [String] -> String
985 #ifdef USE_REPORT_PRELUDE
986 unlines = concatMap (++ "\n")
987 #else
988 -- HBC version (stolen)
989 -- here's a more efficient version
990 unlines [] = []
991 unlines (l:ls) = l ++ '\n' : unlines ls
992 #endif
993
994 -- | 'words' breaks a string up into a list of words, which were delimited
995 -- by white space.
996 words :: String -> [String]
997 words s = case dropWhile {-partain:Char.-}isSpace s of
998 "" -> []
999 s' -> w : words s''
1000 where (w, s'') =
1001 break {-partain:Char.-}isSpace s'
1002
1003 -- | 'unwords' is an inverse operation to 'words'.
1004 -- It joins words with separating spaces.
1005 unwords :: [String] -> String
1006 #ifdef USE_REPORT_PRELUDE
1007 unwords [] = ""
1008 unwords ws = foldr1 (\w s -> w ++ ' ':s) ws
1009 #else
1010 -- HBC version (stolen)
1011 -- here's a more efficient version
1012 unwords [] = ""
1013 unwords [w] = w
1014 unwords (w:ws) = w ++ ' ' : unwords ws
1015 #endif
1016
1017 #else /* !__GLASGOW_HASKELL__ */
1018
1019 errorEmptyList :: String -> a
1020 errorEmptyList fun =
1021 error ("Prelude." ++ fun ++ ": empty list")
1022
1023 #endif /* !__GLASGOW_HASKELL__ */