[project @ 2001-06-28 14:15:04 by simonmar]
[packages/pretty.git] / Data / List.hs
1 {-# OPTIONS -fno-implicit-prelude #-}
2 -----------------------------------------------------------------------------
3 --
4 -- Module : Data.List
5 -- Copyright : (c) The University of Glasgow 2001
6 -- License : BSD-style (see the file libraries/core/LICENSE)
7 --
8 -- Maintainer : libraries@haskell.org
9 -- Stability : provisional
10 -- Portability : portable
11 --
12 -- $Id: List.hs,v 1.1 2001/06/28 14:15:02 simonmar Exp $
13 --
14 -- Operations on lists.
15 --
16 -----------------------------------------------------------------------------
17
18 module Data.List
19 (
20 [] (..),
21
22 , elemIndex -- :: (Eq a) => a -> [a] -> Maybe Int
23 , elemIndices -- :: (Eq a) => a -> [a] -> [Int]
24
25 , find -- :: (a -> Bool) -> [a] -> Maybe a
26 , findIndex -- :: (a -> Bool) -> [a] -> Maybe Int
27 , findIndices -- :: (a -> Bool) -> [a] -> [Int]
28
29 , nub -- :: (Eq a) => [a] -> [a]
30 , nubBy -- :: (a -> a -> Bool) -> [a] -> [a]
31
32 , delete -- :: (Eq a) => a -> [a] -> [a]
33 , deleteBy -- :: (a -> a -> Bool) -> a -> [a] -> [a]
34 , (\\) -- :: (Eq a) => [a] -> [a] -> [a]
35 , deleteFirstsBy -- :: (a -> a -> Bool) -> [a] -> [a] -> [a]
36
37 , union -- :: (Eq a) => [a] -> [a] -> [a]
38 , unionBy -- :: (a -> a -> Bool) -> [a] -> [a] -> [a]
39
40 , intersect -- :: (Eq a) => [a] -> [a] -> [a]
41 , intersectBy -- :: (a -> a -> Bool) -> [a] -> [a] -> [a]
42
43 , intersperse -- :: a -> [a] -> [a]
44 , transpose -- :: [[a]] -> [[a]]
45 , partition -- :: (a -> Bool) -> [a] -> ([a], [a])
46
47 , group -- :: Eq a => [a] -> [[a]]
48 , groupBy -- :: (a -> a -> Bool) -> [a] -> [[a]]
49
50 , inits -- :: [a] -> [[a]]
51 , tails -- :: [a] -> [[a]]
52
53 , isPrefixOf -- :: (Eq a) => [a] -> [a] -> Bool
54 , isSuffixOf -- :: (Eq a) => [a] -> [a] -> Bool
55
56 , mapAccumL -- :: (a -> b -> (a,c)) -> a -> [b] -> (a,[c])
57 , mapAccumR -- :: (a -> b -> (a,c)) -> a -> [b] -> (a,[c])
58
59 , sort -- :: (Ord a) => [a] -> [a]
60 , sortBy -- :: (a -> a -> Ordering) -> [a] -> [a]
61
62 , insert -- :: (Ord a) => a -> [a] -> [a]
63 , insertBy -- :: (a -> a -> Ordering) -> a -> [a] -> [a]
64
65 , maximumBy -- :: (a -> a -> Ordering) -> [a] -> a
66 , minimumBy -- :: (a -> a -> Ordering) -> [a] -> a
67
68 , genericLength -- :: (Integral a) => [b] -> a
69 , genericTake -- :: (Integral a) => a -> [b] -> [b]
70 , genericDrop -- :: (Integral a) => a -> [b] -> [b]
71 , genericSplitAt -- :: (Integral a) => a -> [b] -> ([b], [b])
72 , genericIndex -- :: (Integral a) => [b] -> a -> b
73 , genericReplicate -- :: (Integral a) => a -> b -> [b]
74
75 , unfoldr -- :: (b -> Maybe (a, b)) -> b -> [a]
76
77 , zip4, zip5, zip6, zip7
78 , zipWith4, zipWith5, zipWith6, zipWith7
79 , unzip4, unzip5, unzip6, unzip7
80
81 , map -- :: ( a -> b ) -> [a] -> [b]
82 , (++) -- :: [a] -> [a] -> [a]
83 , concat -- :: [[a]] -> [a]
84 , filter -- :: (a -> Bool) -> [a] -> [a]
85 , head -- :: [a] -> a
86 , last -- :: [a] -> a
87 , tail -- :: [a] -> [a]
88 , init -- :: [a] -> [a]
89 , null -- :: [a] -> Bool
90 , length -- :: [a] -> Int
91 , (!!) -- :: [a] -> Int -> a
92 , foldl -- :: (a -> b -> a) -> a -> [b] -> a
93 , foldl1 -- :: (a -> a -> a) -> [a] -> a
94 , scanl -- :: (a -> b -> a) -> a -> [b] -> [a]
95 , scanl1 -- :: (a -> a -> a) -> [a] -> [a]
96 , foldr -- :: (a -> b -> b) -> b -> [a] -> b
97 , foldr1 -- :: (a -> a -> a) -> [a] -> a
98 , scanr -- :: (a -> b -> b) -> b -> [a] -> [b]
99 , scanr1 -- :: (a -> a -> a) -> [a] -> [a]
100 , iterate -- :: (a -> a) -> a -> [a]
101 , repeat -- :: a -> [a]
102 , replicate -- :: Int -> a -> [a]
103 , cycle -- :: [a] -> [a]
104 , take -- :: Int -> [a] -> [a]
105 , drop -- :: Int -> [a] -> [a]
106 , splitAt -- :: Int -> [a] -> ([a], [a])
107 , takeWhile -- :: (a -> Bool) -> [a] -> [a]
108 , dropWhile -- :: (a -> Bool) -> [a] -> [a]
109 , span -- :: (a -> Bool) -> [a] -> ([a], [a])
110 , break -- :: (a -> Bool) -> [a] -> ([a], [a])
111
112 , lines -- :: String -> [String]
113 , words -- :: String -> [String]
114 , unlines -- :: [String] -> String
115 , unwords -- :: [String] -> String
116 , reverse -- :: [a] -> [a]
117 , and -- :: [Bool] -> Bool
118 , or -- :: [Bool] -> Bool
119 , any -- :: (a -> Bool) -> [a] -> Bool
120 , all -- :: (a -> Bool) -> [a] -> Bool
121 , elem -- :: a -> [a] -> Bool
122 , notElem -- :: a -> [a] -> Bool
123 , lookup -- :: (Eq a) => a -> [(a,b)] -> Maybe b
124 , sum -- :: (Num a) => [a] -> a
125 , product -- :: (Num a) => [a] -> a
126 , maximum -- :: (Ord a) => [a] -> a
127 , minimum -- :: (Ord a) => [a] -> a
128 , concatMap -- :: (a -> [b]) -> [a] -> [b]
129 , zip -- :: [a] -> [b] -> [(a,b)]
130 , zip3
131 , zipWith -- :: (a -> b -> c) -> [a] -> [b] -> [c]
132 , zipWith3
133 , unzip -- :: [(a,b)] -> ([a],[b])
134 , unzip3
135
136 ) where
137
138 import Data.Maybe
139
140 #ifdef __GLASGOW_HASKELL__
141 import GHC.Num
142 import GHC.Real
143 import GHC.List
144 import GHC.Show ( lines, words, unlines, unwords )
145 import GHC.Base
146 #endif
147
148 infix 5 \\
149
150 -- -----------------------------------------------------------------------------
151 -- List functions
152
153 elemIndex :: Eq a => a -> [a] -> Maybe Int
154 elemIndex x = findIndex (x==)
155
156 elemIndices :: Eq a => a -> [a] -> [Int]
157 elemIndices x = findIndices (x==)
158
159 find :: (a -> Bool) -> [a] -> Maybe a
160 find p = listToMaybe . filter p
161
162 findIndex :: (a -> Bool) -> [a] -> Maybe Int
163 findIndex p = listToMaybe . findIndices p
164
165 findIndices :: (a -> Bool) -> [a] -> [Int]
166
167 #ifdef USE_REPORT_PRELUDE
168 findIndices p xs = [ i | (x,i) <- zip xs [0..], p x]
169 #else
170 #ifdef __HUGS__
171 findIndices p xs = [ i | (x,i) <- zip xs [0..], p x]
172 #else
173 -- Efficient definition
174 findIndices p ls = loop 0# ls
175 where
176 loop _ [] = []
177 loop n (x:xs) | p x = I# n : loop (n +# 1#) xs
178 | otherwise = loop (n +# 1#) xs
179 #endif /* __HUGS__ */
180 #endif /* USE_REPORT_PRELUDE */
181
182 isPrefixOf :: (Eq a) => [a] -> [a] -> Bool
183 isPrefixOf [] _ = True
184 isPrefixOf _ [] = False
185 isPrefixOf (x:xs) (y:ys)= x == y && isPrefixOf xs ys
186
187 isSuffixOf :: (Eq a) => [a] -> [a] -> Bool
188 isSuffixOf x y = reverse x `isPrefixOf` reverse y
189
190 -- nub (meaning "essence") remove duplicate elements from its list argument.
191 nub :: (Eq a) => [a] -> [a]
192 #ifdef USE_REPORT_PRELUDE
193 nub = nubBy (==)
194 #else
195 -- stolen from HBC
196 nub l = nub' l [] -- '
197 where
198 nub' [] _ = [] -- '
199 nub' (x:xs) ls -- '
200 | x `elem` ls = nub' xs ls -- '
201 | otherwise = x : nub' xs (x:ls) -- '
202 #endif
203
204 nubBy :: (a -> a -> Bool) -> [a] -> [a]
205 #ifdef USE_REPORT_PRELUDE
206 nubBy eq [] = []
207 nubBy eq (x:xs) = x : nubBy eq (filter (\ y -> not (eq x y)) xs)
208 #else
209 nubBy eq l = nubBy' l []
210 where
211 nubBy' [] _ = []
212 nubBy' (y:ys) xs
213 | elem_by eq y xs = nubBy' ys xs
214 | otherwise = y : nubBy' ys (y:xs)
215
216 -- Not exported:
217 -- Note that we keep the call to `eq` with arguments in the
218 -- same order as in the reference implementation
219 -- 'xs' is the list of things we've seen so far,
220 -- 'y' is the potential new element
221 elem_by :: (a -> a -> Bool) -> a -> [a] -> Bool
222 elem_by _ _ [] = False
223 elem_by eq y (x:xs) = x `eq` y || elem_by eq y xs
224 #endif
225
226
227 -- delete x removes the first occurrence of x from its list argument.
228 delete :: (Eq a) => a -> [a] -> [a]
229 delete = deleteBy (==)
230
231 deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
232 deleteBy _ _ [] = []
233 deleteBy eq x (y:ys) = if x `eq` y then ys else y : deleteBy eq x ys
234
235 -- list difference (non-associative). In the result of xs \\ ys,
236 -- the first occurrence of each element of ys in turn (if any)
237 -- has been removed from xs. Thus, (xs ++ ys) \\ xs == ys.
238 (\\) :: (Eq a) => [a] -> [a] -> [a]
239 (\\) = foldl (flip delete)
240
241 -- List union, remove the elements of first list from second.
242 union :: (Eq a) => [a] -> [a] -> [a]
243 union = unionBy (==)
244
245 unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
246 unionBy eq xs ys = xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs
247
248 intersect :: (Eq a) => [a] -> [a] -> [a]
249 intersect = intersectBy (==)
250
251 intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
252 intersectBy eq xs ys = [x | x <- xs, any (eq x) ys]
253
254 -- intersperse sep inserts sep between the elements of its list argument.
255 -- e.g. intersperse ',' "abcde" == "a,b,c,d,e"
256 intersperse :: a -> [a] -> [a]
257 intersperse _ [] = []
258 intersperse _ [x] = [x]
259 intersperse sep (x:xs) = x : sep : intersperse sep xs
260
261 transpose :: [[a]] -> [[a]]
262 transpose [] = []
263 transpose ([] : xss) = transpose xss
264 transpose ((x:xs) : xss) = (x : [h | (h:t) <- xss]) : transpose (xs : [ t | (h:t) <- xss])
265
266
267 -- partition takes a predicate and a list and returns a pair of lists:
268 -- those elements of the argument list that do and do not satisfy the
269 -- predicate, respectively; i,e,,
270 -- partition p xs == (filter p xs, filter (not . p) xs).
271 partition :: (a -> Bool) -> [a] -> ([a],[a])
272 {-# INLINE partition #-}
273 partition p xs = foldr (select p) ([],[]) xs
274
275 select p x (ts,fs) | p x = (x:ts,fs)
276 | otherwise = (ts, x:fs)
277
278 -- @mapAccumL@ behaves like a combination
279 -- of @map@ and @foldl@;
280 -- it applies a function to each element of a list, passing an accumulating
281 -- parameter from left to right, and returning a final value of this
282 -- accumulator together with the new list.
283
284 mapAccumL :: (acc -> x -> (acc, y)) -- Function of elt of input list
285 -- and accumulator, returning new
286 -- accumulator and elt of result list
287 -> acc -- Initial accumulator
288 -> [x] -- Input list
289 -> (acc, [y]) -- Final accumulator and result list
290 mapAccumL _ s [] = (s, [])
291 mapAccumL f s (x:xs) = (s'',y:ys)
292 where (s', y ) = f s x
293 (s'',ys) = mapAccumL f s' xs
294
295 -- @mapAccumR@ does the same, but working from right to left instead.
296 -- Its type is the same as @mapAccumL@, though.
297
298 mapAccumR :: (acc -> x -> (acc, y)) -- Function of elt of input list
299 -- and accumulator, returning new
300 -- accumulator and elt of result list
301 -> acc -- Initial accumulator
302 -> [x] -- Input list
303 -> (acc, [y]) -- Final accumulator and result list
304 mapAccumR _ s [] = (s, [])
305 mapAccumR f s (x:xs) = (s'', y:ys)
306 where (s'',y ) = f s' x
307 (s', ys) = mapAccumR f s xs
308
309
310 insert :: Ord a => a -> [a] -> [a]
311 insert e ls = insertBy (compare) e ls
312
313 insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a]
314 insertBy _ x [] = [x]
315 insertBy cmp x ys@(y:ys')
316 = case cmp x y of
317 GT -> y : insertBy cmp x ys'
318 _ -> x : ys
319
320 maximumBy :: (a -> a -> a) -> [a] -> a
321 maximumBy _ [] = error "List.maximumBy: empty list"
322 maximumBy max xs = foldl1 max xs
323
324 minimumBy :: (a -> a -> a) -> [a] -> a
325 minimumBy _ [] = error "List.minimumBy: empty list"
326 minimumBy min xs = foldl1 min xs
327
328 genericLength :: (Num i) => [b] -> i
329 genericLength [] = 0
330 genericLength (_:l) = 1 + genericLength l
331
332 genericTake :: (Integral i) => i -> [a] -> [a]
333 genericTake 0 _ = []
334 genericTake _ [] = []
335 genericTake n (x:xs) | n > 0 = x : genericTake (n-1) xs
336 genericTake _ _ = error "List.genericTake: negative argument"
337
338 genericDrop :: (Integral i) => i -> [a] -> [a]
339 genericDrop 0 xs = xs
340 genericDrop _ [] = []
341 genericDrop n (_:xs) | n > 0 = genericDrop (n-1) xs
342 genericDrop _ _ = error "List.genericDrop: negative argument"
343
344 genericSplitAt :: (Integral i) => i -> [b] -> ([b],[b])
345 genericSplitAt 0 xs = ([],xs)
346 genericSplitAt _ [] = ([],[])
347 genericSplitAt n (x:xs) | n > 0 = (x:xs',xs'') where
348 (xs',xs'') = genericSplitAt (n-1) xs
349 genericSplitAt _ _ = error "List.genericSplitAt: negative argument"
350
351
352 genericIndex :: (Integral a) => [b] -> a -> b
353 genericIndex (x:_) 0 = x
354 genericIndex (_:xs) n
355 | n > 0 = genericIndex xs (n-1)
356 | otherwise = error "List.genericIndex: negative argument."
357 genericIndex _ _ = error "List.genericIndex: index too large."
358
359 genericReplicate :: (Integral i) => i -> a -> [a]
360 genericReplicate n x = genericTake n (repeat x)
361
362
363 zip4 :: [a] -> [b] -> [c] -> [d] -> [(a,b,c,d)]
364 zip4 = zipWith4 (,,,)
365
366 zip5 :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a,b,c,d,e)]
367 zip5 = zipWith5 (,,,,)
368
369 zip6 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] ->
370 [(a,b,c,d,e,f)]
371 zip6 = zipWith6 (,,,,,)
372
373 zip7 :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] ->
374 [g] -> [(a,b,c,d,e,f,g)]
375 zip7 = zipWith7 (,,,,,,)
376
377 zipWith4 :: (a->b->c->d->e) -> [a]->[b]->[c]->[d]->[e]
378 zipWith4 z (a:as) (b:bs) (c:cs) (d:ds)
379 = z a b c d : zipWith4 z as bs cs ds
380 zipWith4 _ _ _ _ _ = []
381
382 zipWith5 :: (a->b->c->d->e->f) ->
383 [a]->[b]->[c]->[d]->[e]->[f]
384 zipWith5 z (a:as) (b:bs) (c:cs) (d:ds) (e:es)
385 = z a b c d e : zipWith5 z as bs cs ds es
386 zipWith5 _ _ _ _ _ _ = []
387
388 zipWith6 :: (a->b->c->d->e->f->g) ->
389 [a]->[b]->[c]->[d]->[e]->[f]->[g]
390 zipWith6 z (a:as) (b:bs) (c:cs) (d:ds) (e:es) (f:fs)
391 = z a b c d e f : zipWith6 z as bs cs ds es fs
392 zipWith6 _ _ _ _ _ _ _ = []
393
394 zipWith7 :: (a->b->c->d->e->f->g->h) ->
395 [a]->[b]->[c]->[d]->[e]->[f]->[g]->[h]
396 zipWith7 z (a:as) (b:bs) (c:cs) (d:ds) (e:es) (f:fs) (g:gs)
397 = z a b c d e f g : zipWith7 z as bs cs ds es fs gs
398 zipWith7 _ _ _ _ _ _ _ _ = []
399
400 unzip4 :: [(a,b,c,d)] -> ([a],[b],[c],[d])
401 unzip4 = foldr (\(a,b,c,d) ~(as,bs,cs,ds) ->
402 (a:as,b:bs,c:cs,d:ds))
403 ([],[],[],[])
404
405 unzip5 :: [(a,b,c,d,e)] -> ([a],[b],[c],[d],[e])
406 unzip5 = foldr (\(a,b,c,d,e) ~(as,bs,cs,ds,es) ->
407 (a:as,b:bs,c:cs,d:ds,e:es))
408 ([],[],[],[],[])
409
410 unzip6 :: [(a,b,c,d,e,f)] -> ([a],[b],[c],[d],[e],[f])
411 unzip6 = foldr (\(a,b,c,d,e,f) ~(as,bs,cs,ds,es,fs) ->
412 (a:as,b:bs,c:cs,d:ds,e:es,f:fs))
413 ([],[],[],[],[],[])
414
415 unzip7 :: [(a,b,c,d,e,f,g)] -> ([a],[b],[c],[d],[e],[f],[g])
416 unzip7 = foldr (\(a,b,c,d,e,f,g) ~(as,bs,cs,ds,es,fs,gs) ->
417 (a:as,b:bs,c:cs,d:ds,e:es,f:fs,g:gs))
418 ([],[],[],[],[],[],[])
419
420
421
422 deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
423 deleteFirstsBy eq = foldl (flip (deleteBy eq))
424
425
426 -- group splits its list argument into a list of lists of equal, adjacent
427 -- elements. e.g.,
428 -- group "Mississippi" == ["M","i","ss","i","ss","i","pp","i"]
429 group :: (Eq a) => [a] -> [[a]]
430 group = groupBy (==)
431
432 groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
433 groupBy _ [] = []
434 groupBy eq (x:xs) = (x:ys) : groupBy eq zs
435 where (ys,zs) = span (eq x) xs
436
437 -- inits xs returns the list of initial segments of xs, shortest first.
438 -- e.g., inits "abc" == ["","a","ab","abc"]
439 inits :: [a] -> [[a]]
440 inits [] = [[]]
441 inits (x:xs) = [[]] ++ map (x:) (inits xs)
442
443 -- tails xs returns the list of all final segments of xs, longest first.
444 -- e.g., tails "abc" == ["abc", "bc", "c",""]
445 tails :: [a] -> [[a]]
446 tails [] = [[]]
447 tails xxs@(_:xs) = xxs : tails xs
448
449
450 ------------------------------------------------------------------------------
451 -- Quick Sort algorithm taken from HBC's QSort library.
452
453 sort :: (Ord a) => [a] -> [a]
454 sortBy :: (a -> a -> Ordering) -> [a] -> [a]
455
456 #ifdef USE_REPORT_PRELUDE
457 sort = sortBy compare
458 sortBy cmp = foldr (insertBy cmp) []
459 #else
460
461 sortBy cmp l = qsort cmp l []
462 sort l = qsort compare l []
463
464 -- rest is not exported:
465
466 -- qsort is stable and does not concatenate.
467 qsort :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
468 qsort _ [] r = r
469 qsort _ [x] r = x:r
470 qsort cmp (x:xs) r = qpart cmp x xs [] [] r
471
472 -- qpart partitions and sorts the sublists
473 qpart :: (a -> a -> Ordering) -> a -> [a] -> [a] -> [a] -> [a] -> [a]
474 qpart cmp x [] rlt rge r =
475 -- rlt and rge are in reverse order and must be sorted with an
476 -- anti-stable sorting
477 rqsort cmp rlt (x:rqsort cmp rge r)
478 qpart cmp x (y:ys) rlt rge r =
479 case cmp x y of
480 GT -> qpart cmp x ys (y:rlt) rge r
481 _ -> qpart cmp x ys rlt (y:rge) r
482
483 -- rqsort is as qsort but anti-stable, i.e. reverses equal elements
484 rqsort :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
485 rqsort _ [] r = r
486 rqsort _ [x] r = x:r
487 rqsort cmp (x:xs) r = rqpart cmp x xs [] [] r
488
489 rqpart :: (a -> a -> Ordering) -> a -> [a] -> [a] -> [a] -> [a] -> [a]
490 rqpart cmp x [] rle rgt r =
491 qsort cmp rle (x:qsort cmp rgt r)
492 rqpart cmp x (y:ys) rle rgt r =
493 case cmp y x of
494 GT -> rqpart cmp x ys rle (y:rgt) r
495 _ -> rqpart cmp x ys (y:rle) rgt r
496
497 #endif /* USE_REPORT_PRELUDE */
498
499 {-
500 \begin{verbatim}
501 unfoldr f' (foldr f z xs) == (z,xs)
502
503 if the following holds:
504
505 f' (f x y) = Just (x,y)
506 f' z = Nothing
507 \end{verbatim}
508 -}
509
510 unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
511 unfoldr f b =
512 case f b of
513 Just (a,new_b) -> a : unfoldr f new_b
514 Nothing -> []
515
516 -- -----------------------------------------------------------------------------
517 -- List sum and product
518
519 -- sum and product compute the sum or product of a finite list of numbers.
520 {-# SPECIALISE sum :: [Int] -> Int #-}
521 {-# SPECIALISE sum :: [Integer] -> Integer #-}
522 {-# SPECIALISE product :: [Int] -> Int #-}
523 {-# SPECIALISE product :: [Integer] -> Integer #-}
524 sum, product :: (Num a) => [a] -> a
525 #ifdef USE_REPORT_PRELUDE
526 sum = foldl (+) 0
527 product = foldl (*) 1
528 #else
529 sum l = sum' l 0
530 where
531 sum' [] a = a
532 sum' (x:xs) a = sum' xs (a+x)
533 product l = prod l 1
534 where
535 prod [] a = a
536 prod (x:xs) a = prod xs (a*x)
537 #endif