1 % ------------------------------------------------------------------------------
2 % $Id: List.lhs,v 1.6 2002/02/05 17:32:26 simonmar Exp $
4 % (c) The University of Glasgow, 1994-2000
7 \section[GHC.List]{Module @GHC.List@}
9 The List data type and its operations
12 {-# OPTIONS -fno-implicit-prelude #-}
17 map, (++), filter, concat,
18 head, last, tail, init, null, length, (!!),
19 foldl, foldl1, scanl, scanl1, foldr, foldr1, scanr, scanr1,
20 iterate, repeat, replicate, cycle,
21 take, drop, splitAt, takeWhile, dropWhile, span, break,
23 any, all, elem, notElem, lookup,
24 maximum, minimum, concatMap,
25 zip, zip3, zipWith, zipWith3, unzip, unzip3,
26 #ifdef USE_REPORT_PRELUDE
30 -- non-standard, but hidden when creating the Prelude
38 import {-# SOURCE #-} GHC.Err ( error )
44 infix 4 `elem`, `notElem`
47 %*********************************************************
49 \subsection{List-manipulation functions}
51 %*********************************************************
54 -- head and tail extract the first element and remaining elements,
55 -- respectively, of a list, which must be non-empty. last and init
56 -- are the dual functions working from the end of a finite list,
57 -- rather than the beginning.
63 badHead = errorEmptyList "head"
65 -- This rule is useful in cases like
66 -- head [y | (x,y) <- ps, x==t]
68 "head/build" forall (g::forall b.(Bool->b->b)->b->b) .
69 head (build g) = g (\x _ -> x) badHead
70 "head/augment" forall xs (g::forall b. (a->b->b) -> b -> b) .
71 head (augment g xs) = g (\x _ -> x) (head xs)
76 tail [] = errorEmptyList "tail"
79 #ifdef USE_REPORT_PRELUDE
82 last [] = errorEmptyList "last"
84 -- eliminate repeated cases
85 last [] = errorEmptyList "last"
86 last (x:xs) = last' x xs
88 last' _ (y:ys) = last' y ys
92 #ifdef USE_REPORT_PRELUDE
94 init (x:xs) = x : init xs
95 init [] = errorEmptyList "init"
97 -- eliminate repeated cases
98 init [] = errorEmptyList "init"
99 init (x:xs) = init' x xs
100 where init' _ [] = []
101 init' y (z:zs) = y : init' z zs
108 -- length returns the length of a finite list as an Int; it is an instance
109 -- of the more general genericLength, the result type of which may be
110 -- any kind of number.
114 len :: [a] -> Int# -> Int
116 len (_:xs) a# = len xs (a# +# 1#)
118 -- filter, applied to a predicate and a list, returns the list of those
119 -- elements that satisfy the predicate; i.e.,
120 -- filter p xs = [ x | x <- xs, p x]
121 filter :: (a -> Bool) -> [a] -> [a]
124 | pred x = x : filter pred xs
125 | otherwise = filter pred xs
127 {-# NOINLINE [0] filterFB #-}
128 filterFB c p x r | p x = x `c` r
132 "filter" [~1] forall p xs. filter p xs = build (\c n -> foldr (filterFB c p) n xs)
133 "filterList" [1] forall p. foldr (filterFB (:) p) [] = filter p
134 "filterFB" forall c p q. filterFB (filterFB c p) q = filterFB c (\x -> q x && p x)
137 -- Note the filterFB rule, which has p and q the "wrong way round" in the RHS.
138 -- filterFB (filterFB c p) q a b
139 -- = if q a then filterFB c p a b else b
140 -- = if q a then (if p a then c a b else b) else b
141 -- = if q a && p a then c a b else b
142 -- = filterFB c (\x -> q x && p x) a b
143 -- I originally wrote (\x -> p x && q x), which is wrong, and actually
144 -- gave rise to a live bug report. SLPJ.
147 -- foldl, applied to a binary operator, a starting value (typically the
148 -- left-identity of the operator), and a list, reduces the list using
149 -- the binary operator, from left to right:
150 -- foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
151 -- foldl1 is a variant that has no starting value argument, and thus must
152 -- be applied to non-empty lists. scanl is similar to foldl, but returns
153 -- a list of successive reduced values from the left:
154 -- scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]
155 -- Note that last (scanl f z xs) == foldl f z xs.
156 -- scanl1 is similar, again without the starting element:
157 -- scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
159 -- We write foldl as a non-recursive thing, so that it
160 -- can be inlined, and then (often) strictness-analysed,
161 -- and hence the classic space leak on foldl (+) 0 xs
163 foldl :: (a -> b -> a) -> a -> [b] -> a
164 foldl f z xs = lgo z xs
167 lgo z (x:xs) = lgo (f z x) xs
169 foldl1 :: (a -> a -> a) -> [a] -> a
170 foldl1 f (x:xs) = foldl f x xs
171 foldl1 _ [] = errorEmptyList "foldl1"
173 scanl :: (a -> b -> a) -> a -> [b] -> [a]
174 scanl f q ls = q : (case ls of
176 x:xs -> scanl f (f q x) xs)
178 scanl1 :: (a -> a -> a) -> [a] -> [a]
179 scanl1 f (x:xs) = scanl f x xs
182 -- foldr, foldr1, scanr, and scanr1 are the right-to-left duals of the
185 foldr1 :: (a -> a -> a) -> [a] -> a
187 foldr1 f (x:xs) = f x (foldr1 f xs)
188 foldr1 _ [] = errorEmptyList "foldr1"
190 scanr :: (a -> b -> b) -> b -> [a] -> [b]
192 scanr f q0 (x:xs) = f x q : qs
193 where qs@(q:_) = scanr f q0 xs
195 scanr1 :: (a -> a -> a) -> [a] -> [a]
198 scanr1 f (x:xs) = f x q : qs
199 where qs@(q:_) = scanr1 f xs
201 -- iterate f x returns an infinite list of repeated applications of f to x:
202 -- iterate f x == [x, f x, f (f x), ...]
203 iterate :: (a -> a) -> a -> [a]
204 iterate f x = x : iterate f (f x)
206 iterateFB c f x = x `c` iterateFB c f (f x)
210 "iterate" [~1] forall f x. iterate f x = build (\c _n -> iterateFB c f x)
211 "iterateFB" [1] iterateFB (:) = iterate
215 -- repeat x is an infinite list, with x the value of every element.
217 {-# INLINE [0] repeat #-}
218 -- The pragma just gives the rules more chance to fire
219 repeat x = xs where xs = x : xs
221 {-# INLINE [0] repeatFB #-} -- ditto
222 repeatFB c x = xs where xs = x `c` xs
226 "repeat" [~1] forall x. repeat x = build (\c _n -> repeatFB c x)
227 "repeatFB" [1] repeatFB (:) = repeat
230 -- replicate n x is a list of length n with x the value of every element
231 replicate :: Int -> a -> [a]
232 replicate n x = take n (repeat x)
234 -- cycle ties a finite list into a circular one, or equivalently,
235 -- the infinite repetition of the original list. It is the identity
236 -- on infinite lists.
239 cycle [] = error "Prelude.cycle: empty list"
240 cycle xs = xs' where xs' = xs ++ xs'
242 -- takeWhile, applied to a predicate p and a list xs, returns the longest
243 -- prefix (possibly empty) of xs of elements that satisfy p. dropWhile p xs
244 -- returns the remaining suffix. Span p xs is equivalent to
245 -- (takeWhile p xs, dropWhile p xs), while break p uses the negation of p.
247 takeWhile :: (a -> Bool) -> [a] -> [a]
250 | p x = x : takeWhile p xs
253 dropWhile :: (a -> Bool) -> [a] -> [a]
255 dropWhile p xs@(x:xs')
256 | p x = dropWhile p xs'
259 -- take n, applied to a list xs, returns the prefix of xs of length n,
260 -- or xs itself if n > length xs. drop n xs returns the suffix of xs
261 -- after the first n elements, or [] if n > length xs. splitAt n xs
262 -- is equivalent to (take n xs, drop n xs).
263 #ifdef USE_REPORT_PRELUDE
264 take :: Int -> [a] -> [a]
265 take n _ | n <= 0 = []
267 take n (x:xs) = x : take (n-1) xs
269 drop :: Int -> [a] -> [a]
270 drop n xs | n <= 0 = xs
272 drop n (_:xs) = drop (n-1) xs
274 splitAt :: Int -> [a] -> ([a],[a])
275 splitAt n xs = (take n xs, drop n xs)
277 #else /* hack away */
278 take :: Int -> [b] -> [b]
279 take (I# n#) xs = takeUInt n# xs
281 -- The general code for take, below, checks n <= maxInt
282 -- No need to check for maxInt overflow when specialised
283 -- at type Int or Int# since the Int must be <= maxInt
285 takeUInt :: Int# -> [b] -> [b]
287 | n >=# 0# = take_unsafe_UInt n xs
290 take_unsafe_UInt :: Int# -> [b] -> [b]
291 take_unsafe_UInt 0# _ = []
292 take_unsafe_UInt m ls =
295 (x:xs) -> x : take_unsafe_UInt (m -# 1#) xs
297 takeUInt_append :: Int# -> [b] -> [b] -> [b]
298 takeUInt_append n xs rs
299 | n >=# 0# = take_unsafe_UInt_append n xs rs
302 take_unsafe_UInt_append :: Int# -> [b] -> [b] -> [b]
303 take_unsafe_UInt_append 0# _ rs = rs
304 take_unsafe_UInt_append m ls rs =
307 (x:xs) -> x : take_unsafe_UInt_append (m -# 1#) xs rs
309 drop :: Int -> [b] -> [b]
312 | otherwise = drop# n# ls
314 drop# :: Int# -> [a] -> [a]
317 drop# m# (_:xs) = drop# (m# -# 1#) xs
319 splitAt :: Int -> [b] -> ([b], [b])
321 | n# <# 0# = ([], ls)
322 | otherwise = splitAt# n# ls
324 splitAt# :: Int# -> [a] -> ([a], [a])
325 splitAt# 0# xs = ([], xs)
326 splitAt# _ xs@[] = (xs, xs)
327 splitAt# m# (x:xs) = (x:xs', xs'')
329 (xs', xs'') = splitAt# (m# -# 1#) xs
331 #endif /* USE_REPORT_PRELUDE */
333 span, break :: (a -> Bool) -> [a] -> ([a],[a])
334 span _ xs@[] = (xs, xs)
336 | p x = let (ys,zs) = span p xs' in (x:ys,zs)
337 | otherwise = ([],xs)
339 #ifdef USE_REPORT_PRELUDE
340 break p = span (not . p)
342 -- HBC version (stolen)
343 break _ xs@[] = (xs, xs)
346 | otherwise = let (ys,zs) = break p xs' in (x:ys,zs)
349 -- reverse xs returns the elements of xs in reverse order. xs must be finite.
350 reverse :: [a] -> [a]
351 #ifdef USE_REPORT_PRELUDE
352 reverse = foldl (flip (:)) []
357 rev (x:xs) a = rev xs (x:a)
360 -- and returns the conjunction of a Boolean list. For the result to be
361 -- True, the list must be finite; False, however, results from a False
362 -- value at a finite index of a finite or infinite list. or is the
363 -- disjunctive dual of and.
364 and, or :: [Bool] -> Bool
365 #ifdef USE_REPORT_PRELUDE
366 and = foldr (&&) True
367 or = foldr (||) False
370 and (x:xs) = x && and xs
372 or (x:xs) = x || or xs
375 "and/build" forall (g::forall b.(Bool->b->b)->b->b) .
376 and (build g) = g (&&) True
377 "or/build" forall (g::forall b.(Bool->b->b)->b->b) .
378 or (build g) = g (||) False
382 -- Applied to a predicate and a list, any determines if any element
383 -- of the list satisfies the predicate. Similarly, for all.
384 any, all :: (a -> Bool) -> [a] -> Bool
385 #ifdef USE_REPORT_PRELUDE
390 any p (x:xs) = p x || any p xs
393 all p (x:xs) = p x && all p xs
395 "any/build" forall p (g::forall b.(a->b->b)->b->b) .
396 any p (build g) = g ((||) . p) False
397 "all/build" forall p (g::forall b.(a->b->b)->b->b) .
398 all p (build g) = g ((&&) . p) True
402 -- elem is the list membership predicate, usually written in infix form,
403 -- e.g., x `elem` xs. notElem is the negation.
404 elem, notElem :: (Eq a) => a -> [a] -> Bool
405 #ifdef USE_REPORT_PRELUDE
407 notElem x = all (/= x)
410 elem x (y:ys) = x==y || elem x ys
413 notElem x (y:ys)= x /= y && notElem x ys
416 -- lookup key assocs looks up a key in an association list.
417 lookup :: (Eq a) => a -> [(a,b)] -> Maybe b
418 lookup _key [] = Nothing
419 lookup key ((x,y):xys)
421 | otherwise = lookup key xys
424 -- maximum and minimum return the maximum or minimum value from a list,
425 -- which must be non-empty, finite, and of an ordered type.
426 {-# SPECIALISE maximum :: [Int] -> Int #-}
427 {-# SPECIALISE minimum :: [Int] -> Int #-}
428 maximum, minimum :: (Ord a) => [a] -> a
429 maximum [] = errorEmptyList "maximum"
430 maximum xs = foldl1 max xs
432 minimum [] = errorEmptyList "minimum"
433 minimum xs = foldl1 min xs
435 concatMap :: (a -> [b]) -> [a] -> [b]
436 concatMap f = foldr ((++) . f) []
438 concat :: [[a]] -> [a]
439 concat = foldr (++) []
442 "concat" forall xs. concat xs = build (\c n -> foldr (\x y -> foldr c y x) n xs)
443 -- We don't bother to turn non-fusible applications of concat back into concat
450 -- List index (subscript) operator, 0-origin
451 (!!) :: [a] -> Int -> a
452 #ifdef USE_REPORT_PRELUDE
453 xs !! n | n < 0 = error "Prelude.!!: negative index"
454 [] !! _ = error "Prelude.!!: index too large"
456 (_:xs) !! n = xs !! (n-1)
458 -- HBC version (stolen), then unboxified
459 -- The semantics is not quite the same for error conditions
460 -- in the more efficient version.
462 xs !! (I# n) | n <# 0# = error "Prelude.(!!): negative index\n"
463 | otherwise = sub xs n
465 sub :: [a] -> Int# -> a
466 sub [] _ = error "Prelude.(!!): index too large\n"
467 sub (y:ys) n = if n ==# 0#
469 else sub ys (n -# 1#)
474 %*********************************************************
476 \subsection{The zip family}
478 %*********************************************************
481 foldr2 _k z [] _ys = z
482 foldr2 _k z _xs [] = z
483 foldr2 k z (x:xs) (y:ys) = k x y (foldr2 k z xs ys)
485 foldr2_left _k z _x _r [] = z
486 foldr2_left k _z x r (y:ys) = k x y (r ys)
488 foldr2_right _k z _y _r [] = z
489 foldr2_right k _z y r (x:xs) = k x y (r xs)
491 -- foldr2 k z xs ys = foldr (foldr2_left k z) (\_ -> z) xs ys
492 -- foldr2 k z xs ys = foldr (foldr2_right k z) (\_ -> z) ys xs
494 "foldr2/left" forall k z ys (g::forall b.(a->b->b)->b->b) .
495 foldr2 k z (build g) ys = g (foldr2_left k z) (\_ -> z) ys
497 "foldr2/right" forall k z xs (g::forall b.(a->b->b)->b->b) .
498 foldr2 k z xs (build g) = g (foldr2_right k z) (\_ -> z) xs
502 The foldr2/right rule isn't exactly right, because it changes
503 the strictness of foldr2 (and thereby zip)
505 E.g. main = print (null (zip nonobviousNil (build undefined)))
506 where nonobviousNil = f 3
507 f n = if n == 0 then [] else f (n-1)
509 I'm going to leave it though.
512 zip takes two lists and returns a list of corresponding pairs. If one
513 input list is short, excess elements of the longer list are discarded.
514 zip3 takes three lists and returns a list of triples. Zips for larger
515 tuples are in the List module.
518 ----------------------------------------------
519 zip :: [a] -> [b] -> [(a,b)]
520 zip (a:as) (b:bs) = (a,b) : zip as bs
523 {-# INLINE [0] zipFB #-}
524 zipFB c x y r = (x,y) `c` r
527 "zip" [~1] forall xs ys. zip xs ys = build (\c n -> foldr2 (zipFB c) n xs ys)
528 "zipList" [1] foldr2 (zipFB (:)) [] = zip
533 ----------------------------------------------
534 zip3 :: [a] -> [b] -> [c] -> [(a,b,c)]
536 -- zip3 = zipWith3 (,,)
537 zip3 (a:as) (b:bs) (c:cs) = (a,b,c) : zip3 as bs cs
542 -- The zipWith family generalises the zip family by zipping with the
543 -- function given as the first argument, instead of a tupling function.
544 -- For example, zipWith (+) is applied to two lists to produce the list
545 -- of corresponding sums.
549 ----------------------------------------------
550 zipWith :: (a->b->c) -> [a]->[b]->[c]
551 zipWith f (a:as) (b:bs) = f a b : zipWith f as bs
554 {-# INLINE [0] zipWithFB #-}
555 zipWithFB c f x y r = (x `f` y) `c` r
558 "zipWith" [~1] forall f xs ys. zipWith f xs ys = build (\c n -> foldr2 (zipWithFB c f) n xs ys)
559 "zipWithList" [1] forall f. foldr2 (zipWithFB (:) f) [] = zipWith f
564 zipWith3 :: (a->b->c->d) -> [a]->[b]->[c]->[d]
565 zipWith3 z (a:as) (b:bs) (c:cs)
566 = z a b c : zipWith3 z as bs cs
567 zipWith3 _ _ _ _ = []
569 -- unzip transforms a list of pairs into a pair of lists.
570 unzip :: [(a,b)] -> ([a],[b])
572 unzip = foldr (\(a,b) ~(as,bs) -> (a:as,b:bs)) ([],[])
574 unzip3 :: [(a,b,c)] -> ([a],[b],[c])
575 {-# INLINE unzip3 #-}
576 unzip3 = foldr (\(a,b,c) ~(as,bs,cs) -> (a:as,b:bs,c:cs))
581 %*********************************************************
583 \subsection{Error code}
585 %*********************************************************
587 Common up near identical calls to `error' to reduce the number
588 constant strings created when compiled:
591 errorEmptyList :: String -> a
593 error (prel_list_str ++ fun ++ ": empty list")
595 prel_list_str :: String
596 prel_list_str = "Prelude."