1 % ------------------------------------------------------------------------------
2 % $Id: List.lhs,v 1.5 2001/12/21 15:07:25 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 {-# NOINLINE [1] filter #-}
122 filter :: (a -> Bool) -> [a] -> [a]
125 {-# INLINE [0] filter #-}
126 filterFB c p x r | p x = x `c` r
130 "filter" forall p xs. filter p xs = build (\c n -> foldr (filterFB c p) n xs)
131 "filterFB" forall c p q. filterFB (filterFB c p) q = filterFB c (\x -> q x && p x)
132 "filterList" forall p. foldr (filterFB (:) p) [] = filterList p
135 -- Note the filterFB rule, which has p and q the "wrong way round" in the RHS.
136 -- filterFB (filterFB c p) q a b
137 -- = if q a then filterFB c p a b else b
138 -- = if q a then (if p a then c a b else b) else b
139 -- = if q a && p a then c a b else b
140 -- = filterFB c (\x -> q x && p x) a b
141 -- I originally wrote (\x -> p x && q x), which is wrong, and actually
142 -- gave rise to a live bug report. SLPJ.
144 filterList :: (a -> Bool) -> [a] -> [a]
145 filterList _pred [] = []
146 filterList pred (x:xs)
147 | pred x = x : filterList pred xs
148 | otherwise = filterList pred xs
150 -- foldl, applied to a binary operator, a starting value (typically the
151 -- left-identity of the operator), and a list, reduces the list using
152 -- the binary operator, from left to right:
153 -- foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
154 -- foldl1 is a variant that has no starting value argument, and thus must
155 -- be applied to non-empty lists. scanl is similar to foldl, but returns
156 -- a list of successive reduced values from the left:
157 -- scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]
158 -- Note that last (scanl f z xs) == foldl f z xs.
159 -- scanl1 is similar, again without the starting element:
160 -- scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
162 -- We write foldl as a non-recursive thing, so that it
163 -- can be inlined, and then (often) strictness-analysed,
164 -- and hence the classic space leak on foldl (+) 0 xs
166 foldl :: (a -> b -> a) -> a -> [b] -> a
167 foldl f z xs = lgo z xs
170 lgo z (x:xs) = lgo (f z x) xs
172 foldl1 :: (a -> a -> a) -> [a] -> a
173 foldl1 f (x:xs) = foldl f x xs
174 foldl1 _ [] = errorEmptyList "foldl1"
176 scanl :: (a -> b -> a) -> a -> [b] -> [a]
177 scanl f q ls = q : (case ls of
179 x:xs -> scanl f (f q x) xs)
181 scanl1 :: (a -> a -> a) -> [a] -> [a]
182 scanl1 f (x:xs) = scanl f x xs
185 -- foldr, foldr1, scanr, and scanr1 are the right-to-left duals of the
188 foldr1 :: (a -> a -> a) -> [a] -> a
190 foldr1 f (x:xs) = f x (foldr1 f xs)
191 foldr1 _ [] = errorEmptyList "foldr1"
193 scanr :: (a -> b -> b) -> b -> [a] -> [b]
195 scanr f q0 (x:xs) = f x q : qs
196 where qs@(q:_) = scanr f q0 xs
198 scanr1 :: (a -> a -> a) -> [a] -> [a]
201 scanr1 f (x:xs) = f x q : qs
202 where qs@(q:_) = scanr1 f xs
204 -- iterate f x returns an infinite list of repeated applications of f to x:
205 -- iterate f x == [x, f x, f (f x), ...]
206 iterate :: (a -> a) -> a -> [a]
207 {-# NOINLINE [1] iterate #-}
208 iterate = iterateList
210 iterateFB c f x = x `c` iterateFB c f (f x)
212 iterateList f x = x : iterateList f (f x)
215 "iterate" forall f x. iterate f x = build (\c _n -> iterateFB c f x)
216 "iterateFB" iterateFB (:) = iterateList
220 -- repeat x is an infinite list, with x the value of every element.
222 {-# NOINLINE [1] repeat #-}
225 {-# INLINE [0] repeatFB #-}
226 repeatFB c x = xs where xs = x `c` xs
228 repeatList x = xs where xs = x : xs
231 "repeat" forall x. repeat x = build (\c _n -> repeatFB c x)
232 "repeatFB" repeatFB (:) = repeatList
235 -- replicate n x is a list of length n with x the value of every element
236 replicate :: Int -> a -> [a]
237 replicate n x = take n (repeat x)
239 -- cycle ties a finite list into a circular one, or equivalently,
240 -- the infinite repetition of the original list. It is the identity
241 -- on infinite lists.
244 cycle [] = error "Prelude.cycle: empty list"
245 cycle xs = xs' where xs' = xs ++ xs'
247 -- takeWhile, applied to a predicate p and a list xs, returns the longest
248 -- prefix (possibly empty) of xs of elements that satisfy p. dropWhile p xs
249 -- returns the remaining suffix. Span p xs is equivalent to
250 -- (takeWhile p xs, dropWhile p xs), while break p uses the negation of p.
252 takeWhile :: (a -> Bool) -> [a] -> [a]
255 | p x = x : takeWhile p xs
258 dropWhile :: (a -> Bool) -> [a] -> [a]
260 dropWhile p xs@(x:xs')
261 | p x = dropWhile p xs'
264 -- take n, applied to a list xs, returns the prefix of xs of length n,
265 -- or xs itself if n > length xs. drop n xs returns the suffix of xs
266 -- after the first n elements, or [] if n > length xs. splitAt n xs
267 -- is equivalent to (take n xs, drop n xs).
268 #ifdef USE_REPORT_PRELUDE
269 take :: Int -> [a] -> [a]
270 take n _ | n <= 0 = []
272 take n (x:xs) = x : take (n-1) xs
274 drop :: Int -> [a] -> [a]
275 drop n xs | n <= 0 = xs
277 drop n (_:xs) = drop (n-1) xs
279 splitAt :: Int -> [a] -> ([a],[a])
280 splitAt n xs = (take n xs, drop n xs)
282 #else /* hack away */
283 take :: Int -> [b] -> [b]
284 take (I# n#) xs = takeUInt n# xs
286 -- The general code for take, below, checks n <= maxInt
287 -- No need to check for maxInt overflow when specialised
288 -- at type Int or Int# since the Int must be <= maxInt
290 takeUInt :: Int# -> [b] -> [b]
292 | n >=# 0# = take_unsafe_UInt n xs
295 take_unsafe_UInt :: Int# -> [b] -> [b]
296 take_unsafe_UInt 0# _ = []
297 take_unsafe_UInt m ls =
300 (x:xs) -> x : take_unsafe_UInt (m -# 1#) xs
302 takeUInt_append :: Int# -> [b] -> [b] -> [b]
303 takeUInt_append n xs rs
304 | n >=# 0# = take_unsafe_UInt_append n xs rs
307 take_unsafe_UInt_append :: Int# -> [b] -> [b] -> [b]
308 take_unsafe_UInt_append 0# _ rs = rs
309 take_unsafe_UInt_append m ls rs =
312 (x:xs) -> x : take_unsafe_UInt_append (m -# 1#) xs rs
314 drop :: Int -> [b] -> [b]
317 | otherwise = drop# n# ls
319 drop# :: Int# -> [a] -> [a]
322 drop# m# (_:xs) = drop# (m# -# 1#) xs
324 splitAt :: Int -> [b] -> ([b], [b])
326 | n# <# 0# = ([], ls)
327 | otherwise = splitAt# n# ls
329 splitAt# :: Int# -> [a] -> ([a], [a])
330 splitAt# 0# xs = ([], xs)
331 splitAt# _ xs@[] = (xs, xs)
332 splitAt# m# (x:xs) = (x:xs', xs'')
334 (xs', xs'') = splitAt# (m# -# 1#) xs
336 #endif /* USE_REPORT_PRELUDE */
338 span, break :: (a -> Bool) -> [a] -> ([a],[a])
339 span _ xs@[] = (xs, xs)
341 | p x = let (ys,zs) = span p xs' in (x:ys,zs)
342 | otherwise = ([],xs)
344 #ifdef USE_REPORT_PRELUDE
345 break p = span (not . p)
347 -- HBC version (stolen)
348 break _ xs@[] = (xs, xs)
351 | otherwise = let (ys,zs) = break p xs' in (x:ys,zs)
354 -- reverse xs returns the elements of xs in reverse order. xs must be finite.
355 reverse :: [a] -> [a]
356 #ifdef USE_REPORT_PRELUDE
357 reverse = foldl (flip (:)) []
362 rev (x:xs) a = rev xs (x:a)
365 -- and returns the conjunction of a Boolean list. For the result to be
366 -- True, the list must be finite; False, however, results from a False
367 -- value at a finite index of a finite or infinite list. or is the
368 -- disjunctive dual of and.
369 and, or :: [Bool] -> Bool
370 #ifdef USE_REPORT_PRELUDE
371 and = foldr (&&) True
372 or = foldr (||) False
375 and (x:xs) = x && and xs
377 or (x:xs) = x || or xs
380 "and/build" forall (g::forall b.(Bool->b->b)->b->b) .
381 and (build g) = g (&&) True
382 "or/build" forall (g::forall b.(Bool->b->b)->b->b) .
383 or (build g) = g (||) False
387 -- Applied to a predicate and a list, any determines if any element
388 -- of the list satisfies the predicate. Similarly, for all.
389 any, all :: (a -> Bool) -> [a] -> Bool
390 #ifdef USE_REPORT_PRELUDE
395 any p (x:xs) = p x || any p xs
398 all p (x:xs) = p x && all p xs
400 "any/build" forall p (g::forall b.(a->b->b)->b->b) .
401 any p (build g) = g ((||) . p) False
402 "all/build" forall p (g::forall b.(a->b->b)->b->b) .
403 all p (build g) = g ((&&) . p) True
407 -- elem is the list membership predicate, usually written in infix form,
408 -- e.g., x `elem` xs. notElem is the negation.
409 elem, notElem :: (Eq a) => a -> [a] -> Bool
410 #ifdef USE_REPORT_PRELUDE
412 notElem x = all (/= x)
415 elem x (y:ys) = x==y || elem x ys
418 notElem x (y:ys)= x /= y && notElem x ys
421 -- lookup key assocs looks up a key in an association list.
422 lookup :: (Eq a) => a -> [(a,b)] -> Maybe b
423 lookup _key [] = Nothing
424 lookup key ((x,y):xys)
426 | otherwise = lookup key xys
429 -- maximum and minimum return the maximum or minimum value from a list,
430 -- which must be non-empty, finite, and of an ordered type.
431 {-# SPECIALISE maximum :: [Int] -> Int #-}
432 {-# SPECIALISE minimum :: [Int] -> Int #-}
433 maximum, minimum :: (Ord a) => [a] -> a
434 maximum [] = errorEmptyList "maximum"
435 maximum xs = foldl1 max xs
437 minimum [] = errorEmptyList "minimum"
438 minimum xs = foldl1 min xs
440 concatMap :: (a -> [b]) -> [a] -> [b]
441 concatMap f = foldr ((++) . f) []
443 concat :: [[a]] -> [a]
444 concat = foldr (++) []
447 "concat" forall xs. concat xs = build (\c n -> foldr (\x y -> foldr c y x) n xs)
453 -- List index (subscript) operator, 0-origin
454 (!!) :: [a] -> Int -> a
455 #ifdef USE_REPORT_PRELUDE
456 xs !! n | n < 0 = error "Prelude.!!: negative index"
457 [] !! _ = error "Prelude.!!: index too large"
459 (_:xs) !! n = xs !! (n-1)
461 -- HBC version (stolen), then unboxified
462 -- The semantics is not quite the same for error conditions
463 -- in the more efficient version.
465 xs !! (I# n) | n <# 0# = error "Prelude.(!!): negative index\n"
466 | otherwise = sub xs n
468 sub :: [a] -> Int# -> a
469 sub [] _ = error "Prelude.(!!): index too large\n"
470 sub (y:ys) n = if n ==# 0#
472 else sub ys (n -# 1#)
477 %*********************************************************
479 \subsection{The zip family}
481 %*********************************************************
484 foldr2 _k z [] _ys = z
485 foldr2 _k z _xs [] = z
486 foldr2 k z (x:xs) (y:ys) = k x y (foldr2 k z xs ys)
488 foldr2_left _k z _x _r [] = z
489 foldr2_left k _z x r (y:ys) = k x y (r ys)
491 foldr2_right _k z _y _r [] = z
492 foldr2_right k _z y r (x:xs) = k x y (r xs)
494 -- foldr2 k z xs ys = foldr (foldr2_left k z) (\_ -> z) xs ys
495 -- foldr2 k z xs ys = foldr (foldr2_right k z) (\_ -> z) ys xs
497 "foldr2/left" forall k z ys (g::forall b.(a->b->b)->b->b) .
498 foldr2 k z (build g) ys = g (foldr2_left k z) (\_ -> z) ys
500 "foldr2/right" forall k z xs (g::forall b.(a->b->b)->b->b) .
501 foldr2 k z xs (build g) = g (foldr2_right k z) (\_ -> z) xs
505 The foldr2/right rule isn't exactly right, because it changes
506 the strictness of foldr2 (and thereby zip)
508 E.g. main = print (null (zip nonobviousNil (build undefined)))
509 where nonobviousNil = f 3
510 f n = if n == 0 then [] else f (n-1)
512 I'm going to leave it though.
515 zip takes two lists and returns a list of corresponding pairs. If one
516 input list is short, excess elements of the longer list are discarded.
517 zip3 takes three lists and returns a list of triples. Zips for larger
518 tuples are in the List module.
521 ----------------------------------------------
522 zip :: [a] -> [b] -> [(a,b)]
523 {-# NOINLINE [1] zip #-}
526 {-# INLINE [0] zipFB #-}
527 zipFB c x y r = (x,y) `c` r
530 zipList :: [a] -> [b] -> [(a,b)]
531 zipList (a:as) (b:bs) = (a,b) : zipList as bs
535 "zip" forall xs ys. zip xs ys = build (\c n -> foldr2 (zipFB c) n xs ys)
536 "zipList" foldr2 (zipFB (:)) [] = zipList
541 ----------------------------------------------
542 zip3 :: [a] -> [b] -> [c] -> [(a,b,c)]
544 -- zip3 = zipWith3 (,,)
545 zip3 (a:as) (b:bs) (c:cs) = (a,b,c) : zip3 as bs cs
550 -- The zipWith family generalises the zip family by zipping with the
551 -- function given as the first argument, instead of a tupling function.
552 -- For example, zipWith (+) is applied to two lists to produce the list
553 -- of corresponding sums.
557 ----------------------------------------------
558 zipWith :: (a->b->c) -> [a]->[b]->[c]
559 {-# NOINLINE [1] zipWith #-}
560 zipWith = zipWithList
562 {-# INLINE [0] zipWithFB #-}
563 zipWithFB c f x y r = (x `f` y) `c` r
565 zipWithList :: (a->b->c) -> [a] -> [b] -> [c]
566 zipWithList f (a:as) (b:bs) = f a b : zipWithList f as bs
567 zipWithList _ _ _ = []
570 "zipWith" forall f xs ys. zipWith f xs ys = build (\c n -> foldr2 (zipWithFB c f) n xs ys)
571 "zipWithList" forall f. foldr2 (zipWithFB (:) f) [] = zipWithList f
576 zipWith3 :: (a->b->c->d) -> [a]->[b]->[c]->[d]
577 zipWith3 z (a:as) (b:bs) (c:cs)
578 = z a b c : zipWith3 z as bs cs
579 zipWith3 _ _ _ _ = []
581 -- unzip transforms a list of pairs into a pair of lists.
582 unzip :: [(a,b)] -> ([a],[b])
584 unzip = foldr (\(a,b) ~(as,bs) -> (a:as,b:bs)) ([],[])
586 unzip3 :: [(a,b,c)] -> ([a],[b],[c])
587 {-# INLINE unzip3 #-}
588 unzip3 = foldr (\(a,b,c) ~(as,bs,cs) -> (a:as,b:bs,c:cs))
593 %*********************************************************
595 \subsection{Error code}
597 %*********************************************************
599 Common up near identical calls to `error' to reduce the number
600 constant strings created when compiled:
603 errorEmptyList :: String -> a
605 error (prel_list_str ++ fun ++ ": empty list")
607 prel_list_str :: String
608 prel_list_str = "Prelude."