2 % (c) The AQUA Project, Glasgow University, 1994-1996
5 \section[PrelList]{Module @PrelList@}
7 The List data type and its operations
10 {-# OPTIONS -fno-implicit-prelude #-}
15 map, (++), filter, concat,
16 head, last, tail, init, null, length, (!!),
17 foldl, foldl1, scanl, scanl1, foldr, foldr1, scanr, scanr1,
18 iterate, repeat, replicate, cycle,
19 take, drop, splitAt, takeWhile, dropWhile, span, break,
21 any, all, elem, notElem, lookup,
22 maximum, minimum, concatMap,
23 zip, zip3, zipWith, zipWith3, unzip, unzip3,
25 -- non-standard, but hidden when creating the Prelude
31 import {-# SOURCE #-} PrelErr ( error )
37 infix 4 `elem`, `notElem`
40 %*********************************************************
42 \subsection{List-manipulation functions}
44 %*********************************************************
47 -- head and tail extract the first element and remaining elements,
48 -- respectively, of a list, which must be non-empty. last and init
49 -- are the dual functions working from the end of a finite list,
50 -- rather than the beginning.
54 head [] = errorEmptyList "head"
58 tail [] = errorEmptyList "tail"
61 #ifdef USE_REPORT_PRELUDE
64 last [] = errorEmptyList "last"
66 -- eliminate repeated cases
67 last [] = errorEmptyList "last"
68 last (x:xs) = last' x xs
70 last' _ (y:ys) = last' y ys
74 #ifdef USE_REPORT_PRELUDE
76 init (x:xs) = x : init xs
77 init [] = errorEmptyList "init"
79 -- eliminate repeated cases
80 init [] = errorEmptyList "init"
81 init (x:xs) = init' x xs
83 init' y (z:zs) = y : init' z zs
90 -- length returns the length of a finite list as an Int; it is an instance
91 -- of the more general genericLength, the result type of which may be
92 -- any kind of number.
96 len :: [a] -> Int# -> Int
98 len (_:xs) a# = len xs (a# +# 1#)
100 -- filter, applied to a predicate and a list, returns the list of those
101 -- elements that satisfy the predicate; i.e.,
102 -- filter p xs = [ x | x <- xs, p x]
103 filter :: (a -> Bool) -> [a] -> [a]
104 {-# INLINE filter #-}
105 filter p xs = build (\c n -> foldr (filterFB c p) n xs)
107 filterFB c p x r | p x = x `c` r
111 "filterFB" forall c,p,q. filterFB (filterFB c p) q = filterFB c (\x -> p x && q x)
112 "filterList" forall p. foldr (filterFB (:) p) [] = filterList p
115 filterList :: (a -> Bool) -> [a] -> [a]
116 filterList _pred [] = []
117 filterList pred (x:xs)
118 | pred x = x : filterList pred xs
119 | otherwise = filterList pred xs
121 -- foldl, applied to a binary operator, a starting value (typically the
122 -- left-identity of the operator), and a list, reduces the list using
123 -- the binary operator, from left to right:
124 -- foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
125 -- foldl1 is a variant that has no starting value argument, and thus must
126 -- be applied to non-empty lists. scanl is similar to foldl, but returns
127 -- a list of successive reduced values from the left:
128 -- scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]
129 -- Note that last (scanl f z xs) == foldl f z xs.
130 -- scanl1 is similar, again without the starting element:
131 -- scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
133 foldl :: (a -> b -> a) -> a -> [b] -> a
135 foldl f z (x:xs) = foldl f (f z x) xs
137 foldl1 :: (a -> a -> a) -> [a] -> a
138 foldl1 f (x:xs) = foldl f x xs
139 foldl1 _ [] = errorEmptyList "foldl1"
141 scanl :: (a -> b -> a) -> a -> [b] -> [a]
142 scanl f q ls = q : (case ls of
144 x:xs -> scanl f (f q x) xs)
146 scanl1 :: (a -> a -> a) -> [a] -> [a]
147 scanl1 f (x:xs) = scanl f x xs
148 scanl1 _ [] = errorEmptyList "scanl1"
150 -- foldr, foldr1, scanr, and scanr1 are the right-to-left duals of the
153 foldr1 :: (a -> a -> a) -> [a] -> a
155 foldr1 f (x:xs) = f x (foldr1 f xs)
156 foldr1 _ [] = errorEmptyList "foldr1"
158 scanr :: (a -> b -> b) -> b -> [a] -> [b]
160 scanr f q0 (x:xs) = f x q : qs
161 where qs@(q:_) = scanr f q0 xs
163 scanr1 :: (a -> a -> a) -> [a] -> [a]
165 scanr1 f (x:xs) = f x q : qs
166 where qs@(q:_) = scanr1 f xs
167 scanr1 _ [] = errorEmptyList "scanr1"
169 -- iterate f x returns an infinite list of repeated applications of f to x:
170 -- iterate f x == [x, f x, f (f x), ...]
171 iterate :: (a -> a) -> a -> [a]
172 iterate f x = x : iterate f (f x)
174 -- repeat x is an infinite list, with x the value of every element.
176 repeat x = xs where xs = x:xs
178 -- replicate n x is a list of length n with x the value of every element
179 replicate :: Int -> a -> [a]
180 replicate n x = take n (repeat x)
182 -- cycle ties a finite list into a circular one, or equivalently,
183 -- the infinite repetition of the original list. It is the identity
184 -- on infinite lists.
187 cycle [] = error "Prelude.cycle: empty list"
188 cycle xs = xs' where xs' = xs ++ xs'
190 -- takeWhile, applied to a predicate p and a list xs, returns the longest
191 -- prefix (possibly empty) of xs of elements that satisfy p. dropWhile p xs
192 -- returns the remaining suffix. Span p xs is equivalent to
193 -- (takeWhile p xs, dropWhile p xs), while break p uses the negation of p.
195 takeWhile :: (a -> Bool) -> [a] -> [a]
198 | p x = x : takeWhile p xs
201 dropWhile :: (a -> Bool) -> [a] -> [a]
203 dropWhile p xs@(x:xs')
204 | p x = dropWhile p xs'
207 -- take n, applied to a list xs, returns the prefix of xs of length n,
208 -- or xs itself if n > length xs. drop n xs returns the suffix of xs
209 -- after the first n elements, or [] if n > length xs. splitAt n xs
210 -- is equivalent to (take n xs, drop n xs).
211 #ifdef USE_REPORT_PRELUDE
212 take :: Int -> [a] -> [a]
215 take n (x:xs) | n > 0 = x : take (n-1) xs
216 take _ _ = errorNegativeIdx "take"
218 drop :: Int -> [a] -> [a]
221 drop n (_:xs) | n > 0 = drop (n-1) xs
222 drop _ _ = errorNegativeIdx "drop"
225 splitAt :: Int -> [a] -> ([a],[a])
226 splitAt 0 xs = ([],xs)
227 splitAt _ [] = ([],[])
228 splitAt n (x:xs) | n > 0 = (x:xs',xs'') where (xs',xs'') = splitAt (n-1) xs
229 splitAt _ _ = errorNegativeIdx "splitAt"
231 #else /* hack away */
232 take :: Int -> [b] -> [b]
233 take (I# n#) xs = takeUInt n# xs
235 -- The general code for take, below, checks n <= maxInt
236 -- No need to check for maxInt overflow when specialised
237 -- at type Int or Int# since the Int must be <= maxInt
239 takeUInt :: Int# -> [b] -> [b]
241 | n >=# 0# = take_unsafe_UInt n xs
242 | otherwise = errorNegativeIdx "take"
244 take_unsafe_UInt :: Int# -> [b] -> [b]
245 take_unsafe_UInt 0# _ = []
246 take_unsafe_UInt m ls =
249 (x:xs) -> x : take_unsafe_UInt (m -# 1#) xs
251 takeUInt_append :: Int# -> [b] -> [b] -> [b]
252 takeUInt_append n xs rs
253 | n >=# 0# = take_unsafe_UInt_append n xs rs
254 | otherwise = errorNegativeIdx "take"
256 take_unsafe_UInt_append :: Int# -> [b] -> [b] -> [b]
257 take_unsafe_UInt_append 0# _ rs = rs
258 take_unsafe_UInt_append m ls rs =
261 (x:xs) -> x : take_unsafe_UInt_append (m -# 1#) xs rs
263 drop :: Int -> [b] -> [b]
265 | n# <# 0# = errorNegativeIdx "drop"
266 | otherwise = drop# n# ls
268 drop# :: Int# -> [a] -> [a]
271 drop# m# (_:xs) = drop# (m# -# 1#) xs
273 splitAt :: Int -> [b] -> ([b], [b])
275 | n# <# 0# = errorNegativeIdx "splitAt"
276 | otherwise = splitAt# n# ls
278 splitAt# :: Int# -> [a] -> ([a], [a])
279 splitAt# 0# xs = ([], xs)
280 splitAt# _ xs@[] = (xs, xs)
281 splitAt# m# (x:xs) = (x:xs', xs'')
283 (xs', xs'') = splitAt# (m# -# 1#) xs
285 #endif /* USE_REPORT_PRELUDE */
287 span, break :: (a -> Bool) -> [a] -> ([a],[a])
288 span _ xs@[] = (xs, xs)
290 | p x = let (ys,zs) = span p xs' in (x:ys,zs)
291 | otherwise = ([],xs)
293 #ifdef USE_REPORT_PRELUDE
294 break p = span (not . p)
296 -- HBC version (stolen)
297 break _ xs@[] = (xs, xs)
300 | otherwise = let (ys,zs) = break p xs' in (x:ys,zs)
303 -- reverse xs returns the elements of xs in reverse order. xs must be finite.
304 reverse :: [a] -> [a]
305 #ifdef USE_REPORT_PRELUDE
306 reverse = foldl (flip (:)) []
311 rev (x:xs) a = rev xs (x:a)
314 -- and returns the conjunction of a Boolean list. For the result to be
315 -- True, the list must be finite; False, however, results from a False
316 -- value at a finite index of a finite or infinite list. or is the
317 -- disjunctive dual of and.
318 and, or :: [Bool] -> Bool
319 #ifdef USE_REPORT_PRELUDE
320 and = foldr (&&) True
321 or = foldr (||) False
324 and (x:xs) = x && and xs
326 or (x:xs) = x || or xs
329 "and/build" forall g::forall b.(Bool->b->b)->b->b .
330 and (build g) = g (&&) True
331 "or/build" forall g::forall b.(Bool->b->b)->b->b .
332 or (build g) = g (||) False
336 -- Applied to a predicate and a list, any determines if any element
337 -- of the list satisfies the predicate. Similarly, for all.
338 any, all :: (a -> Bool) -> [a] -> Bool
339 #ifdef USE_REPORT_PRELUDE
344 any p (x:xs) = p x || any p xs
347 all p (x:xs) = p x && all p xs
349 "any/build" forall p, g::forall b.(a->b->b)->b->b .
350 any p (build g) = g ((&&) . p) True
351 "all/build" forall p, g::forall b.(a->b->b)->b->b .
352 all p (build g) = g ((||) . p) False
356 -- elem is the list membership predicate, usually written in infix form,
357 -- e.g., x `elem` xs. notElem is the negation.
358 elem, notElem :: (Eq a) => a -> [a] -> Bool
359 #ifdef USE_REPORT_PRELUDE
361 notElem x = all (/= x)
364 elem x (y:ys) = x==y || elem x ys
367 notElem x (y:ys)= x /= y && notElem x ys
370 -- lookup key assocs looks up a key in an association list.
371 lookup :: (Eq a) => a -> [(a,b)] -> Maybe b
372 lookup _key [] = Nothing
373 lookup key ((x,y):xys)
375 | otherwise = lookup key xys
378 -- maximum and minimum return the maximum or minimum value from a list,
379 -- which must be non-empty, finite, and of an ordered type.
380 {-# SPECIALISE maximum :: [Int] -> Int #-}
381 {-# SPECIALISE minimum :: [Int] -> Int #-}
382 maximum, minimum :: (Ord a) => [a] -> a
383 maximum [] = errorEmptyList "maximum"
384 maximum xs = foldl1 max xs
386 minimum [] = errorEmptyList "minimum"
387 minimum xs = foldl1 min xs
389 concatMap :: (a -> [b]) -> [a] -> [b]
390 concatMap f = foldr ((++) . f) []
392 concat :: [[a]] -> [a]
393 {-# INLINE concat #-}
394 concat = foldr (++) []
399 -- List index (subscript) operator, 0-origin
400 (!!) :: [a] -> Int -> a
401 #ifdef USE_REPORT_PRELUDE
403 (_:xs) !! n | n > 0 = xs !! (n-1)
404 (_:_) !! _ = error "Prelude.(!!): negative index"
405 [] !! _ = error "Prelude.(!!): index too large"
407 -- HBC version (stolen), then unboxified
408 -- The semantics is not quite the same for error conditions
409 -- in the more efficient version.
411 xs !! (I# n) | n <# 0# = error "Prelude.(!!): negative index\n"
412 | otherwise = sub xs n
414 sub :: [a] -> Int# -> a
415 sub [] _ = error "Prelude.(!!): index too large\n"
416 sub (y:ys) n = if n ==# 0#
418 else sub ys (n -# 1#)
423 %*********************************************************
425 \subsection{The zip family}
427 %*********************************************************
432 foldr2 k z (x:xs) (y:ys) = k x y (foldr2 k z xs ys)
434 foldr2_left k z x r [] = z
435 foldr2_left k z x r (y:ys) = k x y (r ys)
437 foldr2_right k z y r [] = z
438 foldr2_right k z y r (x:xs) = k x y (r xs)
440 -- foldr2 k z xs ys = foldr (foldr2_left k z) (\_ -> z) xs ys
441 -- foldr2 k z xs ys = foldr (foldr2_right k z) (\_ -> z) ys xs
443 "foldr2/left" forall k,z,ys,g::forall b.(a->b->b)->b->b .
444 foldr2 k z (build g) ys = g (foldr2_left k z) (\_ -> z) ys
446 "foldr2/right" forall k,z,xs,g::forall b.(a->b->b)->b->b .
447 foldr2 k z xs (build g) = g (foldr2_right k z) (\_ -> z) xs
451 zip takes two lists and returns a list of corresponding pairs. If one
452 input list is short, excess elements of the longer list are discarded.
453 zip3 takes three lists and returns a list of triples. Zips for larger
454 tuples are in the List library
457 ----------------------------------------------
458 zip :: [a] -> [b] -> [(a,b)]
460 zip xs ys = build (\c n -> foldr2 (zipFB c) n xs ys)
462 zipFB c x y r = (x,y) `c` r
465 zipList :: [a] -> [b] -> [(a,b)]
466 zipList (a:as) (b:bs) = (a,b) : zipList as bs
470 "zipList" foldr2 (zipFB (:)) [] = zipList
475 ----------------------------------------------
476 zip3 :: [a] -> [b] -> [c] -> [(a,b,c)]
478 -- zip3 = zipWith3 (,,)
479 zip3 (a:as) (b:bs) (c:cs) = (a,b,c) : zip3 as bs cs
484 -- The zipWith family generalises the zip family by zipping with the
485 -- function given as the first argument, instead of a tupling function.
486 -- For example, zipWith (+) is applied to two lists to produce the list
487 -- of corresponding sums.
491 ----------------------------------------------
492 zipWith :: (a->b->c) -> [a]->[b]->[c]
493 {-# INLINE zipWith #-}
494 zipWith f xs ys = build (\c n -> foldr2 (zipWithFB c f) n xs ys)
496 zipWithFB c f x y r = (x `f` y) `c` r
498 zipWithList :: (a->b->c) -> [a] -> [b] -> [c]
499 zipWithList f (a:as) (b:bs) = f a b : zipWithList f as bs
500 zipWithList f _ _ = []
503 "zipWithList" forall f. foldr2 (zipWithFB (:) f) [] = zipWithList f
508 zipWith3 :: (a->b->c->d) -> [a]->[b]->[c]->[d]
509 zipWith3 z (a:as) (b:bs) (c:cs)
510 = z a b c : zipWith3 z as bs cs
511 zipWith3 _ _ _ _ = []
513 -- unzip transforms a list of pairs into a pair of lists.
514 unzip :: [(a,b)] -> ([a],[b])
515 unzip = foldr (\(a,b) ~(as,bs) -> (a:as,b:bs)) ([],[])
517 unzip3 :: [(a,b,c)] -> ([a],[b],[c])
518 unzip3 = foldr (\(a,b,c) ~(as,bs,cs) -> (a:as,b:bs,c:cs))
523 %*********************************************************
525 \subsection{Error code}
527 %*********************************************************
529 Common up near identical calls to `error' to reduce the number
530 constant strings created when compiled:
533 errorEmptyList :: String -> a
535 error (prel_list_str ++ fun ++ ": empty list")
537 errorNegativeIdx :: String -> a
538 errorNegativeIdx fun =
539 error (prel_list_str ++ fun ++ ": negative index")
541 prel_list_str :: String
542 prel_list_str = "Prelude."