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 #ifdef USE_REPORT_PRELUDE
29 -- non-standard, but hidden when creating the Prelude
37 import {-# SOURCE #-} PrelErr ( error )
43 infix 4 `elem`, `notElem`
46 %*********************************************************
48 \subsection{List-manipulation functions}
50 %*********************************************************
53 -- head and tail extract the first element and remaining elements,
54 -- respectively, of a list, which must be non-empty. last and init
55 -- are the dual functions working from the end of a finite list,
56 -- rather than the beginning.
62 badHead = errorEmptyList "head"
64 -- This rule is useful in cases like
65 -- head [y | (x,y) <- ps, x==t]
67 "head/build" forall (g::forall b.(Bool->b->b)->b->b) .
68 head (build g) = g (\x _ -> x) badHead
69 "head/augment" forall xs (g::forall b. (a->b->b) -> b -> b) .
70 head (augment g xs) = g (\x _ -> x) (head xs)
75 tail [] = errorEmptyList "tail"
78 #ifdef USE_REPORT_PRELUDE
81 last [] = errorEmptyList "last"
83 -- eliminate repeated cases
84 last [] = errorEmptyList "last"
85 last (x:xs) = last' x xs
87 last' _ (y:ys) = last' y ys
91 #ifdef USE_REPORT_PRELUDE
93 init (x:xs) = x : init xs
94 init [] = errorEmptyList "init"
96 -- eliminate repeated cases
97 init [] = errorEmptyList "init"
98 init (x:xs) = init' x xs
100 init' y (z:zs) = y : init' z zs
107 -- length returns the length of a finite list as an Int; it is an instance
108 -- of the more general genericLength, the result type of which may be
109 -- any kind of number.
113 len :: [a] -> Int# -> Int
115 len (_:xs) a# = len xs (a# +# 1#)
117 -- filter, applied to a predicate and a list, returns the list of those
118 -- elements that satisfy the predicate; i.e.,
119 -- filter p xs = [ x | x <- xs, p x]
120 filter :: (a -> Bool) -> [a] -> [a]
123 filterFB c p x r | p x = x `c` r
127 "filter" forall p xs. filter p xs = build (\c n -> foldr (filterFB c p) n xs)
128 "filterFB" forall c p q. filterFB (filterFB c p) q = filterFB c (\x -> p x && q x)
129 "filterList" forall p. foldr (filterFB (:) p) [] = filterList p
132 filterList :: (a -> Bool) -> [a] -> [a]
133 filterList _pred [] = []
134 filterList pred (x:xs)
135 | pred x = x : filterList pred xs
136 | otherwise = filterList pred xs
138 -- foldl, applied to a binary operator, a starting value (typically the
139 -- left-identity of the operator), and a list, reduces the list using
140 -- the binary operator, from left to right:
141 -- foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
142 -- foldl1 is a variant that has no starting value argument, and thus must
143 -- be applied to non-empty lists. scanl is similar to foldl, but returns
144 -- a list of successive reduced values from the left:
145 -- scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]
146 -- Note that last (scanl f z xs) == foldl f z xs.
147 -- scanl1 is similar, again without the starting element:
148 -- scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
150 foldl :: (a -> b -> a) -> a -> [b] -> a
152 foldl f z (x:xs) = foldl f (f z x) xs
154 foldl1 :: (a -> a -> a) -> [a] -> a
155 foldl1 f (x:xs) = foldl f x xs
156 foldl1 _ [] = errorEmptyList "foldl1"
158 scanl :: (a -> b -> a) -> a -> [b] -> [a]
159 scanl f q ls = q : (case ls of
161 x:xs -> scanl f (f q x) xs)
163 scanl1 :: (a -> a -> a) -> [a] -> [a]
164 scanl1 f (x:xs) = scanl f x xs
165 scanl1 _ [] = errorEmptyList "scanl1"
167 -- foldr, foldr1, scanr, and scanr1 are the right-to-left duals of the
170 foldr1 :: (a -> a -> a) -> [a] -> a
172 foldr1 f (x:xs) = f x (foldr1 f xs)
173 foldr1 _ [] = errorEmptyList "foldr1"
175 scanr :: (a -> b -> b) -> b -> [a] -> [b]
177 scanr f q0 (x:xs) = f x q : qs
178 where qs@(q:_) = scanr f q0 xs
180 scanr1 :: (a -> a -> a) -> [a] -> [a]
182 scanr1 f (x:xs) = f x q : qs
183 where qs@(q:_) = scanr1 f xs
184 scanr1 _ [] = errorEmptyList "scanr1"
186 -- iterate f x returns an infinite list of repeated applications of f to x:
187 -- iterate f x == [x, f x, f (f x), ...]
188 iterate :: (a -> a) -> a -> [a]
189 iterate = iterateList
191 iterateFB c f x = x `c` iterateFB c f (f x)
193 iterateList f x = x : iterateList f (f x)
196 "iterate" forall f x. iterate f x = build (\c _n -> iterateFB c f x)
197 "iterateFB" iterateFB (:) = iterateList
201 -- repeat x is an infinite list, with x the value of every element.
205 repeatFB c x = xs where xs = x `c` xs
206 repeatList x = xs where xs = x : xs
209 "repeat" forall x. repeat x = build (\c _n -> repeatFB c x)
210 "repeatFB" repeatFB (:) = repeatList
213 -- replicate n x is a list of length n with x the value of every element
214 replicate :: Int -> a -> [a]
215 replicate n x = take n (repeat x)
217 -- cycle ties a finite list into a circular one, or equivalently,
218 -- the infinite repetition of the original list. It is the identity
219 -- on infinite lists.
222 cycle [] = error "Prelude.cycle: empty list"
223 cycle xs = xs' where xs' = xs ++ xs'
225 -- takeWhile, applied to a predicate p and a list xs, returns the longest
226 -- prefix (possibly empty) of xs of elements that satisfy p. dropWhile p xs
227 -- returns the remaining suffix. Span p xs is equivalent to
228 -- (takeWhile p xs, dropWhile p xs), while break p uses the negation of p.
230 takeWhile :: (a -> Bool) -> [a] -> [a]
233 | p x = x : takeWhile p xs
236 dropWhile :: (a -> Bool) -> [a] -> [a]
238 dropWhile p xs@(x:xs')
239 | p x = dropWhile p xs'
242 -- take n, applied to a list xs, returns the prefix of xs of length n,
243 -- or xs itself if n > length xs. drop n xs returns the suffix of xs
244 -- after the first n elements, or [] if n > length xs. splitAt n xs
245 -- is equivalent to (take n xs, drop n xs).
246 #ifdef USE_REPORT_PRELUDE
247 take :: Int -> [a] -> [a]
250 take n (x:xs) | n > 0 = x : take (minusInt n 1) xs
251 take _ _ = errorNegativeIdx "take"
253 drop :: Int -> [a] -> [a]
256 drop n (_:xs) | n > 0 = drop (minusInt n 1) xs
257 drop _ _ = errorNegativeIdx "drop"
260 splitAt :: Int -> [a] -> ([a],[a])
261 splitAt 0 xs = ([],xs)
262 splitAt _ [] = ([],[])
263 splitAt n (x:xs) | n > 0 = (x:xs',xs'') where (xs',xs'') = splitAt (minusInt n 1) xs
264 splitAt _ _ = errorNegativeIdx "splitAt"
266 #else /* hack away */
267 take :: Int -> [b] -> [b]
268 take (I# n#) xs = takeUInt n# xs
270 -- The general code for take, below, checks n <= maxInt
271 -- No need to check for maxInt overflow when specialised
272 -- at type Int or Int# since the Int must be <= maxInt
274 takeUInt :: Int# -> [b] -> [b]
276 | n >=# 0# = take_unsafe_UInt n xs
277 | otherwise = errorNegativeIdx "take"
279 take_unsafe_UInt :: Int# -> [b] -> [b]
280 take_unsafe_UInt 0# _ = []
281 take_unsafe_UInt m ls =
284 (x:xs) -> x : take_unsafe_UInt (m -# 1#) xs
286 takeUInt_append :: Int# -> [b] -> [b] -> [b]
287 takeUInt_append n xs rs
288 | n >=# 0# = take_unsafe_UInt_append n xs rs
289 | otherwise = errorNegativeIdx "take"
291 take_unsafe_UInt_append :: Int# -> [b] -> [b] -> [b]
292 take_unsafe_UInt_append 0# _ rs = rs
293 take_unsafe_UInt_append m ls rs =
296 (x:xs) -> x : take_unsafe_UInt_append (m -# 1#) xs rs
298 drop :: Int -> [b] -> [b]
300 | n# <# 0# = errorNegativeIdx "drop"
301 | otherwise = drop# n# ls
303 drop# :: Int# -> [a] -> [a]
306 drop# m# (_:xs) = drop# (m# -# 1#) xs
308 splitAt :: Int -> [b] -> ([b], [b])
310 | n# <# 0# = errorNegativeIdx "splitAt"
311 | otherwise = splitAt# n# ls
313 splitAt# :: Int# -> [a] -> ([a], [a])
314 splitAt# 0# xs = ([], xs)
315 splitAt# _ xs@[] = (xs, xs)
316 splitAt# m# (x:xs) = (x:xs', xs'')
318 (xs', xs'') = splitAt# (m# -# 1#) xs
320 #endif /* USE_REPORT_PRELUDE */
322 span, break :: (a -> Bool) -> [a] -> ([a],[a])
323 span _ xs@[] = (xs, xs)
325 | p x = let (ys,zs) = span p xs' in (x:ys,zs)
326 | otherwise = ([],xs)
328 #ifdef USE_REPORT_PRELUDE
329 break p = span (not . p)
331 -- HBC version (stolen)
332 break _ xs@[] = (xs, xs)
335 | otherwise = let (ys,zs) = break p xs' in (x:ys,zs)
338 -- reverse xs returns the elements of xs in reverse order. xs must be finite.
339 reverse :: [a] -> [a]
340 #ifdef USE_REPORT_PRELUDE
341 reverse = foldl (flip (:)) []
346 rev (x:xs) a = rev xs (x:a)
349 -- and returns the conjunction of a Boolean list. For the result to be
350 -- True, the list must be finite; False, however, results from a False
351 -- value at a finite index of a finite or infinite list. or is the
352 -- disjunctive dual of and.
353 and, or :: [Bool] -> Bool
354 #ifdef USE_REPORT_PRELUDE
355 and = foldr (&&) True
356 or = foldr (||) False
359 and (x:xs) = x && and xs
361 or (x:xs) = x || or xs
364 "and/build" forall (g::forall b.(Bool->b->b)->b->b) .
365 and (build g) = g (&&) True
366 "or/build" forall (g::forall b.(Bool->b->b)->b->b) .
367 or (build g) = g (||) False
371 -- Applied to a predicate and a list, any determines if any element
372 -- of the list satisfies the predicate. Similarly, for all.
373 any, all :: (a -> Bool) -> [a] -> Bool
374 #ifdef USE_REPORT_PRELUDE
379 any p (x:xs) = p x || any p xs
382 all p (x:xs) = p x && all p xs
384 "any/build" forall p (g::forall b.(a->b->b)->b->b) .
385 any p (build g) = g ((||) . p) False
386 "all/build" forall p (g::forall b.(a->b->b)->b->b) .
387 all p (build g) = g ((&&) . p) True
391 -- elem is the list membership predicate, usually written in infix form,
392 -- e.g., x `elem` xs. notElem is the negation.
393 elem, notElem :: (Eq a) => a -> [a] -> Bool
394 #ifdef USE_REPORT_PRELUDE
396 notElem x = all (/= x)
399 elem x (y:ys) = x==y || elem x ys
402 notElem x (y:ys)= x /= y && notElem x ys
405 -- lookup key assocs looks up a key in an association list.
406 lookup :: (Eq a) => a -> [(a,b)] -> Maybe b
407 lookup _key [] = Nothing
408 lookup key ((x,y):xys)
410 | otherwise = lookup key xys
413 -- maximum and minimum return the maximum or minimum value from a list,
414 -- which must be non-empty, finite, and of an ordered type.
415 {-# SPECIALISE maximum :: [Int] -> Int #-}
416 {-# SPECIALISE minimum :: [Int] -> Int #-}
417 maximum, minimum :: (Ord a) => [a] -> a
418 maximum [] = errorEmptyList "maximum"
419 maximum xs = foldl1 max xs
421 minimum [] = errorEmptyList "minimum"
422 minimum xs = foldl1 min xs
424 concatMap :: (a -> [b]) -> [a] -> [b]
425 concatMap f = foldr ((++) . f) []
427 concat :: [[a]] -> [a]
428 {-# INLINE concat #-}
429 concat = foldr (++) []
434 -- List index (subscript) operator, 0-origin
435 (!!) :: [a] -> Int -> a
436 #ifdef USE_REPORT_PRELUDE
438 (_:xs) !! n | n > 0 = xs !! (minusInt n 1)
439 (_:_) !! _ = error "Prelude.(!!): negative index"
440 [] !! _ = error "Prelude.(!!): index too large"
442 -- HBC version (stolen), then unboxified
443 -- The semantics is not quite the same for error conditions
444 -- in the more efficient version.
446 xs !! (I# n) | n <# 0# = error "Prelude.(!!): negative index\n"
447 | otherwise = sub xs n
449 sub :: [a] -> Int# -> a
450 sub [] _ = error "Prelude.(!!): index too large\n"
451 sub (y:ys) n = if n ==# 0#
453 else sub ys (n -# 1#)
458 %*********************************************************
460 \subsection{The zip family}
462 %*********************************************************
465 foldr2 _k z [] _ys = z
466 foldr2 _k z _xs [] = z
467 foldr2 k z (x:xs) (y:ys) = k x y (foldr2 k z xs ys)
469 foldr2_left _k z _x _r [] = z
470 foldr2_left k _z x r (y:ys) = k x y (r ys)
472 foldr2_right _k z _y _r [] = z
473 foldr2_right k _z y r (x:xs) = k x y (r xs)
475 -- foldr2 k z xs ys = foldr (foldr2_left k z) (\_ -> z) xs ys
476 -- foldr2 k z xs ys = foldr (foldr2_right k z) (\_ -> z) ys xs
478 "foldr2/left" forall k z ys (g::forall b.(a->b->b)->b->b) .
479 foldr2 k z (build g) ys = g (foldr2_left k z) (\_ -> z) ys
481 "foldr2/right" forall k z xs (g::forall b.(a->b->b)->b->b) .
482 foldr2 k z xs (build g) = g (foldr2_right k z) (\_ -> z) xs
486 zip takes two lists and returns a list of corresponding pairs. If one
487 input list is short, excess elements of the longer list are discarded.
488 zip3 takes three lists and returns a list of triples. Zips for larger
489 tuples are in the List library
492 ----------------------------------------------
493 zip :: [a] -> [b] -> [(a,b)]
496 zipFB c x y r = (x,y) `c` r
499 zipList :: [a] -> [b] -> [(a,b)]
500 zipList (a:as) (b:bs) = (a,b) : zipList as bs
504 "zip" forall xs ys. zip xs ys = build (\c n -> foldr2 (zipFB c) n xs ys)
505 "zipList" foldr2 (zipFB (:)) [] = zipList
510 ----------------------------------------------
511 zip3 :: [a] -> [b] -> [c] -> [(a,b,c)]
513 -- zip3 = zipWith3 (,,)
514 zip3 (a:as) (b:bs) (c:cs) = (a,b,c) : zip3 as bs cs
519 -- The zipWith family generalises the zip family by zipping with the
520 -- function given as the first argument, instead of a tupling function.
521 -- For example, zipWith (+) is applied to two lists to produce the list
522 -- of corresponding sums.
526 ----------------------------------------------
527 zipWith :: (a->b->c) -> [a]->[b]->[c]
528 zipWith = zipWithList
531 zipWithFB c f x y r = (x `f` y) `c` r
533 zipWithList :: (a->b->c) -> [a] -> [b] -> [c]
534 zipWithList f (a:as) (b:bs) = f a b : zipWithList f as bs
535 zipWithList _ _ _ = []
538 "zipWith" forall f xs ys. zipWith f xs ys = build (\c n -> foldr2 (zipWithFB c f) n xs ys)
539 "zipWithList" forall f. foldr2 (zipWithFB (:) f) [] = zipWithList f
544 zipWith3 :: (a->b->c->d) -> [a]->[b]->[c]->[d]
545 zipWith3 z (a:as) (b:bs) (c:cs)
546 = z a b c : zipWith3 z as bs cs
547 zipWith3 _ _ _ _ = []
549 -- unzip transforms a list of pairs into a pair of lists.
550 unzip :: [(a,b)] -> ([a],[b])
552 unzip = foldr (\(a,b) ~(as,bs) -> (a:as,b:bs)) ([],[])
554 unzip3 :: [(a,b,c)] -> ([a],[b],[c])
555 {-# INLINE unzip3 #-}
556 unzip3 = foldr (\(a,b,c) ~(as,bs,cs) -> (a:as,b:bs,c:cs))
561 %*********************************************************
563 \subsection{Error code}
565 %*********************************************************
567 Common up near identical calls to `error' to reduce the number
568 constant strings created when compiled:
571 errorEmptyList :: String -> a
573 error (prel_list_str ++ fun ++ ": empty list")
575 errorNegativeIdx :: String -> a
576 errorNegativeIdx fun =
577 error (prel_list_str ++ fun ++ ": negative index")
579 prel_list_str :: String
580 prel_list_str = "Prelude."