2 % (c) The GRASP/AQUA Project, Glasgow University, 1992-1996
4 \section[Util]{Highly random utility functions}
7 #if defined(COMPILING_GHC)
8 # include "HsVersions.h"
9 # define IF_NOT_GHC(a) {--}
12 # define TAG_ _CMP_TAG
17 # define tagCmp_ _tagCmp
18 # define FAST_STRING String
19 # define ASSERT(x) {-nothing-}
20 # define IF_NOT_GHC(a) a
24 #ifndef __GLASGOW_HASKELL__
33 -- Haskell-version support
34 #ifndef __GLASGOW_HASKELL__
38 -- general list processing
39 IF_NOT_GHC(forall COMMA exists COMMA)
40 zipEqual, zipWithEqual, zipWith3Equal, zipWith4Equal,
42 mapAndUnzip, mapAndUnzip3,
43 nOfThem, lengthExceeds, isSingleton,
45 #if defined(COMPILING_GHC)
53 hasNoDups, equivClasses, runs, removeDups,
56 IF_NOT_GHC(quicksort COMMA stableSortLt COMMA mergesort COMMA)
58 IF_NOT_GHC(mergeSort COMMA) naturalMergeSortLe, -- from Carsten
59 IF_NOT_GHC(naturalMergeSort COMMA mergeSortLe COMMA)
61 -- transitive closures
65 mapAccumL, mapAccumR, mapAccumB,
68 Ord3(..), thenCmp, cmpList,
69 IF_NOT_GHC(cmpString COMMA)
73 IF_NOT_GHC(cfst COMMA applyToPair COMMA applyToFst COMMA)
74 IF_NOT_GHC(applyToSnd COMMA foldPair COMMA)
78 #if defined(COMPILING_GHC)
79 , panic, panic#, pprPanic, pprPanic#, pprError, pprTrace
81 #endif {- COMPILING_GHC -}
85 #if defined(COMPILING_GHC)
87 CHK_Ubiq() -- debugging consistency check
95 %************************************************************************
97 \subsection[Utils-version-support]{Functions to help pre-1.2 versions of (non-Glasgow) Haskell}
99 %************************************************************************
101 This is our own idea:
103 #ifndef __GLASGOW_HASKELL__
104 data TAG_ = LT_ | EQ_ | GT_
106 tagCmp_ :: Ord a => a -> a -> TAG_
107 tagCmp_ a b = if a == b then EQ_ else if a < b then LT_ else GT_
111 %************************************************************************
113 \subsection[Utils-lists]{General list processing}
115 %************************************************************************
117 Quantifiers are not standard in Haskell. The following fill in the gap.
120 forall :: (a -> Bool) -> [a] -> Bool
121 forall pred [] = True
122 forall pred (x:xs) = pred x && forall pred xs
124 exists :: (a -> Bool) -> [a] -> Bool
125 exists pred [] = False
126 exists pred (x:xs) = pred x || exists pred xs
129 A paranoid @zip@ (and some @zipWith@ friends) that checks the lists
130 are of equal length. Alastair Reid thinks this should only happen if
131 DEBUGging on; hey, why not?
134 zipEqual :: String -> [a] -> [b] -> [(a,b)]
135 zipWithEqual :: String -> (a->b->c) -> [a]->[b]->[c]
136 zipWith3Equal :: String -> (a->b->c->d) -> [a]->[b]->[c]->[d]
137 zipWith4Equal :: String -> (a->b->c->d->e) -> [a]->[b]->[c]->[d]->[e]
141 zipWithEqual _ = zipWith
142 zipWith3Equal _ = zipWith3
143 zipWith4Equal _ = zipWith4
145 zipEqual msg [] [] = []
146 zipEqual msg (a:as) (b:bs) = (a,b) : zipEqual msg as bs
147 zipEqual msg as bs = panic ("zipEqual: unequal lists:"++msg)
149 zipWithEqual msg z (a:as) (b:bs)= z a b : zipWithEqual msg z as bs
150 zipWithEqual msg _ [] [] = []
151 zipWithEqual msg _ _ _ = panic ("zipWithEqual: unequal lists:"++msg)
153 zipWith3Equal msg z (a:as) (b:bs) (c:cs)
154 = z a b c : zipWith3Equal msg z as bs cs
155 zipWith3Equal msg _ [] [] [] = []
156 zipWith3Equal msg _ _ _ _ = panic ("zipWith3Equal: unequal lists:"++msg)
158 zipWith4Equal msg z (a:as) (b:bs) (c:cs) (d:ds)
159 = z a b c d : zipWith4Equal msg z as bs cs ds
160 zipWith4Equal msg _ [] [] [] [] = []
161 zipWith4Equal msg _ _ _ _ _ = panic ("zipWith4Equal: unequal lists:"++msg)
166 -- zipLazy is lazy in the second list (observe the ~)
168 zipLazy :: [a] -> [b] -> [(a,b)]
170 zipLazy (x:xs) ~(y:ys) = (x,y) : zipLazy xs ys
174 mapAndUnzip :: (a -> (b, c)) -> [a] -> ([b], [c])
176 mapAndUnzip f [] = ([],[])
180 (rs1, rs2) = mapAndUnzip f xs
184 mapAndUnzip3 :: (a -> (b, c, d)) -> [a] -> ([b], [c], [d])
186 mapAndUnzip3 f [] = ([],[],[])
187 mapAndUnzip3 f (x:xs)
190 (rs1, rs2, rs3) = mapAndUnzip3 f xs
192 (r1:rs1, r2:rs2, r3:rs3)
196 nOfThem :: Int -> a -> [a]
197 nOfThem n thing = take n (repeat thing)
199 lengthExceeds :: [a] -> Int -> Bool
201 [] `lengthExceeds` n = 0 > n
202 (x:xs) `lengthExceeds` n = (1 > n) || (xs `lengthExceeds` (n - 1))
204 isSingleton :: [a] -> Bool
206 isSingleton [x] = True
207 isSingleton _ = False
209 startsWith, endsWith :: String -> String -> Maybe String
211 startsWith [] str = Just str
212 startsWith (c:cs) (s:ss)
213 = if c /= s then Nothing else startsWith cs ss
214 startWith _ [] = Nothing
217 = case (startsWith (reverse cs) (reverse ss)) of
219 Just rs -> Just (reverse rs)
222 Debugging/specialising versions of \tr{elem} and \tr{notElem}
224 #if defined(COMPILING_GHC)
225 isIn, isn'tIn :: (Eq a) => String -> a -> [a] -> Bool
228 isIn msg x ys = elem__ x ys
229 isn'tIn msg x ys = notElem__ x ys
231 --these are here to be SPECIALIZEd (automagically)
233 elem__ x (y:ys) = x==y || elem__ x ys
235 notElem__ x [] = True
236 notElem__ x (y:ys) = x /= y && notElem__ x ys
244 | i _GE_ ILIT(100) = panic ("Over-long elem in: " ++ msg)
245 | otherwise = x == y || elem (i _ADD_ ILIT(1)) x ys
248 = notElem ILIT(0) x ys
250 notElem i x [] = True
252 | i _GE_ ILIT(100) = panic ("Over-long notElem in: " ++ msg)
253 | otherwise = x /= y && notElem (i _ADD_ ILIT(1)) x ys
257 #endif {- COMPILING_GHC -}
260 %************************************************************************
262 \subsection[Utils-assoc]{Association lists}
264 %************************************************************************
266 See also @assocMaybe@ and @mkLookupFun@ in module @Maybes@.
269 assoc :: (Eq a) => String -> [(a, b)] -> a -> b
271 assoc crash_msg lst key
273 then panic ("Failed in assoc: " ++ crash_msg)
275 where res = [ val | (key', val) <- lst, key == key']
278 %************************************************************************
280 \subsection[Utils-dups]{Duplicate-handling}
282 %************************************************************************
285 hasNoDups :: (Eq a) => [a] -> Bool
287 hasNoDups xs = f [] xs
289 f seen_so_far [] = True
290 f seen_so_far (x:xs) = if x `is_elem` seen_so_far then
295 #if defined(COMPILING_GHC)
296 is_elem = isIn "hasNoDups"
303 equivClasses :: (a -> a -> TAG_) -- Comparison
307 equivClasses cmp stuff@[] = []
308 equivClasses cmp stuff@[item] = [stuff]
309 equivClasses cmp items
310 = runs eq (sortLt lt items)
312 eq a b = case cmp a b of { EQ_ -> True; _ -> False }
313 lt a b = case cmp a b of { LT_ -> True; _ -> False }
316 The first cases in @equivClasses@ above are just to cut to the point
319 @runs@ groups a list into a list of lists, each sublist being a run of
320 identical elements of the input list. It is passed a predicate @p@ which
321 tells when two elements are equal.
324 runs :: (a -> a -> Bool) -- Equality
329 runs p (x:xs) = case (span (p x) xs) of
330 (first, rest) -> (x:first) : (runs p rest)
334 removeDups :: (a -> a -> TAG_) -- Comparison function
336 -> ([a], -- List with no duplicates
337 [[a]]) -- List of duplicate groups. One representative from
338 -- each group appears in the first result
340 removeDups cmp [] = ([], [])
341 removeDups cmp [x] = ([x],[])
343 = case (mapAccumR collect_dups [] (equivClasses cmp xs)) of { (dups, xs') ->
346 collect_dups dups_so_far [x] = (dups_so_far, x)
347 collect_dups dups_so_far dups@(x:xs) = (dups:dups_so_far, x)
350 %************************************************************************
352 \subsection[Utils-sorting]{Sorting}
354 %************************************************************************
356 %************************************************************************
358 \subsubsection[Utils-quicksorting]{Quicksorts}
360 %************************************************************************
363 -- tail-recursive, etc., "quicker sort" [as per Meira thesis]
364 quicksort :: (a -> a -> Bool) -- Less-than predicate
366 -> [a] -- Result list in increasing order
369 quicksort lt [x] = [x]
370 quicksort lt (x:xs) = split x [] [] xs
372 split x lo hi [] = quicksort lt lo ++ (x : quicksort lt hi)
373 split x lo hi (y:ys) | y `lt` x = split x (y:lo) hi ys
374 | True = split x lo (y:hi) ys
377 Quicksort variant from Lennart's Haskell-library contribution. This
378 is a {\em stable} sort.
381 stableSortLt = sortLt -- synonym; when we want to highlight stable-ness
383 sortLt :: (a -> a -> Bool) -- Less-than predicate
385 -> [a] -- Result list
387 sortLt lt l = qsort lt l []
389 -- qsort is stable and does not concatenate.
390 qsort :: (a -> a -> Bool) -- Less-than predicate
391 -> [a] -- xs, Input list
392 -> [a] -- r, Concatenate this list to the sorted input list
393 -> [a] -- Result = sort xs ++ r
397 qsort lt (x:xs) r = qpart lt x xs [] [] r
399 -- qpart partitions and sorts the sublists
400 -- rlt contains things less than x,
401 -- rge contains the ones greater than or equal to x.
402 -- Both have equal elements reversed with respect to the original list.
404 qpart lt x [] rlt rge r =
405 -- rlt and rge are in reverse order and must be sorted with an
406 -- anti-stable sorting
407 rqsort lt rlt (x : rqsort lt rge r)
409 qpart lt x (y:ys) rlt rge r =
412 qpart lt x ys (y:rlt) rge r
415 qpart lt x ys rlt (y:rge) r
417 -- rqsort is as qsort but anti-stable, i.e. reverses equal elements
419 rqsort lt [x] r = x:r
420 rqsort lt (x:xs) r = rqpart lt x xs [] [] r
422 rqpart lt x [] rle rgt r =
423 qsort lt rle (x : qsort lt rgt r)
425 rqpart lt x (y:ys) rle rgt r =
428 rqpart lt x ys rle (y:rgt) r
431 rqpart lt x ys (y:rle) rgt r
434 %************************************************************************
436 \subsubsection[Utils-dull-mergesort]{A rather dull mergesort}
438 %************************************************************************
441 mergesort :: (a -> a -> TAG_) -> [a] -> [a]
443 mergesort cmp xs = merge_lists (split_into_runs [] xs)
445 a `le` b = case cmp a b of { LT_ -> True; EQ_ -> True; GT__ -> False }
446 a `ge` b = case cmp a b of { LT_ -> False; EQ_ -> True; GT__ -> True }
448 split_into_runs [] [] = []
449 split_into_runs run [] = [run]
450 split_into_runs [] (x:xs) = split_into_runs [x] xs
451 split_into_runs [r] (x:xs) | x `ge` r = split_into_runs [r,x] xs
452 split_into_runs rl@(r:rs) (x:xs) | x `le` r = split_into_runs (x:rl) xs
453 | True = rl : (split_into_runs [x] xs)
456 merge_lists (x:xs) = merge x (merge_lists xs)
460 merge xl@(x:xs) yl@(y:ys)
462 EQ_ -> x : y : (merge xs ys)
463 LT_ -> x : (merge xs yl)
464 GT__ -> y : (merge xl ys)
467 %************************************************************************
469 \subsubsection[Utils-Carsten-mergesort]{A mergesort from Carsten}
471 %************************************************************************
474 Date: Mon, 3 May 93 20:45:23 +0200
475 From: Carsten Kehler Holst <kehler@cs.chalmers.se>
476 To: partain@dcs.gla.ac.uk
477 Subject: natural merge sort beats quick sort [ and it is prettier ]
479 Here is a piece of Haskell code that I'm rather fond of. See it as an
480 attempt to get rid of the ridiculous quick-sort routine. group is
481 quite useful by itself I think it was John's idea originally though I
482 believe the lazy version is due to me [surprisingly complicated].
483 gamma [used to be called] is called gamma because I got inspired by
484 the Gamma calculus. It is not very close to the calculus but does
485 behave less sequentially than both foldr and foldl. One could imagine
486 a version of gamma that took a unit element as well thereby avoiding
487 the problem with empty lists.
489 I've tried this code against
491 1) insertion sort - as provided by haskell
492 2) the normal implementation of quick sort
493 3) a deforested version of quick sort due to Jan Sparud
494 4) a super-optimized-quick-sort of Lennart's
496 If the list is partially sorted both merge sort and in particular
497 natural merge sort wins. If the list is random [ average length of
498 rising subsequences = approx 2 ] mergesort still wins and natural
499 merge sort is marginally beaten by Lennart's soqs. The space
500 consumption of merge sort is a bit worse than Lennart's quick sort
501 approx a factor of 2. And a lot worse if Sparud's bug-fix [see his
502 fpca article ] isn't used because of group.
509 group :: (a -> a -> Bool) -> [a] -> [[a]]
512 Date: Mon, 12 Feb 1996 15:09:41 +0000
513 From: Andy Gill <andy@dcs.gla.ac.uk>
515 Here is a `better' definition of group.
518 group p (x:xs) = group' xs x x (x :)
520 group' [] _ _ s = [s []]
521 group' (x:xs) x_min x_max s
522 | not (x `p` x_max) = group' xs x_min x (s . (x :))
523 | x `p` x_min = group' xs x x_max ((x :) . s)
524 | otherwise = s [] : group' xs x x (x :)
526 -- This one works forwards *and* backwards, as well as also being
527 -- faster that the one in Util.lhs.
532 let ((h1:t1):tt1) = group p xs
533 (t,tt) = if null xs then ([],[]) else
534 if x `p` h1 then (h1:t1,tt1) else
539 generalMerge :: (a -> a -> Bool) -> [a] -> [a] -> [a]
540 generalMerge p xs [] = xs
541 generalMerge p [] ys = ys
542 generalMerge p (x:xs) (y:ys) | x `p` y = x : generalMerge p xs (y:ys)
543 | otherwise = y : generalMerge p (x:xs) ys
545 -- gamma is now called balancedFold
547 balancedFold :: (a -> a -> a) -> [a] -> a
548 balancedFold f [] = error "can't reduce an empty list using balancedFold"
549 balancedFold f [x] = x
550 balancedFold f l = balancedFold f (balancedFold' f l)
552 balancedFold' :: (a -> a -> a) -> [a] -> [a]
553 balancedFold' f (x:y:xs) = f x y : balancedFold' f xs
554 balancedFold' f xs = xs
556 generalMergeSort p [] = []
557 generalMergeSort p xs = (balancedFold (generalMerge p) . map (: [])) xs
559 generalNaturalMergeSort p [] = []
560 generalNaturalMergeSort p xs = (balancedFold (generalMerge p) . group p) xs
562 mergeSort, naturalMergeSort :: Ord a => [a] -> [a]
564 mergeSort = generalMergeSort (<=)
565 naturalMergeSort = generalNaturalMergeSort (<=)
567 mergeSortLe le = generalMergeSort le
568 naturalMergeSortLe le = generalNaturalMergeSort le
571 %************************************************************************
573 \subsection[Utils-transitive-closure]{Transitive closure}
575 %************************************************************************
577 This algorithm for transitive closure is straightforward, albeit quadratic.
580 transitiveClosure :: (a -> [a]) -- Successor function
581 -> (a -> a -> Bool) -- Equality predicate
583 -> [a] -- The transitive closure
585 transitiveClosure succ eq xs
589 go done (x:xs) | x `is_in` done = go done xs
590 | otherwise = go (x:done) (succ x ++ xs)
593 x `is_in` (y:ys) | eq x y = True
594 | otherwise = x `is_in` ys
597 %************************************************************************
599 \subsection[Utils-accum]{Accumulating}
601 %************************************************************************
603 @mapAccumL@ behaves like a combination
604 of @map@ and @foldl@;
605 it applies a function to each element of a list, passing an accumulating
606 parameter from left to right, and returning a final value of this
607 accumulator together with the new list.
610 mapAccumL :: (acc -> x -> (acc, y)) -- Function of elt of input list
611 -- and accumulator, returning new
612 -- accumulator and elt of result list
613 -> acc -- Initial accumulator
615 -> (acc, [y]) -- Final accumulator and result list
617 mapAccumL f b [] = (b, [])
618 mapAccumL f b (x:xs) = (b'', x':xs') where
620 (b'', xs') = mapAccumL f b' xs
623 @mapAccumR@ does the same, but working from right to left instead. Its type is
624 the same as @mapAccumL@, though.
627 mapAccumR :: (acc -> x -> (acc, y)) -- Function of elt of input list
628 -- and accumulator, returning new
629 -- accumulator and elt of result list
630 -> acc -- Initial accumulator
632 -> (acc, [y]) -- Final accumulator and result list
634 mapAccumR f b [] = (b, [])
635 mapAccumR f b (x:xs) = (b'', x':xs') where
637 (b', xs') = mapAccumR f b xs
640 Here is the bi-directional version, that works from both left and right.
643 mapAccumB :: (accl -> accr -> x -> (accl, accr,y))
644 -- Function of elt of input list
645 -- and accumulator, returning new
646 -- accumulator and elt of result list
647 -> accl -- Initial accumulator from left
648 -> accr -- Initial accumulator from right
650 -> (accl, accr, [y]) -- Final accumulators and result list
652 mapAccumB f a b [] = (a,b,[])
653 mapAccumB f a b (x:xs) = (a'',b'',y:ys)
655 (a',b'',y) = f a b' x
656 (a'',b',ys) = mapAccumB f a' b xs
659 %************************************************************************
661 \subsection[Utils-comparison]{Comparisons}
663 %************************************************************************
665 See also @tagCmp_@ near the versions-compatibility section.
667 The Ord3 class will be subsumed into Ord in Haskell 1.3.
671 cmp :: a -> a -> TAG_
673 thenCmp :: TAG_ -> TAG_ -> TAG_
674 {-# INLINE thenCmp #-}
675 thenCmp EQ_ any = any
676 thenCmp other any = other
678 cmpList :: (a -> a -> TAG_) -> [a] -> [a] -> TAG_
679 -- `cmpList' uses a user-specified comparer
681 cmpList cmp [] [] = EQ_
682 cmpList cmp [] _ = LT_
683 cmpList cmp _ [] = GT_
684 cmpList cmp (a:as) (b:bs)
685 = case cmp a b of { EQ_ -> cmpList cmp as bs; xxx -> xxx }
689 instance Ord3 a => Ord3 [a] where
693 cmp (x:xs) (y:ys) = (x `cmp` y) `thenCmp` (xs `cmp` ys)
695 instance Ord3 a => Ord3 (Maybe a) where
696 cmp Nothing Nothing = EQ_
697 cmp Nothing (Just y) = LT_
698 cmp (Just x) Nothing = GT_
699 cmp (Just x) (Just y) = x `cmp` y
701 instance Ord3 Int where
702 cmp a b | a < b = LT_
708 cmpString :: String -> String -> TAG_
710 cmpString [] [] = EQ_
711 cmpString (x:xs) (y:ys) = if x == y then cmpString xs ys
712 else if x < y then LT_
714 cmpString [] ys = LT_
715 cmpString xs [] = GT_
717 cmpString _ _ = panic# "cmpString"
721 cmpPString :: FAST_STRING -> FAST_STRING -> TAG_
724 = case (_tagCmp x y) of { _LT -> LT_ ; _EQ -> EQ_ ; _GT -> GT_ }
727 %************************************************************************
729 \subsection[Utils-pairs]{Pairs}
731 %************************************************************************
733 The following are curried versions of @fst@ and @snd@.
736 cfst :: a -> b -> a -- stranal-sem only (Note)
740 The following provide us higher order functions that, when applied
741 to a function, operate on pairs.
744 applyToPair :: ((a -> c),(b -> d)) -> (a,b) -> (c,d)
745 applyToPair (f,g) (x,y) = (f x, g y)
747 applyToFst :: (a -> c) -> (a,b)-> (c,b)
748 applyToFst f (x,y) = (f x,y)
750 applyToSnd :: (b -> d) -> (a,b) -> (a,d)
751 applyToSnd f (x,y) = (x,f y)
753 foldPair :: (a->a->a,b->b->b) -> (a,b) -> [(a,b)] -> (a,b)
754 foldPair fg ab [] = ab
755 foldPair fg@(f,g) ab ((a,b):abs) = (f a u,g b v)
756 where (u,v) = foldPair fg ab abs
760 unzipWith :: (a -> b -> c) -> [(a, b)] -> [c]
761 unzipWith f pairs = map ( \ (a, b) -> f a b ) pairs
764 %************************************************************************
766 \subsection[Utils-errors]{Error handling}
768 %************************************************************************
771 #if defined(COMPILING_GHC)
772 panic x = error ("panic! (the `impossible' happened):\n\t"
774 ++ "Please report it as a compiler bug "
775 ++ "to glasgow-haskell-bugs@dcs.glasgow.ac.uk.\n\n" )
777 pprPanic heading pretty_msg = panic (heading++(ppShow 80 pretty_msg))
778 pprError heading pretty_msg = error (heading++(ppShow 80 pretty_msg))
779 pprTrace heading pretty_msg = trace (heading++(ppShow 80 pretty_msg))
781 -- #-versions because panic can't return an unboxed int, and that's
782 -- what TAG_ is with GHC at the moment. Ugh. (Simon)
783 -- No, man -- Too Beautiful! (Will)
785 panic# :: String -> TAG_
786 panic# s = case (panic s) of () -> EQ_
788 pprPanic# heading pretty_msg = panic# (heading++(ppShow 80 pretty_msg))
790 assertPanic :: String -> Int -> a
791 assertPanic file line = panic ("ASSERT failed! file "++file++", line "++show line)
793 #endif {- COMPILING_GHC -}