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
216 = case (startsWith (reverse cs) (reverse ss)) of
218 Just rs -> Just (reverse rs)
221 Debugging/specialising versions of \tr{elem} and \tr{notElem}
223 #if defined(COMPILING_GHC)
224 isIn, isn'tIn :: (Eq a) => String -> a -> [a] -> Bool
227 isIn msg x ys = elem__ x ys
228 isn'tIn msg x ys = notElem__ x ys
230 --these are here to be SPECIALIZEd (automagically)
232 elem__ x (y:ys) = x==y || elem__ x ys
234 notElem__ x [] = True
235 notElem__ x (y:ys) = x /= y && notElem__ x ys
243 | i _GE_ ILIT(100) = panic ("Over-long elem in: " ++ msg)
244 | otherwise = x == y || elem (i _ADD_ ILIT(1)) x ys
247 = notElem ILIT(0) x ys
249 notElem i x [] = True
251 | i _GE_ ILIT(100) = panic ("Over-long notElem in: " ++ msg)
252 | otherwise = x /= y && notElem (i _ADD_ ILIT(1)) x ys
256 #endif {- COMPILING_GHC -}
259 %************************************************************************
261 \subsection[Utils-assoc]{Association lists}
263 %************************************************************************
265 See also @assocMaybe@ and @mkLookupFun@ in module @Maybes@.
268 assoc :: (Eq a) => String -> [(a, b)] -> a -> b
270 assoc crash_msg lst key
272 then panic ("Failed in assoc: " ++ crash_msg)
274 where res = [ val | (key', val) <- lst, key == key']
277 %************************************************************************
279 \subsection[Utils-dups]{Duplicate-handling}
281 %************************************************************************
284 hasNoDups :: (Eq a) => [a] -> Bool
286 hasNoDups xs = f [] xs
288 f seen_so_far [] = True
289 f seen_so_far (x:xs) = if x `is_elem` seen_so_far then
294 #if defined(COMPILING_GHC)
295 is_elem = isIn "hasNoDups"
302 equivClasses :: (a -> a -> TAG_) -- Comparison
306 equivClasses cmp stuff@[] = []
307 equivClasses cmp stuff@[item] = [stuff]
308 equivClasses cmp items
309 = runs eq (sortLt lt items)
311 eq a b = case cmp a b of { EQ_ -> True; _ -> False }
312 lt a b = case cmp a b of { LT_ -> True; _ -> False }
315 The first cases in @equivClasses@ above are just to cut to the point
318 @runs@ groups a list into a list of lists, each sublist being a run of
319 identical elements of the input list. It is passed a predicate @p@ which
320 tells when two elements are equal.
323 runs :: (a -> a -> Bool) -- Equality
328 runs p (x:xs) = case (span (p x) xs) of
329 (first, rest) -> (x:first) : (runs p rest)
333 removeDups :: (a -> a -> TAG_) -- Comparison function
335 -> ([a], -- List with no duplicates
336 [[a]]) -- List of duplicate groups. One representative from
337 -- each group appears in the first result
339 removeDups cmp [] = ([], [])
340 removeDups cmp [x] = ([x],[])
342 = case (mapAccumR collect_dups [] (equivClasses cmp xs)) of { (dups, xs') ->
345 collect_dups dups_so_far [x] = (dups_so_far, x)
346 collect_dups dups_so_far dups@(x:xs) = (dups:dups_so_far, x)
349 %************************************************************************
351 \subsection[Utils-sorting]{Sorting}
353 %************************************************************************
355 %************************************************************************
357 \subsubsection[Utils-quicksorting]{Quicksorts}
359 %************************************************************************
362 -- tail-recursive, etc., "quicker sort" [as per Meira thesis]
363 quicksort :: (a -> a -> Bool) -- Less-than predicate
365 -> [a] -- Result list in increasing order
368 quicksort lt [x] = [x]
369 quicksort lt (x:xs) = split x [] [] xs
371 split x lo hi [] = quicksort lt lo ++ (x : quicksort lt hi)
372 split x lo hi (y:ys) | y `lt` x = split x (y:lo) hi ys
373 | True = split x lo (y:hi) ys
376 Quicksort variant from Lennart's Haskell-library contribution. This
377 is a {\em stable} sort.
380 stableSortLt = sortLt -- synonym; when we want to highlight stable-ness
382 sortLt :: (a -> a -> Bool) -- Less-than predicate
384 -> [a] -- Result list
386 sortLt lt l = qsort lt l []
388 -- qsort is stable and does not concatenate.
389 qsort :: (a -> a -> Bool) -- Less-than predicate
390 -> [a] -- xs, Input list
391 -> [a] -- r, Concatenate this list to the sorted input list
392 -> [a] -- Result = sort xs ++ r
396 qsort lt (x:xs) r = qpart lt x xs [] [] r
398 -- qpart partitions and sorts the sublists
399 -- rlt contains things less than x,
400 -- rge contains the ones greater than or equal to x.
401 -- Both have equal elements reversed with respect to the original list.
403 qpart lt x [] rlt rge r =
404 -- rlt and rge are in reverse order and must be sorted with an
405 -- anti-stable sorting
406 rqsort lt rlt (x : rqsort lt rge r)
408 qpart lt x (y:ys) rlt rge r =
411 qpart lt x ys (y:rlt) rge r
414 qpart lt x ys rlt (y:rge) r
416 -- rqsort is as qsort but anti-stable, i.e. reverses equal elements
418 rqsort lt [x] r = x:r
419 rqsort lt (x:xs) r = rqpart lt x xs [] [] r
421 rqpart lt x [] rle rgt r =
422 qsort lt rle (x : qsort lt rgt r)
424 rqpart lt x (y:ys) rle rgt r =
427 rqpart lt x ys rle (y:rgt) r
430 rqpart lt x ys (y:rle) rgt r
433 %************************************************************************
435 \subsubsection[Utils-dull-mergesort]{A rather dull mergesort}
437 %************************************************************************
440 mergesort :: (a -> a -> TAG_) -> [a] -> [a]
442 mergesort cmp xs = merge_lists (split_into_runs [] xs)
444 a `le` b = case cmp a b of { LT_ -> True; EQ_ -> True; GT__ -> False }
445 a `ge` b = case cmp a b of { LT_ -> False; EQ_ -> True; GT__ -> True }
447 split_into_runs [] [] = []
448 split_into_runs run [] = [run]
449 split_into_runs [] (x:xs) = split_into_runs [x] xs
450 split_into_runs [r] (x:xs) | x `ge` r = split_into_runs [r,x] xs
451 split_into_runs rl@(r:rs) (x:xs) | x `le` r = split_into_runs (x:rl) xs
452 | True = rl : (split_into_runs [x] xs)
455 merge_lists (x:xs) = merge x (merge_lists xs)
459 merge xl@(x:xs) yl@(y:ys)
461 EQ_ -> x : y : (merge xs ys)
462 LT_ -> x : (merge xs yl)
463 GT__ -> y : (merge xl ys)
466 %************************************************************************
468 \subsubsection[Utils-Carsten-mergesort]{A mergesort from Carsten}
470 %************************************************************************
473 Date: Mon, 3 May 93 20:45:23 +0200
474 From: Carsten Kehler Holst <kehler@cs.chalmers.se>
475 To: partain@dcs.gla.ac.uk
476 Subject: natural merge sort beats quick sort [ and it is prettier ]
478 Here is a piece of Haskell code that I'm rather fond of. See it as an
479 attempt to get rid of the ridiculous quick-sort routine. group is
480 quite useful by itself I think it was John's idea originally though I
481 believe the lazy version is due to me [surprisingly complicated].
482 gamma [used to be called] is called gamma because I got inspired by
483 the Gamma calculus. It is not very close to the calculus but does
484 behave less sequentially than both foldr and foldl. One could imagine
485 a version of gamma that took a unit element as well thereby avoiding
486 the problem with empty lists.
488 I've tried this code against
490 1) insertion sort - as provided by haskell
491 2) the normal implementation of quick sort
492 3) a deforested version of quick sort due to Jan Sparud
493 4) a super-optimized-quick-sort of Lennart's
495 If the list is partially sorted both merge sort and in particular
496 natural merge sort wins. If the list is random [ average length of
497 rising subsequences = approx 2 ] mergesort still wins and natural
498 merge sort is marginally beaten by Lennart's soqs. The space
499 consumption of merge sort is a bit worse than Lennart's quick sort
500 approx a factor of 2. And a lot worse if Sparud's bug-fix [see his
501 fpca article ] isn't used because of group.
508 group :: (a -> a -> Bool) -> [a] -> [[a]]
511 Date: Mon, 12 Feb 1996 15:09:41 +0000
512 From: Andy Gill <andy@dcs.gla.ac.uk>
514 Here is a `better' definition of group.
517 group p (x:xs) = group' xs x x (x :)
519 group' [] _ _ s = [s []]
520 group' (x:xs) x_min x_max s
521 | not (x `p` x_max) = group' xs x_min x (s . (x :))
522 | x `p` x_min = group' xs x x_max ((x :) . s)
523 | otherwise = s [] : group' xs x x (x :)
525 -- This one works forwards *and* backwards, as well as also being
526 -- faster that the one in Util.lhs.
531 let ((h1:t1):tt1) = group p xs
532 (t,tt) = if null xs then ([],[]) else
533 if x `p` h1 then (h1:t1,tt1) else
538 generalMerge :: (a -> a -> Bool) -> [a] -> [a] -> [a]
539 generalMerge p xs [] = xs
540 generalMerge p [] ys = ys
541 generalMerge p (x:xs) (y:ys) | x `p` y = x : generalMerge p xs (y:ys)
542 | otherwise = y : generalMerge p (x:xs) ys
544 -- gamma is now called balancedFold
546 balancedFold :: (a -> a -> a) -> [a] -> a
547 balancedFold f [] = error "can't reduce an empty list using balancedFold"
548 balancedFold f [x] = x
549 balancedFold f l = balancedFold f (balancedFold' f l)
551 balancedFold' :: (a -> a -> a) -> [a] -> [a]
552 balancedFold' f (x:y:xs) = f x y : balancedFold' f xs
553 balancedFold' f xs = xs
555 generalMergeSort p [] = []
556 generalMergeSort p xs = (balancedFold (generalMerge p) . map (: [])) xs
558 generalNaturalMergeSort p [] = []
559 generalNaturalMergeSort p xs = (balancedFold (generalMerge p) . group p) xs
561 mergeSort, naturalMergeSort :: Ord a => [a] -> [a]
563 mergeSort = generalMergeSort (<=)
564 naturalMergeSort = generalNaturalMergeSort (<=)
566 mergeSortLe le = generalMergeSort le
567 naturalMergeSortLe le = generalNaturalMergeSort le
570 %************************************************************************
572 \subsection[Utils-transitive-closure]{Transitive closure}
574 %************************************************************************
576 This algorithm for transitive closure is straightforward, albeit quadratic.
579 transitiveClosure :: (a -> [a]) -- Successor function
580 -> (a -> a -> Bool) -- Equality predicate
582 -> [a] -- The transitive closure
584 transitiveClosure succ eq xs
588 go done (x:xs) | x `is_in` done = go done xs
589 | otherwise = go (x:done) (succ x ++ xs)
592 x `is_in` (y:ys) | eq x y = True
593 | otherwise = x `is_in` ys
596 %************************************************************************
598 \subsection[Utils-accum]{Accumulating}
600 %************************************************************************
602 @mapAccumL@ behaves like a combination
603 of @map@ and @foldl@;
604 it applies a function to each element of a list, passing an accumulating
605 parameter from left to right, and returning a final value of this
606 accumulator together with the new list.
609 mapAccumL :: (acc -> x -> (acc, y)) -- Function of elt of input list
610 -- and accumulator, returning new
611 -- accumulator and elt of result list
612 -> acc -- Initial accumulator
614 -> (acc, [y]) -- Final accumulator and result list
616 mapAccumL f b [] = (b, [])
617 mapAccumL f b (x:xs) = (b'', x':xs') where
619 (b'', xs') = mapAccumL f b' xs
622 @mapAccumR@ does the same, but working from right to left instead. Its type is
623 the same as @mapAccumL@, though.
626 mapAccumR :: (acc -> x -> (acc, y)) -- Function of elt of input list
627 -- and accumulator, returning new
628 -- accumulator and elt of result list
629 -> acc -- Initial accumulator
631 -> (acc, [y]) -- Final accumulator and result list
633 mapAccumR f b [] = (b, [])
634 mapAccumR f b (x:xs) = (b'', x':xs') where
636 (b', xs') = mapAccumR f b xs
639 Here is the bi-directional version, that works from both left and right.
642 mapAccumB :: (accl -> accr -> x -> (accl, accr,y))
643 -- Function of elt of input list
644 -- and accumulator, returning new
645 -- accumulator and elt of result list
646 -> accl -- Initial accumulator from left
647 -> accr -- Initial accumulator from right
649 -> (accl, accr, [y]) -- Final accumulators and result list
651 mapAccumB f a b [] = (a,b,[])
652 mapAccumB f a b (x:xs) = (a'',b'',y:ys)
654 (a',b'',y) = f a b' x
655 (a'',b',ys) = mapAccumB f a' b xs
658 %************************************************************************
660 \subsection[Utils-comparison]{Comparisons}
662 %************************************************************************
664 See also @tagCmp_@ near the versions-compatibility section.
666 The Ord3 class will be subsumed into Ord in Haskell 1.3.
670 cmp :: a -> a -> TAG_
672 thenCmp :: TAG_ -> TAG_ -> TAG_
673 {-# INLINE thenCmp #-}
674 thenCmp EQ_ any = any
675 thenCmp other any = other
677 cmpList :: (a -> a -> TAG_) -> [a] -> [a] -> TAG_
678 -- `cmpList' uses a user-specified comparer
680 cmpList cmp [] [] = EQ_
681 cmpList cmp [] _ = LT_
682 cmpList cmp _ [] = GT_
683 cmpList cmp (a:as) (b:bs)
684 = case cmp a b of { EQ_ -> cmpList cmp as bs; xxx -> xxx }
688 instance Ord3 a => Ord3 [a] where
692 cmp (x:xs) (y:ys) = (x `cmp` y) `thenCmp` (xs `cmp` ys)
694 instance Ord3 a => Ord3 (Maybe a) where
695 cmp Nothing Nothing = EQ_
696 cmp Nothing (Just y) = LT_
697 cmp (Just x) Nothing = GT_
698 cmp (Just x) (Just y) = x `cmp` y
700 instance Ord3 Int where
701 cmp a b | a < b = LT_
707 cmpString :: String -> String -> TAG_
709 cmpString [] [] = EQ_
710 cmpString (x:xs) (y:ys) = if x == y then cmpString xs ys
711 else if x < y then LT_
713 cmpString [] ys = LT_
714 cmpString xs [] = GT_
716 cmpString _ _ = panic# "cmpString"
720 cmpPString :: FAST_STRING -> FAST_STRING -> TAG_
723 = case (_tagCmp x y) of { _LT -> LT_ ; _EQ -> EQ_ ; _GT -> GT_ }
726 %************************************************************************
728 \subsection[Utils-pairs]{Pairs}
730 %************************************************************************
732 The following are curried versions of @fst@ and @snd@.
735 cfst :: a -> b -> a -- stranal-sem only (Note)
739 The following provide us higher order functions that, when applied
740 to a function, operate on pairs.
743 applyToPair :: ((a -> c),(b -> d)) -> (a,b) -> (c,d)
744 applyToPair (f,g) (x,y) = (f x, g y)
746 applyToFst :: (a -> c) -> (a,b)-> (c,b)
747 applyToFst f (x,y) = (f x,y)
749 applyToSnd :: (b -> d) -> (a,b) -> (a,d)
750 applyToSnd f (x,y) = (x,f y)
752 foldPair :: (a->a->a,b->b->b) -> (a,b) -> [(a,b)] -> (a,b)
753 foldPair fg ab [] = ab
754 foldPair fg@(f,g) ab ((a,b):abs) = (f a u,g b v)
755 where (u,v) = foldPair fg ab abs
759 unzipWith :: (a -> b -> c) -> [(a, b)] -> [c]
760 unzipWith f pairs = map ( \ (a, b) -> f a b ) pairs
763 %************************************************************************
765 \subsection[Utils-errors]{Error handling}
767 %************************************************************************
770 #if defined(COMPILING_GHC)
771 panic x = error ("panic! (the `impossible' happened):\n\t"
773 ++ "Please report it as a compiler bug "
774 ++ "to glasgow-haskell-bugs@dcs.glasgow.ac.uk.\n\n" )
776 pprPanic heading pretty_msg = panic (heading++(ppShow 80 pretty_msg))
777 pprError heading pretty_msg = error (heading++(ppShow 80 pretty_msg))
778 pprTrace heading pretty_msg = trace (heading++(ppShow 80 pretty_msg))
780 -- #-versions because panic can't return an unboxed int, and that's
781 -- what TAG_ is with GHC at the moment. Ugh. (Simon)
782 -- No, man -- Too Beautiful! (Will)
784 panic# :: String -> TAG_
785 panic# s = case (panic s) of () -> EQ_
787 pprPanic# heading pretty_msg = panic# (heading++(ppShow 80 pretty_msg))
789 assertPanic :: String -> Int -> a
790 assertPanic file line = panic ("ASSERT failed! file "++file++", line "++show line)
792 #endif {- COMPILING_GHC -}