2 % (c) The GRASP/AQUA Project, Glasgow University, 1992-1998
4 \section[Util]{Highly random utility functions}
7 -- IF_NOT_GHC is meant to make this module useful outside the context of GHC
13 Eager, thenEager, returnEager, mapEager, appEager, runEager,
16 -- general list processing
17 zipEqual, zipWithEqual, zipWith3Equal, zipWith4Equal,
18 zipLazy, stretchZipWith,
19 mapAndUnzip, mapAndUnzip3,
20 nOfThem, lengthExceeds, isSingleton, only,
28 IF_NOT_GHC(quicksort COMMA stableSortLt COMMA mergesort COMMA)
30 IF_NOT_GHC(mergeSort COMMA) naturalMergeSortLe, -- from Carsten
31 IF_NOT_GHC(naturalMergeSort COMMA mergeSortLe COMMA)
33 -- transitive closures
37 mapAccumL, mapAccumR, mapAccumB, foldl2, count,
40 thenCmp, cmpList, prefixMatch, postfixMatch,
46 IF_NOT_GHC(cfst COMMA applyToPair COMMA applyToFst COMMA)
47 IF_NOT_GHC(applyToSnd COMMA foldPair COMMA)
51 #if __GLASGOW_HASKELL__ < 402
59 #include "HsVersions.h"
61 import List ( zipWith4 )
62 import Panic ( panic )
63 import IOExts ( IORef, newIORef, unsafePerformIO )
68 %************************************************************************
70 \subsection{The Eager monad}
72 %************************************************************************
74 The @Eager@ monad is just an encoding of continuation-passing style,
75 used to allow you to express "do this and then that", mainly to avoid
76 space leaks. It's done with a type synonym to save bureaucracy.
81 type Eager ans a = (a -> ans) -> ans
83 runEager :: Eager a a -> a
84 runEager m = m (\x -> x)
86 appEager :: Eager ans a -> (a -> ans) -> ans
87 appEager m cont = m cont
89 thenEager :: Eager ans a -> (a -> Eager ans b) -> Eager ans b
90 thenEager m k cont = m (\r -> k r cont)
92 returnEager :: a -> Eager ans a
93 returnEager v cont = cont v
95 mapEager :: (a -> Eager ans b) -> [a] -> Eager ans [b]
96 mapEager f [] = returnEager []
97 mapEager f (x:xs) = f x `thenEager` \ y ->
98 mapEager f xs `thenEager` \ ys ->
103 %************************************************************************
105 \subsection{A for loop}
107 %************************************************************************
110 -- Compose a function with itself n times. (nth rather than twice)
111 nTimes :: Int -> (a -> a) -> (a -> a)
114 nTimes n f = f . nTimes (n-1) f
118 %************************************************************************
120 \subsection[Utils-lists]{General list processing}
122 %************************************************************************
124 A paranoid @zip@ (and some @zipWith@ friends) that checks the lists
125 are of equal length. Alastair Reid thinks this should only happen if
126 DEBUGging on; hey, why not?
129 zipEqual :: String -> [a] -> [b] -> [(a,b)]
130 zipWithEqual :: String -> (a->b->c) -> [a]->[b]->[c]
131 zipWith3Equal :: String -> (a->b->c->d) -> [a]->[b]->[c]->[d]
132 zipWith4Equal :: String -> (a->b->c->d->e) -> [a]->[b]->[c]->[d]->[e]
136 zipWithEqual _ = zipWith
137 zipWith3Equal _ = zipWith3
138 zipWith4Equal _ = zipWith4
140 zipEqual msg [] [] = []
141 zipEqual msg (a:as) (b:bs) = (a,b) : zipEqual msg as bs
142 zipEqual msg as bs = panic ("zipEqual: unequal lists:"++msg)
144 zipWithEqual msg z (a:as) (b:bs)= z a b : zipWithEqual msg z as bs
145 zipWithEqual msg _ [] [] = []
146 zipWithEqual msg _ _ _ = panic ("zipWithEqual: unequal lists:"++msg)
148 zipWith3Equal msg z (a:as) (b:bs) (c:cs)
149 = z a b c : zipWith3Equal msg z as bs cs
150 zipWith3Equal msg _ [] [] [] = []
151 zipWith3Equal msg _ _ _ _ = panic ("zipWith3Equal: unequal lists:"++msg)
153 zipWith4Equal msg z (a:as) (b:bs) (c:cs) (d:ds)
154 = z a b c d : zipWith4Equal msg z as bs cs ds
155 zipWith4Equal msg _ [] [] [] [] = []
156 zipWith4Equal msg _ _ _ _ _ = panic ("zipWith4Equal: unequal lists:"++msg)
161 -- zipLazy is lazy in the second list (observe the ~)
163 zipLazy :: [a] -> [b] -> [(a,b)]
165 zipLazy (x:xs) ~(y:ys) = (x,y) : zipLazy xs ys
170 stretchZipWith :: (a -> Bool) -> b -> (a->b->c) -> [a] -> [b] -> [c]
171 -- (stretchZipWith p z f xs ys) stretches ys by inserting z in
172 -- the places where p returns *True*
174 stretchZipWith p z f [] ys = []
175 stretchZipWith p z f (x:xs) ys
176 | p x = f x z : stretchZipWith p z f xs ys
177 | otherwise = case ys of
179 (y:ys) -> f x y : stretchZipWith p z f xs ys
184 mapAndUnzip :: (a -> (b, c)) -> [a] -> ([b], [c])
186 mapAndUnzip f [] = ([],[])
190 (rs1, rs2) = mapAndUnzip f xs
194 mapAndUnzip3 :: (a -> (b, c, d)) -> [a] -> ([b], [c], [d])
196 mapAndUnzip3 f [] = ([],[],[])
197 mapAndUnzip3 f (x:xs)
200 (rs1, rs2, rs3) = mapAndUnzip3 f xs
202 (r1:rs1, r2:rs2, r3:rs3)
206 nOfThem :: Int -> a -> [a]
207 nOfThem n thing = replicate n thing
209 lengthExceeds :: [a] -> Int -> Bool
210 -- (lengthExceeds xs n) is True if length xs > n
211 (x:xs) `lengthExceeds` n = n < 1 || xs `lengthExceeds` (n - 1)
212 [] `lengthExceeds` n = n < 0
214 isSingleton :: [a] -> Bool
215 isSingleton [x] = True
216 isSingleton _ = False
227 snocView :: [a] -> ([a], a) -- Split off the last element
228 snocView xs = go xs []
230 go [x] acc = (reverse acc, x)
231 go (x:xs) acc = go xs (x:acc)
234 Debugging/specialising versions of \tr{elem} and \tr{notElem}
237 isIn, isn'tIn :: (Eq a) => String -> a -> [a] -> Bool
240 isIn msg x ys = elem__ x ys
241 isn'tIn msg x ys = notElem__ x ys
243 --these are here to be SPECIALIZEd (automagically)
245 elem__ x (y:ys) = x==y || elem__ x ys
247 notElem__ x [] = True
248 notElem__ x (y:ys) = x /= y && notElem__ x ys
256 | i _GE_ ILIT(100) = panic ("Over-long elem in: " ++ msg)
257 | otherwise = x == y || elem (i _ADD_ ILIT(1)) x ys
260 = notElem ILIT(0) x ys
262 notElem i x [] = True
264 | i _GE_ ILIT(100) = panic ("Over-long notElem in: " ++ msg)
265 | otherwise = x /= y && notElem (i _ADD_ ILIT(1)) x ys
271 %************************************************************************
273 \subsection[Utils-sorting]{Sorting}
275 %************************************************************************
277 %************************************************************************
279 \subsubsection[Utils-quicksorting]{Quicksorts}
281 %************************************************************************
286 -- tail-recursive, etc., "quicker sort" [as per Meira thesis]
287 quicksort :: (a -> a -> Bool) -- Less-than predicate
289 -> [a] -- Result list in increasing order
292 quicksort lt [x] = [x]
293 quicksort lt (x:xs) = split x [] [] xs
295 split x lo hi [] = quicksort lt lo ++ (x : quicksort lt hi)
296 split x lo hi (y:ys) | y `lt` x = split x (y:lo) hi ys
297 | True = split x lo (y:hi) ys
301 Quicksort variant from Lennart's Haskell-library contribution. This
302 is a {\em stable} sort.
305 stableSortLt = sortLt -- synonym; when we want to highlight stable-ness
307 sortLt :: (a -> a -> Bool) -- Less-than predicate
309 -> [a] -- Result list
311 sortLt lt l = qsort lt l []
313 -- qsort is stable and does not concatenate.
314 qsort :: (a -> a -> Bool) -- Less-than predicate
315 -> [a] -- xs, Input list
316 -> [a] -- r, Concatenate this list to the sorted input list
317 -> [a] -- Result = sort xs ++ r
321 qsort lt (x:xs) r = qpart lt x xs [] [] r
323 -- qpart partitions and sorts the sublists
324 -- rlt contains things less than x,
325 -- rge contains the ones greater than or equal to x.
326 -- Both have equal elements reversed with respect to the original list.
328 qpart lt x [] rlt rge r =
329 -- rlt and rge are in reverse order and must be sorted with an
330 -- anti-stable sorting
331 rqsort lt rlt (x : rqsort lt rge r)
333 qpart lt x (y:ys) rlt rge r =
336 qpart lt x ys (y:rlt) rge r
339 qpart lt x ys rlt (y:rge) r
341 -- rqsort is as qsort but anti-stable, i.e. reverses equal elements
343 rqsort lt [x] r = x:r
344 rqsort lt (x:xs) r = rqpart lt x xs [] [] r
346 rqpart lt x [] rle rgt r =
347 qsort lt rle (x : qsort lt rgt r)
349 rqpart lt x (y:ys) rle rgt r =
352 rqpart lt x ys rle (y:rgt) r
355 rqpart lt x ys (y:rle) rgt r
358 %************************************************************************
360 \subsubsection[Utils-dull-mergesort]{A rather dull mergesort}
362 %************************************************************************
366 mergesort :: (a -> a -> Ordering) -> [a] -> [a]
368 mergesort cmp xs = merge_lists (split_into_runs [] xs)
370 a `le` b = case cmp a b of { LT -> True; EQ -> True; GT -> False }
371 a `ge` b = case cmp a b of { LT -> False; EQ -> True; GT -> True }
373 split_into_runs [] [] = []
374 split_into_runs run [] = [run]
375 split_into_runs [] (x:xs) = split_into_runs [x] xs
376 split_into_runs [r] (x:xs) | x `ge` r = split_into_runs [r,x] xs
377 split_into_runs rl@(r:rs) (x:xs) | x `le` r = split_into_runs (x:rl) xs
378 | True = rl : (split_into_runs [x] xs)
381 merge_lists (x:xs) = merge x (merge_lists xs)
385 merge xl@(x:xs) yl@(y:ys)
387 EQ -> x : y : (merge xs ys)
388 LT -> x : (merge xs yl)
389 GT -> y : (merge xl ys)
393 %************************************************************************
395 \subsubsection[Utils-Carsten-mergesort]{A mergesort from Carsten}
397 %************************************************************************
400 Date: Mon, 3 May 93 20:45:23 +0200
401 From: Carsten Kehler Holst <kehler@cs.chalmers.se>
402 To: partain@dcs.gla.ac.uk
403 Subject: natural merge sort beats quick sort [ and it is prettier ]
405 Here is a piece of Haskell code that I'm rather fond of. See it as an
406 attempt to get rid of the ridiculous quick-sort routine. group is
407 quite useful by itself I think it was John's idea originally though I
408 believe the lazy version is due to me [surprisingly complicated].
409 gamma [used to be called] is called gamma because I got inspired by
410 the Gamma calculus. It is not very close to the calculus but does
411 behave less sequentially than both foldr and foldl. One could imagine
412 a version of gamma that took a unit element as well thereby avoiding
413 the problem with empty lists.
415 I've tried this code against
417 1) insertion sort - as provided by haskell
418 2) the normal implementation of quick sort
419 3) a deforested version of quick sort due to Jan Sparud
420 4) a super-optimized-quick-sort of Lennart's
422 If the list is partially sorted both merge sort and in particular
423 natural merge sort wins. If the list is random [ average length of
424 rising subsequences = approx 2 ] mergesort still wins and natural
425 merge sort is marginally beaten by Lennart's soqs. The space
426 consumption of merge sort is a bit worse than Lennart's quick sort
427 approx a factor of 2. And a lot worse if Sparud's bug-fix [see his
428 fpca article ] isn't used because of group.
435 group :: (a -> a -> Bool) -> [a] -> [[a]]
438 Date: Mon, 12 Feb 1996 15:09:41 +0000
439 From: Andy Gill <andy@dcs.gla.ac.uk>
441 Here is a `better' definition of group.
444 group p (x:xs) = group' xs x x (x :)
446 group' [] _ _ s = [s []]
447 group' (x:xs) x_min x_max s
448 | not (x `p` x_max) = group' xs x_min x (s . (x :))
449 | x `p` x_min = group' xs x x_max ((x :) . s)
450 | otherwise = s [] : group' xs x x (x :)
452 -- This one works forwards *and* backwards, as well as also being
453 -- faster that the one in Util.lhs.
458 let ((h1:t1):tt1) = group p xs
459 (t,tt) = if null xs then ([],[]) else
460 if x `p` h1 then (h1:t1,tt1) else
465 generalMerge :: (a -> a -> Bool) -> [a] -> [a] -> [a]
466 generalMerge p xs [] = xs
467 generalMerge p [] ys = ys
468 generalMerge p (x:xs) (y:ys) | x `p` y = x : generalMerge p xs (y:ys)
469 | otherwise = y : generalMerge p (x:xs) ys
471 -- gamma is now called balancedFold
473 balancedFold :: (a -> a -> a) -> [a] -> a
474 balancedFold f [] = error "can't reduce an empty list using balancedFold"
475 balancedFold f [x] = x
476 balancedFold f l = balancedFold f (balancedFold' f l)
478 balancedFold' :: (a -> a -> a) -> [a] -> [a]
479 balancedFold' f (x:y:xs) = f x y : balancedFold' f xs
480 balancedFold' f xs = xs
482 generalMergeSort p [] = []
483 generalMergeSort p xs = (balancedFold (generalMerge p) . map (: [])) xs
485 generalNaturalMergeSort p [] = []
486 generalNaturalMergeSort p xs = (balancedFold (generalMerge p) . group p) xs
488 mergeSort, naturalMergeSort :: Ord a => [a] -> [a]
490 mergeSort = generalMergeSort (<=)
491 naturalMergeSort = generalNaturalMergeSort (<=)
493 mergeSortLe le = generalMergeSort le
494 naturalMergeSortLe le = generalNaturalMergeSort le
497 %************************************************************************
499 \subsection[Utils-transitive-closure]{Transitive closure}
501 %************************************************************************
503 This algorithm for transitive closure is straightforward, albeit quadratic.
506 transitiveClosure :: (a -> [a]) -- Successor function
507 -> (a -> a -> Bool) -- Equality predicate
509 -> [a] -- The transitive closure
511 transitiveClosure succ eq xs
515 go done (x:xs) | x `is_in` done = go done xs
516 | otherwise = go (x:done) (succ x ++ xs)
519 x `is_in` (y:ys) | eq x y = True
520 | otherwise = x `is_in` ys
523 %************************************************************************
525 \subsection[Utils-accum]{Accumulating}
527 %************************************************************************
529 @mapAccumL@ behaves like a combination
530 of @map@ and @foldl@;
531 it applies a function to each element of a list, passing an accumulating
532 parameter from left to right, and returning a final value of this
533 accumulator together with the new list.
536 mapAccumL :: (acc -> x -> (acc, y)) -- Function of elt of input list
537 -- and accumulator, returning new
538 -- accumulator and elt of result list
539 -> acc -- Initial accumulator
541 -> (acc, [y]) -- Final accumulator and result list
543 mapAccumL f b [] = (b, [])
544 mapAccumL f b (x:xs) = (b'', x':xs') where
546 (b'', xs') = mapAccumL f b' xs
549 @mapAccumR@ does the same, but working from right to left instead. Its type is
550 the same as @mapAccumL@, though.
553 mapAccumR :: (acc -> x -> (acc, y)) -- Function of elt of input list
554 -- and accumulator, returning new
555 -- accumulator and elt of result list
556 -> acc -- Initial accumulator
558 -> (acc, [y]) -- Final accumulator and result list
560 mapAccumR f b [] = (b, [])
561 mapAccumR f b (x:xs) = (b'', x':xs') where
563 (b', xs') = mapAccumR f b xs
566 Here is the bi-directional version, that works from both left and right.
569 mapAccumB :: (accl -> accr -> x -> (accl, accr,y))
570 -- Function of elt of input list
571 -- and accumulator, returning new
572 -- accumulator and elt of result list
573 -> accl -- Initial accumulator from left
574 -> accr -- Initial accumulator from right
576 -> (accl, accr, [y]) -- Final accumulators and result list
578 mapAccumB f a b [] = (a,b,[])
579 mapAccumB f a b (x:xs) = (a'',b'',y:ys)
581 (a',b'',y) = f a b' x
582 (a'',b',ys) = mapAccumB f a' b xs
585 A combination of foldl with zip. It works with equal length lists.
588 foldl2 :: (acc -> a -> b -> acc) -> acc -> [a] -> [b] -> acc
590 foldl2 k z (a:as) (b:bs) = foldl2 k (k z a b) as bs
593 Count the number of times a predicate is true
596 count :: (a -> Bool) -> [a] -> Int
598 count p (x:xs) | p x = 1 + count p xs
599 | otherwise = count p xs
603 %************************************************************************
605 \subsection[Utils-comparison]{Comparisons}
607 %************************************************************************
610 thenCmp :: Ordering -> Ordering -> Ordering
611 {-# INLINE thenCmp #-}
613 thenCmp other any = other
615 cmpList :: (a -> a -> Ordering) -> [a] -> [a] -> Ordering
616 -- `cmpList' uses a user-specified comparer
618 cmpList cmp [] [] = EQ
619 cmpList cmp [] _ = LT
620 cmpList cmp _ [] = GT
621 cmpList cmp (a:as) (b:bs)
622 = case cmp a b of { EQ -> cmpList cmp as bs; xxx -> xxx }
626 prefixMatch :: Eq a => [a] -> [a] -> Bool
627 prefixMatch [] _str = True
628 prefixMatch _pat [] = False
629 prefixMatch (p:ps) (s:ss) | p == s = prefixMatch ps ss
632 postfixMatch :: Eq a => [a] -> [a] -> Bool
633 postfixMatch pat str = prefixMatch (reverse pat) (reverse str)
636 %************************************************************************
638 \subsection[Utils-pairs]{Pairs}
640 %************************************************************************
642 The following are curried versions of @fst@ and @snd@.
645 cfst :: a -> b -> a -- stranal-sem only (Note)
649 The following provide us higher order functions that, when applied
650 to a function, operate on pairs.
653 applyToPair :: ((a -> c),(b -> d)) -> (a,b) -> (c,d)
654 applyToPair (f,g) (x,y) = (f x, g y)
656 applyToFst :: (a -> c) -> (a,b)-> (c,b)
657 applyToFst f (x,y) = (f x,y)
659 applyToSnd :: (b -> d) -> (a,b) -> (a,d)
660 applyToSnd f (x,y) = (x,f y)
662 foldPair :: (a->a->a,b->b->b) -> (a,b) -> [(a,b)] -> (a,b)
663 foldPair fg ab [] = ab
664 foldPair fg@(f,g) ab ((a,b):abs) = (f a u,g b v)
665 where (u,v) = foldPair fg ab abs
669 unzipWith :: (a -> b -> c) -> [(a, b)] -> [c]
670 unzipWith f pairs = map ( \ (a, b) -> f a b ) pairs
675 seqList :: [a] -> b -> b
677 seqList :: (Eval a) => [a] -> b -> b
680 seqList (x:xs) b = x `seq` seqList xs b
682 #if __HASKELL1__ <= 4
683 ($!) :: (Eval a) => (a -> b) -> a -> b
689 #if __GLASGOW_HASKELL__ < 402
690 bracket :: IO a -> (a -> IO b) -> (a -> IO c) -> IO c
691 bracket before after thing = do
693 r <- (thing a) `catch` (\err -> after a >> fail err)
702 global :: a -> IORef a
703 global a = unsafePerformIO (newIORef a)