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 )
69 %************************************************************************
71 \subsection{The Eager monad}
73 %************************************************************************
75 The @Eager@ monad is just an encoding of continuation-passing style,
76 used to allow you to express "do this and then that", mainly to avoid
77 space leaks. It's done with a type synonym to save bureaucracy.
82 type Eager ans a = (a -> ans) -> ans
84 runEager :: Eager a a -> a
85 runEager m = m (\x -> x)
87 appEager :: Eager ans a -> (a -> ans) -> ans
88 appEager m cont = m cont
90 thenEager :: Eager ans a -> (a -> Eager ans b) -> Eager ans b
91 thenEager m k cont = m (\r -> k r cont)
93 returnEager :: a -> Eager ans a
94 returnEager v cont = cont v
96 mapEager :: (a -> Eager ans b) -> [a] -> Eager ans [b]
97 mapEager f [] = returnEager []
98 mapEager f (x:xs) = f x `thenEager` \ y ->
99 mapEager f xs `thenEager` \ ys ->
104 %************************************************************************
106 \subsection{A for loop}
108 %************************************************************************
111 -- Compose a function with itself n times. (nth rather than twice)
112 nTimes :: Int -> (a -> a) -> (a -> a)
115 nTimes n f = f . nTimes (n-1) f
119 %************************************************************************
121 \subsection[Utils-lists]{General list processing}
123 %************************************************************************
125 A paranoid @zip@ (and some @zipWith@ friends) that checks the lists
126 are of equal length. Alastair Reid thinks this should only happen if
127 DEBUGging on; hey, why not?
130 zipEqual :: String -> [a] -> [b] -> [(a,b)]
131 zipWithEqual :: String -> (a->b->c) -> [a]->[b]->[c]
132 zipWith3Equal :: String -> (a->b->c->d) -> [a]->[b]->[c]->[d]
133 zipWith4Equal :: String -> (a->b->c->d->e) -> [a]->[b]->[c]->[d]->[e]
137 zipWithEqual _ = zipWith
138 zipWith3Equal _ = zipWith3
139 zipWith4Equal _ = zipWith4
141 zipEqual msg [] [] = []
142 zipEqual msg (a:as) (b:bs) = (a,b) : zipEqual msg as bs
143 zipEqual msg as bs = panic ("zipEqual: unequal lists:"++msg)
145 zipWithEqual msg z (a:as) (b:bs)= z a b : zipWithEqual msg z as bs
146 zipWithEqual msg _ [] [] = []
147 zipWithEqual msg _ _ _ = panic ("zipWithEqual: unequal lists:"++msg)
149 zipWith3Equal msg z (a:as) (b:bs) (c:cs)
150 = z a b c : zipWith3Equal msg z as bs cs
151 zipWith3Equal msg _ [] [] [] = []
152 zipWith3Equal msg _ _ _ _ = panic ("zipWith3Equal: unequal lists:"++msg)
154 zipWith4Equal msg z (a:as) (b:bs) (c:cs) (d:ds)
155 = z a b c d : zipWith4Equal msg z as bs cs ds
156 zipWith4Equal msg _ [] [] [] [] = []
157 zipWith4Equal msg _ _ _ _ _ = panic ("zipWith4Equal: unequal lists:"++msg)
162 -- zipLazy is lazy in the second list (observe the ~)
164 zipLazy :: [a] -> [b] -> [(a,b)]
166 zipLazy (x:xs) ~(y:ys) = (x,y) : zipLazy xs ys
171 stretchZipWith :: (a -> Bool) -> b -> (a->b->c) -> [a] -> [b] -> [c]
172 -- (stretchZipWith p z f xs ys) stretches ys by inserting z in
173 -- the places where p returns *True*
175 stretchZipWith p z f [] ys = []
176 stretchZipWith p z f (x:xs) ys
177 | p x = f x z : stretchZipWith p z f xs ys
178 | otherwise = case ys of
180 (y:ys) -> f x y : stretchZipWith p z f xs ys
185 mapAndUnzip :: (a -> (b, c)) -> [a] -> ([b], [c])
187 mapAndUnzip f [] = ([],[])
191 (rs1, rs2) = mapAndUnzip f xs
195 mapAndUnzip3 :: (a -> (b, c, d)) -> [a] -> ([b], [c], [d])
197 mapAndUnzip3 f [] = ([],[],[])
198 mapAndUnzip3 f (x:xs)
201 (rs1, rs2, rs3) = mapAndUnzip3 f xs
203 (r1:rs1, r2:rs2, r3:rs3)
207 nOfThem :: Int -> a -> [a]
208 nOfThem n thing = replicate n thing
210 lengthExceeds :: [a] -> Int -> Bool
211 -- (lengthExceeds xs n) is True if length xs > n
212 (x:xs) `lengthExceeds` n = n < 1 || xs `lengthExceeds` (n - 1)
213 [] `lengthExceeds` n = n < 0
215 isSingleton :: [a] -> Bool
216 isSingleton [x] = True
217 isSingleton _ = False
228 snocView :: [a] -> ([a], a) -- Split off the last element
229 snocView xs = go xs []
231 go [x] acc = (reverse acc, x)
232 go (x:xs) acc = go xs (x:acc)
235 Debugging/specialising versions of \tr{elem} and \tr{notElem}
238 isIn, isn'tIn :: (Eq a) => String -> a -> [a] -> Bool
241 isIn msg x ys = elem__ x ys
242 isn'tIn msg x ys = notElem__ x ys
244 --these are here to be SPECIALIZEd (automagically)
246 elem__ x (y:ys) = x==y || elem__ x ys
248 notElem__ x [] = True
249 notElem__ x (y:ys) = x /= y && notElem__ x ys
253 = elem (_ILIT 0) x ys
257 | i ># _ILIT 100 = panic ("Over-long elem in: " ++ msg)
258 | otherwise = x == y || elem (i +# _ILIT(1)) x ys
261 = notElem (_ILIT 0) x ys
263 notElem i x [] = True
265 | i ># _ILIT 100 = panic ("Over-long notElem in: " ++ msg)
266 | otherwise = x /= y && notElem (i +# _ILIT(1)) x ys
272 %************************************************************************
274 \subsection[Utils-sorting]{Sorting}
276 %************************************************************************
278 %************************************************************************
280 \subsubsection[Utils-quicksorting]{Quicksorts}
282 %************************************************************************
287 -- tail-recursive, etc., "quicker sort" [as per Meira thesis]
288 quicksort :: (a -> a -> Bool) -- Less-than predicate
290 -> [a] -- Result list in increasing order
293 quicksort lt [x] = [x]
294 quicksort lt (x:xs) = split x [] [] xs
296 split x lo hi [] = quicksort lt lo ++ (x : quicksort lt hi)
297 split x lo hi (y:ys) | y `lt` x = split x (y:lo) hi ys
298 | True = split x lo (y:hi) ys
302 Quicksort variant from Lennart's Haskell-library contribution. This
303 is a {\em stable} sort.
306 stableSortLt = sortLt -- synonym; when we want to highlight stable-ness
308 sortLt :: (a -> a -> Bool) -- Less-than predicate
310 -> [a] -- Result list
312 sortLt lt l = qsort lt l []
314 -- qsort is stable and does not concatenate.
315 qsort :: (a -> a -> Bool) -- Less-than predicate
316 -> [a] -- xs, Input list
317 -> [a] -- r, Concatenate this list to the sorted input list
318 -> [a] -- Result = sort xs ++ r
322 qsort lt (x:xs) r = qpart lt x xs [] [] r
324 -- qpart partitions and sorts the sublists
325 -- rlt contains things less than x,
326 -- rge contains the ones greater than or equal to x.
327 -- Both have equal elements reversed with respect to the original list.
329 qpart lt x [] rlt rge r =
330 -- rlt and rge are in reverse order and must be sorted with an
331 -- anti-stable sorting
332 rqsort lt rlt (x : rqsort lt rge r)
334 qpart lt x (y:ys) rlt rge r =
337 qpart lt x ys (y:rlt) rge r
340 qpart lt x ys rlt (y:rge) r
342 -- rqsort is as qsort but anti-stable, i.e. reverses equal elements
344 rqsort lt [x] r = x:r
345 rqsort lt (x:xs) r = rqpart lt x xs [] [] r
347 rqpart lt x [] rle rgt r =
348 qsort lt rle (x : qsort lt rgt r)
350 rqpart lt x (y:ys) rle rgt r =
353 rqpart lt x ys rle (y:rgt) r
356 rqpart lt x ys (y:rle) rgt r
359 %************************************************************************
361 \subsubsection[Utils-dull-mergesort]{A rather dull mergesort}
363 %************************************************************************
367 mergesort :: (a -> a -> Ordering) -> [a] -> [a]
369 mergesort cmp xs = merge_lists (split_into_runs [] xs)
371 a `le` b = case cmp a b of { LT -> True; EQ -> True; GT -> False }
372 a `ge` b = case cmp a b of { LT -> False; EQ -> True; GT -> True }
374 split_into_runs [] [] = []
375 split_into_runs run [] = [run]
376 split_into_runs [] (x:xs) = split_into_runs [x] xs
377 split_into_runs [r] (x:xs) | x `ge` r = split_into_runs [r,x] xs
378 split_into_runs rl@(r:rs) (x:xs) | x `le` r = split_into_runs (x:rl) xs
379 | True = rl : (split_into_runs [x] xs)
382 merge_lists (x:xs) = merge x (merge_lists xs)
386 merge xl@(x:xs) yl@(y:ys)
388 EQ -> x : y : (merge xs ys)
389 LT -> x : (merge xs yl)
390 GT -> y : (merge xl ys)
394 %************************************************************************
396 \subsubsection[Utils-Carsten-mergesort]{A mergesort from Carsten}
398 %************************************************************************
401 Date: Mon, 3 May 93 20:45:23 +0200
402 From: Carsten Kehler Holst <kehler@cs.chalmers.se>
403 To: partain@dcs.gla.ac.uk
404 Subject: natural merge sort beats quick sort [ and it is prettier ]
406 Here is a piece of Haskell code that I'm rather fond of. See it as an
407 attempt to get rid of the ridiculous quick-sort routine. group is
408 quite useful by itself I think it was John's idea originally though I
409 believe the lazy version is due to me [surprisingly complicated].
410 gamma [used to be called] is called gamma because I got inspired by
411 the Gamma calculus. It is not very close to the calculus but does
412 behave less sequentially than both foldr and foldl. One could imagine
413 a version of gamma that took a unit element as well thereby avoiding
414 the problem with empty lists.
416 I've tried this code against
418 1) insertion sort - as provided by haskell
419 2) the normal implementation of quick sort
420 3) a deforested version of quick sort due to Jan Sparud
421 4) a super-optimized-quick-sort of Lennart's
423 If the list is partially sorted both merge sort and in particular
424 natural merge sort wins. If the list is random [ average length of
425 rising subsequences = approx 2 ] mergesort still wins and natural
426 merge sort is marginally beaten by Lennart's soqs. The space
427 consumption of merge sort is a bit worse than Lennart's quick sort
428 approx a factor of 2. And a lot worse if Sparud's bug-fix [see his
429 fpca article ] isn't used because of group.
436 group :: (a -> a -> Bool) -> [a] -> [[a]]
439 Date: Mon, 12 Feb 1996 15:09:41 +0000
440 From: Andy Gill <andy@dcs.gla.ac.uk>
442 Here is a `better' definition of group.
445 group p (x:xs) = group' xs x x (x :)
447 group' [] _ _ s = [s []]
448 group' (x:xs) x_min x_max s
449 | not (x `p` x_max) = group' xs x_min x (s . (x :))
450 | x `p` x_min = group' xs x x_max ((x :) . s)
451 | otherwise = s [] : group' xs x x (x :)
453 -- This one works forwards *and* backwards, as well as also being
454 -- faster that the one in Util.lhs.
459 let ((h1:t1):tt1) = group p xs
460 (t,tt) = if null xs then ([],[]) else
461 if x `p` h1 then (h1:t1,tt1) else
466 generalMerge :: (a -> a -> Bool) -> [a] -> [a] -> [a]
467 generalMerge p xs [] = xs
468 generalMerge p [] ys = ys
469 generalMerge p (x:xs) (y:ys) | x `p` y = x : generalMerge p xs (y:ys)
470 | otherwise = y : generalMerge p (x:xs) ys
472 -- gamma is now called balancedFold
474 balancedFold :: (a -> a -> a) -> [a] -> a
475 balancedFold f [] = error "can't reduce an empty list using balancedFold"
476 balancedFold f [x] = x
477 balancedFold f l = balancedFold f (balancedFold' f l)
479 balancedFold' :: (a -> a -> a) -> [a] -> [a]
480 balancedFold' f (x:y:xs) = f x y : balancedFold' f xs
481 balancedFold' f xs = xs
483 generalMergeSort p [] = []
484 generalMergeSort p xs = (balancedFold (generalMerge p) . map (: [])) xs
486 generalNaturalMergeSort p [] = []
487 generalNaturalMergeSort p xs = (balancedFold (generalMerge p) . group p) xs
489 mergeSort, naturalMergeSort :: Ord a => [a] -> [a]
491 mergeSort = generalMergeSort (<=)
492 naturalMergeSort = generalNaturalMergeSort (<=)
494 mergeSortLe le = generalMergeSort le
495 naturalMergeSortLe le = generalNaturalMergeSort le
498 %************************************************************************
500 \subsection[Utils-transitive-closure]{Transitive closure}
502 %************************************************************************
504 This algorithm for transitive closure is straightforward, albeit quadratic.
507 transitiveClosure :: (a -> [a]) -- Successor function
508 -> (a -> a -> Bool) -- Equality predicate
510 -> [a] -- The transitive closure
512 transitiveClosure succ eq xs
516 go done (x:xs) | x `is_in` done = go done xs
517 | otherwise = go (x:done) (succ x ++ xs)
520 x `is_in` (y:ys) | eq x y = True
521 | otherwise = x `is_in` ys
524 %************************************************************************
526 \subsection[Utils-accum]{Accumulating}
528 %************************************************************************
530 @mapAccumL@ behaves like a combination
531 of @map@ and @foldl@;
532 it applies a function to each element of a list, passing an accumulating
533 parameter from left to right, and returning a final value of this
534 accumulator together with the new list.
537 mapAccumL :: (acc -> x -> (acc, y)) -- Function of elt of input list
538 -- and accumulator, returning new
539 -- accumulator and elt of result list
540 -> acc -- Initial accumulator
542 -> (acc, [y]) -- Final accumulator and result list
544 mapAccumL f b [] = (b, [])
545 mapAccumL f b (x:xs) = (b'', x':xs') where
547 (b'', xs') = mapAccumL f b' xs
550 @mapAccumR@ does the same, but working from right to left instead. Its type is
551 the same as @mapAccumL@, though.
554 mapAccumR :: (acc -> x -> (acc, y)) -- Function of elt of input list
555 -- and accumulator, returning new
556 -- accumulator and elt of result list
557 -> acc -- Initial accumulator
559 -> (acc, [y]) -- Final accumulator and result list
561 mapAccumR f b [] = (b, [])
562 mapAccumR f b (x:xs) = (b'', x':xs') where
564 (b', xs') = mapAccumR f b xs
567 Here is the bi-directional version, that works from both left and right.
570 mapAccumB :: (accl -> accr -> x -> (accl, accr,y))
571 -- Function of elt of input list
572 -- and accumulator, returning new
573 -- accumulator and elt of result list
574 -> accl -- Initial accumulator from left
575 -> accr -- Initial accumulator from right
577 -> (accl, accr, [y]) -- Final accumulators and result list
579 mapAccumB f a b [] = (a,b,[])
580 mapAccumB f a b (x:xs) = (a'',b'',y:ys)
582 (a',b'',y) = f a b' x
583 (a'',b',ys) = mapAccumB f a' b xs
586 A combination of foldl with zip. It works with equal length lists.
589 foldl2 :: (acc -> a -> b -> acc) -> acc -> [a] -> [b] -> acc
591 foldl2 k z (a:as) (b:bs) = foldl2 k (k z a b) as bs
594 Count the number of times a predicate is true
597 count :: (a -> Bool) -> [a] -> Int
599 count p (x:xs) | p x = 1 + count p xs
600 | otherwise = count p xs
604 %************************************************************************
606 \subsection[Utils-comparison]{Comparisons}
608 %************************************************************************
611 thenCmp :: Ordering -> Ordering -> Ordering
612 {-# INLINE thenCmp #-}
614 thenCmp other any = other
616 cmpList :: (a -> a -> Ordering) -> [a] -> [a] -> Ordering
617 -- `cmpList' uses a user-specified comparer
619 cmpList cmp [] [] = EQ
620 cmpList cmp [] _ = LT
621 cmpList cmp _ [] = GT
622 cmpList cmp (a:as) (b:bs)
623 = case cmp a b of { EQ -> cmpList cmp as bs; xxx -> xxx }
627 prefixMatch :: Eq a => [a] -> [a] -> Bool
628 prefixMatch [] _str = True
629 prefixMatch _pat [] = False
630 prefixMatch (p:ps) (s:ss) | p == s = prefixMatch ps ss
633 postfixMatch :: Eq a => [a] -> [a] -> Bool
634 postfixMatch pat str = prefixMatch (reverse pat) (reverse str)
637 %************************************************************************
639 \subsection[Utils-pairs]{Pairs}
641 %************************************************************************
643 The following are curried versions of @fst@ and @snd@.
646 cfst :: a -> b -> a -- stranal-sem only (Note)
650 The following provide us higher order functions that, when applied
651 to a function, operate on pairs.
654 applyToPair :: ((a -> c),(b -> d)) -> (a,b) -> (c,d)
655 applyToPair (f,g) (x,y) = (f x, g y)
657 applyToFst :: (a -> c) -> (a,b)-> (c,b)
658 applyToFst f (x,y) = (f x,y)
660 applyToSnd :: (b -> d) -> (a,b) -> (a,d)
661 applyToSnd f (x,y) = (x,f y)
663 foldPair :: (a->a->a,b->b->b) -> (a,b) -> [(a,b)] -> (a,b)
664 foldPair fg ab [] = ab
665 foldPair fg@(f,g) ab ((a,b):abs) = (f a u,g b v)
666 where (u,v) = foldPair fg ab abs
670 unzipWith :: (a -> b -> c) -> [(a, b)] -> [c]
671 unzipWith f pairs = map ( \ (a, b) -> f a b ) pairs
676 seqList :: [a] -> b -> b
678 seqList :: (Eval a) => [a] -> b -> b
681 seqList (x:xs) b = x `seq` seqList xs b
683 #if __HASKELL1__ <= 4
684 ($!) :: (Eval a) => (a -> b) -> a -> b
690 #if __GLASGOW_HASKELL__ < 402
691 bracket :: IO a -> (a -> IO b) -> (a -> IO c) -> IO c
692 bracket before after thing = do
694 r <- (thing a) `catch` (\err -> after a >> fail err)
703 global :: a -> IORef a
704 global a = unsafePerformIO (newIORef a)