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,
31 IF_NOT_GHC(quicksort COMMA stableSortLt COMMA mergesort COMMA)
33 IF_NOT_GHC(mergeSort COMMA) naturalMergeSortLe, -- from Carsten
34 IF_NOT_GHC(naturalMergeSort COMMA mergeSortLe COMMA)
36 -- transitive closures
40 mapAccumL, mapAccumR, mapAccumB, foldl2, count,
43 thenCmp, cmpList, prefixMatch, postfixMatch,
49 IF_NOT_GHC(cfst COMMA applyToPair COMMA applyToFst COMMA)
50 IF_NOT_GHC(applyToSnd COMMA foldPair COMMA)
54 #if __GLASGOW_HASKELL__ < 402
61 #if __GLASGOW_HASKELL__ <= 408
69 #include "HsVersions.h"
71 import List ( zipWith4 )
72 import Maybe ( Maybe(..) )
73 import Panic ( panic )
74 import IOExts ( IORef, newIORef, unsafePerformIO )
76 #if __GLASGOW_HASKELL__ <= 408
77 import Exception ( catchIO, justIoErrors, raiseInThread )
79 #ifndef mingw32_TARGET_OS
85 %************************************************************************
87 \subsection{The Eager monad}
89 %************************************************************************
91 The @Eager@ monad is just an encoding of continuation-passing style,
92 used to allow you to express "do this and then that", mainly to avoid
93 space leaks. It's done with a type synonym to save bureaucracy.
98 type Eager ans a = (a -> ans) -> ans
100 runEager :: Eager a a -> a
101 runEager m = m (\x -> x)
103 appEager :: Eager ans a -> (a -> ans) -> ans
104 appEager m cont = m cont
106 thenEager :: Eager ans a -> (a -> Eager ans b) -> Eager ans b
107 thenEager m k cont = m (\r -> k r cont)
109 returnEager :: a -> Eager ans a
110 returnEager v cont = cont v
112 mapEager :: (a -> Eager ans b) -> [a] -> Eager ans [b]
113 mapEager f [] = returnEager []
114 mapEager f (x:xs) = f x `thenEager` \ y ->
115 mapEager f xs `thenEager` \ ys ->
120 %************************************************************************
122 \subsection{A for loop}
124 %************************************************************************
127 -- Compose a function with itself n times. (nth rather than twice)
128 nTimes :: Int -> (a -> a) -> (a -> a)
131 nTimes n f = f . nTimes (n-1) f
134 %************************************************************************
136 \subsection{Maybe-ery}
138 %************************************************************************
141 unJust :: String -> Maybe a -> a
142 unJust who (Just x) = x
143 unJust who Nothing = panic ("unJust of Nothing, called by " ++ who)
146 %************************************************************************
148 \subsection[Utils-lists]{General list processing}
150 %************************************************************************
152 A paranoid @zip@ (and some @zipWith@ friends) that checks the lists
153 are of equal length. Alastair Reid thinks this should only happen if
154 DEBUGging on; hey, why not?
157 zipEqual :: String -> [a] -> [b] -> [(a,b)]
158 zipWithEqual :: String -> (a->b->c) -> [a]->[b]->[c]
159 zipWith3Equal :: String -> (a->b->c->d) -> [a]->[b]->[c]->[d]
160 zipWith4Equal :: String -> (a->b->c->d->e) -> [a]->[b]->[c]->[d]->[e]
164 zipWithEqual _ = zipWith
165 zipWith3Equal _ = zipWith3
166 zipWith4Equal _ = zipWith4
168 zipEqual msg [] [] = []
169 zipEqual msg (a:as) (b:bs) = (a,b) : zipEqual msg as bs
170 zipEqual msg as bs = panic ("zipEqual: unequal lists:"++msg)
172 zipWithEqual msg z (a:as) (b:bs)= z a b : zipWithEqual msg z as bs
173 zipWithEqual msg _ [] [] = []
174 zipWithEqual msg _ _ _ = panic ("zipWithEqual: unequal lists:"++msg)
176 zipWith3Equal msg z (a:as) (b:bs) (c:cs)
177 = z a b c : zipWith3Equal msg z as bs cs
178 zipWith3Equal msg _ [] [] [] = []
179 zipWith3Equal msg _ _ _ _ = panic ("zipWith3Equal: unequal lists:"++msg)
181 zipWith4Equal msg z (a:as) (b:bs) (c:cs) (d:ds)
182 = z a b c d : zipWith4Equal msg z as bs cs ds
183 zipWith4Equal msg _ [] [] [] [] = []
184 zipWith4Equal msg _ _ _ _ _ = panic ("zipWith4Equal: unequal lists:"++msg)
189 -- zipLazy is lazy in the second list (observe the ~)
191 zipLazy :: [a] -> [b] -> [(a,b)]
193 zipLazy (x:xs) ~(y:ys) = (x,y) : zipLazy xs ys
198 stretchZipWith :: (a -> Bool) -> b -> (a->b->c) -> [a] -> [b] -> [c]
199 -- (stretchZipWith p z f xs ys) stretches ys by inserting z in
200 -- the places where p returns *True*
202 stretchZipWith p z f [] ys = []
203 stretchZipWith p z f (x:xs) ys
204 | p x = f x z : stretchZipWith p z f xs ys
205 | otherwise = case ys of
207 (y:ys) -> f x y : stretchZipWith p z f xs ys
212 mapAndUnzip :: (a -> (b, c)) -> [a] -> ([b], [c])
214 mapAndUnzip f [] = ([],[])
218 (rs1, rs2) = mapAndUnzip f xs
222 mapAndUnzip3 :: (a -> (b, c, d)) -> [a] -> ([b], [c], [d])
224 mapAndUnzip3 f [] = ([],[],[])
225 mapAndUnzip3 f (x:xs)
228 (rs1, rs2, rs3) = mapAndUnzip3 f xs
230 (r1:rs1, r2:rs2, r3:rs3)
234 nOfThem :: Int -> a -> [a]
235 nOfThem n thing = replicate n thing
237 lengthExceeds :: [a] -> Int -> Bool
238 -- (lengthExceeds xs n) is True if length xs > n
239 (x:xs) `lengthExceeds` n = n < 1 || xs `lengthExceeds` (n - 1)
240 [] `lengthExceeds` n = n < 0
242 isSingleton :: [a] -> Bool
243 isSingleton [x] = True
244 isSingleton _ = False
255 snocView :: [a] -> ([a], a) -- Split off the last element
256 snocView xs = go xs []
258 go [x] acc = (reverse acc, x)
259 go (x:xs) acc = go xs (x:acc)
262 Debugging/specialising versions of \tr{elem} and \tr{notElem}
265 isIn, isn'tIn :: (Eq a) => String -> a -> [a] -> Bool
268 isIn msg x ys = elem__ x ys
269 isn'tIn msg x ys = notElem__ x ys
271 --these are here to be SPECIALIZEd (automagically)
273 elem__ x (y:ys) = x==y || elem__ x ys
275 notElem__ x [] = True
276 notElem__ x (y:ys) = x /= y && notElem__ x ys
280 = elem (_ILIT 0) x ys
284 | i ># _ILIT 100 = panic ("Over-long elem in: " ++ msg)
285 | otherwise = x == y || elem (i +# _ILIT(1)) x ys
288 = notElem (_ILIT 0) x ys
290 notElem i x [] = True
292 | i ># _ILIT 100 = panic ("Over-long notElem in: " ++ msg)
293 | otherwise = x /= y && notElem (i +# _ILIT(1)) x ys
299 %************************************************************************
301 \subsection[Utils-sorting]{Sorting}
303 %************************************************************************
305 %************************************************************************
307 \subsubsection[Utils-quicksorting]{Quicksorts}
309 %************************************************************************
314 -- tail-recursive, etc., "quicker sort" [as per Meira thesis]
315 quicksort :: (a -> a -> Bool) -- Less-than predicate
317 -> [a] -- Result list in increasing order
320 quicksort lt [x] = [x]
321 quicksort lt (x:xs) = split x [] [] xs
323 split x lo hi [] = quicksort lt lo ++ (x : quicksort lt hi)
324 split x lo hi (y:ys) | y `lt` x = split x (y:lo) hi ys
325 | True = split x lo (y:hi) ys
329 Quicksort variant from Lennart's Haskell-library contribution. This
330 is a {\em stable} sort.
333 stableSortLt = sortLt -- synonym; when we want to highlight stable-ness
335 sortLt :: (a -> a -> Bool) -- Less-than predicate
337 -> [a] -- Result list
339 sortLt lt l = qsort lt l []
341 -- qsort is stable and does not concatenate.
342 qsort :: (a -> a -> Bool) -- Less-than predicate
343 -> [a] -- xs, Input list
344 -> [a] -- r, Concatenate this list to the sorted input list
345 -> [a] -- Result = sort xs ++ r
349 qsort lt (x:xs) r = qpart lt x xs [] [] r
351 -- qpart partitions and sorts the sublists
352 -- rlt contains things less than x,
353 -- rge contains the ones greater than or equal to x.
354 -- Both have equal elements reversed with respect to the original list.
356 qpart lt x [] rlt rge r =
357 -- rlt and rge are in reverse order and must be sorted with an
358 -- anti-stable sorting
359 rqsort lt rlt (x : rqsort lt rge r)
361 qpart lt x (y:ys) rlt rge r =
364 qpart lt x ys (y:rlt) rge r
367 qpart lt x ys rlt (y:rge) r
369 -- rqsort is as qsort but anti-stable, i.e. reverses equal elements
371 rqsort lt [x] r = x:r
372 rqsort lt (x:xs) r = rqpart lt x xs [] [] r
374 rqpart lt x [] rle rgt r =
375 qsort lt rle (x : qsort lt rgt r)
377 rqpart lt x (y:ys) rle rgt r =
380 rqpart lt x ys rle (y:rgt) r
383 rqpart lt x ys (y:rle) rgt r
386 %************************************************************************
388 \subsubsection[Utils-dull-mergesort]{A rather dull mergesort}
390 %************************************************************************
394 mergesort :: (a -> a -> Ordering) -> [a] -> [a]
396 mergesort cmp xs = merge_lists (split_into_runs [] xs)
398 a `le` b = case cmp a b of { LT -> True; EQ -> True; GT -> False }
399 a `ge` b = case cmp a b of { LT -> False; EQ -> True; GT -> True }
401 split_into_runs [] [] = []
402 split_into_runs run [] = [run]
403 split_into_runs [] (x:xs) = split_into_runs [x] xs
404 split_into_runs [r] (x:xs) | x `ge` r = split_into_runs [r,x] xs
405 split_into_runs rl@(r:rs) (x:xs) | x `le` r = split_into_runs (x:rl) xs
406 | True = rl : (split_into_runs [x] xs)
409 merge_lists (x:xs) = merge x (merge_lists xs)
413 merge xl@(x:xs) yl@(y:ys)
415 EQ -> x : y : (merge xs ys)
416 LT -> x : (merge xs yl)
417 GT -> y : (merge xl ys)
421 %************************************************************************
423 \subsubsection[Utils-Carsten-mergesort]{A mergesort from Carsten}
425 %************************************************************************
428 Date: Mon, 3 May 93 20:45:23 +0200
429 From: Carsten Kehler Holst <kehler@cs.chalmers.se>
430 To: partain@dcs.gla.ac.uk
431 Subject: natural merge sort beats quick sort [ and it is prettier ]
433 Here is a piece of Haskell code that I'm rather fond of. See it as an
434 attempt to get rid of the ridiculous quick-sort routine. group is
435 quite useful by itself I think it was John's idea originally though I
436 believe the lazy version is due to me [surprisingly complicated].
437 gamma [used to be called] is called gamma because I got inspired by
438 the Gamma calculus. It is not very close to the calculus but does
439 behave less sequentially than both foldr and foldl. One could imagine
440 a version of gamma that took a unit element as well thereby avoiding
441 the problem with empty lists.
443 I've tried this code against
445 1) insertion sort - as provided by haskell
446 2) the normal implementation of quick sort
447 3) a deforested version of quick sort due to Jan Sparud
448 4) a super-optimized-quick-sort of Lennart's
450 If the list is partially sorted both merge sort and in particular
451 natural merge sort wins. If the list is random [ average length of
452 rising subsequences = approx 2 ] mergesort still wins and natural
453 merge sort is marginally beaten by Lennart's soqs. The space
454 consumption of merge sort is a bit worse than Lennart's quick sort
455 approx a factor of 2. And a lot worse if Sparud's bug-fix [see his
456 fpca article ] isn't used because of group.
463 group :: (a -> a -> Bool) -> [a] -> [[a]]
466 Date: Mon, 12 Feb 1996 15:09:41 +0000
467 From: Andy Gill <andy@dcs.gla.ac.uk>
469 Here is a `better' definition of group.
472 group p (x:xs) = group' xs x x (x :)
474 group' [] _ _ s = [s []]
475 group' (x:xs) x_min x_max s
476 | not (x `p` x_max) = group' xs x_min x (s . (x :))
477 | x `p` x_min = group' xs x x_max ((x :) . s)
478 | otherwise = s [] : group' xs x x (x :)
480 -- This one works forwards *and* backwards, as well as also being
481 -- faster that the one in Util.lhs.
486 let ((h1:t1):tt1) = group p xs
487 (t,tt) = if null xs then ([],[]) else
488 if x `p` h1 then (h1:t1,tt1) else
493 generalMerge :: (a -> a -> Bool) -> [a] -> [a] -> [a]
494 generalMerge p xs [] = xs
495 generalMerge p [] ys = ys
496 generalMerge p (x:xs) (y:ys) | x `p` y = x : generalMerge p xs (y:ys)
497 | otherwise = y : generalMerge p (x:xs) ys
499 -- gamma is now called balancedFold
501 balancedFold :: (a -> a -> a) -> [a] -> a
502 balancedFold f [] = error "can't reduce an empty list using balancedFold"
503 balancedFold f [x] = x
504 balancedFold f l = balancedFold f (balancedFold' f l)
506 balancedFold' :: (a -> a -> a) -> [a] -> [a]
507 balancedFold' f (x:y:xs) = f x y : balancedFold' f xs
508 balancedFold' f xs = xs
510 generalMergeSort p [] = []
511 generalMergeSort p xs = (balancedFold (generalMerge p) . map (: [])) xs
513 generalNaturalMergeSort p [] = []
514 generalNaturalMergeSort p xs = (balancedFold (generalMerge p) . group p) xs
516 mergeSort, naturalMergeSort :: Ord a => [a] -> [a]
518 mergeSort = generalMergeSort (<=)
519 naturalMergeSort = generalNaturalMergeSort (<=)
521 mergeSortLe le = generalMergeSort le
522 naturalMergeSortLe le = generalNaturalMergeSort le
525 %************************************************************************
527 \subsection[Utils-transitive-closure]{Transitive closure}
529 %************************************************************************
531 This algorithm for transitive closure is straightforward, albeit quadratic.
534 transitiveClosure :: (a -> [a]) -- Successor function
535 -> (a -> a -> Bool) -- Equality predicate
537 -> [a] -- The transitive closure
539 transitiveClosure succ eq xs
543 go done (x:xs) | x `is_in` done = go done xs
544 | otherwise = go (x:done) (succ x ++ xs)
547 x `is_in` (y:ys) | eq x y = True
548 | otherwise = x `is_in` ys
551 %************************************************************************
553 \subsection[Utils-accum]{Accumulating}
555 %************************************************************************
557 @mapAccumL@ behaves like a combination
558 of @map@ and @foldl@;
559 it applies a function to each element of a list, passing an accumulating
560 parameter from left to right, and returning a final value of this
561 accumulator together with the new list.
564 mapAccumL :: (acc -> x -> (acc, y)) -- Function of elt of input list
565 -- and accumulator, returning new
566 -- accumulator and elt of result list
567 -> acc -- Initial accumulator
569 -> (acc, [y]) -- Final accumulator and result list
571 mapAccumL f b [] = (b, [])
572 mapAccumL f b (x:xs) = (b'', x':xs') where
574 (b'', xs') = mapAccumL f b' xs
577 @mapAccumR@ does the same, but working from right to left instead. Its type is
578 the same as @mapAccumL@, though.
581 mapAccumR :: (acc -> x -> (acc, y)) -- Function of elt of input list
582 -- and accumulator, returning new
583 -- accumulator and elt of result list
584 -> acc -- Initial accumulator
586 -> (acc, [y]) -- Final accumulator and result list
588 mapAccumR f b [] = (b, [])
589 mapAccumR f b (x:xs) = (b'', x':xs') where
591 (b', xs') = mapAccumR f b xs
594 Here is the bi-directional version, that works from both left and right.
597 mapAccumB :: (accl -> accr -> x -> (accl, accr,y))
598 -- Function of elt of input list
599 -- and accumulator, returning new
600 -- accumulator and elt of result list
601 -> accl -- Initial accumulator from left
602 -> accr -- Initial accumulator from right
604 -> (accl, accr, [y]) -- Final accumulators and result list
606 mapAccumB f a b [] = (a,b,[])
607 mapAccumB f a b (x:xs) = (a'',b'',y:ys)
609 (a',b'',y) = f a b' x
610 (a'',b',ys) = mapAccumB f a' b xs
613 A combination of foldl with zip. It works with equal length lists.
616 foldl2 :: (acc -> a -> b -> acc) -> acc -> [a] -> [b] -> acc
618 foldl2 k z (a:as) (b:bs) = foldl2 k (k z a b) as bs
621 Count the number of times a predicate is true
624 count :: (a -> Bool) -> [a] -> Int
626 count p (x:xs) | p x = 1 + count p xs
627 | otherwise = count p xs
631 %************************************************************************
633 \subsection[Utils-comparison]{Comparisons}
635 %************************************************************************
638 thenCmp :: Ordering -> Ordering -> Ordering
639 {-# INLINE thenCmp #-}
641 thenCmp other any = other
643 cmpList :: (a -> a -> Ordering) -> [a] -> [a] -> Ordering
644 -- `cmpList' uses a user-specified comparer
646 cmpList cmp [] [] = EQ
647 cmpList cmp [] _ = LT
648 cmpList cmp _ [] = GT
649 cmpList cmp (a:as) (b:bs)
650 = case cmp a b of { EQ -> cmpList cmp as bs; xxx -> xxx }
654 prefixMatch :: Eq a => [a] -> [a] -> Bool
655 prefixMatch [] _str = True
656 prefixMatch _pat [] = False
657 prefixMatch (p:ps) (s:ss) | p == s = prefixMatch ps ss
660 postfixMatch :: Eq a => [a] -> [a] -> Bool
661 postfixMatch pat str = prefixMatch (reverse pat) (reverse str)
664 %************************************************************************
666 \subsection[Utils-pairs]{Pairs}
668 %************************************************************************
670 The following are curried versions of @fst@ and @snd@.
673 cfst :: a -> b -> a -- stranal-sem only (Note)
677 The following provide us higher order functions that, when applied
678 to a function, operate on pairs.
681 applyToPair :: ((a -> c),(b -> d)) -> (a,b) -> (c,d)
682 applyToPair (f,g) (x,y) = (f x, g y)
684 applyToFst :: (a -> c) -> (a,b)-> (c,b)
685 applyToFst f (x,y) = (f x,y)
687 applyToSnd :: (b -> d) -> (a,b) -> (a,d)
688 applyToSnd f (x,y) = (x,f y)
690 foldPair :: (a->a->a,b->b->b) -> (a,b) -> [(a,b)] -> (a,b)
691 foldPair fg ab [] = ab
692 foldPair fg@(f,g) ab ((a,b):abs) = (f a u,g b v)
693 where (u,v) = foldPair fg ab abs
697 unzipWith :: (a -> b -> c) -> [(a, b)] -> [c]
698 unzipWith f pairs = map ( \ (a, b) -> f a b ) pairs
703 seqList :: [a] -> b -> b
705 seqList :: (Eval a) => [a] -> b -> b
708 seqList (x:xs) b = x `seq` seqList xs b
710 #if __HASKELL1__ <= 4
711 ($!) :: (Eval a) => (a -> b) -> a -> b
717 #if __GLASGOW_HASKELL__ < 402
718 bracket :: IO a -> (a -> IO b) -> (a -> IO c) -> IO c
719 bracket before after thing = do
721 r <- (thing a) `catch` (\err -> after a >> fail err)
730 global :: a -> IORef a
731 global a = unsafePerformIO (newIORef a)
737 #if __GLASGOW_HASKELL__ <= 408
739 ioErrors = justIoErrors
740 throwTo = raiseInThread
743 #ifdef mingw32_TARGET_OS
744 foreign import "_getpid" myGetProcessID :: IO Int
746 myGetProcessID :: IO Int
747 myGetProcessID = Posix.getProcessID