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,
44 thenCmp, cmpList, prefixMatch, suffixMatch,
50 IF_NOT_GHC(cfst COMMA applyToPair COMMA applyToFst COMMA)
51 IF_NOT_GHC(applyToSnd COMMA foldPair COMMA)
57 #if __GLASGOW_HASKELL__ <= 408
65 #include "../includes/config.h"
66 #include "HsVersions.h"
68 import List ( zipWith4 )
69 import Maybe ( Maybe(..) )
70 import Panic ( panic )
71 import IOExts ( IORef, newIORef, unsafePerformIO )
73 #if __GLASGOW_HASKELL__ <= 408
74 import Exception ( catchIO, justIoErrors, raiseInThread )
76 #ifndef mingw32_TARGET_OS
82 %************************************************************************
84 \subsection{The Eager monad}
86 %************************************************************************
88 The @Eager@ monad is just an encoding of continuation-passing style,
89 used to allow you to express "do this and then that", mainly to avoid
90 space leaks. It's done with a type synonym to save bureaucracy.
95 type Eager ans a = (a -> ans) -> ans
97 runEager :: Eager a a -> a
98 runEager m = m (\x -> x)
100 appEager :: Eager ans a -> (a -> ans) -> ans
101 appEager m cont = m cont
103 thenEager :: Eager ans a -> (a -> Eager ans b) -> Eager ans b
104 thenEager m k cont = m (\r -> k r cont)
106 returnEager :: a -> Eager ans a
107 returnEager v cont = cont v
109 mapEager :: (a -> Eager ans b) -> [a] -> Eager ans [b]
110 mapEager f [] = returnEager []
111 mapEager f (x:xs) = f x `thenEager` \ y ->
112 mapEager f xs `thenEager` \ ys ->
117 %************************************************************************
119 \subsection{A for loop}
121 %************************************************************************
124 -- Compose a function with itself n times. (nth rather than twice)
125 nTimes :: Int -> (a -> a) -> (a -> a)
128 nTimes n f = f . nTimes (n-1) f
131 %************************************************************************
133 \subsection{Maybe-ery}
135 %************************************************************************
138 unJust :: String -> Maybe a -> a
139 unJust who (Just x) = x
140 unJust who Nothing = panic ("unJust of Nothing, called by " ++ who)
143 %************************************************************************
145 \subsection[Utils-lists]{General list processing}
147 %************************************************************************
149 A paranoid @zip@ (and some @zipWith@ friends) that checks the lists
150 are of equal length. Alastair Reid thinks this should only happen if
151 DEBUGging on; hey, why not?
154 zipEqual :: String -> [a] -> [b] -> [(a,b)]
155 zipWithEqual :: String -> (a->b->c) -> [a]->[b]->[c]
156 zipWith3Equal :: String -> (a->b->c->d) -> [a]->[b]->[c]->[d]
157 zipWith4Equal :: String -> (a->b->c->d->e) -> [a]->[b]->[c]->[d]->[e]
161 zipWithEqual _ = zipWith
162 zipWith3Equal _ = zipWith3
163 zipWith4Equal _ = zipWith4
165 zipEqual msg [] [] = []
166 zipEqual msg (a:as) (b:bs) = (a,b) : zipEqual msg as bs
167 zipEqual msg as bs = panic ("zipEqual: unequal lists:"++msg)
169 zipWithEqual msg z (a:as) (b:bs)= z a b : zipWithEqual msg z as bs
170 zipWithEqual msg _ [] [] = []
171 zipWithEqual msg _ _ _ = panic ("zipWithEqual: unequal lists:"++msg)
173 zipWith3Equal msg z (a:as) (b:bs) (c:cs)
174 = z a b c : zipWith3Equal msg z as bs cs
175 zipWith3Equal msg _ [] [] [] = []
176 zipWith3Equal msg _ _ _ _ = panic ("zipWith3Equal: unequal lists:"++msg)
178 zipWith4Equal msg z (a:as) (b:bs) (c:cs) (d:ds)
179 = z a b c d : zipWith4Equal msg z as bs cs ds
180 zipWith4Equal msg _ [] [] [] [] = []
181 zipWith4Equal msg _ _ _ _ _ = panic ("zipWith4Equal: unequal lists:"++msg)
186 -- zipLazy is lazy in the second list (observe the ~)
188 zipLazy :: [a] -> [b] -> [(a,b)]
190 zipLazy (x:xs) ~(y:ys) = (x,y) : zipLazy xs ys
195 stretchZipWith :: (a -> Bool) -> b -> (a->b->c) -> [a] -> [b] -> [c]
196 -- (stretchZipWith p z f xs ys) stretches ys by inserting z in
197 -- the places where p returns *True*
199 stretchZipWith p z f [] ys = []
200 stretchZipWith p z f (x:xs) ys
201 | p x = f x z : stretchZipWith p z f xs ys
202 | otherwise = case ys of
204 (y:ys) -> f x y : stretchZipWith p z f xs ys
209 mapAndUnzip :: (a -> (b, c)) -> [a] -> ([b], [c])
211 mapAndUnzip f [] = ([],[])
215 (rs1, rs2) = mapAndUnzip f xs
219 mapAndUnzip3 :: (a -> (b, c, d)) -> [a] -> ([b], [c], [d])
221 mapAndUnzip3 f [] = ([],[],[])
222 mapAndUnzip3 f (x:xs)
225 (rs1, rs2, rs3) = mapAndUnzip3 f xs
227 (r1:rs1, r2:rs2, r3:rs3)
231 nOfThem :: Int -> a -> [a]
232 nOfThem n thing = replicate n thing
234 lengthExceeds :: [a] -> Int -> Bool
235 -- (lengthExceeds xs n) is True if length xs > n
236 (x:xs) `lengthExceeds` n = n < 1 || xs `lengthExceeds` (n - 1)
237 [] `lengthExceeds` n = n < 0
239 isSingleton :: [a] -> Bool
240 isSingleton [x] = True
241 isSingleton _ = False
252 snocView :: [a] -> ([a], a) -- Split off the last element
253 snocView xs = go xs []
255 go [x] acc = (reverse acc, x)
256 go (x:xs) acc = go xs (x:acc)
259 Debugging/specialising versions of \tr{elem} and \tr{notElem}
262 isIn, isn'tIn :: (Eq a) => String -> a -> [a] -> Bool
265 isIn msg x ys = elem__ x ys
266 isn'tIn msg x ys = notElem__ x ys
268 --these are here to be SPECIALIZEd (automagically)
270 elem__ x (y:ys) = x==y || elem__ x ys
272 notElem__ x [] = True
273 notElem__ x (y:ys) = x /= y && notElem__ x ys
277 = elem (_ILIT 0) x ys
281 | i ># _ILIT 100 = panic ("Over-long elem in: " ++ msg)
282 | otherwise = x == y || elem (i +# _ILIT(1)) x ys
285 = notElem (_ILIT 0) x ys
287 notElem i x [] = True
289 | i ># _ILIT 100 = panic ("Over-long notElem in: " ++ msg)
290 | otherwise = x /= y && notElem (i +# _ILIT(1)) x ys
296 %************************************************************************
298 \subsection[Utils-sorting]{Sorting}
300 %************************************************************************
302 %************************************************************************
304 \subsubsection[Utils-quicksorting]{Quicksorts}
306 %************************************************************************
311 -- tail-recursive, etc., "quicker sort" [as per Meira thesis]
312 quicksort :: (a -> a -> Bool) -- Less-than predicate
314 -> [a] -- Result list in increasing order
317 quicksort lt [x] = [x]
318 quicksort lt (x:xs) = split x [] [] xs
320 split x lo hi [] = quicksort lt lo ++ (x : quicksort lt hi)
321 split x lo hi (y:ys) | y `lt` x = split x (y:lo) hi ys
322 | True = split x lo (y:hi) ys
326 Quicksort variant from Lennart's Haskell-library contribution. This
327 is a {\em stable} sort.
330 stableSortLt = sortLt -- synonym; when we want to highlight stable-ness
332 sortLt :: (a -> a -> Bool) -- Less-than predicate
334 -> [a] -- Result list
336 sortLt lt l = qsort lt l []
338 -- qsort is stable and does not concatenate.
339 qsort :: (a -> a -> Bool) -- Less-than predicate
340 -> [a] -- xs, Input list
341 -> [a] -- r, Concatenate this list to the sorted input list
342 -> [a] -- Result = sort xs ++ r
346 qsort lt (x:xs) r = qpart lt x xs [] [] r
348 -- qpart partitions and sorts the sublists
349 -- rlt contains things less than x,
350 -- rge contains the ones greater than or equal to x.
351 -- Both have equal elements reversed with respect to the original list.
353 qpart lt x [] rlt rge r =
354 -- rlt and rge are in reverse order and must be sorted with an
355 -- anti-stable sorting
356 rqsort lt rlt (x : rqsort lt rge r)
358 qpart lt x (y:ys) rlt rge r =
361 qpart lt x ys (y:rlt) rge r
364 qpart lt x ys rlt (y:rge) r
366 -- rqsort is as qsort but anti-stable, i.e. reverses equal elements
368 rqsort lt [x] r = x:r
369 rqsort lt (x:xs) r = rqpart lt x xs [] [] r
371 rqpart lt x [] rle rgt r =
372 qsort lt rle (x : qsort lt rgt r)
374 rqpart lt x (y:ys) rle rgt r =
377 rqpart lt x ys rle (y:rgt) r
380 rqpart lt x ys (y:rle) rgt r
383 %************************************************************************
385 \subsubsection[Utils-dull-mergesort]{A rather dull mergesort}
387 %************************************************************************
391 mergesort :: (a -> a -> Ordering) -> [a] -> [a]
393 mergesort cmp xs = merge_lists (split_into_runs [] xs)
395 a `le` b = case cmp a b of { LT -> True; EQ -> True; GT -> False }
396 a `ge` b = case cmp a b of { LT -> False; EQ -> True; GT -> True }
398 split_into_runs [] [] = []
399 split_into_runs run [] = [run]
400 split_into_runs [] (x:xs) = split_into_runs [x] xs
401 split_into_runs [r] (x:xs) | x `ge` r = split_into_runs [r,x] xs
402 split_into_runs rl@(r:rs) (x:xs) | x `le` r = split_into_runs (x:rl) xs
403 | True = rl : (split_into_runs [x] xs)
406 merge_lists (x:xs) = merge x (merge_lists xs)
410 merge xl@(x:xs) yl@(y:ys)
412 EQ -> x : y : (merge xs ys)
413 LT -> x : (merge xs yl)
414 GT -> y : (merge xl ys)
418 %************************************************************************
420 \subsubsection[Utils-Carsten-mergesort]{A mergesort from Carsten}
422 %************************************************************************
425 Date: Mon, 3 May 93 20:45:23 +0200
426 From: Carsten Kehler Holst <kehler@cs.chalmers.se>
427 To: partain@dcs.gla.ac.uk
428 Subject: natural merge sort beats quick sort [ and it is prettier ]
430 Here is a piece of Haskell code that I'm rather fond of. See it as an
431 attempt to get rid of the ridiculous quick-sort routine. group is
432 quite useful by itself I think it was John's idea originally though I
433 believe the lazy version is due to me [surprisingly complicated].
434 gamma [used to be called] is called gamma because I got inspired by
435 the Gamma calculus. It is not very close to the calculus but does
436 behave less sequentially than both foldr and foldl. One could imagine
437 a version of gamma that took a unit element as well thereby avoiding
438 the problem with empty lists.
440 I've tried this code against
442 1) insertion sort - as provided by haskell
443 2) the normal implementation of quick sort
444 3) a deforested version of quick sort due to Jan Sparud
445 4) a super-optimized-quick-sort of Lennart's
447 If the list is partially sorted both merge sort and in particular
448 natural merge sort wins. If the list is random [ average length of
449 rising subsequences = approx 2 ] mergesort still wins and natural
450 merge sort is marginally beaten by Lennart's soqs. The space
451 consumption of merge sort is a bit worse than Lennart's quick sort
452 approx a factor of 2. And a lot worse if Sparud's bug-fix [see his
453 fpca article ] isn't used because of group.
460 group :: (a -> a -> Bool) -> [a] -> [[a]]
463 Date: Mon, 12 Feb 1996 15:09:41 +0000
464 From: Andy Gill <andy@dcs.gla.ac.uk>
466 Here is a `better' definition of group.
469 group p (x:xs) = group' xs x x (x :)
471 group' [] _ _ s = [s []]
472 group' (x:xs) x_min x_max s
473 | not (x `p` x_max) = group' xs x_min x (s . (x :))
474 | x `p` x_min = group' xs x x_max ((x :) . s)
475 | otherwise = s [] : group' xs x x (x :)
477 -- This one works forwards *and* backwards, as well as also being
478 -- faster that the one in Util.lhs.
483 let ((h1:t1):tt1) = group p xs
484 (t,tt) = if null xs then ([],[]) else
485 if x `p` h1 then (h1:t1,tt1) else
490 generalMerge :: (a -> a -> Bool) -> [a] -> [a] -> [a]
491 generalMerge p xs [] = xs
492 generalMerge p [] ys = ys
493 generalMerge p (x:xs) (y:ys) | x `p` y = x : generalMerge p xs (y:ys)
494 | otherwise = y : generalMerge p (x:xs) ys
496 -- gamma is now called balancedFold
498 balancedFold :: (a -> a -> a) -> [a] -> a
499 balancedFold f [] = error "can't reduce an empty list using balancedFold"
500 balancedFold f [x] = x
501 balancedFold f l = balancedFold f (balancedFold' f l)
503 balancedFold' :: (a -> a -> a) -> [a] -> [a]
504 balancedFold' f (x:y:xs) = f x y : balancedFold' f xs
505 balancedFold' f xs = xs
507 generalMergeSort p [] = []
508 generalMergeSort p xs = (balancedFold (generalMerge p) . map (: [])) xs
510 generalNaturalMergeSort p [] = []
511 generalNaturalMergeSort p xs = (balancedFold (generalMerge p) . group p) xs
513 mergeSort, naturalMergeSort :: Ord a => [a] -> [a]
515 mergeSort = generalMergeSort (<=)
516 naturalMergeSort = generalNaturalMergeSort (<=)
518 mergeSortLe le = generalMergeSort le
519 naturalMergeSortLe le = generalNaturalMergeSort le
522 %************************************************************************
524 \subsection[Utils-transitive-closure]{Transitive closure}
526 %************************************************************************
528 This algorithm for transitive closure is straightforward, albeit quadratic.
531 transitiveClosure :: (a -> [a]) -- Successor function
532 -> (a -> a -> Bool) -- Equality predicate
534 -> [a] -- The transitive closure
536 transitiveClosure succ eq xs
540 go done (x:xs) | x `is_in` done = go done xs
541 | otherwise = go (x:done) (succ x ++ xs)
544 x `is_in` (y:ys) | eq x y = True
545 | otherwise = x `is_in` ys
548 %************************************************************************
550 \subsection[Utils-accum]{Accumulating}
552 %************************************************************************
554 @mapAccumL@ behaves like a combination
555 of @map@ and @foldl@;
556 it applies a function to each element of a list, passing an accumulating
557 parameter from left to right, and returning a final value of this
558 accumulator together with the new list.
561 mapAccumL :: (acc -> x -> (acc, y)) -- Function of elt of input list
562 -- and accumulator, returning new
563 -- accumulator and elt of result list
564 -> acc -- Initial accumulator
566 -> (acc, [y]) -- Final accumulator and result list
568 mapAccumL f b [] = (b, [])
569 mapAccumL f b (x:xs) = (b'', x':xs') where
571 (b'', xs') = mapAccumL f b' xs
574 @mapAccumR@ does the same, but working from right to left instead. Its type is
575 the same as @mapAccumL@, though.
578 mapAccumR :: (acc -> x -> (acc, y)) -- Function of elt of input list
579 -- and accumulator, returning new
580 -- accumulator and elt of result list
581 -> acc -- Initial accumulator
583 -> (acc, [y]) -- Final accumulator and result list
585 mapAccumR f b [] = (b, [])
586 mapAccumR f b (x:xs) = (b'', x':xs') where
588 (b', xs') = mapAccumR f b xs
591 Here is the bi-directional version, that works from both left and right.
594 mapAccumB :: (accl -> accr -> x -> (accl, accr,y))
595 -- Function of elt of input list
596 -- and accumulator, returning new
597 -- accumulator and elt of result list
598 -> accl -- Initial accumulator from left
599 -> accr -- Initial accumulator from right
601 -> (accl, accr, [y]) -- Final accumulators and result list
603 mapAccumB f a b [] = (a,b,[])
604 mapAccumB f a b (x:xs) = (a'',b'',y:ys)
606 (a',b'',y) = f a b' x
607 (a'',b',ys) = mapAccumB f a' b xs
610 A strict version of foldl.
613 foldl' :: (a -> b -> a) -> a -> [b] -> a
614 foldl' f z xs = lgo z xs
617 lgo z (x:xs) = (lgo $! (f z x)) xs
620 A combination of foldl with zip. It works with equal length lists.
623 foldl2 :: (acc -> a -> b -> acc) -> acc -> [a] -> [b] -> acc
625 foldl2 k z (a:as) (b:bs) = foldl2 k (k z a b) as bs
628 Count the number of times a predicate is true
631 count :: (a -> Bool) -> [a] -> Int
633 count p (x:xs) | p x = 1 + count p xs
634 | otherwise = count p xs
638 %************************************************************************
640 \subsection[Utils-comparison]{Comparisons}
642 %************************************************************************
645 thenCmp :: Ordering -> Ordering -> Ordering
646 {-# INLINE thenCmp #-}
648 thenCmp other any = other
650 cmpList :: (a -> a -> Ordering) -> [a] -> [a] -> Ordering
651 -- `cmpList' uses a user-specified comparer
653 cmpList cmp [] [] = EQ
654 cmpList cmp [] _ = LT
655 cmpList cmp _ [] = GT
656 cmpList cmp (a:as) (b:bs)
657 = case cmp a b of { EQ -> cmpList cmp as bs; xxx -> xxx }
661 prefixMatch :: Eq a => [a] -> [a] -> Bool
662 prefixMatch [] _str = True
663 prefixMatch _pat [] = False
664 prefixMatch (p:ps) (s:ss) | p == s = prefixMatch ps ss
667 suffixMatch :: Eq a => [a] -> [a] -> Bool
668 suffixMatch pat str = prefixMatch (reverse pat) (reverse str)
671 %************************************************************************
673 \subsection[Utils-pairs]{Pairs}
675 %************************************************************************
677 The following are curried versions of @fst@ and @snd@.
680 cfst :: a -> b -> a -- stranal-sem only (Note)
684 The following provide us higher order functions that, when applied
685 to a function, operate on pairs.
688 applyToPair :: ((a -> c),(b -> d)) -> (a,b) -> (c,d)
689 applyToPair (f,g) (x,y) = (f x, g y)
691 applyToFst :: (a -> c) -> (a,b)-> (c,b)
692 applyToFst f (x,y) = (f x,y)
694 applyToSnd :: (b -> d) -> (a,b) -> (a,d)
695 applyToSnd f (x,y) = (x,f y)
697 foldPair :: (a->a->a,b->b->b) -> (a,b) -> [(a,b)] -> (a,b)
698 foldPair fg ab [] = ab
699 foldPair fg@(f,g) ab ((a,b):abs) = (f a u,g b v)
700 where (u,v) = foldPair fg ab abs
704 unzipWith :: (a -> b -> c) -> [(a, b)] -> [c]
705 unzipWith f pairs = map ( \ (a, b) -> f a b ) pairs
709 seqList :: [a] -> b -> b
711 seqList (x:xs) b = x `seq` seqList xs b
717 global :: a -> IORef a
718 global a = unsafePerformIO (newIORef a)
724 #if __GLASGOW_HASKELL__ <= 408
726 ioErrors = justIoErrors
727 throwTo = raiseInThread
730 #ifdef mingw32_TARGET_OS
731 foreign import "_getpid" myGetProcessID :: IO Int
733 myGetProcessID :: IO Int
734 myGetProcessID = Posix.getProcessID