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,
46 IF_NOT_GHC(cfst COMMA applyToPair COMMA applyToFst COMMA)
47 IF_NOT_GHC(applyToSnd COMMA foldPair COMMA)
51 #if __GLASGOW_HASKELL__ < 402
57 #include "HsVersions.h"
59 import List ( zipWith4 )
60 import Panic ( panic )
61 import Unique ( Unique )
62 import UniqFM ( eltsUFM, emptyUFM, addToUFM_C )
67 %************************************************************************
69 \subsection{The Eager monad}
71 %************************************************************************
73 The @Eager@ monad is just an encoding of continuation-passing style,
74 used to allow you to express "do this and then that", mainly to avoid
75 space leaks. It's done with a type synonym to save bureaucracy.
80 type Eager ans a = (a -> ans) -> ans
82 runEager :: Eager a a -> a
83 runEager m = m (\x -> x)
85 appEager :: Eager ans a -> (a -> ans) -> ans
86 appEager m cont = m cont
88 thenEager :: Eager ans a -> (a -> Eager ans b) -> Eager ans b
89 thenEager m k cont = m (\r -> k r cont)
91 returnEager :: a -> Eager ans a
92 returnEager v cont = cont v
94 mapEager :: (a -> Eager ans b) -> [a] -> Eager ans [b]
95 mapEager f [] = returnEager []
96 mapEager f (x:xs) = f x `thenEager` \ y ->
97 mapEager f xs `thenEager` \ ys ->
102 %************************************************************************
104 \subsection{A for loop}
106 %************************************************************************
109 -- Compose a function with itself n times. (nth rather than twice)
110 nTimes :: Int -> (a -> a) -> (a -> a)
113 nTimes n f = f . nTimes (n-1) f
117 %************************************************************************
119 \subsection[Utils-lists]{General list processing}
121 %************************************************************************
123 A paranoid @zip@ (and some @zipWith@ friends) that checks the lists
124 are of equal length. Alastair Reid thinks this should only happen if
125 DEBUGging on; hey, why not?
128 zipEqual :: String -> [a] -> [b] -> [(a,b)]
129 zipWithEqual :: String -> (a->b->c) -> [a]->[b]->[c]
130 zipWith3Equal :: String -> (a->b->c->d) -> [a]->[b]->[c]->[d]
131 zipWith4Equal :: String -> (a->b->c->d->e) -> [a]->[b]->[c]->[d]->[e]
135 zipWithEqual _ = zipWith
136 zipWith3Equal _ = zipWith3
137 zipWith4Equal _ = zipWith4
139 zipEqual msg [] [] = []
140 zipEqual msg (a:as) (b:bs) = (a,b) : zipEqual msg as bs
141 zipEqual msg as bs = panic ("zipEqual: unequal lists:"++msg)
143 zipWithEqual msg z (a:as) (b:bs)= z a b : zipWithEqual msg z as bs
144 zipWithEqual msg _ [] [] = []
145 zipWithEqual msg _ _ _ = panic ("zipWithEqual: unequal lists:"++msg)
147 zipWith3Equal msg z (a:as) (b:bs) (c:cs)
148 = z a b c : zipWith3Equal msg z as bs cs
149 zipWith3Equal msg _ [] [] [] = []
150 zipWith3Equal msg _ _ _ _ = panic ("zipWith3Equal: unequal lists:"++msg)
152 zipWith4Equal msg z (a:as) (b:bs) (c:cs) (d:ds)
153 = z a b c d : zipWith4Equal msg z as bs cs ds
154 zipWith4Equal msg _ [] [] [] [] = []
155 zipWith4Equal msg _ _ _ _ _ = panic ("zipWith4Equal: unequal lists:"++msg)
160 -- zipLazy is lazy in the second list (observe the ~)
162 zipLazy :: [a] -> [b] -> [(a,b)]
164 zipLazy (x:xs) ~(y:ys) = (x,y) : zipLazy xs ys
169 stretchZipWith :: (a -> Bool) -> b -> (a->b->c) -> [a] -> [b] -> [c]
170 -- (stretchZipWith p z f xs ys) stretches ys by inserting z in
171 -- the places where p returns *True*
173 stretchZipWith p z f [] ys = []
174 stretchZipWith p z f (x:xs) ys
175 | p x = f x z : stretchZipWith p z f xs ys
176 | otherwise = case ys of
178 (y:ys) -> f x y : stretchZipWith p z f xs ys
183 mapAndUnzip :: (a -> (b, c)) -> [a] -> ([b], [c])
185 mapAndUnzip f [] = ([],[])
189 (rs1, rs2) = mapAndUnzip f xs
193 mapAndUnzip3 :: (a -> (b, c, d)) -> [a] -> ([b], [c], [d])
195 mapAndUnzip3 f [] = ([],[],[])
196 mapAndUnzip3 f (x:xs)
199 (rs1, rs2, rs3) = mapAndUnzip3 f xs
201 (r1:rs1, r2:rs2, r3:rs3)
205 nOfThem :: Int -> a -> [a]
206 nOfThem n thing = replicate n thing
208 lengthExceeds :: [a] -> Int -> Bool
209 -- (lengthExceeds xs n) is True if length xs > n
210 (x:xs) `lengthExceeds` n = n < 1 || xs `lengthExceeds` (n - 1)
211 [] `lengthExceeds` n = n < 0
213 isSingleton :: [a] -> Bool
214 isSingleton [x] = True
215 isSingleton _ = False
226 snocView :: [a] -> ([a], a) -- Split off the last element
227 snocView xs = go xs []
229 go [x] acc = (reverse acc, x)
230 go (x:xs) acc = go xs (x:acc)
233 Debugging/specialising versions of \tr{elem} and \tr{notElem}
236 isIn, isn'tIn :: (Eq a) => String -> a -> [a] -> Bool
239 isIn msg x ys = elem__ x ys
240 isn'tIn msg x ys = notElem__ x ys
242 --these are here to be SPECIALIZEd (automagically)
244 elem__ x (y:ys) = x==y || elem__ x ys
246 notElem__ x [] = True
247 notElem__ x (y:ys) = x /= y && notElem__ x ys
255 | i _GE_ ILIT(100) = panic ("Over-long elem in: " ++ msg)
256 | otherwise = x == y || elem (i _ADD_ ILIT(1)) x ys
259 = notElem ILIT(0) x ys
261 notElem i x [] = True
263 | i _GE_ ILIT(100) = panic ("Over-long notElem in: " ++ msg)
264 | otherwise = x /= y && notElem (i _ADD_ ILIT(1)) x ys
270 %************************************************************************
272 \subsection[Utils-sorting]{Sorting}
274 %************************************************************************
276 %************************************************************************
278 \subsubsection[Utils-quicksorting]{Quicksorts}
280 %************************************************************************
285 -- tail-recursive, etc., "quicker sort" [as per Meira thesis]
286 quicksort :: (a -> a -> Bool) -- Less-than predicate
288 -> [a] -- Result list in increasing order
291 quicksort lt [x] = [x]
292 quicksort lt (x:xs) = split x [] [] xs
294 split x lo hi [] = quicksort lt lo ++ (x : quicksort lt hi)
295 split x lo hi (y:ys) | y `lt` x = split x (y:lo) hi ys
296 | True = split x lo (y:hi) ys
300 Quicksort variant from Lennart's Haskell-library contribution. This
301 is a {\em stable} sort.
304 stableSortLt = sortLt -- synonym; when we want to highlight stable-ness
306 sortLt :: (a -> a -> Bool) -- Less-than predicate
308 -> [a] -- Result list
310 sortLt lt l = qsort lt l []
312 -- qsort is stable and does not concatenate.
313 qsort :: (a -> a -> Bool) -- Less-than predicate
314 -> [a] -- xs, Input list
315 -> [a] -- r, Concatenate this list to the sorted input list
316 -> [a] -- Result = sort xs ++ r
320 qsort lt (x:xs) r = qpart lt x xs [] [] r
322 -- qpart partitions and sorts the sublists
323 -- rlt contains things less than x,
324 -- rge contains the ones greater than or equal to x.
325 -- Both have equal elements reversed with respect to the original list.
327 qpart lt x [] rlt rge r =
328 -- rlt and rge are in reverse order and must be sorted with an
329 -- anti-stable sorting
330 rqsort lt rlt (x : rqsort lt rge r)
332 qpart lt x (y:ys) rlt rge r =
335 qpart lt x ys (y:rlt) rge r
338 qpart lt x ys rlt (y:rge) r
340 -- rqsort is as qsort but anti-stable, i.e. reverses equal elements
342 rqsort lt [x] r = x:r
343 rqsort lt (x:xs) r = rqpart lt x xs [] [] r
345 rqpart lt x [] rle rgt r =
346 qsort lt rle (x : qsort lt rgt r)
348 rqpart lt x (y:ys) rle rgt r =
351 rqpart lt x ys rle (y:rgt) r
354 rqpart lt x ys (y:rle) rgt r
357 %************************************************************************
359 \subsubsection[Utils-dull-mergesort]{A rather dull mergesort}
361 %************************************************************************
365 mergesort :: (a -> a -> Ordering) -> [a] -> [a]
367 mergesort cmp xs = merge_lists (split_into_runs [] xs)
369 a `le` b = case cmp a b of { LT -> True; EQ -> True; GT -> False }
370 a `ge` b = case cmp a b of { LT -> False; EQ -> True; GT -> True }
372 split_into_runs [] [] = []
373 split_into_runs run [] = [run]
374 split_into_runs [] (x:xs) = split_into_runs [x] xs
375 split_into_runs [r] (x:xs) | x `ge` r = split_into_runs [r,x] xs
376 split_into_runs rl@(r:rs) (x:xs) | x `le` r = split_into_runs (x:rl) xs
377 | True = rl : (split_into_runs [x] xs)
380 merge_lists (x:xs) = merge x (merge_lists xs)
384 merge xl@(x:xs) yl@(y:ys)
386 EQ -> x : y : (merge xs ys)
387 LT -> x : (merge xs yl)
388 GT -> y : (merge xl ys)
392 %************************************************************************
394 \subsubsection[Utils-Carsten-mergesort]{A mergesort from Carsten}
396 %************************************************************************
399 Date: Mon, 3 May 93 20:45:23 +0200
400 From: Carsten Kehler Holst <kehler@cs.chalmers.se>
401 To: partain@dcs.gla.ac.uk
402 Subject: natural merge sort beats quick sort [ and it is prettier ]
404 Here is a piece of Haskell code that I'm rather fond of. See it as an
405 attempt to get rid of the ridiculous quick-sort routine. group is
406 quite useful by itself I think it was John's idea originally though I
407 believe the lazy version is due to me [surprisingly complicated].
408 gamma [used to be called] is called gamma because I got inspired by
409 the Gamma calculus. It is not very close to the calculus but does
410 behave less sequentially than both foldr and foldl. One could imagine
411 a version of gamma that took a unit element as well thereby avoiding
412 the problem with empty lists.
414 I've tried this code against
416 1) insertion sort - as provided by haskell
417 2) the normal implementation of quick sort
418 3) a deforested version of quick sort due to Jan Sparud
419 4) a super-optimized-quick-sort of Lennart's
421 If the list is partially sorted both merge sort and in particular
422 natural merge sort wins. If the list is random [ average length of
423 rising subsequences = approx 2 ] mergesort still wins and natural
424 merge sort is marginally beaten by Lennart's soqs. The space
425 consumption of merge sort is a bit worse than Lennart's quick sort
426 approx a factor of 2. And a lot worse if Sparud's bug-fix [see his
427 fpca article ] isn't used because of group.
434 group :: (a -> a -> Bool) -> [a] -> [[a]]
437 Date: Mon, 12 Feb 1996 15:09:41 +0000
438 From: Andy Gill <andy@dcs.gla.ac.uk>
440 Here is a `better' definition of group.
443 group p (x:xs) = group' xs x x (x :)
445 group' [] _ _ s = [s []]
446 group' (x:xs) x_min x_max s
447 | not (x `p` x_max) = group' xs x_min x (s . (x :))
448 | x `p` x_min = group' xs x x_max ((x :) . s)
449 | otherwise = s [] : group' xs x x (x :)
451 -- This one works forwards *and* backwards, as well as also being
452 -- faster that the one in Util.lhs.
457 let ((h1:t1):tt1) = group p xs
458 (t,tt) = if null xs then ([],[]) else
459 if x `p` h1 then (h1:t1,tt1) else
464 generalMerge :: (a -> a -> Bool) -> [a] -> [a] -> [a]
465 generalMerge p xs [] = xs
466 generalMerge p [] ys = ys
467 generalMerge p (x:xs) (y:ys) | x `p` y = x : generalMerge p xs (y:ys)
468 | otherwise = y : generalMerge p (x:xs) ys
470 -- gamma is now called balancedFold
472 balancedFold :: (a -> a -> a) -> [a] -> a
473 balancedFold f [] = error "can't reduce an empty list using balancedFold"
474 balancedFold f [x] = x
475 balancedFold f l = balancedFold f (balancedFold' f l)
477 balancedFold' :: (a -> a -> a) -> [a] -> [a]
478 balancedFold' f (x:y:xs) = f x y : balancedFold' f xs
479 balancedFold' f xs = xs
481 generalMergeSort p [] = []
482 generalMergeSort p xs = (balancedFold (generalMerge p) . map (: [])) xs
484 generalNaturalMergeSort p [] = []
485 generalNaturalMergeSort p xs = (balancedFold (generalMerge p) . group p) xs
487 mergeSort, naturalMergeSort :: Ord a => [a] -> [a]
489 mergeSort = generalMergeSort (<=)
490 naturalMergeSort = generalNaturalMergeSort (<=)
492 mergeSortLe le = generalMergeSort le
493 naturalMergeSortLe le = generalNaturalMergeSort le
496 %************************************************************************
498 \subsection[Utils-transitive-closure]{Transitive closure}
500 %************************************************************************
502 This algorithm for transitive closure is straightforward, albeit quadratic.
505 transitiveClosure :: (a -> [a]) -- Successor function
506 -> (a -> a -> Bool) -- Equality predicate
508 -> [a] -- The transitive closure
510 transitiveClosure succ eq xs
514 go done (x:xs) | x `is_in` done = go done xs
515 | otherwise = go (x:done) (succ x ++ xs)
518 x `is_in` (y:ys) | eq x y = True
519 | otherwise = x `is_in` ys
522 %************************************************************************
524 \subsection[Utils-accum]{Accumulating}
526 %************************************************************************
528 @mapAccumL@ behaves like a combination
529 of @map@ and @foldl@;
530 it applies a function to each element of a list, passing an accumulating
531 parameter from left to right, and returning a final value of this
532 accumulator together with the new list.
535 mapAccumL :: (acc -> x -> (acc, y)) -- Function of elt of input list
536 -- and accumulator, returning new
537 -- accumulator and elt of result list
538 -> acc -- Initial accumulator
540 -> (acc, [y]) -- Final accumulator and result list
542 mapAccumL f b [] = (b, [])
543 mapAccumL f b (x:xs) = (b'', x':xs') where
545 (b'', xs') = mapAccumL f b' xs
548 @mapAccumR@ does the same, but working from right to left instead. Its type is
549 the same as @mapAccumL@, though.
552 mapAccumR :: (acc -> x -> (acc, y)) -- Function of elt of input list
553 -- and accumulator, returning new
554 -- accumulator and elt of result list
555 -> acc -- Initial accumulator
557 -> (acc, [y]) -- Final accumulator and result list
559 mapAccumR f b [] = (b, [])
560 mapAccumR f b (x:xs) = (b'', x':xs') where
562 (b', xs') = mapAccumR f b xs
565 Here is the bi-directional version, that works from both left and right.
568 mapAccumB :: (accl -> accr -> x -> (accl, accr,y))
569 -- Function of elt of input list
570 -- and accumulator, returning new
571 -- accumulator and elt of result list
572 -> accl -- Initial accumulator from left
573 -> accr -- Initial accumulator from right
575 -> (accl, accr, [y]) -- Final accumulators and result list
577 mapAccumB f a b [] = (a,b,[])
578 mapAccumB f a b (x:xs) = (a'',b'',y:ys)
580 (a',b'',y) = f a b' x
581 (a'',b',ys) = mapAccumB f a' b xs
584 A combination of foldl with zip. It works with equal length lists.
587 foldl2 :: (acc -> a -> b -> acc) -> acc -> [a] -> [b] -> acc
589 foldl2 k z (a:as) (b:bs) = foldl2 k (k z a b) as bs
592 Count the number of times a predicate is true
595 count :: (a -> Bool) -> [a] -> Int
597 count p (x:xs) | p x = 1 + count p xs
598 | otherwise = count p xs
602 %************************************************************************
604 \subsection[Utils-comparison]{Comparisons}
606 %************************************************************************
609 thenCmp :: Ordering -> Ordering -> Ordering
610 {-# INLINE thenCmp #-}
612 thenCmp other any = other
614 cmpList :: (a -> a -> Ordering) -> [a] -> [a] -> Ordering
615 -- `cmpList' uses a user-specified comparer
617 cmpList cmp [] [] = EQ
618 cmpList cmp [] _ = LT
619 cmpList cmp _ [] = GT
620 cmpList cmp (a:as) (b:bs)
621 = case cmp a b of { EQ -> cmpList cmp as bs; xxx -> xxx }
625 cmpString :: String -> String -> Ordering
628 cmpString (x:xs) (y:ys) = if x == y then cmpString xs ys
629 else if x < y then LT
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)