Util.lhs 20 KB
 partain committed Jan 08, 1996 1 %  simonm committed Dec 02, 1998 2 % (c) The GRASP/AQUA Project, Glasgow University, 1992-1998  partain committed Jan 08, 1996 3 4 5 6 % \section[Util]{Highly random utility functions} \begin{code}  simonm committed Jan 08, 1998 7 8 -- IF_NOT_GHC is meant to make this module useful outside the context of GHC #define IF_NOT_GHC(a)  partain committed Jan 08, 1996 9 10  module Util (  simonmar committed Jun 03, 1999 11 #if NOT_USED  sof committed May 18, 1997 12  -- The Eager monad  simonm committed Jan 08, 1998 13  Eager, thenEager, returnEager, mapEager, appEager, runEager,  simonmar committed Jun 03, 1999 14 #endif  sof committed May 18, 1997 15   partain committed Jan 08, 1996 16  -- general list processing  partain committed Mar 19, 1996 17  zipEqual, zipWithEqual, zipWith3Equal, zipWith4Equal,  simonpj committed Mar 23, 2000 18  zipLazy, stretchZipWith,  partain committed May 17, 1996 19  mapAndUnzip, mapAndUnzip3,  simonm committed Apr 27, 1999 20  nOfThem, lengthExceeds, isSingleton, only,  simonpj committed Dec 18, 1998 21  snocView,  partain committed Jan 08, 1996 22 23  isIn, isn'tIn,  simonpj committed Mar 23, 2000 24 25 26  -- for-loop nTimes,  sewardj committed Oct 30, 2000 27 28 29  -- maybe-ish unJust,  partain committed Jan 08, 1996 30 31 32 33 34 35 36 37 38 39  -- sorting IF_NOT_GHC(quicksort COMMA stableSortLt COMMA mergesort COMMA) sortLt, IF_NOT_GHC(mergeSort COMMA) naturalMergeSortLe, -- from Carsten IF_NOT_GHC(naturalMergeSort COMMA mergeSortLe COMMA) -- transitive closures transitiveClosure, -- accumulating  simonmar committed Mar 01, 2001 40 41  mapAccumL, mapAccumR, mapAccumB, foldl2, count,  partain committed Jan 08, 1996 42 43  -- comparisons  simonpj committed Jul 19, 2001 44  eqListBy, thenCmp, cmpList, prefixMatch, suffixMatch,  partain committed May 17, 1996 45   simonm committed Mar 04, 1999 46  -- strictness  simonmar committed Mar 01, 2001 47  foldl', seqList,  simonm committed Mar 04, 1999 48   partain committed Jan 08, 1996 49 50 51  -- pairs IF_NOT_GHC(cfst COMMA applyToPair COMMA applyToFst COMMA) IF_NOT_GHC(applyToSnd COMMA foldPair COMMA)  simonpj committed Dec 18, 1998 52  unzipWith  simonmar committed Jun 03, 1999 53   simonmar committed Oct 11, 2000 54  , global  sewardj committed Oct 27, 2000 55 56 57 58 59 60  #if __GLASGOW_HASKELL__ <= 408 , catchJust , ioErrors , throwTo #endif  simonmar committed Oct 11, 2000 61   partain committed Jan 08, 1996 62 63  ) where  rrt committed Dec 08, 2000 64 #include "../includes/config.h"  simonm committed Jan 08, 1998 65 66 67 #include "HsVersions.h" import List ( zipWith4 )  sewardj committed Oct 30, 2000 68 import Maybe ( Maybe(..) )  simonpj committed Dec 18, 1998 69 import Panic ( panic )  simonmar committed Oct 11, 2000 70 import IOExts ( IORef, newIORef, unsafePerformIO )  simonmar committed Oct 12, 2000 71 import FastTypes  simonmar committed Oct 27, 2000 72 #if __GLASGOW_HASKELL__ <= 408  sewardj committed Oct 27, 2000 73 74 import Exception ( catchIO, justIoErrors, raiseInThread ) #endif  sof committed May 28, 2001 75   partain committed May 16, 1996 76 infixr 9 thenCmp  partain committed Jan 08, 1996 77 78 \end{code}  sof committed May 18, 1997 79 80 81 82 83 84 85 86 87 88 89 %************************************************************************ %* * \subsection{The Eager monad} %* * %************************************************************************ The @Eager@ monad is just an encoding of continuation-passing style, used to allow you to express "do this and then that", mainly to avoid space leaks. It's done with a type synonym to save bureaucracy. \begin{code}  simonmar committed Jun 03, 1999 90 91 #if NOT_USED  sof committed May 18, 1997 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 type Eager ans a = (a -> ans) -> ans runEager :: Eager a a -> a runEager m = m (\x -> x) appEager :: Eager ans a -> (a -> ans) -> ans appEager m cont = m cont thenEager :: Eager ans a -> (a -> Eager ans b) -> Eager ans b thenEager m k cont = m (\r -> k r cont) returnEager :: a -> Eager ans a returnEager v cont = cont v mapEager :: (a -> Eager ans b) -> [a] -> Eager ans [b] mapEager f [] = returnEager [] mapEager f (x:xs) = f x thenEager \ y -> mapEager f xs thenEager \ ys -> returnEager (y:ys)  simonmar committed Jun 03, 1999 111 #endif  sof committed May 18, 1997 112 113 \end{code}  simonpj committed Mar 23, 2000 114 115 116 117 118 119 120 121 122 123 124 125 126 127 %************************************************************************ %* * \subsection{A for loop} %* * %************************************************************************ \begin{code} -- Compose a function with itself n times. (nth rather than twice) nTimes :: Int -> (a -> a) -> (a -> a) nTimes 0 _ = id nTimes 1 f = f nTimes n f = f . nTimes (n-1) f \end{code}  sewardj committed Oct 30, 2000 128 129 130 131 132 133 134 %************************************************************************ %* * \subsection{Maybe-ery} %* * %************************************************************************ \begin{code}  sewardj committed Nov 20, 2000 135 136 137 unJust :: String -> Maybe a -> a unJust who (Just x) = x unJust who Nothing = panic ("unJust of Nothing, called by " ++ who)  sewardj committed Oct 30, 2000 138 \end{code}  simonpj committed Mar 23, 2000 139   partain committed Jan 08, 1996 140 141 142 143 144 145 %************************************************************************ %* * \subsection[Utils-lists]{General list processing} %* * %************************************************************************  partain committed Mar 19, 1996 146 147 148 A paranoid @zip@ (and some @zipWith@ friends) that checks the lists are of equal length. Alastair Reid thinks this should only happen if DEBUGging on; hey, why not?  partain committed Jan 08, 1996 149 150  \begin{code}  partain committed May 16, 1996 151 152 153 154 zipEqual :: String -> [a] -> [b] -> [(a,b)] zipWithEqual :: String -> (a->b->c) -> [a]->[b]->[c] zipWith3Equal :: String -> (a->b->c->d) -> [a]->[b]->[c]->[d] zipWith4Equal :: String -> (a->b->c->d->e) -> [a]->[b]->[c]->[d]->[e]  partain committed Jan 08, 1996 155 156  #ifndef DEBUG  partain committed May 16, 1996 157 158 159 160 zipEqual _ = zip zipWithEqual _ = zipWith zipWith3Equal _ = zipWith3 zipWith4Equal _ = zipWith4  partain committed Jan 08, 1996 161 #else  partain committed May 16, 1996 162 163 zipEqual msg [] [] = [] zipEqual msg (a:as) (b:bs) = (a,b) : zipEqual msg as bs  simonpj committed May 18, 1999 164 zipEqual msg as bs = panic ("zipEqual: unequal lists:"++msg)  partain committed May 16, 1996 165 166 167  zipWithEqual msg z (a:as) (b:bs)= z a b : zipWithEqual msg z as bs zipWithEqual msg _ [] [] = []  simonpj committed May 18, 1999 168 zipWithEqual msg _ _ _ = panic ("zipWithEqual: unequal lists:"++msg)  partain committed May 16, 1996 169 170 171 172  zipWith3Equal msg z (a:as) (b:bs) (c:cs) = z a b c : zipWith3Equal msg z as bs cs zipWith3Equal msg _ [] [] [] = []  simonpj committed May 18, 1999 173 zipWith3Equal msg _ _ _ _ = panic ("zipWith3Equal: unequal lists:"++msg)  partain committed May 16, 1996 174 175 176 177  zipWith4Equal msg z (a:as) (b:bs) (c:cs) (d:ds) = z a b c d : zipWith4Equal msg z as bs cs ds zipWith4Equal msg _ [] [] [] [] = []  simonpj committed May 18, 1999 178 zipWith4Equal msg _ _ _ _ _ = panic ("zipWith4Equal: unequal lists:"++msg)  partain committed Jan 08, 1996 179 180 181 #endif \end{code}  partain committed Mar 19, 1996 182 183 184 185 186 187 188 189 \begin{code} -- zipLazy is lazy in the second list (observe the ~) zipLazy :: [a] -> [b] -> [(a,b)] zipLazy [] ys = [] zipLazy (x:xs) ~(y:ys) = (x,y) : zipLazy xs ys \end{code}  simonm committed Dec 02, 1998 190 191  \begin{code}  simonpj committed Mar 23, 2000 192 193 194 195 196 197 198 199 200 201 stretchZipWith :: (a -> Bool) -> b -> (a->b->c) -> [a] -> [b] -> [c] -- (stretchZipWith p z f xs ys) stretches ys by inserting z in -- the places where p returns *True* stretchZipWith p z f [] ys = [] stretchZipWith p z f (x:xs) ys | p x = f x z : stretchZipWith p z f xs ys | otherwise = case ys of [] -> [] (y:ys) -> f x y : stretchZipWith p z f xs ys  simonm committed Dec 02, 1998 202 203 204 \end{code}  partain committed Apr 30, 1996 205 206 207 208 209 210 211 212 213 214 \begin{code} mapAndUnzip :: (a -> (b, c)) -> [a] -> ([b], [c]) mapAndUnzip f [] = ([],[]) mapAndUnzip f (x:xs) = let (r1, r2) = f x (rs1, rs2) = mapAndUnzip f xs in (r1:rs1, r2:rs2)  partain committed May 17, 1996 215 216 217 218 219 220 221 222 223 224  mapAndUnzip3 :: (a -> (b, c, d)) -> [a] -> ([b], [c], [d]) mapAndUnzip3 f [] = ([],[],[]) mapAndUnzip3 f (x:xs) = let (r1, r2, r3) = f x (rs1, rs2, rs3) = mapAndUnzip3 f xs in (r1:rs1, r2:rs2, r3:rs3)  partain committed Apr 30, 1996 225 226 \end{code}  partain committed Jan 08, 1996 227 228 \begin{code} nOfThem :: Int -> a -> [a]  sof committed Mar 01, 1999 229 nOfThem n thing = replicate n thing  partain committed Jan 08, 1996 230 231  lengthExceeds :: [a] -> Int -> Bool  simonpj committed May 18, 1999 232 233 234 -- (lengthExceeds xs n) is True if length xs > n (x:xs) lengthExceeds n = n < 1 || xs lengthExceeds (n - 1) [] lengthExceeds n = n < 0  partain committed Jan 08, 1996 235 236 237 238  isSingleton :: [a] -> Bool isSingleton [x] = True isSingleton _ = False  simonm committed Apr 27, 1999 239 240 241 242 243 244 245  only :: [a] -> a #ifdef DEBUG only [a] = a #else only (a:_) = a #endif  partain committed Jan 08, 1996 246 247 \end{code}  simonm committed Jan 08, 1998 248 249 250 251 252 253 254 255 \begin{code} snocView :: [a] -> ([a], a) -- Split off the last element snocView xs = go xs [] where go [x] acc = (reverse acc, x) go (x:xs) acc = go xs (x:acc) \end{code}  partain committed Jan 08, 1996 256 Debugging/specialising versions of \tr{elem} and \tr{notElem}  simonm committed Jan 08, 1998 257   partain committed Jan 08, 1996 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 \begin{code} isIn, isn'tIn :: (Eq a) => String -> a -> [a] -> Bool # ifndef DEBUG isIn msg x ys = elem__ x ys isn'tIn msg x ys = notElem__ x ys --these are here to be SPECIALIZEd (automagically) elem__ _ [] = False elem__ x (y:ys) = x==y || elem__ x ys notElem__ x [] = True notElem__ x (y:ys) = x /= y && notElem__ x ys # else {- DEBUG -} isIn msg x ys  simonmar committed Oct 12, 2000 274  = elem (_ILIT 0) x ys  partain committed Jan 08, 1996 275 276 277  where elem i _ [] = False elem i x (y:ys)  simonmar committed Oct 12, 2000 278 279  | i ># _ILIT 100 = panic ("Over-long elem in: " ++ msg) | otherwise = x == y || elem (i +# _ILIT(1)) x ys  partain committed Jan 08, 1996 280 281  isn'tIn msg x ys  simonmar committed Oct 12, 2000 282  = notElem (_ILIT 0) x ys  partain committed Jan 08, 1996 283 284 285  where notElem i x [] = True notElem i x (y:ys)  simonmar committed Oct 12, 2000 286 287  | i ># _ILIT 100 = panic ("Over-long notElem in: " ++ msg) | otherwise = x /= y && notElem (i +# _ILIT(1)) x ys  partain committed Jan 08, 1996 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305  # endif {- DEBUG -} \end{code} %************************************************************************ %* * \subsection[Utils-sorting]{Sorting} %* * %************************************************************************ %************************************************************************ %* * \subsubsection[Utils-quicksorting]{Quicksorts} %* * %************************************************************************ \begin{code}  simonmar committed Jun 03, 1999 306 307 #if NOT_USED  partain committed Jan 08, 1996 308 309 310 311 312 313 314 315 316 317 318 319 -- tail-recursive, etc., "quicker sort" [as per Meira thesis] quicksort :: (a -> a -> Bool) -- Less-than predicate -> [a] -- Input list -> [a] -- Result list in increasing order quicksort lt [] = [] quicksort lt [x] = [x] quicksort lt (x:xs) = split x [] [] xs where split x lo hi [] = quicksort lt lo ++ (x : quicksort lt hi) split x lo hi (y:ys) | y lt x = split x (y:lo) hi ys | True = split x lo (y:hi) ys  simonmar committed Jun 03, 1999 320 #endif  partain committed Jan 08, 1996 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 \end{code} Quicksort variant from Lennart's Haskell-library contribution. This is a {\em stable} sort. \begin{code} stableSortLt = sortLt -- synonym; when we want to highlight stable-ness sortLt :: (a -> a -> Bool) -- Less-than predicate -> [a] -- Input list -> [a] -- Result list sortLt lt l = qsort lt l [] -- qsort is stable and does not concatenate. qsort :: (a -> a -> Bool) -- Less-than predicate -> [a] -- xs, Input list -> [a] -- r, Concatenate this list to the sorted input list -> [a] -- Result = sort xs ++ r qsort lt [] r = r qsort lt [x] r = x:r qsort lt (x:xs) r = qpart lt x xs [] [] r -- qpart partitions and sorts the sublists  partain committed Mar 19, 1996 346 -- rlt contains things less than x,  partain committed Jan 08, 1996 347 348 349 350 351 352 353 354 355 356 357 358 -- rge contains the ones greater than or equal to x. -- Both have equal elements reversed with respect to the original list. qpart lt x [] rlt rge r = -- rlt and rge are in reverse order and must be sorted with an -- anti-stable sorting rqsort lt rlt (x : rqsort lt rge r) qpart lt x (y:ys) rlt rge r = if lt y x then -- y < x qpart lt x ys (y:rlt) rge r  partain committed Mar 19, 1996 359  else  partain committed Jan 08, 1996 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386  -- y >= x qpart lt x ys rlt (y:rge) r -- rqsort is as qsort but anti-stable, i.e. reverses equal elements rqsort lt [] r = r rqsort lt [x] r = x:r rqsort lt (x:xs) r = rqpart lt x xs [] [] r rqpart lt x [] rle rgt r = qsort lt rle (x : qsort lt rgt r) rqpart lt x (y:ys) rle rgt r = if lt x y then -- y > x rqpart lt x ys rle (y:rgt) r else -- y <= x rqpart lt x ys (y:rle) rgt r \end{code} %************************************************************************ %* * \subsubsection[Utils-dull-mergesort]{A rather dull mergesort} %* * %************************************************************************ \begin{code}  simonmar committed Jun 03, 1999 387 #if NOT_USED  simonm committed Jan 08, 1998 388 mergesort :: (a -> a -> Ordering) -> [a] -> [a]  partain committed Jan 08, 1996 389 390 391  mergesort cmp xs = merge_lists (split_into_runs [] xs) where  simonm committed Jan 08, 1998 392 393  a le b = case cmp a b of { LT -> True; EQ -> True; GT -> False } a ge b = case cmp a b of { LT -> False; EQ -> True; GT -> True }  partain committed Jan 08, 1996 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408  split_into_runs [] [] = [] split_into_runs run [] = [run] split_into_runs [] (x:xs) = split_into_runs [x] xs split_into_runs [r] (x:xs) | x ge r = split_into_runs [r,x] xs split_into_runs rl@(r:rs) (x:xs) | x le r = split_into_runs (x:rl) xs | True = rl : (split_into_runs [x] xs) merge_lists [] = [] merge_lists (x:xs) = merge x (merge_lists xs) merge [] ys = ys merge xs [] = xs merge xl@(x:xs) yl@(y:ys) = case cmp x y of  simonm committed Jan 08, 1998 409 410 411  EQ -> x : y : (merge xs ys) LT -> x : (merge xs yl) GT -> y : (merge xl ys)  simonmar committed Jun 03, 1999 412 #endif  partain committed Jan 08, 1996 413 414 415 416 417 418 419 420 421 422 423 424 425 426 \end{code} %************************************************************************ %* * \subsubsection[Utils-Carsten-mergesort]{A mergesort from Carsten} %* * %************************************************************************ \begin{display} Date: Mon, 3 May 93 20:45:23 +0200 From: Carsten Kehler Holst To: partain@dcs.gla.ac.uk Subject: natural merge sort beats quick sort [ and it is prettier ]  partain committed Mar 19, 1996 427 Here is a piece of Haskell code that I'm rather fond of. See it as an  partain committed Jan 11, 1996 428 429 attempt to get rid of the ridiculous quick-sort routine. group is quite useful by itself I think it was John's idea originally though I  partain committed Jan 08, 1996 430 believe the lazy version is due to me [surprisingly complicated].  partain committed Jan 11, 1996 431 432 gamma [used to be called] is called gamma because I got inspired by the Gamma calculus. It is not very close to the calculus but does  partain committed Mar 19, 1996 433 434 435 behave less sequentially than both foldr and foldl. One could imagine a version of gamma that took a unit element as well thereby avoiding the problem with empty lists.  partain committed Jan 08, 1996 436 437 438 439 440 441  I've tried this code against 1) insertion sort - as provided by haskell 2) the normal implementation of quick sort 3) a deforested version of quick sort due to Jan Sparud  partain committed Jan 22, 1996 442  4) a super-optimized-quick-sort of Lennart's  partain committed Jan 08, 1996 443 444 445 446  If the list is partially sorted both merge sort and in particular natural merge sort wins. If the list is random [ average length of rising subsequences = approx 2 ] mergesort still wins and natural  partain committed Jan 22, 1996 447 merge sort is marginally beaten by Lennart's soqs. The space  partain committed Jan 11, 1996 448 consumption of merge sort is a bit worse than Lennart's quick sort  partain committed Jan 08, 1996 449 450 451 approx a factor of 2. And a lot worse if Sparud's bug-fix [see his fpca article ] isn't used because of group.  partain committed Mar 19, 1996 452 have fun  partain committed Jan 08, 1996 453 454 455 456 457 Carsten \end{display} \begin{code} group :: (a -> a -> Bool) -> [a] -> [[a]]  partain committed Jan 11, 1996 458   partain committed Mar 19, 1996 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 {- Date: Mon, 12 Feb 1996 15:09:41 +0000 From: Andy Gill Here is a better' definition of group. -} group p [] = [] group p (x:xs) = group' xs x x (x :) where group' [] _ _ s = [s []] group' (x:xs) x_min x_max s | not (x p x_max) = group' xs x_min x (s . (x :)) | x p x_min = group' xs x x_max ((x :) . s) | otherwise = s [] : group' xs x x (x :) -- This one works forwards *and* backwards, as well as also being -- faster that the one in Util.lhs. {- ORIG:  partain committed Jan 08, 1996 478 group p [] = [[]]  partain committed Mar 19, 1996 479 group p (x:xs) =  partain committed Jan 08, 1996 480 481  let ((h1:t1):tt1) = group p xs (t,tt) = if null xs then ([],[]) else  partain committed Mar 19, 1996 482 483  if x p h1 then (h1:t1,tt1) else ([], (h1:t1):tt1)  partain committed Jan 08, 1996 484  in ((x:t):tt)  partain committed Mar 19, 1996 485 -}  partain committed Jan 08, 1996 486 487 488 489  generalMerge :: (a -> a -> Bool) -> [a] -> [a] -> [a] generalMerge p xs [] = xs generalMerge p [] ys = ys  partain committed Jan 11, 1996 490 generalMerge p (x:xs) (y:ys) | x p y = x : generalMerge p xs (y:ys)  partain committed Mar 19, 1996 491  | otherwise = y : generalMerge p (x:xs) ys  partain committed Jan 08, 1996 492 493 494 495 496 497 498 499 500 501 502 503  -- gamma is now called balancedFold balancedFold :: (a -> a -> a) -> [a] -> a balancedFold f [] = error "can't reduce an empty list using balancedFold" balancedFold f [x] = x balancedFold f l = balancedFold f (balancedFold' f l) balancedFold' :: (a -> a -> a) -> [a] -> [a] balancedFold' f (x:y:xs) = f x y : balancedFold' f xs balancedFold' f xs = xs  partain committed Jan 11, 1996 504 505 506 507 508 generalMergeSort p [] = [] generalMergeSort p xs = (balancedFold (generalMerge p) . map (: [])) xs generalNaturalMergeSort p [] = [] generalNaturalMergeSort p xs = (balancedFold (generalMerge p) . group p) xs  partain committed Jan 08, 1996 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529  mergeSort, naturalMergeSort :: Ord a => [a] -> [a] mergeSort = generalMergeSort (<=) naturalMergeSort = generalNaturalMergeSort (<=) mergeSortLe le = generalMergeSort le naturalMergeSortLe le = generalNaturalMergeSort le \end{code} %************************************************************************ %* * \subsection[Utils-transitive-closure]{Transitive closure} %* * %************************************************************************ This algorithm for transitive closure is straightforward, albeit quadratic. \begin{code} transitiveClosure :: (a -> [a]) -- Successor function -> (a -> a -> Bool) -- Equality predicate  partain committed Mar 19, 1996 530  -> [a]  partain committed Jan 08, 1996 531 532 533  -> [a] -- The transitive closure transitiveClosure succ eq xs  partain committed Jun 05, 1996 534  = go [] xs  partain committed Jan 08, 1996 535  where  partain committed Jun 05, 1996 536 537 538  go done [] = done go done (x:xs) | x is_in done = go done xs | otherwise = go (x:done) (succ x ++ xs)  partain committed Jan 08, 1996 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594  x is_in [] = False x is_in (y:ys) | eq x y = True | otherwise = x is_in ys \end{code} %************************************************************************ %* * \subsection[Utils-accum]{Accumulating} %* * %************************************************************************ @mapAccumL@ behaves like a combination of @map@ and @foldl@; it applies a function to each element of a list, passing an accumulating parameter from left to right, and returning a final value of this accumulator together with the new list. \begin{code} mapAccumL :: (acc -> x -> (acc, y)) -- Function of elt of input list -- and accumulator, returning new -- accumulator and elt of result list -> acc -- Initial accumulator -> [x] -- Input list -> (acc, [y]) -- Final accumulator and result list mapAccumL f b [] = (b, []) mapAccumL f b (x:xs) = (b'', x':xs') where (b', x') = f b x (b'', xs') = mapAccumL f b' xs \end{code} @mapAccumR@ does the same, but working from right to left instead. Its type is the same as @mapAccumL@, though. \begin{code} mapAccumR :: (acc -> x -> (acc, y)) -- Function of elt of input list -- and accumulator, returning new -- accumulator and elt of result list -> acc -- Initial accumulator -> [x] -- Input list -> (acc, [y]) -- Final accumulator and result list mapAccumR f b [] = (b, []) mapAccumR f b (x:xs) = (b'', x':xs') where (b'', x') = f b' x (b', xs') = mapAccumR f b xs \end{code} Here is the bi-directional version, that works from both left and right. \begin{code} mapAccumB :: (accl -> accr -> x -> (accl, accr,y)) -- Function of elt of input list -- and accumulator, returning new -- accumulator and elt of result list  partain committed Mar 19, 1996 595 596 597 598  -> accl -- Initial accumulator from left -> accr -- Initial accumulator from right -> [x] -- Input list -> (accl, accr, [y]) -- Final accumulators and result list  partain committed Jan 08, 1996 599 600 601 602 603 604 605 606  mapAccumB f a b [] = (a,b,[]) mapAccumB f a b (x:xs) = (a'',b'',y:ys) where (a',b'',y) = f a b' x (a'',b',ys) = mapAccumB f a' b xs \end{code}  simonmar committed Mar 01, 2001 607 608 609 610 611 612 613 614 615 616 A strict version of foldl. \begin{code} foldl' :: (a -> b -> a) -> a -> [b] -> a foldl' f z xs = lgo z xs where lgo z [] = z lgo z (x:xs) = (lgo \$! (f z x)) xs \end{code}  simonpj committed May 18, 1999 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 A combination of foldl with zip. It works with equal length lists. \begin{code} foldl2 :: (acc -> a -> b -> acc) -> acc -> [a] -> [b] -> acc foldl2 k z [] [] = z foldl2 k z (a:as) (b:bs) = foldl2 k (k z a b) as bs \end{code} Count the number of times a predicate is true \begin{code} count :: (a -> Bool) -> [a] -> Int count p [] = 0 count p (x:xs) | p x = 1 + count p xs | otherwise = count p xs \end{code}  partain committed Jan 08, 1996 635 636 637 638 639 640 %************************************************************************ %* * \subsection[Utils-comparison]{Comparisons} %* * %************************************************************************  partain committed Mar 19, 1996 641 \begin{code}  simonpj committed Jul 19, 2001 642 643 644 645 646 eqListBy :: (a->a->Bool) -> [a] -> [a] -> Bool eqListBy eq [] [] = True eqListBy eq (x:xs) (y:ys) = eq x y && eqListBy eq xs ys eqListBy eq xs ys = False  simonm committed Jan 08, 1998 647 thenCmp :: Ordering -> Ordering -> Ordering  partain committed Mar 19, 1996 648 {-# INLINE thenCmp #-}  simonm committed Jan 08, 1998 649 thenCmp EQ any = any  partain committed Mar 19, 1996 650 651 thenCmp other any = other  simonm committed Jan 08, 1998 652 cmpList :: (a -> a -> Ordering) -> [a] -> [a] -> Ordering  partain committed Mar 19, 1996 653 654  -- cmpList' uses a user-specified comparer  simonm committed Jan 08, 1998 655 656 657 cmpList cmp [] [] = EQ cmpList cmp [] _ = LT cmpList cmp _ [] = GT  partain committed Mar 19, 1996 658 cmpList cmp (a:as) (b:bs)  simonm committed Jan 08, 1998 659  = case cmp a b of { EQ -> cmpList cmp as bs; xxx -> xxx }  partain committed Mar 19, 1996 660 661 \end{code}  partain committed Jan 08, 1996 662 \begin{code}  simonmar committed Oct 11, 2000 663 664 665 666 667 668 prefixMatch :: Eq a => [a] -> [a] -> Bool prefixMatch [] _str = True prefixMatch _pat [] = False prefixMatch (p:ps) (s:ss) | p == s = prefixMatch ps ss | otherwise = False  sewardj committed Dec 05, 2000 669 670 suffixMatch :: Eq a => [a] -> [a] -> Bool suffixMatch pat str = prefixMatch (reverse pat) (reverse str)  partain committed Jan 08, 1996 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 \end{code} %************************************************************************ %* * \subsection[Utils-pairs]{Pairs} %* * %************************************************************************ The following are curried versions of @fst@ and @snd@. \begin{code} cfst :: a -> b -> a -- stranal-sem only (Note) cfst x y = x \end{code} The following provide us higher order functions that, when applied to a function, operate on pairs. \begin{code} applyToPair :: ((a -> c),(b -> d)) -> (a,b) -> (c,d) applyToPair (f,g) (x,y) = (f x, g y) applyToFst :: (a -> c) -> (a,b)-> (c,b) applyToFst f (x,y) = (f x,y) applyToSnd :: (b -> d) -> (a,b) -> (a,d) applyToSnd f (x,y) = (x,f y) foldPair :: (a->a->a,b->b->b) -> (a,b) -> [(a,b)] -> (a,b) foldPair fg ab [] = ab foldPair fg@(f,g) ab ((a,b):abs) = (f a u,g b v)  partain committed Mar 19, 1996 702  where (u,v) = foldPair fg ab abs  partain committed Jan 08, 1996 703 704 705 706 707 708 709 \end{code} \begin{code} unzipWith :: (a -> b -> c) -> [(a, b)] -> [c] unzipWith f pairs = map ( \ (a, b) -> f a b ) pairs \end{code}  simonm committed Mar 04, 1999 710 711 712 713 \begin{code} seqList :: [a] -> b -> b seqList [] b = b seqList (x:xs) b = x seq seqList xs b  simonmar committed Jun 01, 1999 714 \end{code}  simonmar committed Oct 11, 2000 715 716 717 718 719 720 721 722  Global variables: \begin{code} global :: a -> IORef a global a = unsafePerformIO (newIORef a) \end{code}  sewardj committed Oct 27, 2000 723 724 725 726 727 728 729 730 731 Compatibility stuff: \begin{code} #if __GLASGOW_HASKELL__ <= 408 catchJust = catchIO ioErrors = justIoErrors throwTo = raiseInThread #endif \end{code}