Data/List.hs

   1 {-# OPTIONS -fno-implicit-prelude #-}
   2 -----------------------------------------------------------------------------
   3 --
   4 -- Module      :  Data.List
   5 -- Copyright   :  (c) The University of Glasgow 2001
   6 -- License     :  BSD-style (see the file libraries/core/LICENSE)
   7 --
   8 -- Maintainer  :  libraries@haskell.org
   9 -- Stability   :  provisional
  10 -- Portability :  portable
  11 --
  12 -- $Id: List.hs,v 1.1 2001/06/28 14:15:02 simonmar Exp $
  13 --
  14 -- Operations on lists.
  15 --
  16 -----------------------------------------------------------------------------
  17
  18 module Data.List
  19    (
  20     [] (..),
  21
  22    , elemIndex         -- :: (Eq a) => a -> [a] -> Maybe Int
  23    , elemIndices       -- :: (Eq a) => a -> [a] -> [Int]
  24
  25    , find              -- :: (a -> Bool) -> [a] -> Maybe a
  26    , findIndex         -- :: (a -> Bool) -> [a] -> Maybe Int
  27    , findIndices       -- :: (a -> Bool) -> [a] -> [Int]
  28
  29    , nub               -- :: (Eq a) => [a] -> [a]
  30    , nubBy             -- :: (a -> a -> Bool) -> [a] -> [a]
  31
  32    , delete            -- :: (Eq a) => a -> [a] -> [a]
  33    , deleteBy          -- :: (a -> a -> Bool) -> a -> [a] -> [a]
  34    , (\\)              -- :: (Eq a) => [a] -> [a] -> [a]
  35    , deleteFirstsBy    -- :: (a -> a -> Bool) -> [a] -> [a] -> [a]
  36
  37    , union             -- :: (Eq a) => [a] -> [a] -> [a]
  38    , unionBy           -- :: (a -> a -> Bool) -> [a] -> [a] -> [a]
  39
  40    , intersect         -- :: (Eq a) => [a] -> [a] -> [a]
  41    , intersectBy       -- :: (a -> a -> Bool) -> [a] -> [a] -> [a]
  42
  43    , intersperse       -- :: a -> [a] -> [a]
  44    , transpose         -- :: [[a]] -> [[a]]
  45    , partition         -- :: (a -> Bool) -> [a] -> ([a], [a])
  46
  47    , group             -- :: Eq a => [a] -> [[a]]
  48    , groupBy           -- :: (a -> a -> Bool) -> [a] -> [[a]]
  49
  50    , inits             -- :: [a] -> [[a]]
  51    , tails             -- :: [a] -> [[a]]
  52
  53    , isPrefixOf        -- :: (Eq a) => [a] -> [a] -> Bool
  54    , isSuffixOf        -- :: (Eq a) => [a] -> [a] -> Bool
  55
  56    , mapAccumL         -- :: (a -> b -> (a,c)) -> a -> [b] -> (a,[c])
  57    , mapAccumR         -- :: (a -> b -> (a,c)) -> a -> [b] -> (a,[c])
  58
  59    , sort              -- :: (Ord a) => [a] -> [a]
  60    , sortBy            -- :: (a -> a -> Ordering) -> [a] -> [a]
  61
  62    , insert            -- :: (Ord a) => a -> [a] -> [a]
  63    , insertBy          -- :: (a -> a -> Ordering) -> a -> [a] -> [a]
  64
  65    , maximumBy         -- :: (a -> a -> Ordering) -> [a] -> a
  66    , minimumBy         -- :: (a -> a -> Ordering) -> [a] -> a
  67
  68    , genericLength     -- :: (Integral a) => [b] -> a
  69    , genericTake       -- :: (Integral a) => a -> [b] -> [b]
  70    , genericDrop       -- :: (Integral a) => a -> [b] -> [b]
  71    , genericSplitAt    -- :: (Integral a) => a -> [b] -> ([b], [b])
  72    , genericIndex      -- :: (Integral a) => [b] -> a -> b
  73    , genericReplicate  -- :: (Integral a) => a -> b -> [b]
  74
  75    , unfoldr            -- :: (b -> Maybe (a, b)) -> b -> [a]
  76
  77    , zip4, zip5, zip6, zip7
  78    , zipWith4, zipWith5, zipWith6, zipWith7
  79    , unzip4, unzip5, unzip6, unzip7
  80
  81    , map               -- :: ( a -> b ) -> [a] -> [b]
  82    , (++)              -- :: [a] -> [a] -> [a]
  83    , concat            -- :: [[a]] -> [a]
  84    , filter            -- :: (a -> Bool) -> [a] -> [a]
  85    , head              -- :: [a] -> a
  86    , last              -- :: [a] -> a
  87    , tail              -- :: [a] -> [a]
  88    , init              -- :: [a] -> [a]
  89    , null              -- :: [a] -> Bool
  90    , length            -- :: [a] -> Int
  91    , (!!)              -- :: [a] -> Int -> a
  92    , foldl             -- :: (a -> b -> a) -> a -> [b] -> a
  93    , foldl1            -- :: (a -> a -> a) -> [a] -> a
  94    , scanl             -- :: (a -> b -> a) -> a -> [b] -> [a]
  95    , scanl1            -- :: (a -> a -> a) -> [a] -> [a]
  96    , foldr             -- :: (a -> b -> b) -> b -> [a] -> b
  97    , foldr1            -- :: (a -> a -> a) -> [a] -> a
  98    , scanr             -- :: (a -> b -> b) -> b -> [a] -> [b]
  99    , scanr1            -- :: (a -> a -> a) -> [a] -> [a]
 100    , iterate           -- :: (a -> a) -> a -> [a]
 101    , repeat            -- :: a -> [a]
 102    , replicate         -- :: Int -> a -> [a]
 103    , cycle             -- :: [a] -> [a]
 104    , take              -- :: Int -> [a] -> [a]
 105    , drop              -- :: Int -> [a] -> [a]
 106    , splitAt           -- :: Int -> [a] -> ([a], [a])
 107    , takeWhile         -- :: (a -> Bool) -> [a] -> [a]
 108    , dropWhile         -- :: (a -> Bool) -> [a] -> [a]
 109    , span              -- :: (a -> Bool) -> [a] -> ([a], [a])
 110    , break             -- :: (a -> Bool) -> [a] -> ([a], [a])
 111
 112    , lines             -- :: String   -> [String]
 113    , words             -- :: String   -> [String]
 114    , unlines           -- :: [String] -> String
 115    , unwords           -- :: [String] -> String
 116    , reverse           -- :: [a] -> [a]
 117    , and               -- :: [Bool] -> Bool
 118    , or                -- :: [Bool] -> Bool
 119    , any               -- :: (a -> Bool) -> [a] -> Bool
 120    , all               -- :: (a -> Bool) -> [a] -> Bool
 121    , elem              -- :: a -> [a] -> Bool
 122    , notElem           -- :: a -> [a] -> Bool
 123    , lookup            -- :: (Eq a) => a -> [(a,b)] -> Maybe b
 124    , sum               -- :: (Num a) => [a] -> a
 125    , product           -- :: (Num a) => [a] -> a
 126    , maximum           -- :: (Ord a) => [a] -> a
 127    , minimum           -- :: (Ord a) => [a] -> a
 128    , concatMap         -- :: (a -> [b]) -> [a] -> [b]
 129    , zip               -- :: [a] -> [b] -> [(a,b)]
 130    , zip3
 131    , zipWith           -- :: (a -> b -> c) -> [a] -> [b] -> [c]
 132    , zipWith3
 133    , unzip             -- :: [(a,b)] -> ([a],[b])
 134    , unzip3
 135
 136    ) where
 137
 138 import Data.Maybe
 139
 140 #ifdef __GLASGOW_HASKELL__
 141 import GHC.Num
 142 import GHC.Real
 143 import GHC.List
 144 import GHC.Show ( lines, words, unlines, unwords )
 145 import GHC.Base
 146 #endif
 147
 148 infix 5 \\
 149
 150 -- -----------------------------------------------------------------------------
 151 -- List functions
 152
 153 elemIndex       :: Eq a => a -> [a] -> Maybe Int
 154 elemIndex x     = findIndex (x==)
 155
 156 elemIndices     :: Eq a => a -> [a] -> [Int]
 157 elemIndices x   = findIndices (x==)
 158
 159 find            :: (a -> Bool) -> [a] -> Maybe a
 160 find p          = listToMaybe . filter p
 161
 162 findIndex       :: (a -> Bool) -> [a] -> Maybe Int
 163 findIndex p     = listToMaybe . findIndices p
 164
 165 findIndices      :: (a -> Bool) -> [a] -> [Int]
 166
 167 #ifdef USE_REPORT_PRELUDE
 168 findIndices p xs = [ i | (x,i) <- zip xs [0..], p x]
 169 #else
 170 #ifdef __HUGS__
 171 findIndices p xs = [ i | (x,i) <- zip xs [0..], p x]
 172 #else
 173 -- Efficient definition
 174 findIndices p ls = loop 0# ls
 175                  where
 176                    loop _ [] = []
 177                    loop n (x:xs) | p x       = I# n : loop (n +# 1#) xs
 178                                  | otherwise = loop (n +# 1#) xs
 179 #endif  /* __HUGS__ */
 180 #endif  /* USE_REPORT_PRELUDE */
 181
 182 isPrefixOf              :: (Eq a) => [a] -> [a] -> Bool
 183 isPrefixOf [] _         =  True
 184 isPrefixOf _  []        =  False
 185 isPrefixOf (x:xs) (y:ys)=  x == y && isPrefixOf xs ys
 186
 187 isSuffixOf              :: (Eq a) => [a] -> [a] -> Bool
 188 isSuffixOf x y          =  reverse x `isPrefixOf` reverse y
 189
 190 -- nub (meaning "essence") remove duplicate elements from its list argument.
 191 nub                     :: (Eq a) => [a] -> [a]
 192 #ifdef USE_REPORT_PRELUDE
 193 nub                     =  nubBy (==)
 194 #else
 195 -- stolen from HBC
 196 nub l                   = nub' l []             -- '
 197   where
 198     nub' [] _           = []                    -- '
 199     nub' (x:xs) ls                              -- '
 200         | x `elem` ls   = nub' xs ls            -- '
 201         | otherwise     = x : nub' xs (x:ls)    -- '
 202 #endif
 203
 204 nubBy                   :: (a -> a -> Bool) -> [a] -> [a]
 205 #ifdef USE_REPORT_PRELUDE
 206 nubBy eq []             =  []
 207 nubBy eq (x:xs)         =  x : nubBy eq (filter (\ y -> not (eq x y)) xs)
 208 #else
 209 nubBy eq l              = nubBy' l []
 210   where
 211     nubBy' [] _         = []
 212     nubBy' (y:ys) xs
 213        | elem_by eq y xs = nubBy' ys xs
 214        | otherwise       = y : nubBy' ys (y:xs)
 215
 216 -- Not exported:
 217 -- Note that we keep the call to `eq` with arguments in the
 218 -- same order as in the reference implementation
 219 -- 'xs' is the list of things we've seen so far,
 220 -- 'y' is the potential new element
 221 elem_by :: (a -> a -> Bool) -> a -> [a] -> Bool
 222 elem_by _  _ []         =  False
 223 elem_by eq y (x:xs)     =  x `eq` y || elem_by eq y xs
 224 #endif
 225
 226
 227 -- delete x removes the first occurrence of x from its list argument.
 228 delete                  :: (Eq a) => a -> [a] -> [a]
 229 delete                  =  deleteBy (==)
 230
 231 deleteBy                :: (a -> a -> Bool) -> a -> [a] -> [a]
 232 deleteBy _  _ []        = []
 233 deleteBy eq x (y:ys)    = if x `eq` y then ys else y : deleteBy eq x ys
 234
 235 -- list difference (non-associative).  In the result of xs \\ ys,
 236 -- the first occurrence of each element of ys in turn (if any)
 237 -- has been removed from xs.  Thus, (xs ++ ys) \\ xs == ys.
 238 (\\)                    :: (Eq a) => [a] -> [a] -> [a]
 239 (\\)                    =  foldl (flip delete)
 240
 241 -- List union, remove the elements of first list from second.
 242 union                   :: (Eq a) => [a] -> [a] -> [a]
 243 union                   = unionBy (==)
 244
 245 unionBy                 :: (a -> a -> Bool) -> [a] -> [a] -> [a]
 246 unionBy eq xs ys        =  xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs
 247
 248 intersect               :: (Eq a) => [a] -> [a] -> [a]
 249 intersect               =  intersectBy (==)
 250
 251 intersectBy             :: (a -> a -> Bool) -> [a] -> [a] -> [a]
 252 intersectBy eq xs ys    =  [x | x <- xs, any (eq x) ys]
 253
 254 -- intersperse sep inserts sep between the elements of its list argument.
 255 -- e.g. intersperse ',' "abcde" == "a,b,c,d,e"
 256 intersperse             :: a -> [a] -> [a]
 257 intersperse _   []      = []
 258 intersperse _   [x]     = [x]
 259 intersperse sep (x:xs)  = x : sep : intersperse sep xs
 260
 261 transpose               :: [[a]] -> [[a]]
 262 transpose []             = []
 263 transpose ([]   : xss)   = transpose xss
 264 transpose ((x:xs) : xss) = (x : [h | (h:t) <- xss]) : transpose (xs : [ t | (h:t) <- xss])
 265
 266
 267 -- partition takes a predicate and a list and returns a pair of lists:
 268 -- those elements of the argument list that do and do not satisfy the
 269 -- predicate, respectively; i,e,,
 270 -- partition p xs == (filter p xs, filter (not . p) xs).
 271 partition               :: (a -> Bool) -> [a] -> ([a],[a])
 272 {-# INLINE partition #-}
 273 partition p xs = foldr (select p) ([],[]) xs
 274
 275 select p x (ts,fs) | p x       = (x:ts,fs)
 276                    | otherwise = (ts, x:fs)
 277
 278 -- @mapAccumL@ behaves like a combination
 279 -- of  @map@ and @foldl@;
 280 -- it applies a function to each element of a list, passing an accumulating
 281 -- parameter from left to right, and returning a final value of this
 282 -- accumulator together with the new list.
 283
 284 mapAccumL :: (acc -> x -> (acc, y)) -- Function of elt of input list
 285                                     -- and accumulator, returning new
 286                                     -- accumulator and elt of result list
 287           -> acc            -- Initial accumulator
 288           -> [x]            -- Input list
 289           -> (acc, [y])     -- Final accumulator and result list
 290 mapAccumL _ s []        =  (s, [])
 291 mapAccumL f s (x:xs)    =  (s'',y:ys)
 292                            where (s', y ) = f s x
 293                                  (s'',ys) = mapAccumL f s' xs
 294
 295 -- @mapAccumR@ does the same, but working from right to left instead.
 296 -- Its type is the same as @mapAccumL@, though.
 297
 298 mapAccumR :: (acc -> x -> (acc, y))     -- Function of elt of input list
 299                                         -- and accumulator, returning new
 300                                         -- accumulator and elt of result list
 301             -> acc              -- Initial accumulator
 302             -> [x]              -- Input list
 303             -> (acc, [y])               -- Final accumulator and result list
 304 mapAccumR _ s []        =  (s, [])
 305 mapAccumR f s (x:xs)    =  (s'', y:ys)
 306                            where (s'',y ) = f s' x
 307                                  (s', ys) = mapAccumR f s xs
 308
 309
 310 insert :: Ord a => a -> [a] -> [a]
 311 insert e ls = insertBy (compare) e ls
 312
 313 insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a]
 314 insertBy _   x [] = [x]
 315 insertBy cmp x ys@(y:ys')
 316  = case cmp x y of
 317      GT -> y : insertBy cmp x ys'
 318      _  -> x : ys
 319
 320 maximumBy               :: (a -> a -> a) -> [a] -> a
 321 maximumBy _   []        =  error "List.maximumBy: empty list"
 322 maximumBy max xs        =  foldl1 max xs
 323
 324 minimumBy               :: (a -> a -> a) -> [a] -> a
 325 minimumBy _   []        =  error "List.minimumBy: empty list"
 326 minimumBy min xs        =  foldl1 min xs
 327
 328 genericLength           :: (Num i) => [b] -> i
 329 genericLength []        =  0
 330 genericLength (_:l)     =  1 + genericLength l
 331
 332 genericTake             :: (Integral i) => i -> [a] -> [a]
 333 genericTake 0 _         =  []
 334 genericTake _ []        =  []
 335 genericTake n (x:xs) | n > 0  =  x : genericTake (n-1) xs
 336 genericTake _  _        =  error "List.genericTake: negative argument"
 337
 338 genericDrop             :: (Integral i) => i -> [a] -> [a]
 339 genericDrop 0 xs        =  xs
 340 genericDrop _ []        =  []
 341 genericDrop n (_:xs) | n > 0  =  genericDrop (n-1) xs
 342 genericDrop _ _         =  error "List.genericDrop: negative argument"
 343
 344 genericSplitAt          :: (Integral i) => i -> [b] -> ([b],[b])
 345 genericSplitAt 0 xs     =  ([],xs)
 346 genericSplitAt _ []     =  ([],[])
 347 genericSplitAt n (x:xs) | n > 0  =  (x:xs',xs'') where
 348                                (xs',xs'') = genericSplitAt (n-1) xs
 349 genericSplitAt _ _      =  error "List.genericSplitAt: negative argument"
 350
 351
 352 genericIndex :: (Integral a) => [b] -> a -> b
 353 genericIndex (x:_)  0 = x
 354 genericIndex (_:xs) n
 355  | n > 0     = genericIndex xs (n-1)
 356  | otherwise = error "List.genericIndex: negative argument."
 357 genericIndex _ _      = error "List.genericIndex: index too large."
 358
 359 genericReplicate        :: (Integral i) => i -> a -> [a]
 360 genericReplicate n x    =  genericTake n (repeat x)
 361
 362
 363 zip4                    :: [a] -> [b] -> [c] -> [d] -> [(a,b,c,d)]
 364 zip4                    =  zipWith4 (,,,)
 365
 366 zip5                    :: [a] -> [b] -> [c] -> [d] -> [e] -> [(a,b,c,d,e)]
 367 zip5                    =  zipWith5 (,,,,)
 368
 369 zip6                    :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] ->
 370                               [(a,b,c,d,e,f)]
 371 zip6                    =  zipWith6 (,,,,,)
 372
 373 zip7                    :: [a] -> [b] -> [c] -> [d] -> [e] -> [f] ->
 374                               [g] -> [(a,b,c,d,e,f,g)]
 375 zip7                    =  zipWith7 (,,,,,,)
 376
 377 zipWith4                :: (a->b->c->d->e) -> [a]->[b]->[c]->[d]->[e]
 378 zipWith4 z (a:as) (b:bs) (c:cs) (d:ds)
 379                         =  z a b c d : zipWith4 z as bs cs ds
 380 zipWith4 _ _ _ _ _      =  []
 381
 382 zipWith5                :: (a->b->c->d->e->f) ->
 383                            [a]->[b]->[c]->[d]->[e]->[f]
 384 zipWith5 z (a:as) (b:bs) (c:cs) (d:ds) (e:es)
 385                         =  z a b c d e : zipWith5 z as bs cs ds es
 386 zipWith5 _ _ _ _ _ _    = []
 387
 388 zipWith6                :: (a->b->c->d->e->f->g) ->
 389                            [a]->[b]->[c]->[d]->[e]->[f]->[g]
 390 zipWith6 z (a:as) (b:bs) (c:cs) (d:ds) (e:es) (f:fs)
 391                         =  z a b c d e f : zipWith6 z as bs cs ds es fs
 392 zipWith6 _ _ _ _ _ _ _  = []
 393
 394 zipWith7                :: (a->b->c->d->e->f->g->h) ->
 395                            [a]->[b]->[c]->[d]->[e]->[f]->[g]->[h]
 396 zipWith7 z (a:as) (b:bs) (c:cs) (d:ds) (e:es) (f:fs) (g:gs)
 397                    =  z a b c d e f g : zipWith7 z as bs cs ds es fs gs
 398 zipWith7 _ _ _ _ _ _ _ _ = []
 399
 400 unzip4                  :: [(a,b,c,d)] -> ([a],[b],[c],[d])
 401 unzip4                  =  foldr (\(a,b,c,d) ~(as,bs,cs,ds) ->
 402                                         (a:as,b:bs,c:cs,d:ds))
 403                                  ([],[],[],[])
 404
 405 unzip5                  :: [(a,b,c,d,e)] -> ([a],[b],[c],[d],[e])
 406 unzip5                  =  foldr (\(a,b,c,d,e) ~(as,bs,cs,ds,es) ->
 407                                         (a:as,b:bs,c:cs,d:ds,e:es))
 408                                  ([],[],[],[],[])
 409
 410 unzip6                  :: [(a,b,c,d,e,f)] -> ([a],[b],[c],[d],[e],[f])
 411 unzip6                  =  foldr (\(a,b,c,d,e,f) ~(as,bs,cs,ds,es,fs) ->
 412                                         (a:as,b:bs,c:cs,d:ds,e:es,f:fs))
 413                                  ([],[],[],[],[],[])
 414
 415 unzip7          :: [(a,b,c,d,e,f,g)] -> ([a],[b],[c],[d],[e],[f],[g])
 416 unzip7          =  foldr (\(a,b,c,d,e,f,g) ~(as,bs,cs,ds,es,fs,gs) ->
 417                                 (a:as,b:bs,c:cs,d:ds,e:es,f:fs,g:gs))
 418                          ([],[],[],[],[],[],[])
 419
 420
 421
 422 deleteFirstsBy          :: (a -> a -> Bool) -> [a] -> [a] -> [a]
 423 deleteFirstsBy eq       =  foldl (flip (deleteBy eq))
 424
 425
 426 -- group splits its list argument into a list of lists of equal, adjacent
 427 -- elements.  e.g.,
 428 -- group "Mississippi" == ["M","i","ss","i","ss","i","pp","i"]
 429 group                   :: (Eq a) => [a] -> [[a]]
 430 group                   =  groupBy (==)
 431
 432 groupBy                 :: (a -> a -> Bool) -> [a] -> [[a]]
 433 groupBy _  []           =  []
 434 groupBy eq (x:xs)       =  (x:ys) : groupBy eq zs
 435                            where (ys,zs) = span (eq x) xs
 436
 437 -- inits xs returns the list of initial segments of xs, shortest first.
 438 -- e.g., inits "abc" == ["","a","ab","abc"]
 439 inits                   :: [a] -> [[a]]
 440 inits []                =  [[]]
 441 inits (x:xs)            =  [[]] ++ map (x:) (inits xs)
 442
 443 -- tails xs returns the list of all final segments of xs, longest first.
 444 -- e.g., tails "abc" == ["abc", "bc", "c",""]
 445 tails                   :: [a] -> [[a]]
 446 tails []                =  [[]]
 447 tails xxs@(_:xs)        =  xxs : tails xs
 448
 449
 450 ------------------------------------------------------------------------------
 451 -- Quick Sort algorithm taken from HBC's QSort library.
 452
 453 sort :: (Ord a) => [a] -> [a]
 454 sortBy :: (a -> a -> Ordering) -> [a] -> [a]
 455
 456 #ifdef USE_REPORT_PRELUDE
 457 sort = sortBy compare
 458 sortBy cmp = foldr (insertBy cmp) []
 459 #else
 460
 461 sortBy cmp l = qsort cmp l []
 462 sort l = qsort compare l []
 463
 464 -- rest is not exported:
 465
 466 -- qsort is stable and does not concatenate.
 467 qsort :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
 468 qsort _   []     r = r
 469 qsort _   [x]    r = x:r
 470 qsort cmp (x:xs) r = qpart cmp x xs [] [] r
 471
 472 -- qpart partitions and sorts the sublists
 473 qpart :: (a -> a -> Ordering) -> a -> [a] -> [a] -> [a] -> [a] -> [a]
 474 qpart cmp x [] rlt rge r =
 475     -- rlt and rge are in reverse order and must be sorted with an
 476     -- anti-stable sorting
 477     rqsort cmp rlt (x:rqsort cmp rge r)
 478 qpart cmp x (y:ys) rlt rge r =
 479     case cmp x y of
 480         GT -> qpart cmp x ys (y:rlt) rge r
 481         _  -> qpart cmp x ys rlt (y:rge) r
 482
 483 -- rqsort is as qsort but anti-stable, i.e. reverses equal elements
 484 rqsort :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
 485 rqsort _   []     r = r
 486 rqsort _   [x]    r = x:r
 487 rqsort cmp (x:xs) r = rqpart cmp x xs [] [] r
 488
 489 rqpart :: (a -> a -> Ordering) -> a -> [a] -> [a] -> [a] -> [a] -> [a]
 490 rqpart cmp x [] rle rgt r =
 491     qsort cmp rle (x:qsort cmp rgt r)
 492 rqpart cmp x (y:ys) rle rgt r =
 493     case cmp y x of
 494         GT -> rqpart cmp x ys rle (y:rgt) r
 495         _  -> rqpart cmp x ys (y:rle) rgt r
 496
 497 #endif /* USE_REPORT_PRELUDE */
 498
 499 {-
 500 \begin{verbatim}
 501   unfoldr f' (foldr f z xs) == (z,xs)
 502
 503  if the following holds:
 504
 505    f' (f x y) = Just (x,y)
 506    f' z       = Nothing
 507 \end{verbatim}
 508 -}
 509
 510 unfoldr      :: (b -> Maybe (a, b)) -> b -> [a]
 511 unfoldr f b  =
 512   case f b of
 513    Just (a,new_b) -> a : unfoldr f new_b
 514    Nothing        -> []
 515
 516 -- -----------------------------------------------------------------------------
 517 -- List sum and product
 518
 519 -- sum and product compute the sum or product of a finite list of numbers.
 520 {-# SPECIALISE sum     :: [Int] -> Int #-}
 521 {-# SPECIALISE sum     :: [Integer] -> Integer #-}
 522 {-# SPECIALISE product :: [Int] -> Int #-}
 523 {-# SPECIALISE product :: [Integer] -> Integer #-}
 524 sum, product            :: (Num a) => [a] -> a
 525 #ifdef USE_REPORT_PRELUDE
 526 sum                     =  foldl (+) 0
 527 product                 =  foldl (*) 1
 528 #else
 529 sum     l       = sum' l 0
 530   where
 531     sum' []     a = a
 532     sum' (x:xs) a = sum' xs (a+x)
 533 product l       = prod l 1
 534   where
 535     prod []     a = a
 536     prod (x:xs) a = prod xs (a*x)
 537 #endif