Remove Control.Parallel*, now in package parallel
[packages/random.git] / Data / Map.hs
1 {-# OPTIONS_GHC -fno-bang-patterns #-}
2
3 -----------------------------------------------------------------------------
4 -- |
5 -- Module : Data.Map
6 -- Copyright : (c) Daan Leijen 2002
7 -- License : BSD-style
8 -- Maintainer : libraries@haskell.org
9 -- Stability : provisional
10 -- Portability : portable
11 --
12 -- An efficient implementation of maps from keys to values (dictionaries).
13 --
14 -- Since many function names (but not the type name) clash with
15 -- "Prelude" names, this module is usually imported @qualified@, e.g.
16 --
17 -- > import Data.Map (Map)
18 -- > import qualified Data.Map as Map
19 --
20 -- The implementation of 'Map' is based on /size balanced/ binary trees (or
21 -- trees of /bounded balance/) as described by:
22 --
23 -- * Stephen Adams, \"/Efficient sets: a balancing act/\",
24 -- Journal of Functional Programming 3(4):553-562, October 1993,
25 -- <http://www.swiss.ai.mit.edu/~adams/BB>.
26 --
27 -- * J. Nievergelt and E.M. Reingold,
28 -- \"/Binary search trees of bounded balance/\",
29 -- SIAM journal of computing 2(1), March 1973.
30 --
31 -- Note that the implementation is /left-biased/ -- the elements of a
32 -- first argument are always preferred to the second, for example in
33 -- 'union' or 'insert'.
34 -----------------------------------------------------------------------------
35
36 module Data.Map (
37 -- * Map type
38 Map -- instance Eq,Show,Read
39
40 -- * Operators
41 , (!), (\\)
42
43
44 -- * Query
45 , null
46 , size
47 , member
48 , notMember
49 , lookup
50 , findWithDefault
51
52 -- * Construction
53 , empty
54 , singleton
55
56 -- ** Insertion
57 , insert
58 , insertWith, insertWithKey, insertLookupWithKey
59 , insertWith', insertWithKey'
60
61 -- ** Delete\/Update
62 , delete
63 , adjust
64 , adjustWithKey
65 , update
66 , updateWithKey
67 , updateLookupWithKey
68 , alter
69
70 -- * Combine
71
72 -- ** Union
73 , union
74 , unionWith
75 , unionWithKey
76 , unions
77 , unionsWith
78
79 -- ** Difference
80 , difference
81 , differenceWith
82 , differenceWithKey
83
84 -- ** Intersection
85 , intersection
86 , intersectionWith
87 , intersectionWithKey
88
89 -- * Traversal
90 -- ** Map
91 , map
92 , mapWithKey
93 , mapAccum
94 , mapAccumWithKey
95 , mapKeys
96 , mapKeysWith
97 , mapKeysMonotonic
98
99 -- ** Fold
100 , fold
101 , foldWithKey
102
103 -- * Conversion
104 , elems
105 , keys
106 , keysSet
107 , assocs
108
109 -- ** Lists
110 , toList
111 , fromList
112 , fromListWith
113 , fromListWithKey
114
115 -- ** Ordered lists
116 , toAscList
117 , fromAscList
118 , fromAscListWith
119 , fromAscListWithKey
120 , fromDistinctAscList
121
122 -- * Filter
123 , filter
124 , filterWithKey
125 , partition
126 , partitionWithKey
127
128 , mapMaybe
129 , mapMaybeWithKey
130 , mapEither
131 , mapEitherWithKey
132
133 , split
134 , splitLookup
135
136 -- * Submap
137 , isSubmapOf, isSubmapOfBy
138 , isProperSubmapOf, isProperSubmapOfBy
139
140 -- * Indexed
141 , lookupIndex
142 , findIndex
143 , elemAt
144 , updateAt
145 , deleteAt
146
147 -- * Min\/Max
148 , findMin
149 , findMax
150 , deleteMin
151 , deleteMax
152 , deleteFindMin
153 , deleteFindMax
154 , updateMin
155 , updateMax
156 , updateMinWithKey
157 , updateMaxWithKey
158 , minView
159 , maxView
160 , minViewWithKey
161 , maxViewWithKey
162
163 -- * Debugging
164 , showTree
165 , showTreeWith
166 , valid
167 ) where
168
169 import Prelude hiding (lookup,map,filter,foldr,foldl,null)
170 import qualified Data.Set as Set
171 import qualified Data.List as List
172 import Data.Monoid (Monoid(..))
173 import Data.Typeable
174 import Control.Applicative (Applicative(..), (<$>))
175 import Data.Traversable (Traversable(traverse))
176 import Data.Foldable (Foldable(foldMap))
177
178 {-
179 -- for quick check
180 import qualified Prelude
181 import qualified List
182 import Debug.QuickCheck
183 import List(nub,sort)
184 -}
185
186 #if __GLASGOW_HASKELL__
187 import Text.Read
188 import Data.Generics.Basics
189 import Data.Generics.Instances
190 #endif
191
192 {--------------------------------------------------------------------
193 Operators
194 --------------------------------------------------------------------}
195 infixl 9 !,\\ --
196
197 -- | /O(log n)/. Find the value at a key.
198 -- Calls 'error' when the element can not be found.
199 (!) :: Ord k => Map k a -> k -> a
200 m ! k = find k m
201
202 -- | /O(n+m)/. See 'difference'.
203 (\\) :: Ord k => Map k a -> Map k b -> Map k a
204 m1 \\ m2 = difference m1 m2
205
206 {--------------------------------------------------------------------
207 Size balanced trees.
208 --------------------------------------------------------------------}
209 -- | A Map from keys @k@ to values @a@.
210 data Map k a = Tip
211 | Bin {-# UNPACK #-} !Size !k a !(Map k a) !(Map k a)
212
213 type Size = Int
214
215 instance (Ord k) => Monoid (Map k v) where
216 mempty = empty
217 mappend = union
218 mconcat = unions
219
220 #if __GLASGOW_HASKELL__
221
222 {--------------------------------------------------------------------
223 A Data instance
224 --------------------------------------------------------------------}
225
226 -- This instance preserves data abstraction at the cost of inefficiency.
227 -- We omit reflection services for the sake of data abstraction.
228
229 instance (Data k, Data a, Ord k) => Data (Map k a) where
230 gfoldl f z map = z fromList `f` (toList map)
231 toConstr _ = error "toConstr"
232 gunfold _ _ = error "gunfold"
233 dataTypeOf _ = mkNorepType "Data.Map.Map"
234 dataCast2 f = gcast2 f
235
236 #endif
237
238 {--------------------------------------------------------------------
239 Query
240 --------------------------------------------------------------------}
241 -- | /O(1)/. Is the map empty?
242 null :: Map k a -> Bool
243 null t
244 = case t of
245 Tip -> True
246 Bin sz k x l r -> False
247
248 -- | /O(1)/. The number of elements in the map.
249 size :: Map k a -> Int
250 size t
251 = case t of
252 Tip -> 0
253 Bin sz k x l r -> sz
254
255
256 -- | /O(log n)/. Lookup the value at a key in the map.
257 --
258 -- The function will
259 -- @return@ the result in the monad or @fail@ in it the key isn't in the
260 -- map. Often, the monad to use is 'Maybe', so you get either
261 -- @('Just' result)@ or @'Nothing'@.
262 lookup :: (Monad m,Ord k) => k -> Map k a -> m a
263 lookup k t = case lookup' k t of
264 Just x -> return x
265 Nothing -> fail "Data.Map.lookup: Key not found"
266 lookup' :: Ord k => k -> Map k a -> Maybe a
267 lookup' k t
268 = case t of
269 Tip -> Nothing
270 Bin sz kx x l r
271 -> case compare k kx of
272 LT -> lookup' k l
273 GT -> lookup' k r
274 EQ -> Just x
275
276 lookupAssoc :: Ord k => k -> Map k a -> Maybe (k,a)
277 lookupAssoc k t
278 = case t of
279 Tip -> Nothing
280 Bin sz kx x l r
281 -> case compare k kx of
282 LT -> lookupAssoc k l
283 GT -> lookupAssoc k r
284 EQ -> Just (kx,x)
285
286 -- | /O(log n)/. Is the key a member of the map?
287 member :: Ord k => k -> Map k a -> Bool
288 member k m
289 = case lookup k m of
290 Nothing -> False
291 Just x -> True
292
293 -- | /O(log n)/. Is the key not a member of the map?
294 notMember :: Ord k => k -> Map k a -> Bool
295 notMember k m = not $ member k m
296
297 -- | /O(log n)/. Find the value at a key.
298 -- Calls 'error' when the element can not be found.
299 find :: Ord k => k -> Map k a -> a
300 find k m
301 = case lookup k m of
302 Nothing -> error "Map.find: element not in the map"
303 Just x -> x
304
305 -- | /O(log n)/. The expression @('findWithDefault' def k map)@ returns
306 -- the value at key @k@ or returns @def@ when the key is not in the map.
307 findWithDefault :: Ord k => a -> k -> Map k a -> a
308 findWithDefault def k m
309 = case lookup k m of
310 Nothing -> def
311 Just x -> x
312
313
314
315 {--------------------------------------------------------------------
316 Construction
317 --------------------------------------------------------------------}
318 -- | /O(1)/. The empty map.
319 empty :: Map k a
320 empty
321 = Tip
322
323 -- | /O(1)/. A map with a single element.
324 singleton :: k -> a -> Map k a
325 singleton k x
326 = Bin 1 k x Tip Tip
327
328 {--------------------------------------------------------------------
329 Insertion
330 --------------------------------------------------------------------}
331 -- | /O(log n)/. Insert a new key and value in the map.
332 -- If the key is already present in the map, the associated value is
333 -- replaced with the supplied value, i.e. 'insert' is equivalent to
334 -- @'insertWith' 'const'@.
335 insert :: Ord k => k -> a -> Map k a -> Map k a
336 insert kx x t
337 = case t of
338 Tip -> singleton kx x
339 Bin sz ky y l r
340 -> case compare kx ky of
341 LT -> balance ky y (insert kx x l) r
342 GT -> balance ky y l (insert kx x r)
343 EQ -> Bin sz kx x l r
344
345 -- | /O(log n)/. Insert with a combining function.
346 -- @'insertWith' f key value mp@
347 -- will insert the pair (key, value) into @mp@ if key does
348 -- not exist in the map. If the key does exist, the function will
349 -- insert the pair @(key, f new_value old_value)@.
350 insertWith :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
351 insertWith f k x m
352 = insertWithKey (\k x y -> f x y) k x m
353
354 -- | Same as 'insertWith', but the combining function is applied strictly.
355 insertWith' :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
356 insertWith' f k x m
357 = insertWithKey' (\k x y -> f x y) k x m
358
359
360 -- | /O(log n)/. Insert with a combining function.
361 -- @'insertWithKey' f key value mp@
362 -- will insert the pair (key, value) into @mp@ if key does
363 -- not exist in the map. If the key does exist, the function will
364 -- insert the pair @(key,f key new_value old_value)@.
365 -- Note that the key passed to f is the same key passed to 'insertWithKey'.
366 insertWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
367 insertWithKey f kx x t
368 = case t of
369 Tip -> singleton kx x
370 Bin sy ky y l r
371 -> case compare kx ky of
372 LT -> balance ky y (insertWithKey f kx x l) r
373 GT -> balance ky y l (insertWithKey f kx x r)
374 EQ -> Bin sy kx (f kx x y) l r
375
376 -- | Same as 'insertWithKey', but the combining function is applied strictly.
377 insertWithKey' :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
378 insertWithKey' f kx x t
379 = case t of
380 Tip -> singleton kx x
381 Bin sy ky y l r
382 -> case compare kx ky of
383 LT -> balance ky y (insertWithKey' f kx x l) r
384 GT -> balance ky y l (insertWithKey' f kx x r)
385 EQ -> let x' = f kx x y in seq x' (Bin sy kx x' l r)
386
387
388 -- | /O(log n)/. The expression (@'insertLookupWithKey' f k x map@)
389 -- is a pair where the first element is equal to (@'lookup' k map@)
390 -- and the second element equal to (@'insertWithKey' f k x map@).
391 insertLookupWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> (Maybe a,Map k a)
392 insertLookupWithKey f kx x t
393 = case t of
394 Tip -> (Nothing, singleton kx x)
395 Bin sy ky y l r
396 -> case compare kx ky of
397 LT -> let (found,l') = insertLookupWithKey f kx x l in (found,balance ky y l' r)
398 GT -> let (found,r') = insertLookupWithKey f kx x r in (found,balance ky y l r')
399 EQ -> (Just y, Bin sy kx (f kx x y) l r)
400
401 {--------------------------------------------------------------------
402 Deletion
403 [delete] is the inlined version of [deleteWith (\k x -> Nothing)]
404 --------------------------------------------------------------------}
405 -- | /O(log n)/. Delete a key and its value from the map. When the key is not
406 -- a member of the map, the original map is returned.
407 delete :: Ord k => k -> Map k a -> Map k a
408 delete k t
409 = case t of
410 Tip -> Tip
411 Bin sx kx x l r
412 -> case compare k kx of
413 LT -> balance kx x (delete k l) r
414 GT -> balance kx x l (delete k r)
415 EQ -> glue l r
416
417 -- | /O(log n)/. Adjust a value at a specific key. When the key is not
418 -- a member of the map, the original map is returned.
419 adjust :: Ord k => (a -> a) -> k -> Map k a -> Map k a
420 adjust f k m
421 = adjustWithKey (\k x -> f x) k m
422
423 -- | /O(log n)/. Adjust a value at a specific key. When the key is not
424 -- a member of the map, the original map is returned.
425 adjustWithKey :: Ord k => (k -> a -> a) -> k -> Map k a -> Map k a
426 adjustWithKey f k m
427 = updateWithKey (\k x -> Just (f k x)) k m
428
429 -- | /O(log n)/. The expression (@'update' f k map@) updates the value @x@
430 -- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is
431 -- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@.
432 update :: Ord k => (a -> Maybe a) -> k -> Map k a -> Map k a
433 update f k m
434 = updateWithKey (\k x -> f x) k m
435
436 -- | /O(log n)/. The expression (@'updateWithKey' f k map@) updates the
437 -- value @x@ at @k@ (if it is in the map). If (@f k x@) is 'Nothing',
438 -- the element is deleted. If it is (@'Just' y@), the key @k@ is bound
439 -- to the new value @y@.
440 updateWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a
441 updateWithKey f k t
442 = case t of
443 Tip -> Tip
444 Bin sx kx x l r
445 -> case compare k kx of
446 LT -> balance kx x (updateWithKey f k l) r
447 GT -> balance kx x l (updateWithKey f k r)
448 EQ -> case f kx x of
449 Just x' -> Bin sx kx x' l r
450 Nothing -> glue l r
451
452 -- | /O(log n)/. Lookup and update.
453 updateLookupWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> (Maybe a,Map k a)
454 updateLookupWithKey f k t
455 = case t of
456 Tip -> (Nothing,Tip)
457 Bin sx kx x l r
458 -> case compare k kx of
459 LT -> let (found,l') = updateLookupWithKey f k l in (found,balance kx x l' r)
460 GT -> let (found,r') = updateLookupWithKey f k r in (found,balance kx x l r')
461 EQ -> case f kx x of
462 Just x' -> (Just x',Bin sx kx x' l r)
463 Nothing -> (Just x,glue l r)
464
465 -- | /O(log n)/. The expression (@'alter' f k map@) alters the value @x@ at @k@, or absence thereof.
466 -- 'alter' can be used to insert, delete, or update a value in a 'Map'.
467 -- In short : @'lookup' k ('alter' f k m) = f ('lookup' k m)@
468 alter :: Ord k => (Maybe a -> Maybe a) -> k -> Map k a -> Map k a
469 alter f k t
470 = case t of
471 Tip -> case f Nothing of
472 Nothing -> Tip
473 Just x -> singleton k x
474 Bin sx kx x l r
475 -> case compare k kx of
476 LT -> balance kx x (alter f k l) r
477 GT -> balance kx x l (alter f k r)
478 EQ -> case f (Just x) of
479 Just x' -> Bin sx kx x' l r
480 Nothing -> glue l r
481
482 {--------------------------------------------------------------------
483 Indexing
484 --------------------------------------------------------------------}
485 -- | /O(log n)/. Return the /index/ of a key. The index is a number from
486 -- /0/ up to, but not including, the 'size' of the map. Calls 'error' when
487 -- the key is not a 'member' of the map.
488 findIndex :: Ord k => k -> Map k a -> Int
489 findIndex k t
490 = case lookupIndex k t of
491 Nothing -> error "Map.findIndex: element is not in the map"
492 Just idx -> idx
493
494 -- | /O(log n)/. Lookup the /index/ of a key. The index is a number from
495 -- /0/ up to, but not including, the 'size' of the map.
496 lookupIndex :: (Monad m,Ord k) => k -> Map k a -> m Int
497 lookupIndex k t = case lookup 0 t of
498 Nothing -> fail "Data.Map.lookupIndex: Key not found."
499 Just x -> return x
500 where
501 lookup idx Tip = Nothing
502 lookup idx (Bin _ kx x l r)
503 = case compare k kx of
504 LT -> lookup idx l
505 GT -> lookup (idx + size l + 1) r
506 EQ -> Just (idx + size l)
507
508 -- | /O(log n)/. Retrieve an element by /index/. Calls 'error' when an
509 -- invalid index is used.
510 elemAt :: Int -> Map k a -> (k,a)
511 elemAt i Tip = error "Map.elemAt: index out of range"
512 elemAt i (Bin _ kx x l r)
513 = case compare i sizeL of
514 LT -> elemAt i l
515 GT -> elemAt (i-sizeL-1) r
516 EQ -> (kx,x)
517 where
518 sizeL = size l
519
520 -- | /O(log n)/. Update the element at /index/. Calls 'error' when an
521 -- invalid index is used.
522 updateAt :: (k -> a -> Maybe a) -> Int -> Map k a -> Map k a
523 updateAt f i Tip = error "Map.updateAt: index out of range"
524 updateAt f i (Bin sx kx x l r)
525 = case compare i sizeL of
526 LT -> updateAt f i l
527 GT -> updateAt f (i-sizeL-1) r
528 EQ -> case f kx x of
529 Just x' -> Bin sx kx x' l r
530 Nothing -> glue l r
531 where
532 sizeL = size l
533
534 -- | /O(log n)/. Delete the element at /index/.
535 -- Defined as (@'deleteAt' i map = 'updateAt' (\k x -> 'Nothing') i map@).
536 deleteAt :: Int -> Map k a -> Map k a
537 deleteAt i map
538 = updateAt (\k x -> Nothing) i map
539
540
541 {--------------------------------------------------------------------
542 Minimal, Maximal
543 --------------------------------------------------------------------}
544 -- | /O(log n)/. The minimal key of the map.
545 findMin :: Map k a -> (k,a)
546 findMin (Bin _ kx x Tip r) = (kx,x)
547 findMin (Bin _ kx x l r) = findMin l
548 findMin Tip = error "Map.findMin: empty map has no minimal element"
549
550 -- | /O(log n)/. The maximal key of the map.
551 findMax :: Map k a -> (k,a)
552 findMax (Bin _ kx x l Tip) = (kx,x)
553 findMax (Bin _ kx x l r) = findMax r
554 findMax Tip = error "Map.findMax: empty map has no maximal element"
555
556 -- | /O(log n)/. Delete the minimal key.
557 deleteMin :: Map k a -> Map k a
558 deleteMin (Bin _ kx x Tip r) = r
559 deleteMin (Bin _ kx x l r) = balance kx x (deleteMin l) r
560 deleteMin Tip = Tip
561
562 -- | /O(log n)/. Delete the maximal key.
563 deleteMax :: Map k a -> Map k a
564 deleteMax (Bin _ kx x l Tip) = l
565 deleteMax (Bin _ kx x l r) = balance kx x l (deleteMax r)
566 deleteMax Tip = Tip
567
568 -- | /O(log n)/. Update the value at the minimal key.
569 updateMin :: (a -> Maybe a) -> Map k a -> Map k a
570 updateMin f m
571 = updateMinWithKey (\k x -> f x) m
572
573 -- | /O(log n)/. Update the value at the maximal key.
574 updateMax :: (a -> Maybe a) -> Map k a -> Map k a
575 updateMax f m
576 = updateMaxWithKey (\k x -> f x) m
577
578
579 -- | /O(log n)/. Update the value at the minimal key.
580 updateMinWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a
581 updateMinWithKey f t
582 = case t of
583 Bin sx kx x Tip r -> case f kx x of
584 Nothing -> r
585 Just x' -> Bin sx kx x' Tip r
586 Bin sx kx x l r -> balance kx x (updateMinWithKey f l) r
587 Tip -> Tip
588
589 -- | /O(log n)/. Update the value at the maximal key.
590 updateMaxWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a
591 updateMaxWithKey f t
592 = case t of
593 Bin sx kx x l Tip -> case f kx x of
594 Nothing -> l
595 Just x' -> Bin sx kx x' l Tip
596 Bin sx kx x l r -> balance kx x l (updateMaxWithKey f r)
597 Tip -> Tip
598
599 -- | /O(log n)/. Retrieves the minimal (key,value) pair of the map, and the map stripped from that element
600 -- @fail@s (in the monad) when passed an empty map.
601 minViewWithKey :: Monad m => Map k a -> m ((k,a), Map k a)
602 minViewWithKey Tip = fail "Map.minView: empty map"
603 minViewWithKey x = return (deleteFindMin x)
604
605 -- | /O(log n)/. Retrieves the maximal (key,value) pair of the map, and the map stripped from that element
606 -- @fail@s (in the monad) when passed an empty map.
607 maxViewWithKey :: Monad m => Map k a -> m ((k,a), Map k a)
608 maxViewWithKey Tip = fail "Map.maxView: empty map"
609 maxViewWithKey x = return (deleteFindMax x)
610
611 -- | /O(log n)/. Retrieves the minimal key\'s value of the map, and the map stripped from that element
612 -- @fail@s (in the monad) when passed an empty map.
613 minView :: Monad m => Map k a -> m (a, Map k a)
614 minView Tip = fail "Map.minView: empty map"
615 minView x = return (first snd $ deleteFindMin x)
616
617 -- | /O(log n)/. Retrieves the maximal key\'s value of the map, and the map stripped from that element
618 -- @fail@s (in the monad) when passed an empty map.
619 maxView :: Monad m => Map k a -> m (a, Map k a)
620 maxView Tip = fail "Map.maxView: empty map"
621 maxView x = return (first snd $ deleteFindMax x)
622
623 -- Update the 1st component of a tuple (special case of Control.Arrow.first)
624 first :: (a -> b) -> (a,c) -> (b,c)
625 first f (x,y) = (f x, y)
626
627 {--------------------------------------------------------------------
628 Union.
629 --------------------------------------------------------------------}
630 -- | The union of a list of maps:
631 -- (@'unions' == 'Prelude.foldl' 'union' 'empty'@).
632 unions :: Ord k => [Map k a] -> Map k a
633 unions ts
634 = foldlStrict union empty ts
635
636 -- | The union of a list of maps, with a combining operation:
637 -- (@'unionsWith' f == 'Prelude.foldl' ('unionWith' f) 'empty'@).
638 unionsWith :: Ord k => (a->a->a) -> [Map k a] -> Map k a
639 unionsWith f ts
640 = foldlStrict (unionWith f) empty ts
641
642 -- | /O(n+m)/.
643 -- The expression (@'union' t1 t2@) takes the left-biased union of @t1@ and @t2@.
644 -- It prefers @t1@ when duplicate keys are encountered,
645 -- i.e. (@'union' == 'unionWith' 'const'@).
646 -- The implementation uses the efficient /hedge-union/ algorithm.
647 -- Hedge-union is more efficient on (bigset `union` smallset)
648 union :: Ord k => Map k a -> Map k a -> Map k a
649 union Tip t2 = t2
650 union t1 Tip = t1
651 union t1 t2 = hedgeUnionL (const LT) (const GT) t1 t2
652
653 -- left-biased hedge union
654 hedgeUnionL cmplo cmphi t1 Tip
655 = t1
656 hedgeUnionL cmplo cmphi Tip (Bin _ kx x l r)
657 = join kx x (filterGt cmplo l) (filterLt cmphi r)
658 hedgeUnionL cmplo cmphi (Bin _ kx x l r) t2
659 = join kx x (hedgeUnionL cmplo cmpkx l (trim cmplo cmpkx t2))
660 (hedgeUnionL cmpkx cmphi r (trim cmpkx cmphi t2))
661 where
662 cmpkx k = compare kx k
663
664 -- right-biased hedge union
665 hedgeUnionR cmplo cmphi t1 Tip
666 = t1
667 hedgeUnionR cmplo cmphi Tip (Bin _ kx x l r)
668 = join kx x (filterGt cmplo l) (filterLt cmphi r)
669 hedgeUnionR cmplo cmphi (Bin _ kx x l r) t2
670 = join kx newx (hedgeUnionR cmplo cmpkx l lt)
671 (hedgeUnionR cmpkx cmphi r gt)
672 where
673 cmpkx k = compare kx k
674 lt = trim cmplo cmpkx t2
675 (found,gt) = trimLookupLo kx cmphi t2
676 newx = case found of
677 Nothing -> x
678 Just (_,y) -> y
679
680 {--------------------------------------------------------------------
681 Union with a combining function
682 --------------------------------------------------------------------}
683 -- | /O(n+m)/. Union with a combining function. The implementation uses the efficient /hedge-union/ algorithm.
684 unionWith :: Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a
685 unionWith f m1 m2
686 = unionWithKey (\k x y -> f x y) m1 m2
687
688 -- | /O(n+m)/.
689 -- Union with a combining function. The implementation uses the efficient /hedge-union/ algorithm.
690 -- Hedge-union is more efficient on (bigset `union` smallset).
691 unionWithKey :: Ord k => (k -> a -> a -> a) -> Map k a -> Map k a -> Map k a
692 unionWithKey f Tip t2 = t2
693 unionWithKey f t1 Tip = t1
694 unionWithKey f t1 t2 = hedgeUnionWithKey f (const LT) (const GT) t1 t2
695
696 hedgeUnionWithKey f cmplo cmphi t1 Tip
697 = t1
698 hedgeUnionWithKey f cmplo cmphi Tip (Bin _ kx x l r)
699 = join kx x (filterGt cmplo l) (filterLt cmphi r)
700 hedgeUnionWithKey f cmplo cmphi (Bin _ kx x l r) t2
701 = join kx newx (hedgeUnionWithKey f cmplo cmpkx l lt)
702 (hedgeUnionWithKey f cmpkx cmphi r gt)
703 where
704 cmpkx k = compare kx k
705 lt = trim cmplo cmpkx t2
706 (found,gt) = trimLookupLo kx cmphi t2
707 newx = case found of
708 Nothing -> x
709 Just (_,y) -> f kx x y
710
711 {--------------------------------------------------------------------
712 Difference
713 --------------------------------------------------------------------}
714 -- | /O(n+m)/. Difference of two maps.
715 -- The implementation uses an efficient /hedge/ algorithm comparable with /hedge-union/.
716 difference :: Ord k => Map k a -> Map k b -> Map k a
717 difference Tip t2 = Tip
718 difference t1 Tip = t1
719 difference t1 t2 = hedgeDiff (const LT) (const GT) t1 t2
720
721 hedgeDiff cmplo cmphi Tip t
722 = Tip
723 hedgeDiff cmplo cmphi (Bin _ kx x l r) Tip
724 = join kx x (filterGt cmplo l) (filterLt cmphi r)
725 hedgeDiff cmplo cmphi t (Bin _ kx x l r)
726 = merge (hedgeDiff cmplo cmpkx (trim cmplo cmpkx t) l)
727 (hedgeDiff cmpkx cmphi (trim cmpkx cmphi t) r)
728 where
729 cmpkx k = compare kx k
730
731 -- | /O(n+m)/. Difference with a combining function.
732 -- The implementation uses an efficient /hedge/ algorithm comparable with /hedge-union/.
733 differenceWith :: Ord k => (a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a
734 differenceWith f m1 m2
735 = differenceWithKey (\k x y -> f x y) m1 m2
736
737 -- | /O(n+m)/. Difference with a combining function. When two equal keys are
738 -- encountered, the combining function is applied to the key and both values.
739 -- If it returns 'Nothing', the element is discarded (proper set difference). If
740 -- it returns (@'Just' y@), the element is updated with a new value @y@.
741 -- The implementation uses an efficient /hedge/ algorithm comparable with /hedge-union/.
742 differenceWithKey :: Ord k => (k -> a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a
743 differenceWithKey f Tip t2 = Tip
744 differenceWithKey f t1 Tip = t1
745 differenceWithKey f t1 t2 = hedgeDiffWithKey f (const LT) (const GT) t1 t2
746
747 hedgeDiffWithKey f cmplo cmphi Tip t
748 = Tip
749 hedgeDiffWithKey f cmplo cmphi (Bin _ kx x l r) Tip
750 = join kx x (filterGt cmplo l) (filterLt cmphi r)
751 hedgeDiffWithKey f cmplo cmphi t (Bin _ kx x l r)
752 = case found of
753 Nothing -> merge tl tr
754 Just (ky,y) ->
755 case f ky y x of
756 Nothing -> merge tl tr
757 Just z -> join ky z tl tr
758 where
759 cmpkx k = compare kx k
760 lt = trim cmplo cmpkx t
761 (found,gt) = trimLookupLo kx cmphi t
762 tl = hedgeDiffWithKey f cmplo cmpkx lt l
763 tr = hedgeDiffWithKey f cmpkx cmphi gt r
764
765
766
767 {--------------------------------------------------------------------
768 Intersection
769 --------------------------------------------------------------------}
770 -- | /O(n+m)/. Intersection of two maps. The values in the first
771 -- map are returned, i.e. (@'intersection' m1 m2 == 'intersectionWith' 'const' m1 m2@).
772 intersection :: Ord k => Map k a -> Map k b -> Map k a
773 intersection m1 m2
774 = intersectionWithKey (\k x y -> x) m1 m2
775
776 -- | /O(n+m)/. Intersection with a combining function.
777 intersectionWith :: Ord k => (a -> b -> c) -> Map k a -> Map k b -> Map k c
778 intersectionWith f m1 m2
779 = intersectionWithKey (\k x y -> f x y) m1 m2
780
781 -- | /O(n+m)/. Intersection with a combining function.
782 -- Intersection is more efficient on (bigset `intersection` smallset)
783 --intersectionWithKey :: Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c
784 --intersectionWithKey f Tip t = Tip
785 --intersectionWithKey f t Tip = Tip
786 --intersectionWithKey f t1 t2 = intersectWithKey f t1 t2
787 --
788 --intersectWithKey f Tip t = Tip
789 --intersectWithKey f t Tip = Tip
790 --intersectWithKey f t (Bin _ kx x l r)
791 -- = case found of
792 -- Nothing -> merge tl tr
793 -- Just y -> join kx (f kx y x) tl tr
794 -- where
795 -- (lt,found,gt) = splitLookup kx t
796 -- tl = intersectWithKey f lt l
797 -- tr = intersectWithKey f gt r
798
799
800 intersectionWithKey :: Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c
801 intersectionWithKey f Tip t = Tip
802 intersectionWithKey f t Tip = Tip
803 intersectionWithKey f t1@(Bin s1 k1 x1 l1 r1) t2@(Bin s2 k2 x2 l2 r2) =
804 if s1 >= s2 then
805 let (lt,found,gt) = splitLookupWithKey k2 t1
806 tl = intersectionWithKey f lt l2
807 tr = intersectionWithKey f gt r2
808 in case found of
809 Just (k,x) -> join k (f k x x2) tl tr
810 Nothing -> merge tl tr
811 else let (lt,found,gt) = splitLookup k1 t2
812 tl = intersectionWithKey f l1 lt
813 tr = intersectionWithKey f r1 gt
814 in case found of
815 Just x -> join k1 (f k1 x1 x) tl tr
816 Nothing -> merge tl tr
817
818
819
820 {--------------------------------------------------------------------
821 Submap
822 --------------------------------------------------------------------}
823 -- | /O(n+m)/.
824 -- This function is defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@).
825 isSubmapOf :: (Ord k,Eq a) => Map k a -> Map k a -> Bool
826 isSubmapOf m1 m2
827 = isSubmapOfBy (==) m1 m2
828
829 {- | /O(n+m)/.
830 The expression (@'isSubmapOfBy' f t1 t2@) returns 'True' if
831 all keys in @t1@ are in tree @t2@, and when @f@ returns 'True' when
832 applied to their respective values. For example, the following
833 expressions are all 'True':
834
835 > isSubmapOfBy (==) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
836 > isSubmapOfBy (<=) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
837 > isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1),('b',2)])
838
839 But the following are all 'False':
840
841 > isSubmapOfBy (==) (fromList [('a',2)]) (fromList [('a',1),('b',2)])
842 > isSubmapOfBy (<) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
843 > isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1)])
844 -}
845 isSubmapOfBy :: Ord k => (a->b->Bool) -> Map k a -> Map k b -> Bool
846 isSubmapOfBy f t1 t2
847 = (size t1 <= size t2) && (submap' f t1 t2)
848
849 submap' f Tip t = True
850 submap' f t Tip = False
851 submap' f (Bin _ kx x l r) t
852 = case found of
853 Nothing -> False
854 Just y -> f x y && submap' f l lt && submap' f r gt
855 where
856 (lt,found,gt) = splitLookup kx t
857
858 -- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
859 -- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@).
860 isProperSubmapOf :: (Ord k,Eq a) => Map k a -> Map k a -> Bool
861 isProperSubmapOf m1 m2
862 = isProperSubmapOfBy (==) m1 m2
863
864 {- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
865 The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when
866 @m1@ and @m2@ are not equal,
867 all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
868 applied to their respective values. For example, the following
869 expressions are all 'True':
870
871 > isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
872 > isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
873
874 But the following are all 'False':
875
876 > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
877 > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
878 > isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
879 -}
880 isProperSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool
881 isProperSubmapOfBy f t1 t2
882 = (size t1 < size t2) && (submap' f t1 t2)
883
884 {--------------------------------------------------------------------
885 Filter and partition
886 --------------------------------------------------------------------}
887 -- | /O(n)/. Filter all values that satisfy the predicate.
888 filter :: Ord k => (a -> Bool) -> Map k a -> Map k a
889 filter p m
890 = filterWithKey (\k x -> p x) m
891
892 -- | /O(n)/. Filter all keys\/values that satisfy the predicate.
893 filterWithKey :: Ord k => (k -> a -> Bool) -> Map k a -> Map k a
894 filterWithKey p Tip = Tip
895 filterWithKey p (Bin _ kx x l r)
896 | p kx x = join kx x (filterWithKey p l) (filterWithKey p r)
897 | otherwise = merge (filterWithKey p l) (filterWithKey p r)
898
899
900 -- | /O(n)/. partition the map according to a predicate. The first
901 -- map contains all elements that satisfy the predicate, the second all
902 -- elements that fail the predicate. See also 'split'.
903 partition :: Ord k => (a -> Bool) -> Map k a -> (Map k a,Map k a)
904 partition p m
905 = partitionWithKey (\k x -> p x) m
906
907 -- | /O(n)/. partition the map according to a predicate. The first
908 -- map contains all elements that satisfy the predicate, the second all
909 -- elements that fail the predicate. See also 'split'.
910 partitionWithKey :: Ord k => (k -> a -> Bool) -> Map k a -> (Map k a,Map k a)
911 partitionWithKey p Tip = (Tip,Tip)
912 partitionWithKey p (Bin _ kx x l r)
913 | p kx x = (join kx x l1 r1,merge l2 r2)
914 | otherwise = (merge l1 r1,join kx x l2 r2)
915 where
916 (l1,l2) = partitionWithKey p l
917 (r1,r2) = partitionWithKey p r
918
919 -- | /O(n)/. Map values and collect the 'Just' results.
920 mapMaybe :: Ord k => (a -> Maybe b) -> Map k a -> Map k b
921 mapMaybe f m
922 = mapMaybeWithKey (\k x -> f x) m
923
924 -- | /O(n)/. Map keys\/values and collect the 'Just' results.
925 mapMaybeWithKey :: Ord k => (k -> a -> Maybe b) -> Map k a -> Map k b
926 mapMaybeWithKey f Tip = Tip
927 mapMaybeWithKey f (Bin _ kx x l r) = case f kx x of
928 Just y -> join kx y (mapMaybeWithKey f l) (mapMaybeWithKey f r)
929 Nothing -> merge (mapMaybeWithKey f l) (mapMaybeWithKey f r)
930
931 -- | /O(n)/. Map values and separate the 'Left' and 'Right' results.
932 mapEither :: Ord k => (a -> Either b c) -> Map k a -> (Map k b, Map k c)
933 mapEither f m
934 = mapEitherWithKey (\k x -> f x) m
935
936 -- | /O(n)/. Map keys\/values and separate the 'Left' and 'Right' results.
937 mapEitherWithKey :: Ord k =>
938 (k -> a -> Either b c) -> Map k a -> (Map k b, Map k c)
939 mapEitherWithKey f Tip = (Tip, Tip)
940 mapEitherWithKey f (Bin _ kx x l r) = case f kx x of
941 Left y -> (join kx y l1 r1, merge l2 r2)
942 Right z -> (merge l1 r1, join kx z l2 r2)
943 where
944 (l1,l2) = mapEitherWithKey f l
945 (r1,r2) = mapEitherWithKey f r
946
947 {--------------------------------------------------------------------
948 Mapping
949 --------------------------------------------------------------------}
950 -- | /O(n)/. Map a function over all values in the map.
951 map :: (a -> b) -> Map k a -> Map k b
952 map f m
953 = mapWithKey (\k x -> f x) m
954
955 -- | /O(n)/. Map a function over all values in the map.
956 mapWithKey :: (k -> a -> b) -> Map k a -> Map k b
957 mapWithKey f Tip = Tip
958 mapWithKey f (Bin sx kx x l r)
959 = Bin sx kx (f kx x) (mapWithKey f l) (mapWithKey f r)
960
961 -- | /O(n)/. The function 'mapAccum' threads an accumulating
962 -- argument through the map in ascending order of keys.
963 mapAccum :: (a -> b -> (a,c)) -> a -> Map k b -> (a,Map k c)
964 mapAccum f a m
965 = mapAccumWithKey (\a k x -> f a x) a m
966
967 -- | /O(n)/. The function 'mapAccumWithKey' threads an accumulating
968 -- argument through the map in ascending order of keys.
969 mapAccumWithKey :: (a -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c)
970 mapAccumWithKey f a t
971 = mapAccumL f a t
972
973 -- | /O(n)/. The function 'mapAccumL' threads an accumulating
974 -- argument throught the map in ascending order of keys.
975 mapAccumL :: (a -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c)
976 mapAccumL f a t
977 = case t of
978 Tip -> (a,Tip)
979 Bin sx kx x l r
980 -> let (a1,l') = mapAccumL f a l
981 (a2,x') = f a1 kx x
982 (a3,r') = mapAccumL f a2 r
983 in (a3,Bin sx kx x' l' r')
984
985 -- | /O(n)/. The function 'mapAccumR' threads an accumulating
986 -- argument throught the map in descending order of keys.
987 mapAccumR :: (a -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c)
988 mapAccumR f a t
989 = case t of
990 Tip -> (a,Tip)
991 Bin sx kx x l r
992 -> let (a1,r') = mapAccumR f a r
993 (a2,x') = f a1 kx x
994 (a3,l') = mapAccumR f a2 l
995 in (a3,Bin sx kx x' l' r')
996
997 -- | /O(n*log n)/.
998 -- @'mapKeys' f s@ is the map obtained by applying @f@ to each key of @s@.
999 --
1000 -- The size of the result may be smaller if @f@ maps two or more distinct
1001 -- keys to the same new key. In this case the value at the smallest of
1002 -- these keys is retained.
1003
1004 mapKeys :: Ord k2 => (k1->k2) -> Map k1 a -> Map k2 a
1005 mapKeys = mapKeysWith (\x y->x)
1006
1007 -- | /O(n*log n)/.
1008 -- @'mapKeysWith' c f s@ is the map obtained by applying @f@ to each key of @s@.
1009 --
1010 -- The size of the result may be smaller if @f@ maps two or more distinct
1011 -- keys to the same new key. In this case the associated values will be
1012 -- combined using @c@.
1013
1014 mapKeysWith :: Ord k2 => (a -> a -> a) -> (k1->k2) -> Map k1 a -> Map k2 a
1015 mapKeysWith c f = fromListWith c . List.map fFirst . toList
1016 where fFirst (x,y) = (f x, y)
1017
1018
1019 -- | /O(n)/.
1020 -- @'mapKeysMonotonic' f s == 'mapKeys' f s@, but works only when @f@
1021 -- is strictly monotonic.
1022 -- /The precondition is not checked./
1023 -- Semi-formally, we have:
1024 --
1025 -- > and [x < y ==> f x < f y | x <- ls, y <- ls]
1026 -- > ==> mapKeysMonotonic f s == mapKeys f s
1027 -- > where ls = keys s
1028
1029 mapKeysMonotonic :: (k1->k2) -> Map k1 a -> Map k2 a
1030 mapKeysMonotonic f Tip = Tip
1031 mapKeysMonotonic f (Bin sz k x l r) =
1032 Bin sz (f k) x (mapKeysMonotonic f l) (mapKeysMonotonic f r)
1033
1034 {--------------------------------------------------------------------
1035 Folds
1036 --------------------------------------------------------------------}
1037
1038 -- | /O(n)/. Fold the values in the map, such that
1039 -- @'fold' f z == 'Prelude.foldr' f z . 'elems'@.
1040 -- For example,
1041 --
1042 -- > elems map = fold (:) [] map
1043 --
1044 fold :: (a -> b -> b) -> b -> Map k a -> b
1045 fold f z m
1046 = foldWithKey (\k x z -> f x z) z m
1047
1048 -- | /O(n)/. Fold the keys and values in the map, such that
1049 -- @'foldWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@.
1050 -- For example,
1051 --
1052 -- > keys map = foldWithKey (\k x ks -> k:ks) [] map
1053 --
1054 foldWithKey :: (k -> a -> b -> b) -> b -> Map k a -> b
1055 foldWithKey f z t
1056 = foldr f z t
1057
1058 -- | /O(n)/. In-order fold.
1059 foldi :: (k -> a -> b -> b -> b) -> b -> Map k a -> b
1060 foldi f z Tip = z
1061 foldi f z (Bin _ kx x l r) = f kx x (foldi f z l) (foldi f z r)
1062
1063 -- | /O(n)/. Post-order fold.
1064 foldr :: (k -> a -> b -> b) -> b -> Map k a -> b
1065 foldr f z Tip = z
1066 foldr f z (Bin _ kx x l r) = foldr f (f kx x (foldr f z r)) l
1067
1068 -- | /O(n)/. Pre-order fold.
1069 foldl :: (b -> k -> a -> b) -> b -> Map k a -> b
1070 foldl f z Tip = z
1071 foldl f z (Bin _ kx x l r) = foldl f (f (foldl f z l) kx x) r
1072
1073 {--------------------------------------------------------------------
1074 List variations
1075 --------------------------------------------------------------------}
1076 -- | /O(n)/.
1077 -- Return all elements of the map in the ascending order of their keys.
1078 elems :: Map k a -> [a]
1079 elems m
1080 = [x | (k,x) <- assocs m]
1081
1082 -- | /O(n)/. Return all keys of the map in ascending order.
1083 keys :: Map k a -> [k]
1084 keys m
1085 = [k | (k,x) <- assocs m]
1086
1087 -- | /O(n)/. The set of all keys of the map.
1088 keysSet :: Map k a -> Set.Set k
1089 keysSet m = Set.fromDistinctAscList (keys m)
1090
1091 -- | /O(n)/. Return all key\/value pairs in the map in ascending key order.
1092 assocs :: Map k a -> [(k,a)]
1093 assocs m
1094 = toList m
1095
1096 {--------------------------------------------------------------------
1097 Lists
1098 use [foldlStrict] to reduce demand on the control-stack
1099 --------------------------------------------------------------------}
1100 -- | /O(n*log n)/. Build a map from a list of key\/value pairs. See also 'fromAscList'.
1101 fromList :: Ord k => [(k,a)] -> Map k a
1102 fromList xs
1103 = foldlStrict ins empty xs
1104 where
1105 ins t (k,x) = insert k x t
1106
1107 -- | /O(n*log n)/. Build a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'.
1108 fromListWith :: Ord k => (a -> a -> a) -> [(k,a)] -> Map k a
1109 fromListWith f xs
1110 = fromListWithKey (\k x y -> f x y) xs
1111
1112 -- | /O(n*log n)/. Build a map from a list of key\/value pairs with a combining function. See also 'fromAscListWithKey'.
1113 fromListWithKey :: Ord k => (k -> a -> a -> a) -> [(k,a)] -> Map k a
1114 fromListWithKey f xs
1115 = foldlStrict ins empty xs
1116 where
1117 ins t (k,x) = insertWithKey f k x t
1118
1119 -- | /O(n)/. Convert to a list of key\/value pairs.
1120 toList :: Map k a -> [(k,a)]
1121 toList t = toAscList t
1122
1123 -- | /O(n)/. Convert to an ascending list.
1124 toAscList :: Map k a -> [(k,a)]
1125 toAscList t = foldr (\k x xs -> (k,x):xs) [] t
1126
1127 -- | /O(n)/.
1128 toDescList :: Map k a -> [(k,a)]
1129 toDescList t = foldl (\xs k x -> (k,x):xs) [] t
1130
1131
1132 {--------------------------------------------------------------------
1133 Building trees from ascending/descending lists can be done in linear time.
1134
1135 Note that if [xs] is ascending that:
1136 fromAscList xs == fromList xs
1137 fromAscListWith f xs == fromListWith f xs
1138 --------------------------------------------------------------------}
1139 -- | /O(n)/. Build a map from an ascending list in linear time.
1140 -- /The precondition (input list is ascending) is not checked./
1141 fromAscList :: Eq k => [(k,a)] -> Map k a
1142 fromAscList xs
1143 = fromAscListWithKey (\k x y -> x) xs
1144
1145 -- | /O(n)/. Build a map from an ascending list in linear time with a combining function for equal keys.
1146 -- /The precondition (input list is ascending) is not checked./
1147 fromAscListWith :: Eq k => (a -> a -> a) -> [(k,a)] -> Map k a
1148 fromAscListWith f xs
1149 = fromAscListWithKey (\k x y -> f x y) xs
1150
1151 -- | /O(n)/. Build a map from an ascending list in linear time with a
1152 -- combining function for equal keys.
1153 -- /The precondition (input list is ascending) is not checked./
1154 fromAscListWithKey :: Eq k => (k -> a -> a -> a) -> [(k,a)] -> Map k a
1155 fromAscListWithKey f xs
1156 = fromDistinctAscList (combineEq f xs)
1157 where
1158 -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs]
1159 combineEq f xs
1160 = case xs of
1161 [] -> []
1162 [x] -> [x]
1163 (x:xx) -> combineEq' x xx
1164
1165 combineEq' z [] = [z]
1166 combineEq' z@(kz,zz) (x@(kx,xx):xs)
1167 | kx==kz = let yy = f kx xx zz in combineEq' (kx,yy) xs
1168 | otherwise = z:combineEq' x xs
1169
1170
1171 -- | /O(n)/. Build a map from an ascending list of distinct elements in linear time.
1172 -- /The precondition is not checked./
1173 fromDistinctAscList :: [(k,a)] -> Map k a
1174 fromDistinctAscList xs
1175 = build const (length xs) xs
1176 where
1177 -- 1) use continutations so that we use heap space instead of stack space.
1178 -- 2) special case for n==5 to build bushier trees.
1179 build c 0 xs = c Tip xs
1180 build c 5 xs = case xs of
1181 ((k1,x1):(k2,x2):(k3,x3):(k4,x4):(k5,x5):xx)
1182 -> c (bin k4 x4 (bin k2 x2 (singleton k1 x1) (singleton k3 x3)) (singleton k5 x5)) xx
1183 build c n xs = seq nr $ build (buildR nr c) nl xs
1184 where
1185 nl = n `div` 2
1186 nr = n - nl - 1
1187
1188 buildR n c l ((k,x):ys) = build (buildB l k x c) n ys
1189 buildB l k x c r zs = c (bin k x l r) zs
1190
1191
1192
1193 {--------------------------------------------------------------------
1194 Utility functions that return sub-ranges of the original
1195 tree. Some functions take a comparison function as argument to
1196 allow comparisons against infinite values. A function [cmplo k]
1197 should be read as [compare lo k].
1198
1199 [trim cmplo cmphi t] A tree that is either empty or where [cmplo k == LT]
1200 and [cmphi k == GT] for the key [k] of the root.
1201 [filterGt cmp t] A tree where for all keys [k]. [cmp k == LT]
1202 [filterLt cmp t] A tree where for all keys [k]. [cmp k == GT]
1203
1204 [split k t] Returns two trees [l] and [r] where all keys
1205 in [l] are <[k] and all keys in [r] are >[k].
1206 [splitLookup k t] Just like [split] but also returns whether [k]
1207 was found in the tree.
1208 --------------------------------------------------------------------}
1209
1210 {--------------------------------------------------------------------
1211 [trim lo hi t] trims away all subtrees that surely contain no
1212 values between the range [lo] to [hi]. The returned tree is either
1213 empty or the key of the root is between @lo@ and @hi@.
1214 --------------------------------------------------------------------}
1215 trim :: (k -> Ordering) -> (k -> Ordering) -> Map k a -> Map k a
1216 trim cmplo cmphi Tip = Tip
1217 trim cmplo cmphi t@(Bin sx kx x l r)
1218 = case cmplo kx of
1219 LT -> case cmphi kx of
1220 GT -> t
1221 le -> trim cmplo cmphi l
1222 ge -> trim cmplo cmphi r
1223
1224 trimLookupLo :: Ord k => k -> (k -> Ordering) -> Map k a -> (Maybe (k,a), Map k a)
1225 trimLookupLo lo cmphi Tip = (Nothing,Tip)
1226 trimLookupLo lo cmphi t@(Bin sx kx x l r)
1227 = case compare lo kx of
1228 LT -> case cmphi kx of
1229 GT -> (lookupAssoc lo t, t)
1230 le -> trimLookupLo lo cmphi l
1231 GT -> trimLookupLo lo cmphi r
1232 EQ -> (Just (kx,x),trim (compare lo) cmphi r)
1233
1234
1235 {--------------------------------------------------------------------
1236 [filterGt k t] filter all keys >[k] from tree [t]
1237 [filterLt k t] filter all keys <[k] from tree [t]
1238 --------------------------------------------------------------------}
1239 filterGt :: Ord k => (k -> Ordering) -> Map k a -> Map k a
1240 filterGt cmp Tip = Tip
1241 filterGt cmp (Bin sx kx x l r)
1242 = case cmp kx of
1243 LT -> join kx x (filterGt cmp l) r
1244 GT -> filterGt cmp r
1245 EQ -> r
1246
1247 filterLt :: Ord k => (k -> Ordering) -> Map k a -> Map k a
1248 filterLt cmp Tip = Tip
1249 filterLt cmp (Bin sx kx x l r)
1250 = case cmp kx of
1251 LT -> filterLt cmp l
1252 GT -> join kx x l (filterLt cmp r)
1253 EQ -> l
1254
1255 {--------------------------------------------------------------------
1256 Split
1257 --------------------------------------------------------------------}
1258 -- | /O(log n)/. The expression (@'split' k map@) is a pair @(map1,map2)@ where
1259 -- the keys in @map1@ are smaller than @k@ and the keys in @map2@ larger than @k@. Any key equal to @k@ is found in neither @map1@ nor @map2@.
1260 split :: Ord k => k -> Map k a -> (Map k a,Map k a)
1261 split k Tip = (Tip,Tip)
1262 split k (Bin sx kx x l r)
1263 = case compare k kx of
1264 LT -> let (lt,gt) = split k l in (lt,join kx x gt r)
1265 GT -> let (lt,gt) = split k r in (join kx x l lt,gt)
1266 EQ -> (l,r)
1267
1268 -- | /O(log n)/. The expression (@'splitLookup' k map@) splits a map just
1269 -- like 'split' but also returns @'lookup' k map@.
1270 splitLookup :: Ord k => k -> Map k a -> (Map k a,Maybe a,Map k a)
1271 splitLookup k Tip = (Tip,Nothing,Tip)
1272 splitLookup k (Bin sx kx x l r)
1273 = case compare k kx of
1274 LT -> let (lt,z,gt) = splitLookup k l in (lt,z,join kx x gt r)
1275 GT -> let (lt,z,gt) = splitLookup k r in (join kx x l lt,z,gt)
1276 EQ -> (l,Just x,r)
1277
1278 -- | /O(log n)/.
1279 splitLookupWithKey :: Ord k => k -> Map k a -> (Map k a,Maybe (k,a),Map k a)
1280 splitLookupWithKey k Tip = (Tip,Nothing,Tip)
1281 splitLookupWithKey k (Bin sx kx x l r)
1282 = case compare k kx of
1283 LT -> let (lt,z,gt) = splitLookupWithKey k l in (lt,z,join kx x gt r)
1284 GT -> let (lt,z,gt) = splitLookupWithKey k r in (join kx x l lt,z,gt)
1285 EQ -> (l,Just (kx, x),r)
1286
1287 -- | /O(log n)/. Performs a 'split' but also returns whether the pivot
1288 -- element was found in the original set.
1289 splitMember :: Ord k => k -> Map k a -> (Map k a,Bool,Map k a)
1290 splitMember x t = let (l,m,r) = splitLookup x t in
1291 (l,maybe False (const True) m,r)
1292
1293
1294 {--------------------------------------------------------------------
1295 Utility functions that maintain the balance properties of the tree.
1296 All constructors assume that all values in [l] < [k] and all values
1297 in [r] > [k], and that [l] and [r] are valid trees.
1298
1299 In order of sophistication:
1300 [Bin sz k x l r] The type constructor.
1301 [bin k x l r] Maintains the correct size, assumes that both [l]
1302 and [r] are balanced with respect to each other.
1303 [balance k x l r] Restores the balance and size.
1304 Assumes that the original tree was balanced and
1305 that [l] or [r] has changed by at most one element.
1306 [join k x l r] Restores balance and size.
1307
1308 Furthermore, we can construct a new tree from two trees. Both operations
1309 assume that all values in [l] < all values in [r] and that [l] and [r]
1310 are valid:
1311 [glue l r] Glues [l] and [r] together. Assumes that [l] and
1312 [r] are already balanced with respect to each other.
1313 [merge l r] Merges two trees and restores balance.
1314
1315 Note: in contrast to Adam's paper, we use (<=) comparisons instead
1316 of (<) comparisons in [join], [merge] and [balance].
1317 Quickcheck (on [difference]) showed that this was necessary in order
1318 to maintain the invariants. It is quite unsatisfactory that I haven't
1319 been able to find out why this is actually the case! Fortunately, it
1320 doesn't hurt to be a bit more conservative.
1321 --------------------------------------------------------------------}
1322
1323 {--------------------------------------------------------------------
1324 Join
1325 --------------------------------------------------------------------}
1326 join :: Ord k => k -> a -> Map k a -> Map k a -> Map k a
1327 join kx x Tip r = insertMin kx x r
1328 join kx x l Tip = insertMax kx x l
1329 join kx x l@(Bin sizeL ky y ly ry) r@(Bin sizeR kz z lz rz)
1330 | delta*sizeL <= sizeR = balance kz z (join kx x l lz) rz
1331 | delta*sizeR <= sizeL = balance ky y ly (join kx x ry r)
1332 | otherwise = bin kx x l r
1333
1334
1335 -- insertMin and insertMax don't perform potentially expensive comparisons.
1336 insertMax,insertMin :: k -> a -> Map k a -> Map k a
1337 insertMax kx x t
1338 = case t of
1339 Tip -> singleton kx x
1340 Bin sz ky y l r
1341 -> balance ky y l (insertMax kx x r)
1342
1343 insertMin kx x t
1344 = case t of
1345 Tip -> singleton kx x
1346 Bin sz ky y l r
1347 -> balance ky y (insertMin kx x l) r
1348
1349 {--------------------------------------------------------------------
1350 [merge l r]: merges two trees.
1351 --------------------------------------------------------------------}
1352 merge :: Map k a -> Map k a -> Map k a
1353 merge Tip r = r
1354 merge l Tip = l
1355 merge l@(Bin sizeL kx x lx rx) r@(Bin sizeR ky y ly ry)
1356 | delta*sizeL <= sizeR = balance ky y (merge l ly) ry
1357 | delta*sizeR <= sizeL = balance kx x lx (merge rx r)
1358 | otherwise = glue l r
1359
1360 {--------------------------------------------------------------------
1361 [glue l r]: glues two trees together.
1362 Assumes that [l] and [r] are already balanced with respect to each other.
1363 --------------------------------------------------------------------}
1364 glue :: Map k a -> Map k a -> Map k a
1365 glue Tip r = r
1366 glue l Tip = l
1367 glue l r
1368 | size l > size r = let ((km,m),l') = deleteFindMax l in balance km m l' r
1369 | otherwise = let ((km,m),r') = deleteFindMin r in balance km m l r'
1370
1371
1372 -- | /O(log n)/. Delete and find the minimal element.
1373 deleteFindMin :: Map k a -> ((k,a),Map k a)
1374 deleteFindMin t
1375 = case t of
1376 Bin _ k x Tip r -> ((k,x),r)
1377 Bin _ k x l r -> let (km,l') = deleteFindMin l in (km,balance k x l' r)
1378 Tip -> (error "Map.deleteFindMin: can not return the minimal element of an empty map", Tip)
1379
1380 -- | /O(log n)/. Delete and find the maximal element.
1381 deleteFindMax :: Map k a -> ((k,a),Map k a)
1382 deleteFindMax t
1383 = case t of
1384 Bin _ k x l Tip -> ((k,x),l)
1385 Bin _ k x l r -> let (km,r') = deleteFindMax r in (km,balance k x l r')
1386 Tip -> (error "Map.deleteFindMax: can not return the maximal element of an empty map", Tip)
1387
1388
1389 {--------------------------------------------------------------------
1390 [balance l x r] balances two trees with value x.
1391 The sizes of the trees should balance after decreasing the
1392 size of one of them. (a rotation).
1393
1394 [delta] is the maximal relative difference between the sizes of
1395 two trees, it corresponds with the [w] in Adams' paper.
1396 [ratio] is the ratio between an outer and inner sibling of the
1397 heavier subtree in an unbalanced setting. It determines
1398 whether a double or single rotation should be performed
1399 to restore balance. It is correspondes with the inverse
1400 of $\alpha$ in Adam's article.
1401
1402 Note that:
1403 - [delta] should be larger than 4.646 with a [ratio] of 2.
1404 - [delta] should be larger than 3.745 with a [ratio] of 1.534.
1405
1406 - A lower [delta] leads to a more 'perfectly' balanced tree.
1407 - A higher [delta] performs less rebalancing.
1408
1409 - Balancing is automatic for random data and a balancing
1410 scheme is only necessary to avoid pathological worst cases.
1411 Almost any choice will do, and in practice, a rather large
1412 [delta] may perform better than smaller one.
1413
1414 Note: in contrast to Adam's paper, we use a ratio of (at least) [2]
1415 to decide whether a single or double rotation is needed. Allthough
1416 he actually proves that this ratio is needed to maintain the
1417 invariants, his implementation uses an invalid ratio of [1].
1418 --------------------------------------------------------------------}
1419 delta,ratio :: Int
1420 delta = 5
1421 ratio = 2
1422
1423 balance :: k -> a -> Map k a -> Map k a -> Map k a
1424 balance k x l r
1425 | sizeL + sizeR <= 1 = Bin sizeX k x l r
1426 | sizeR >= delta*sizeL = rotateL k x l r
1427 | sizeL >= delta*sizeR = rotateR k x l r
1428 | otherwise = Bin sizeX k x l r
1429 where
1430 sizeL = size l
1431 sizeR = size r
1432 sizeX = sizeL + sizeR + 1
1433
1434 -- rotate
1435 rotateL k x l r@(Bin _ _ _ ly ry)
1436 | size ly < ratio*size ry = singleL k x l r
1437 | otherwise = doubleL k x l r
1438
1439 rotateR k x l@(Bin _ _ _ ly ry) r
1440 | size ry < ratio*size ly = singleR k x l r
1441 | otherwise = doubleR k x l r
1442
1443 -- basic rotations
1444 singleL k1 x1 t1 (Bin _ k2 x2 t2 t3) = bin k2 x2 (bin k1 x1 t1 t2) t3
1445 singleR k1 x1 (Bin _ k2 x2 t1 t2) t3 = bin k2 x2 t1 (bin k1 x1 t2 t3)
1446
1447 doubleL k1 x1 t1 (Bin _ k2 x2 (Bin _ k3 x3 t2 t3) t4) = bin k3 x3 (bin k1 x1 t1 t2) (bin k2 x2 t3 t4)
1448 doubleR k1 x1 (Bin _ k2 x2 t1 (Bin _ k3 x3 t2 t3)) t4 = bin k3 x3 (bin k2 x2 t1 t2) (bin k1 x1 t3 t4)
1449
1450
1451 {--------------------------------------------------------------------
1452 The bin constructor maintains the size of the tree
1453 --------------------------------------------------------------------}
1454 bin :: k -> a -> Map k a -> Map k a -> Map k a
1455 bin k x l r
1456 = Bin (size l + size r + 1) k x l r
1457
1458
1459 {--------------------------------------------------------------------
1460 Eq converts the tree to a list. In a lazy setting, this
1461 actually seems one of the faster methods to compare two trees
1462 and it is certainly the simplest :-)
1463 --------------------------------------------------------------------}
1464 instance (Eq k,Eq a) => Eq (Map k a) where
1465 t1 == t2 = (size t1 == size t2) && (toAscList t1 == toAscList t2)
1466
1467 {--------------------------------------------------------------------
1468 Ord
1469 --------------------------------------------------------------------}
1470
1471 instance (Ord k, Ord v) => Ord (Map k v) where
1472 compare m1 m2 = compare (toAscList m1) (toAscList m2)
1473
1474 {--------------------------------------------------------------------
1475 Functor
1476 --------------------------------------------------------------------}
1477 instance Functor (Map k) where
1478 fmap f m = map f m
1479
1480 instance Traversable (Map k) where
1481 traverse f Tip = pure Tip
1482 traverse f (Bin s k v l r)
1483 = flip (Bin s k) <$> traverse f l <*> f v <*> traverse f r
1484
1485 instance Foldable (Map k) where
1486 foldMap _f Tip = mempty
1487 foldMap f (Bin _s _k v l r)
1488 = foldMap f l `mappend` f v `mappend` foldMap f r
1489
1490 {--------------------------------------------------------------------
1491 Read
1492 --------------------------------------------------------------------}
1493 instance (Ord k, Read k, Read e) => Read (Map k e) where
1494 #ifdef __GLASGOW_HASKELL__
1495 readPrec = parens $ prec 10 $ do
1496 Ident "fromList" <- lexP
1497 xs <- readPrec
1498 return (fromList xs)
1499
1500 readListPrec = readListPrecDefault
1501 #else
1502 readsPrec p = readParen (p > 10) $ \ r -> do
1503 ("fromList",s) <- lex r
1504 (xs,t) <- reads s
1505 return (fromList xs,t)
1506 #endif
1507
1508 -- parses a pair of things with the syntax a:=b
1509 readPair :: (Read a, Read b) => ReadS (a,b)
1510 readPair s = do (a, ct1) <- reads s
1511 (":=", ct2) <- lex ct1
1512 (b, ct3) <- reads ct2
1513 return ((a,b), ct3)
1514
1515 {--------------------------------------------------------------------
1516 Show
1517 --------------------------------------------------------------------}
1518 instance (Show k, Show a) => Show (Map k a) where
1519 showsPrec d m = showParen (d > 10) $
1520 showString "fromList " . shows (toList m)
1521
1522 showMap :: (Show k,Show a) => [(k,a)] -> ShowS
1523 showMap []
1524 = showString "{}"
1525 showMap (x:xs)
1526 = showChar '{' . showElem x . showTail xs
1527 where
1528 showTail [] = showChar '}'
1529 showTail (x:xs) = showString ", " . showElem x . showTail xs
1530
1531 showElem (k,x) = shows k . showString " := " . shows x
1532
1533
1534 -- | /O(n)/. Show the tree that implements the map. The tree is shown
1535 -- in a compressed, hanging format.
1536 showTree :: (Show k,Show a) => Map k a -> String
1537 showTree m
1538 = showTreeWith showElem True False m
1539 where
1540 showElem k x = show k ++ ":=" ++ show x
1541
1542
1543 {- | /O(n)/. The expression (@'showTreeWith' showelem hang wide map@) shows
1544 the tree that implements the map. Elements are shown using the @showElem@ function. If @hang@ is
1545 'True', a /hanging/ tree is shown otherwise a rotated tree is shown. If
1546 @wide@ is 'True', an extra wide version is shown.
1547
1548 > Map> let t = fromDistinctAscList [(x,()) | x <- [1..5]]
1549 > Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True False t
1550 > (4,())
1551 > +--(2,())
1552 > | +--(1,())
1553 > | +--(3,())
1554 > +--(5,())
1555 >
1556 > Map> putStrLn $ showTreeWith (\k x -> show (k,x)) True True t
1557 > (4,())
1558 > |
1559 > +--(2,())
1560 > | |
1561 > | +--(1,())
1562 > | |
1563 > | +--(3,())
1564 > |
1565 > +--(5,())
1566 >
1567 > Map> putStrLn $ showTreeWith (\k x -> show (k,x)) False True t
1568 > +--(5,())
1569 > |
1570 > (4,())
1571 > |
1572 > | +--(3,())
1573 > | |
1574 > +--(2,())
1575 > |
1576 > +--(1,())
1577
1578 -}
1579 showTreeWith :: (k -> a -> String) -> Bool -> Bool -> Map k a -> String
1580 showTreeWith showelem hang wide t
1581 | hang = (showsTreeHang showelem wide [] t) ""
1582 | otherwise = (showsTree showelem wide [] [] t) ""
1583
1584 showsTree :: (k -> a -> String) -> Bool -> [String] -> [String] -> Map k a -> ShowS
1585 showsTree showelem wide lbars rbars t
1586 = case t of
1587 Tip -> showsBars lbars . showString "|\n"
1588 Bin sz kx x Tip Tip
1589 -> showsBars lbars . showString (showelem kx x) . showString "\n"
1590 Bin sz kx x l r
1591 -> showsTree showelem wide (withBar rbars) (withEmpty rbars) r .
1592 showWide wide rbars .
1593 showsBars lbars . showString (showelem kx x) . showString "\n" .
1594 showWide wide lbars .
1595 showsTree showelem wide (withEmpty lbars) (withBar lbars) l
1596
1597 showsTreeHang :: (k -> a -> String) -> Bool -> [String] -> Map k a -> ShowS
1598 showsTreeHang showelem wide bars t
1599 = case t of
1600 Tip -> showsBars bars . showString "|\n"
1601 Bin sz kx x Tip Tip
1602 -> showsBars bars . showString (showelem kx x) . showString "\n"
1603 Bin sz kx x l r
1604 -> showsBars bars . showString (showelem kx x) . showString "\n" .
1605 showWide wide bars .
1606 showsTreeHang showelem wide (withBar bars) l .
1607 showWide wide bars .
1608 showsTreeHang showelem wide (withEmpty bars) r
1609
1610
1611 showWide wide bars
1612 | wide = showString (concat (reverse bars)) . showString "|\n"
1613 | otherwise = id
1614
1615 showsBars :: [String] -> ShowS
1616 showsBars bars
1617 = case bars of
1618 [] -> id
1619 _ -> showString (concat (reverse (tail bars))) . showString node
1620
1621 node = "+--"
1622 withBar bars = "| ":bars
1623 withEmpty bars = " ":bars
1624
1625 {--------------------------------------------------------------------
1626 Typeable
1627 --------------------------------------------------------------------}
1628
1629 #include "Typeable.h"
1630 INSTANCE_TYPEABLE2(Map,mapTc,"Map")
1631
1632 {--------------------------------------------------------------------
1633 Assertions
1634 --------------------------------------------------------------------}
1635 -- | /O(n)/. Test if the internal map structure is valid.
1636 valid :: Ord k => Map k a -> Bool
1637 valid t
1638 = balanced t && ordered t && validsize t
1639
1640 ordered t
1641 = bounded (const True) (const True) t
1642 where
1643 bounded lo hi t
1644 = case t of
1645 Tip -> True
1646 Bin sz kx x l r -> (lo kx) && (hi kx) && bounded lo (<kx) l && bounded (>kx) hi r
1647
1648 -- | Exported only for "Debug.QuickCheck"
1649 balanced :: Map k a -> Bool
1650 balanced t
1651 = case t of
1652 Tip -> True
1653 Bin sz kx x l r -> (size l + size r <= 1 || (size l <= delta*size r && size r <= delta*size l)) &&
1654 balanced l && balanced r
1655
1656
1657 validsize t
1658 = (realsize t == Just (size t))
1659 where
1660 realsize t
1661 = case t of
1662 Tip -> Just 0
1663 Bin sz kx x l r -> case (realsize l,realsize r) of
1664 (Just n,Just m) | n+m+1 == sz -> Just sz
1665 other -> Nothing
1666
1667 {--------------------------------------------------------------------
1668 Utilities
1669 --------------------------------------------------------------------}
1670 foldlStrict f z xs
1671 = case xs of
1672 [] -> z
1673 (x:xx) -> let z' = f z x in seq z' (foldlStrict f z' xx)
1674
1675
1676 {-
1677 {--------------------------------------------------------------------
1678 Testing
1679 --------------------------------------------------------------------}
1680 testTree xs = fromList [(x,"*") | x <- xs]
1681 test1 = testTree [1..20]
1682 test2 = testTree [30,29..10]
1683 test3 = testTree [1,4,6,89,2323,53,43,234,5,79,12,9,24,9,8,423,8,42,4,8,9,3]
1684
1685 {--------------------------------------------------------------------
1686 QuickCheck
1687 --------------------------------------------------------------------}
1688 qcheck prop
1689 = check config prop
1690 where
1691 config = Config
1692 { configMaxTest = 500
1693 , configMaxFail = 5000
1694 , configSize = \n -> (div n 2 + 3)
1695 , configEvery = \n args -> let s = show n in s ++ [ '\b' | _ <- s ]
1696 }
1697
1698
1699 {--------------------------------------------------------------------
1700 Arbitrary, reasonably balanced trees
1701 --------------------------------------------------------------------}
1702 instance (Enum k,Arbitrary a) => Arbitrary (Map k a) where
1703 arbitrary = sized (arbtree 0 maxkey)
1704 where maxkey = 10000
1705
1706 arbtree :: (Enum k,Arbitrary a) => Int -> Int -> Int -> Gen (Map k a)
1707 arbtree lo hi n
1708 | n <= 0 = return Tip
1709 | lo >= hi = return Tip
1710 | otherwise = do{ x <- arbitrary
1711 ; i <- choose (lo,hi)
1712 ; m <- choose (1,30)
1713 ; let (ml,mr) | m==(1::Int)= (1,2)
1714 | m==2 = (2,1)
1715 | m==3 = (1,1)
1716 | otherwise = (2,2)
1717 ; l <- arbtree lo (i-1) (n `div` ml)
1718 ; r <- arbtree (i+1) hi (n `div` mr)
1719 ; return (bin (toEnum i) x l r)
1720 }
1721
1722
1723 {--------------------------------------------------------------------
1724 Valid tree's
1725 --------------------------------------------------------------------}
1726 forValid :: (Show k,Enum k,Show a,Arbitrary a,Testable b) => (Map k a -> b) -> Property
1727 forValid f
1728 = forAll arbitrary $ \t ->
1729 -- classify (balanced t) "balanced" $
1730 classify (size t == 0) "empty" $
1731 classify (size t > 0 && size t <= 10) "small" $
1732 classify (size t > 10 && size t <= 64) "medium" $
1733 classify (size t > 64) "large" $
1734 balanced t ==> f t
1735
1736 forValidIntTree :: Testable a => (Map Int Int -> a) -> Property
1737 forValidIntTree f
1738 = forValid f
1739
1740 forValidUnitTree :: Testable a => (Map Int () -> a) -> Property
1741 forValidUnitTree f
1742 = forValid f
1743
1744
1745 prop_Valid
1746 = forValidUnitTree $ \t -> valid t
1747
1748 {--------------------------------------------------------------------
1749 Single, Insert, Delete
1750 --------------------------------------------------------------------}
1751 prop_Single :: Int -> Int -> Bool
1752 prop_Single k x
1753 = (insert k x empty == singleton k x)
1754
1755 prop_InsertValid :: Int -> Property
1756 prop_InsertValid k
1757 = forValidUnitTree $ \t -> valid (insert k () t)
1758
1759 prop_InsertDelete :: Int -> Map Int () -> Property
1760 prop_InsertDelete k t
1761 = (lookup k t == Nothing) ==> delete k (insert k () t) == t
1762
1763 prop_DeleteValid :: Int -> Property
1764 prop_DeleteValid k
1765 = forValidUnitTree $ \t ->
1766 valid (delete k (insert k () t))
1767
1768 {--------------------------------------------------------------------
1769 Balance
1770 --------------------------------------------------------------------}
1771 prop_Join :: Int -> Property
1772 prop_Join k
1773 = forValidUnitTree $ \t ->
1774 let (l,r) = split k t
1775 in valid (join k () l r)
1776
1777 prop_Merge :: Int -> Property
1778 prop_Merge k
1779 = forValidUnitTree $ \t ->
1780 let (l,r) = split k t
1781 in valid (merge l r)
1782
1783
1784 {--------------------------------------------------------------------
1785 Union
1786 --------------------------------------------------------------------}
1787 prop_UnionValid :: Property
1788 prop_UnionValid
1789 = forValidUnitTree $ \t1 ->
1790 forValidUnitTree $ \t2 ->
1791 valid (union t1 t2)
1792
1793 prop_UnionInsert :: Int -> Int -> Map Int Int -> Bool
1794 prop_UnionInsert k x t
1795 = union (singleton k x) t == insert k x t
1796
1797 prop_UnionAssoc :: Map Int Int -> Map Int Int -> Map Int Int -> Bool
1798 prop_UnionAssoc t1 t2 t3
1799 = union t1 (union t2 t3) == union (union t1 t2) t3
1800
1801 prop_UnionComm :: Map Int Int -> Map Int Int -> Bool
1802 prop_UnionComm t1 t2
1803 = (union t1 t2 == unionWith (\x y -> y) t2 t1)
1804
1805 prop_UnionWithValid
1806 = forValidIntTree $ \t1 ->
1807 forValidIntTree $ \t2 ->
1808 valid (unionWithKey (\k x y -> x+y) t1 t2)
1809
1810 prop_UnionWith :: [(Int,Int)] -> [(Int,Int)] -> Bool
1811 prop_UnionWith xs ys
1812 = sum (elems (unionWith (+) (fromListWith (+) xs) (fromListWith (+) ys)))
1813 == (sum (Prelude.map snd xs) + sum (Prelude.map snd ys))
1814
1815 prop_DiffValid
1816 = forValidUnitTree $ \t1 ->
1817 forValidUnitTree $ \t2 ->
1818 valid (difference t1 t2)
1819
1820 prop_Diff :: [(Int,Int)] -> [(Int,Int)] -> Bool
1821 prop_Diff xs ys
1822 = List.sort (keys (difference (fromListWith (+) xs) (fromListWith (+) ys)))
1823 == List.sort ((List.\\) (nub (Prelude.map fst xs)) (nub (Prelude.map fst ys)))
1824
1825 prop_IntValid
1826 = forValidUnitTree $ \t1 ->
1827 forValidUnitTree $ \t2 ->
1828 valid (intersection t1 t2)
1829
1830 prop_Int :: [(Int,Int)] -> [(Int,Int)] -> Bool
1831 prop_Int xs ys
1832 = List.sort (keys (intersection (fromListWith (+) xs) (fromListWith (+) ys)))
1833 == List.sort (nub ((List.intersect) (Prelude.map fst xs) (Prelude.map fst ys)))
1834
1835 {--------------------------------------------------------------------
1836 Lists
1837 --------------------------------------------------------------------}
1838 prop_Ordered
1839 = forAll (choose (5,100)) $ \n ->
1840 let xs = [(x,()) | x <- [0..n::Int]]
1841 in fromAscList xs == fromList xs
1842
1843 prop_List :: [Int] -> Bool
1844 prop_List xs
1845 = (sort (nub xs) == [x | (x,()) <- toList (fromList [(x,()) | x <- xs])])
1846 -}