137.93/108.33 MAYBE 140.44/109.08 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 140.44/109.08 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 140.44/109.08 140.44/109.08 140.44/109.08 H-Termination with start terms of the given HASKELL could not be shown: 140.44/109.08 140.44/109.08 (0) HASKELL 140.44/109.08 (1) LR [EQUIVALENT, 0 ms] 140.44/109.08 (2) HASKELL 140.44/109.08 (3) CR [EQUIVALENT, 0 ms] 140.44/109.08 (4) HASKELL 140.44/109.08 (5) IFR [EQUIVALENT, 0 ms] 140.44/109.08 (6) HASKELL 140.44/109.08 (7) BR [EQUIVALENT, 0 ms] 140.44/109.08 (8) HASKELL 140.44/109.08 (9) COR [EQUIVALENT, 0 ms] 140.44/109.08 (10) HASKELL 140.44/109.08 (11) LetRed [EQUIVALENT, 0 ms] 140.44/109.08 (12) HASKELL 140.44/109.08 (13) NumRed [SOUND, 27 ms] 140.44/109.08 (14) HASKELL 140.44/109.08 140.44/109.08 140.44/109.08 ---------------------------------------- 140.44/109.08 140.44/109.08 (0) 140.44/109.08 Obligation: 140.44/109.08 mainModule Main 140.44/109.08 module FiniteMap where { 140.44/109.08 import qualified Main; 140.44/109.08 import qualified Maybe; 140.44/109.08 import qualified Prelude; 140.44/109.08 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 140.44/109.08 140.44/109.08 instance (Eq a, Eq b) => Eq FiniteMap a b where { 140.44/109.08 (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; 140.44/109.08 } 140.44/109.08 addToFM :: Ord a => FiniteMap a b -> a -> b -> FiniteMap a b; 140.44/109.08 addToFM fm key elt = addToFM_C (\old new ->new) fm key elt; 140.44/109.08 140.44/109.08 addToFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> a -> b -> FiniteMap a b; 140.44/109.08 addToFM_C combiner EmptyFM key elt = unitFM key elt; 140.44/109.08 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r 140.44/109.08 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) 140.44/109.08 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; 140.44/109.08 140.44/109.08 emptyFM :: FiniteMap b a; 140.44/109.08 emptyFM = EmptyFM; 140.44/109.08 140.44/109.08 findMax :: FiniteMap a b -> (a,b); 140.44/109.08 findMax (Branch key elt _ _ EmptyFM) = (key,elt); 140.44/109.08 findMax (Branch key elt _ _ fm_r) = findMax fm_r; 140.44/109.08 140.44/109.08 findMin :: FiniteMap b a -> (b,a); 140.44/109.08 findMin (Branch key elt _ EmptyFM _) = (key,elt); 140.44/109.08 findMin (Branch key elt _ fm_l _) = findMin fm_l; 140.44/109.08 140.44/109.08 fmToList :: FiniteMap b a -> [(b,a)]; 140.44/109.08 fmToList fm = foldFM (\key elt rest ->(key,elt) : rest) [] fm; 140.44/109.08 140.44/109.08 foldFM :: (c -> b -> a -> a) -> a -> FiniteMap c b -> a; 140.44/109.08 foldFM k z EmptyFM = z; 140.44/109.08 foldFM k z (Branch key elt _ fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; 140.44/109.08 140.44/109.08 lookupFM :: Ord a => FiniteMap a b -> a -> Maybe b; 140.44/109.08 lookupFM EmptyFM key = Nothing; 140.44/109.08 lookupFM (Branch key elt _ fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find 140.44/109.08 | key_to_find > key = lookupFM fm_r key_to_find 140.44/109.08 | otherwise = Just elt; 140.44/109.08 140.44/109.08 mkBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 140.44/109.08 mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R 140.44/109.08 | size_r > sIZE_RATIO * size_l = case fm_R of { 140.44/109.08 Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R 140.44/109.08 | otherwise -> double_L fm_L fm_R; 140.44/109.08 } 140.44/109.08 | size_l > sIZE_RATIO * size_r = case fm_L of { 140.44/109.08 Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R 140.44/109.08 | otherwise -> double_R fm_L fm_R; 140.44/109.08 } 140.44/109.08 | otherwise = mkBranch 2 key elt fm_L fm_R where { 140.44/109.08 double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 140.44/109.08 double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 140.44/109.08 single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 140.44/109.08 single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 140.44/109.08 size_l = sizeFM fm_L; 140.44/109.08 size_r = sizeFM fm_R; 140.44/109.08 }; 140.44/109.08 140.44/109.08 mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 140.44/109.08 mkBranch which key elt fm_l fm_r = let { 140.44/109.08 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 140.44/109.08 } in result where { 140.44/109.08 balance_ok = True; 140.44/109.08 left_ok = case fm_l of { 140.44/109.08 EmptyFM-> True; 140.44/109.08 Branch left_key _ _ _ _-> let { 140.44/109.08 biggest_left_key = fst (findMax fm_l); 140.44/109.08 } in biggest_left_key < key; 140.44/109.08 } ; 140.44/109.08 left_size = sizeFM fm_l; 140.44/109.08 right_ok = case fm_r of { 140.44/109.08 EmptyFM-> True; 140.44/109.08 Branch right_key _ _ _ _-> let { 140.44/109.08 smallest_right_key = fst (findMin fm_r); 140.44/109.08 } in key < smallest_right_key; 140.44/109.08 } ; 140.44/109.08 right_size = sizeFM fm_r; 140.44/109.08 unbox :: Int -> Int; 140.44/109.08 unbox x = x; 140.44/109.08 }; 140.44/109.08 140.44/109.08 mkVBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 140.44/109.08 mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; 140.44/109.08 mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; 140.44/109.08 mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) | sIZE_RATIO * size_l < size_r = mkBalBranch key_r elt_r (mkVBalBranch key elt fm_l fm_rl) fm_rr 140.44/109.08 | sIZE_RATIO * size_r < size_l = mkBalBranch key_l elt_l fm_ll (mkVBalBranch key elt fm_lr fm_r) 140.44/109.08 | otherwise = mkBranch 13 key elt fm_l fm_r where { 140.44/109.08 size_l = sizeFM fm_l; 140.44/109.08 size_r = sizeFM fm_r; 140.44/109.08 }; 140.44/109.08 140.44/109.08 plusFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 140.44/109.08 plusFM_C combiner EmptyFM fm2 = fm2; 140.44/109.08 plusFM_C combiner fm1 EmptyFM = fm1; 140.44/109.08 plusFM_C combiner fm1 (Branch split_key elt2 _ left right) = mkVBalBranch split_key new_elt (plusFM_C combiner lts left) (plusFM_C combiner gts right) where { 140.44/109.08 gts = splitGT fm1 split_key; 140.44/109.08 lts = splitLT fm1 split_key; 140.44/109.08 new_elt = case lookupFM fm1 split_key of { 140.44/109.08 Nothing-> elt2; 140.44/109.08 Just elt1-> combiner elt1 elt2; 140.44/109.08 } ; 140.44/109.08 }; 140.44/109.08 140.44/109.08 sIZE_RATIO :: Int; 140.44/109.08 sIZE_RATIO = 5; 140.44/109.08 140.44/109.08 sizeFM :: FiniteMap a b -> Int; 140.44/109.08 sizeFM EmptyFM = 0; 140.44/109.08 sizeFM (Branch _ _ size _ _) = size; 140.44/109.08 140.44/109.08 splitGT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 140.44/109.08 splitGT EmptyFM split_key = emptyFM; 140.44/109.08 splitGT (Branch key elt _ fm_l fm_r) split_key | split_key > key = splitGT fm_r split_key 140.44/109.08 | split_key < key = mkVBalBranch key elt (splitGT fm_l split_key) fm_r 140.44/109.08 | otherwise = fm_r; 140.44/109.08 140.44/109.08 splitLT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 140.44/109.08 splitLT EmptyFM split_key = emptyFM; 140.44/109.08 splitLT (Branch key elt _ fm_l fm_r) split_key | split_key < key = splitLT fm_l split_key 140.44/109.08 | split_key > key = mkVBalBranch key elt fm_l (splitLT fm_r split_key) 140.44/109.08 | otherwise = fm_l; 140.44/109.08 140.44/109.08 unitFM :: a -> b -> FiniteMap a b; 140.44/109.08 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 140.44/109.08 140.44/109.08 } 140.44/109.08 module Maybe where { 140.44/109.08 import qualified FiniteMap; 140.44/109.08 import qualified Main; 140.44/109.08 import qualified Prelude; 140.44/109.08 } 140.44/109.08 module Main where { 140.44/109.08 import qualified FiniteMap; 140.44/109.08 import qualified Maybe; 140.44/109.08 import qualified Prelude; 140.44/109.08 } 140.44/109.08 140.44/109.08 ---------------------------------------- 140.44/109.08 140.44/109.08 (1) LR (EQUIVALENT) 140.44/109.08 Lambda Reductions: 140.44/109.08 The following Lambda expression 140.44/109.08 "\oldnew->new" 140.44/109.08 is transformed to 140.44/109.08 "addToFM0 old new = new; 140.44/109.08 " 140.44/109.08 The following Lambda expression 140.44/109.08 "\keyeltrest->(key,elt) : rest" 140.44/109.08 is transformed to 140.44/109.08 "fmToList0 key elt rest = (key,elt) : rest; 140.44/109.08 " 140.44/109.08 140.44/109.08 ---------------------------------------- 140.44/109.08 140.44/109.08 (2) 140.44/109.08 Obligation: 140.44/109.08 mainModule Main 140.44/109.08 module FiniteMap where { 140.44/109.08 import qualified Main; 140.44/109.08 import qualified Maybe; 140.44/109.08 import qualified Prelude; 140.44/109.08 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 140.44/109.08 140.44/109.08 instance (Eq a, Eq b) => Eq FiniteMap a b where { 140.44/109.08 (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; 140.44/109.08 } 140.44/109.08 addToFM :: Ord a => FiniteMap a b -> a -> b -> FiniteMap a b; 140.44/109.08 addToFM fm key elt = addToFM_C addToFM0 fm key elt; 140.44/109.08 140.44/109.08 addToFM0 old new = new; 140.44/109.08 140.44/109.08 addToFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> a -> b -> FiniteMap a b; 140.44/109.08 addToFM_C combiner EmptyFM key elt = unitFM key elt; 140.44/109.08 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r 140.44/109.08 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) 140.44/109.08 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; 140.44/109.08 140.44/109.08 emptyFM :: FiniteMap a b; 140.44/109.08 emptyFM = EmptyFM; 140.44/109.08 140.44/109.08 findMax :: FiniteMap b a -> (b,a); 140.44/109.08 findMax (Branch key elt _ _ EmptyFM) = (key,elt); 140.44/109.08 findMax (Branch key elt _ _ fm_r) = findMax fm_r; 140.44/109.08 140.44/109.08 findMin :: FiniteMap b a -> (b,a); 140.44/109.08 findMin (Branch key elt _ EmptyFM _) = (key,elt); 140.44/109.08 findMin (Branch key elt _ fm_l _) = findMin fm_l; 140.44/109.08 140.44/109.08 fmToList :: FiniteMap a b -> [(a,b)]; 140.44/109.08 fmToList fm = foldFM fmToList0 [] fm; 140.44/109.08 140.44/109.08 fmToList0 key elt rest = (key,elt) : rest; 140.44/109.08 140.44/109.08 foldFM :: (c -> b -> a -> a) -> a -> FiniteMap c b -> a; 140.44/109.08 foldFM k z EmptyFM = z; 140.44/109.08 foldFM k z (Branch key elt _ fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; 140.44/109.08 140.44/109.08 lookupFM :: Ord b => FiniteMap b a -> b -> Maybe a; 140.44/109.08 lookupFM EmptyFM key = Nothing; 140.44/109.08 lookupFM (Branch key elt _ fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find 140.44/109.08 | key_to_find > key = lookupFM fm_r key_to_find 140.44/109.08 | otherwise = Just elt; 140.44/109.08 140.44/109.08 mkBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 140.44/109.08 mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R 140.44/109.08 | size_r > sIZE_RATIO * size_l = case fm_R of { 140.44/109.08 Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R 140.44/109.08 | otherwise -> double_L fm_L fm_R; 140.44/109.08 } 140.44/109.08 | size_l > sIZE_RATIO * size_r = case fm_L of { 140.44/109.08 Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R 140.44/109.08 | otherwise -> double_R fm_L fm_R; 140.44/109.08 } 140.44/109.08 | otherwise = mkBranch 2 key elt fm_L fm_R where { 140.44/109.08 double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 140.44/109.08 double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 140.44/109.08 single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 140.44/109.08 single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 140.44/109.08 size_l = sizeFM fm_L; 140.44/109.08 size_r = sizeFM fm_R; 140.44/109.08 }; 140.44/109.08 140.44/109.08 mkBranch :: Ord a => Int -> a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 140.44/109.08 mkBranch which key elt fm_l fm_r = let { 140.44/109.08 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 140.44/109.08 } in result where { 140.44/109.08 balance_ok = True; 140.44/109.08 left_ok = case fm_l of { 140.44/109.08 EmptyFM-> True; 140.44/109.08 Branch left_key _ _ _ _-> let { 140.44/109.08 biggest_left_key = fst (findMax fm_l); 140.44/109.08 } in biggest_left_key < key; 140.44/109.08 } ; 140.44/109.08 left_size = sizeFM fm_l; 140.44/109.08 right_ok = case fm_r of { 140.44/109.08 EmptyFM-> True; 140.44/109.08 Branch right_key _ _ _ _-> let { 140.44/109.08 smallest_right_key = fst (findMin fm_r); 140.44/109.08 } in key < smallest_right_key; 140.44/109.08 } ; 140.44/109.08 right_size = sizeFM fm_r; 140.44/109.08 unbox :: Int -> Int; 140.44/109.08 unbox x = x; 140.44/109.08 }; 140.44/109.08 140.44/109.08 mkVBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 140.44/109.08 mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; 140.44/109.08 mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; 140.44/109.08 mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) | sIZE_RATIO * size_l < size_r = mkBalBranch key_r elt_r (mkVBalBranch key elt fm_l fm_rl) fm_rr 140.44/109.08 | sIZE_RATIO * size_r < size_l = mkBalBranch key_l elt_l fm_ll (mkVBalBranch key elt fm_lr fm_r) 140.44/109.08 | otherwise = mkBranch 13 key elt fm_l fm_r where { 140.44/109.08 size_l = sizeFM fm_l; 140.44/109.08 size_r = sizeFM fm_r; 140.44/109.08 }; 140.44/109.08 140.44/109.08 plusFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 140.44/109.08 plusFM_C combiner EmptyFM fm2 = fm2; 140.44/109.08 plusFM_C combiner fm1 EmptyFM = fm1; 140.44/109.08 plusFM_C combiner fm1 (Branch split_key elt2 _ left right) = mkVBalBranch split_key new_elt (plusFM_C combiner lts left) (plusFM_C combiner gts right) where { 140.44/109.08 gts = splitGT fm1 split_key; 140.44/109.08 lts = splitLT fm1 split_key; 140.44/109.08 new_elt = case lookupFM fm1 split_key of { 140.44/109.08 Nothing-> elt2; 140.44/109.08 Just elt1-> combiner elt1 elt2; 140.44/109.08 } ; 140.44/109.08 }; 140.44/109.08 140.44/109.08 sIZE_RATIO :: Int; 140.44/109.08 sIZE_RATIO = 5; 140.44/109.08 140.44/109.08 sizeFM :: FiniteMap a b -> Int; 140.44/109.08 sizeFM EmptyFM = 0; 140.44/109.08 sizeFM (Branch _ _ size _ _) = size; 140.44/109.08 140.44/109.08 splitGT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 140.44/109.08 splitGT EmptyFM split_key = emptyFM; 140.44/109.08 splitGT (Branch key elt _ fm_l fm_r) split_key | split_key > key = splitGT fm_r split_key 140.44/109.08 | split_key < key = mkVBalBranch key elt (splitGT fm_l split_key) fm_r 140.44/109.08 | otherwise = fm_r; 140.44/109.08 140.44/109.08 splitLT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 140.44/109.08 splitLT EmptyFM split_key = emptyFM; 140.44/109.08 splitLT (Branch key elt _ fm_l fm_r) split_key | split_key < key = splitLT fm_l split_key 140.44/109.08 | split_key > key = mkVBalBranch key elt fm_l (splitLT fm_r split_key) 140.44/109.08 | otherwise = fm_l; 140.44/109.08 140.44/109.08 unitFM :: a -> b -> FiniteMap a b; 140.44/109.08 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 140.44/109.08 140.44/109.08 } 140.44/109.08 module Maybe where { 140.44/109.08 import qualified FiniteMap; 140.44/109.08 import qualified Main; 140.44/109.08 import qualified Prelude; 140.44/109.08 } 140.44/109.08 module Main where { 140.44/109.08 import qualified FiniteMap; 140.44/109.08 import qualified Maybe; 140.44/109.08 import qualified Prelude; 140.44/109.08 } 140.44/109.08 140.44/109.08 ---------------------------------------- 140.44/109.08 140.44/109.08 (3) CR (EQUIVALENT) 140.44/109.08 Case Reductions: 140.44/109.08 The following Case expression 140.44/109.08 "case compare x y of { 140.44/109.08 EQ -> o; 140.44/109.08 LT -> LT; 140.44/109.08 GT -> GT} 140.44/109.08 " 140.44/109.08 is transformed to 140.44/109.08 "primCompAux0 o EQ = o; 140.44/109.08 primCompAux0 o LT = LT; 140.44/109.08 primCompAux0 o GT = GT; 140.44/109.08 " 140.44/109.08 The following Case expression 140.44/109.08 "case lookupFM fm1 split_key of { 140.44/109.08 Nothing -> elt2; 140.44/109.08 Just elt1 -> combiner elt1 elt2} 140.44/109.08 " 140.44/109.08 is transformed to 140.44/109.08 "new_elt0 elt2 combiner Nothing = elt2; 140.44/109.08 new_elt0 elt2 combiner (Just elt1) = combiner elt1 elt2; 140.44/109.08 " 140.44/109.08 The following Case expression 140.44/109.08 "case fm_r of { 140.44/109.08 EmptyFM -> True; 140.44/109.08 Branch right_key _ _ _ _ -> let { 140.44/109.08 smallest_right_key = fst (findMin fm_r); 140.44/109.08 } in key < smallest_right_key} 140.44/109.08 " 140.44/109.08 is transformed to 140.44/109.08 "right_ok0 fm_r key EmptyFM = True; 140.44/109.08 right_ok0 fm_r key (Branch right_key _ _ _ _) = let { 140.44/109.08 smallest_right_key = fst (findMin fm_r); 140.44/109.08 } in key < smallest_right_key; 140.44/109.08 " 140.44/109.08 The following Case expression 140.44/109.08 "case fm_l of { 140.44/109.08 EmptyFM -> True; 140.44/109.08 Branch left_key _ _ _ _ -> let { 140.44/109.08 biggest_left_key = fst (findMax fm_l); 140.44/109.08 } in biggest_left_key < key} 140.44/109.08 " 140.44/109.08 is transformed to 140.44/109.08 "left_ok0 fm_l key EmptyFM = True; 140.44/109.08 left_ok0 fm_l key (Branch left_key _ _ _ _) = let { 140.44/109.08 biggest_left_key = fst (findMax fm_l); 140.44/109.08 } in biggest_left_key < key; 140.44/109.08 " 140.44/109.08 The following Case expression 140.44/109.08 "case fm_R of { 140.44/109.08 Branch _ _ _ fm_rl fm_rr |sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R} 140.44/109.08 " 140.44/109.08 is transformed to 140.44/109.08 "mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R; 140.44/109.08 " 140.44/109.08 The following Case expression 140.44/109.08 "case fm_L of { 140.44/109.08 Branch _ _ _ fm_ll fm_lr |sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R} 140.44/109.08 " 140.44/109.08 is transformed to 140.44/109.08 "mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R; 140.44/109.08 " 140.44/109.08 140.44/109.08 ---------------------------------------- 140.44/109.08 140.44/109.08 (4) 140.44/109.08 Obligation: 140.44/109.08 mainModule Main 140.44/109.08 module FiniteMap where { 140.44/109.08 import qualified Main; 140.44/109.08 import qualified Maybe; 140.44/109.08 import qualified Prelude; 140.44/109.08 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 140.44/109.08 140.44/109.08 instance (Eq a, Eq b) => Eq FiniteMap b a where { 140.44/109.08 (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; 140.44/109.08 } 140.44/109.08 addToFM :: Ord b => FiniteMap b a -> b -> a -> FiniteMap b a; 140.44/109.08 addToFM fm key elt = addToFM_C addToFM0 fm key elt; 140.44/109.08 140.44/109.08 addToFM0 old new = new; 140.44/109.08 140.44/109.08 addToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> b -> a -> FiniteMap b a; 140.44/109.08 addToFM_C combiner EmptyFM key elt = unitFM key elt; 140.44/109.08 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r 140.44/109.08 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) 140.44/109.08 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; 140.44/109.08 140.44/109.08 emptyFM :: FiniteMap a b; 140.44/109.08 emptyFM = EmptyFM; 140.44/109.08 140.44/109.08 findMax :: FiniteMap b a -> (b,a); 140.44/109.08 findMax (Branch key elt _ _ EmptyFM) = (key,elt); 140.44/109.08 findMax (Branch key elt _ _ fm_r) = findMax fm_r; 140.44/109.08 140.44/109.08 findMin :: FiniteMap a b -> (a,b); 140.44/109.08 findMin (Branch key elt _ EmptyFM _) = (key,elt); 140.44/109.08 findMin (Branch key elt _ fm_l _) = findMin fm_l; 140.44/109.08 140.44/109.08 fmToList :: FiniteMap b a -> [(b,a)]; 140.44/109.08 fmToList fm = foldFM fmToList0 [] fm; 140.44/109.08 140.44/109.08 fmToList0 key elt rest = (key,elt) : rest; 140.44/109.08 140.44/109.08 foldFM :: (a -> b -> c -> c) -> c -> FiniteMap a b -> c; 140.44/109.08 foldFM k z EmptyFM = z; 140.44/109.08 foldFM k z (Branch key elt _ fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; 140.44/109.08 140.44/109.08 lookupFM :: Ord b => FiniteMap b a -> b -> Maybe a; 140.44/109.08 lookupFM EmptyFM key = Nothing; 140.44/109.08 lookupFM (Branch key elt _ fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find 140.44/109.08 | key_to_find > key = lookupFM fm_r key_to_find 140.44/109.08 | otherwise = Just elt; 140.44/109.08 140.44/109.08 mkBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 140.44/109.08 mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R 140.44/109.08 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R 140.44/109.08 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L 141.35/109.34 | otherwise = mkBranch 2 key elt fm_L fm_R where { 141.35/109.34 double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 141.35/109.34 double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 141.35/109.34 mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr) | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R 141.35/109.34 | otherwise = double_L fm_L fm_R; 141.35/109.34 mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr) | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R 141.35/109.34 | otherwise = double_R fm_L fm_R; 141.35/109.34 single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 141.35/109.34 single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 141.35/109.34 size_l = sizeFM fm_L; 141.35/109.34 size_r = sizeFM fm_R; 141.35/109.34 }; 141.35/109.34 141.35/109.34 mkBranch :: Ord a => Int -> a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 141.35/109.34 mkBranch which key elt fm_l fm_r = let { 141.35/109.34 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 141.35/109.34 } in result where { 141.35/109.34 balance_ok = True; 141.35/109.34 left_ok = left_ok0 fm_l key fm_l; 141.35/109.34 left_ok0 fm_l key EmptyFM = True; 141.35/109.34 left_ok0 fm_l key (Branch left_key _ _ _ _) = let { 141.35/109.34 biggest_left_key = fst (findMax fm_l); 141.35/109.34 } in biggest_left_key < key; 141.35/109.34 left_size = sizeFM fm_l; 141.35/109.34 right_ok = right_ok0 fm_r key fm_r; 141.35/109.34 right_ok0 fm_r key EmptyFM = True; 141.35/109.34 right_ok0 fm_r key (Branch right_key _ _ _ _) = let { 141.35/109.34 smallest_right_key = fst (findMin fm_r); 141.35/109.34 } in key < smallest_right_key; 141.35/109.34 right_size = sizeFM fm_r; 141.35/109.34 unbox :: Int -> Int; 141.35/109.34 unbox x = x; 141.35/109.34 }; 141.35/109.34 141.35/109.34 mkVBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 141.35/109.34 mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; 141.35/109.34 mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; 141.35/109.34 mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) | sIZE_RATIO * size_l < size_r = mkBalBranch key_r elt_r (mkVBalBranch key elt fm_l fm_rl) fm_rr 141.35/109.34 | sIZE_RATIO * size_r < size_l = mkBalBranch key_l elt_l fm_ll (mkVBalBranch key elt fm_lr fm_r) 141.35/109.34 | otherwise = mkBranch 13 key elt fm_l fm_r where { 141.35/109.34 size_l = sizeFM fm_l; 141.35/109.34 size_r = sizeFM fm_r; 141.35/109.34 }; 141.35/109.34 141.35/109.34 plusFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 141.35/109.34 plusFM_C combiner EmptyFM fm2 = fm2; 141.35/109.34 plusFM_C combiner fm1 EmptyFM = fm1; 141.35/109.34 plusFM_C combiner fm1 (Branch split_key elt2 _ left right) = mkVBalBranch split_key new_elt (plusFM_C combiner lts left) (plusFM_C combiner gts right) where { 141.35/109.34 gts = splitGT fm1 split_key; 141.35/109.34 lts = splitLT fm1 split_key; 141.35/109.34 new_elt = new_elt0 elt2 combiner (lookupFM fm1 split_key); 141.35/109.34 new_elt0 elt2 combiner Nothing = elt2; 141.35/109.34 new_elt0 elt2 combiner (Just elt1) = combiner elt1 elt2; 141.35/109.34 }; 141.35/109.34 141.35/109.34 sIZE_RATIO :: Int; 141.35/109.34 sIZE_RATIO = 5; 141.35/109.34 141.35/109.34 sizeFM :: FiniteMap b a -> Int; 141.35/109.34 sizeFM EmptyFM = 0; 141.35/109.34 sizeFM (Branch _ _ size _ _) = size; 141.35/109.34 141.35/109.34 splitGT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; 141.35/109.34 splitGT EmptyFM split_key = emptyFM; 141.35/109.34 splitGT (Branch key elt _ fm_l fm_r) split_key | split_key > key = splitGT fm_r split_key 141.35/109.34 | split_key < key = mkVBalBranch key elt (splitGT fm_l split_key) fm_r 141.35/109.34 | otherwise = fm_r; 141.35/109.34 141.35/109.34 splitLT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; 141.35/109.34 splitLT EmptyFM split_key = emptyFM; 141.35/109.34 splitLT (Branch key elt _ fm_l fm_r) split_key | split_key < key = splitLT fm_l split_key 141.35/109.34 | split_key > key = mkVBalBranch key elt fm_l (splitLT fm_r split_key) 141.35/109.34 | otherwise = fm_l; 141.35/109.34 141.35/109.34 unitFM :: b -> a -> FiniteMap b a; 141.35/109.34 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 141.35/109.34 141.35/109.34 } 141.35/109.34 module Maybe where { 141.35/109.34 import qualified FiniteMap; 141.35/109.34 import qualified Main; 141.35/109.34 import qualified Prelude; 141.35/109.34 } 141.35/109.34 module Main where { 141.35/109.34 import qualified FiniteMap; 141.35/109.34 import qualified Maybe; 141.35/109.34 import qualified Prelude; 141.35/109.34 } 141.35/109.34 141.35/109.34 ---------------------------------------- 141.35/109.34 141.35/109.34 (5) IFR (EQUIVALENT) 141.35/109.34 If Reductions: 141.35/109.34 The following If expression 141.35/109.34 "if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero" 141.35/109.34 is transformed to 141.35/109.34 "primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y)); 141.35/109.34 primDivNatS0 x y False = Zero; 141.35/109.34 " 141.35/109.34 The following If expression 141.35/109.34 "if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x" 141.35/109.34 is transformed to 141.35/109.34 "primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y); 141.35/109.34 primModNatS0 x y False = Succ x; 141.35/109.34 " 141.35/109.34 141.35/109.34 ---------------------------------------- 141.35/109.34 141.35/109.34 (6) 141.35/109.34 Obligation: 141.35/109.34 mainModule Main 141.35/109.34 module FiniteMap where { 141.35/109.34 import qualified Main; 141.35/109.34 import qualified Maybe; 141.35/109.34 import qualified Prelude; 141.35/109.34 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 141.35/109.34 141.35/109.34 instance (Eq a, Eq b) => Eq FiniteMap b a where { 141.35/109.34 (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; 141.35/109.34 } 141.35/109.34 addToFM :: Ord a => FiniteMap a b -> a -> b -> FiniteMap a b; 141.35/109.34 addToFM fm key elt = addToFM_C addToFM0 fm key elt; 141.35/109.34 141.35/109.34 addToFM0 old new = new; 141.35/109.34 141.35/109.34 addToFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> a -> b -> FiniteMap a b; 141.35/109.34 addToFM_C combiner EmptyFM key elt = unitFM key elt; 141.35/109.34 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r 141.35/109.34 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) 141.35/109.34 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; 141.35/109.34 141.35/109.34 emptyFM :: FiniteMap a b; 141.35/109.34 emptyFM = EmptyFM; 141.35/109.34 141.35/109.34 findMax :: FiniteMap b a -> (b,a); 141.35/109.34 findMax (Branch key elt _ _ EmptyFM) = (key,elt); 141.35/109.34 findMax (Branch key elt _ _ fm_r) = findMax fm_r; 141.35/109.34 141.35/109.34 findMin :: FiniteMap b a -> (b,a); 141.35/109.34 findMin (Branch key elt _ EmptyFM _) = (key,elt); 141.35/109.34 findMin (Branch key elt _ fm_l _) = findMin fm_l; 141.35/109.34 141.35/109.34 fmToList :: FiniteMap a b -> [(a,b)]; 141.35/109.34 fmToList fm = foldFM fmToList0 [] fm; 141.35/109.34 141.35/109.34 fmToList0 key elt rest = (key,elt) : rest; 141.35/109.34 141.35/109.34 foldFM :: (a -> c -> b -> b) -> b -> FiniteMap a c -> b; 141.35/109.34 foldFM k z EmptyFM = z; 141.35/109.34 foldFM k z (Branch key elt _ fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; 141.35/109.34 141.35/109.34 lookupFM :: Ord b => FiniteMap b a -> b -> Maybe a; 141.35/109.34 lookupFM EmptyFM key = Nothing; 141.35/109.34 lookupFM (Branch key elt _ fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find 141.35/109.34 | key_to_find > key = lookupFM fm_r key_to_find 141.35/109.34 | otherwise = Just elt; 141.35/109.34 141.35/109.34 mkBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 141.35/109.34 mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R 141.35/109.34 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R 141.35/109.34 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L 141.35/109.34 | otherwise = mkBranch 2 key elt fm_L fm_R where { 141.35/109.34 double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 141.35/109.34 double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 141.35/109.34 mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr) | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R 141.35/109.34 | otherwise = double_L fm_L fm_R; 141.35/109.34 mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr) | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R 141.35/109.34 | otherwise = double_R fm_L fm_R; 141.35/109.34 single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 141.35/109.34 single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 141.35/109.34 size_l = sizeFM fm_L; 141.35/109.34 size_r = sizeFM fm_R; 141.35/109.34 }; 141.35/109.34 141.35/109.34 mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 141.35/109.34 mkBranch which key elt fm_l fm_r = let { 141.35/109.34 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 141.35/109.34 } in result where { 141.35/109.34 balance_ok = True; 141.35/109.34 left_ok = left_ok0 fm_l key fm_l; 141.35/109.34 left_ok0 fm_l key EmptyFM = True; 141.35/109.34 left_ok0 fm_l key (Branch left_key _ _ _ _) = let { 141.35/109.34 biggest_left_key = fst (findMax fm_l); 141.35/109.34 } in biggest_left_key < key; 141.35/109.34 left_size = sizeFM fm_l; 141.35/109.34 right_ok = right_ok0 fm_r key fm_r; 141.35/109.34 right_ok0 fm_r key EmptyFM = True; 141.35/109.34 right_ok0 fm_r key (Branch right_key _ _ _ _) = let { 141.35/109.34 smallest_right_key = fst (findMin fm_r); 141.35/109.34 } in key < smallest_right_key; 141.35/109.34 right_size = sizeFM fm_r; 141.35/109.34 unbox :: Int -> Int; 141.35/109.34 unbox x = x; 141.35/109.34 }; 141.35/109.34 141.35/109.34 mkVBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 141.35/109.34 mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; 141.35/109.34 mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; 141.35/109.34 mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) | sIZE_RATIO * size_l < size_r = mkBalBranch key_r elt_r (mkVBalBranch key elt fm_l fm_rl) fm_rr 141.35/109.34 | sIZE_RATIO * size_r < size_l = mkBalBranch key_l elt_l fm_ll (mkVBalBranch key elt fm_lr fm_r) 141.35/109.34 | otherwise = mkBranch 13 key elt fm_l fm_r where { 141.35/109.34 size_l = sizeFM fm_l; 141.35/109.34 size_r = sizeFM fm_r; 141.35/109.34 }; 141.35/109.34 141.35/109.34 plusFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 141.35/109.34 plusFM_C combiner EmptyFM fm2 = fm2; 141.35/109.34 plusFM_C combiner fm1 EmptyFM = fm1; 141.35/109.34 plusFM_C combiner fm1 (Branch split_key elt2 _ left right) = mkVBalBranch split_key new_elt (plusFM_C combiner lts left) (plusFM_C combiner gts right) where { 141.35/109.34 gts = splitGT fm1 split_key; 141.35/109.34 lts = splitLT fm1 split_key; 141.35/109.34 new_elt = new_elt0 elt2 combiner (lookupFM fm1 split_key); 141.35/109.34 new_elt0 elt2 combiner Nothing = elt2; 141.35/109.34 new_elt0 elt2 combiner (Just elt1) = combiner elt1 elt2; 141.35/109.34 }; 141.35/109.34 141.35/109.34 sIZE_RATIO :: Int; 141.35/109.34 sIZE_RATIO = 5; 141.35/109.34 141.35/109.34 sizeFM :: FiniteMap b a -> Int; 141.35/109.34 sizeFM EmptyFM = 0; 141.35/109.34 sizeFM (Branch _ _ size _ _) = size; 141.35/109.34 141.35/109.34 splitGT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; 141.35/109.34 splitGT EmptyFM split_key = emptyFM; 141.35/109.34 splitGT (Branch key elt _ fm_l fm_r) split_key | split_key > key = splitGT fm_r split_key 141.35/109.34 | split_key < key = mkVBalBranch key elt (splitGT fm_l split_key) fm_r 141.35/109.34 | otherwise = fm_r; 141.35/109.34 141.35/109.34 splitLT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 141.35/109.34 splitLT EmptyFM split_key = emptyFM; 141.35/109.34 splitLT (Branch key elt _ fm_l fm_r) split_key | split_key < key = splitLT fm_l split_key 141.35/109.34 | split_key > key = mkVBalBranch key elt fm_l (splitLT fm_r split_key) 141.35/109.34 | otherwise = fm_l; 141.35/109.34 141.35/109.34 unitFM :: b -> a -> FiniteMap b a; 141.35/109.34 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 141.35/109.34 141.35/109.34 } 141.35/109.34 module Maybe where { 141.35/109.34 import qualified FiniteMap; 141.35/109.34 import qualified Main; 141.35/109.34 import qualified Prelude; 141.35/109.34 } 141.35/109.34 module Main where { 141.35/109.34 import qualified FiniteMap; 141.35/109.34 import qualified Maybe; 141.35/109.34 import qualified Prelude; 141.35/109.34 } 141.35/109.34 141.35/109.34 ---------------------------------------- 141.35/109.34 141.35/109.34 (7) BR (EQUIVALENT) 141.35/109.34 Replaced joker patterns by fresh variables and removed binding patterns. 141.35/109.34 141.35/109.34 Binding Reductions: 141.35/109.34 The bind variable of the following binding Pattern 141.35/109.34 "fm_l@(Branch vuv vuw vux vuy vuz)" 141.35/109.34 is replaced by the following term 141.35/109.34 "Branch vuv vuw vux vuy vuz" 141.35/109.34 The bind variable of the following binding Pattern 141.35/109.34 "fm_r@(Branch vvv vvw vvx vvy vvz)" 141.35/109.34 is replaced by the following term 141.35/109.34 "Branch vvv vvw vvx vvy vvz" 141.35/109.34 141.35/109.34 ---------------------------------------- 141.35/109.34 141.35/109.34 (8) 141.35/109.34 Obligation: 141.35/109.34 mainModule Main 141.35/109.34 module FiniteMap where { 141.35/109.34 import qualified Main; 141.35/109.34 import qualified Maybe; 141.35/109.34 import qualified Prelude; 141.35/109.34 data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; 141.35/109.34 141.35/109.34 instance (Eq a, Eq b) => Eq FiniteMap b a where { 141.35/109.34 (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; 141.35/109.34 } 141.35/109.34 addToFM :: Ord b => FiniteMap b a -> b -> a -> FiniteMap b a; 141.35/109.34 addToFM fm key elt = addToFM_C addToFM0 fm key elt; 141.35/109.34 141.35/109.34 addToFM0 old new = new; 141.35/109.34 141.35/109.34 addToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> b -> a -> FiniteMap b a; 141.35/109.34 addToFM_C combiner EmptyFM key elt = unitFM key elt; 141.35/109.34 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r 141.35/109.34 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) 141.35/109.34 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; 141.35/109.34 141.35/109.34 emptyFM :: FiniteMap a b; 141.35/109.34 emptyFM = EmptyFM; 141.35/109.34 141.35/109.34 findMax :: FiniteMap a b -> (a,b); 141.35/109.34 findMax (Branch key elt vxy vxz EmptyFM) = (key,elt); 141.35/109.34 findMax (Branch key elt vyu vyv fm_r) = findMax fm_r; 141.35/109.34 141.35/109.34 findMin :: FiniteMap b a -> (b,a); 141.35/109.34 findMin (Branch key elt wvw EmptyFM wvx) = (key,elt); 141.35/109.34 findMin (Branch key elt wvy fm_l wvz) = findMin fm_l; 141.35/109.34 141.35/109.34 fmToList :: FiniteMap a b -> [(a,b)]; 141.35/109.34 fmToList fm = foldFM fmToList0 [] fm; 141.35/109.34 141.35/109.34 fmToList0 key elt rest = (key,elt) : rest; 141.35/109.34 141.35/109.34 foldFM :: (b -> a -> c -> c) -> c -> FiniteMap b a -> c; 141.35/109.34 foldFM k z EmptyFM = z; 141.35/109.34 foldFM k z (Branch key elt wuw fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; 141.35/109.34 141.35/109.34 lookupFM :: Ord a => FiniteMap a b -> a -> Maybe b; 141.35/109.34 lookupFM EmptyFM key = Nothing; 141.35/109.34 lookupFM (Branch key elt wvv fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find 141.35/109.34 | key_to_find > key = lookupFM fm_r key_to_find 141.35/109.34 | otherwise = Just elt; 141.35/109.34 141.35/109.34 mkBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 141.35/109.34 mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R 141.35/109.34 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R 141.35/109.34 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L 141.35/109.34 | otherwise = mkBranch 2 key elt fm_L fm_R where { 141.35/109.34 double_L fm_l (Branch key_r elt_r vzw (Branch key_rl elt_rl vzx fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 141.35/109.34 double_R (Branch key_l elt_l vyx fm_ll (Branch key_lr elt_lr vyy fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 141.35/109.34 mkBalBranch0 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R 141.35/109.34 | otherwise = double_L fm_L fm_R; 141.35/109.34 mkBalBranch1 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R 141.35/109.34 | otherwise = double_R fm_L fm_R; 141.35/109.34 single_L fm_l (Branch key_r elt_r wuv fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 141.35/109.34 single_R (Branch key_l elt_l vyw fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 141.35/109.34 size_l = sizeFM fm_L; 141.35/109.34 size_r = sizeFM fm_R; 141.35/109.34 }; 141.35/109.34 141.35/109.34 mkBranch :: Ord a => Int -> a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 141.35/109.34 mkBranch which key elt fm_l fm_r = let { 141.35/109.34 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 141.35/109.34 } in result where { 141.35/109.34 balance_ok = True; 141.35/109.34 left_ok = left_ok0 fm_l key fm_l; 141.35/109.34 left_ok0 fm_l key EmptyFM = True; 141.35/109.34 left_ok0 fm_l key (Branch left_key vww vwx vwy vwz) = let { 141.35/109.34 biggest_left_key = fst (findMax fm_l); 141.35/109.34 } in biggest_left_key < key; 141.35/109.34 left_size = sizeFM fm_l; 141.35/109.34 right_ok = right_ok0 fm_r key fm_r; 141.35/109.34 right_ok0 fm_r key EmptyFM = True; 141.35/109.34 right_ok0 fm_r key (Branch right_key vxu vxv vxw vxx) = let { 141.35/109.34 smallest_right_key = fst (findMin fm_r); 141.35/109.34 } in key < smallest_right_key; 141.35/109.34 right_size = sizeFM fm_r; 141.35/109.34 unbox :: Int -> Int; 141.35/109.34 unbox x = x; 141.35/109.34 }; 141.35/109.34 141.35/109.34 mkVBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 141.35/109.34 mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; 141.35/109.34 mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; 141.35/109.34 mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) | sIZE_RATIO * size_l < size_r = mkBalBranch vvv vvw (mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) vvy) vvz 141.35/109.34 | sIZE_RATIO * size_r < size_l = mkBalBranch vuv vuw vuy (mkVBalBranch key elt vuz (Branch vvv vvw vvx vvy vvz)) 141.35/109.34 | otherwise = mkBranch 13 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) where { 141.35/109.34 size_l = sizeFM (Branch vuv vuw vux vuy vuz); 141.35/109.34 size_r = sizeFM (Branch vvv vvw vvx vvy vvz); 141.35/109.34 }; 141.35/109.34 141.35/109.34 plusFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 141.35/109.34 plusFM_C combiner EmptyFM fm2 = fm2; 141.35/109.34 plusFM_C combiner fm1 EmptyFM = fm1; 141.35/109.34 plusFM_C combiner fm1 (Branch split_key elt2 zz left right) = mkVBalBranch split_key new_elt (plusFM_C combiner lts left) (plusFM_C combiner gts right) where { 141.35/109.34 gts = splitGT fm1 split_key; 141.35/109.34 lts = splitLT fm1 split_key; 141.35/109.34 new_elt = new_elt0 elt2 combiner (lookupFM fm1 split_key); 141.35/109.34 new_elt0 elt2 combiner Nothing = elt2; 141.35/109.34 new_elt0 elt2 combiner (Just elt1) = combiner elt1 elt2; 141.35/109.34 }; 141.35/109.34 141.35/109.34 sIZE_RATIO :: Int; 141.35/109.34 sIZE_RATIO = 5; 141.35/109.34 141.35/109.34 sizeFM :: FiniteMap b a -> Int; 141.35/109.34 sizeFM EmptyFM = 0; 141.35/109.34 sizeFM (Branch wux wuy size wuz wvu) = size; 141.35/109.34 141.35/109.34 splitGT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; 141.35/109.34 splitGT EmptyFM split_key = emptyFM; 141.35/109.34 splitGT (Branch key elt vwu fm_l fm_r) split_key | split_key > key = splitGT fm_r split_key 141.35/109.34 | split_key < key = mkVBalBranch key elt (splitGT fm_l split_key) fm_r 141.35/109.34 | otherwise = fm_r; 141.35/109.34 141.35/109.34 splitLT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; 141.35/109.34 splitLT EmptyFM split_key = emptyFM; 141.35/109.34 splitLT (Branch key elt vwv fm_l fm_r) split_key | split_key < key = splitLT fm_l split_key 141.35/109.34 | split_key > key = mkVBalBranch key elt fm_l (splitLT fm_r split_key) 141.35/109.34 | otherwise = fm_l; 141.35/109.34 141.35/109.34 unitFM :: b -> a -> FiniteMap b a; 141.35/109.34 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 141.35/109.34 141.35/109.34 } 141.35/109.34 module Maybe where { 141.35/109.34 import qualified FiniteMap; 141.35/109.34 import qualified Main; 141.35/109.34 import qualified Prelude; 141.35/109.34 } 141.35/109.34 module Main where { 141.35/109.34 import qualified FiniteMap; 141.35/109.34 import qualified Maybe; 141.35/109.34 import qualified Prelude; 141.35/109.34 } 141.35/109.34 141.35/109.34 ---------------------------------------- 141.35/109.34 141.35/109.34 (9) COR (EQUIVALENT) 141.35/109.34 Cond Reductions: 141.35/109.34 The following Function with conditions 141.35/109.34 "compare x y|x == yEQ|x <= yLT|otherwiseGT; 141.35/109.34 " 141.35/109.34 is transformed to 141.35/109.34 "compare x y = compare3 x y; 141.35/109.34 " 141.35/109.34 "compare2 x y True = EQ; 141.35/109.34 compare2 x y False = compare1 x y (x <= y); 141.35/109.34 " 141.35/109.34 "compare0 x y True = GT; 141.35/109.34 " 141.35/109.34 "compare1 x y True = LT; 141.35/109.34 compare1 x y False = compare0 x y otherwise; 141.35/109.34 " 141.35/109.34 "compare3 x y = compare2 x y (x == y); 141.35/109.34 " 141.35/109.34 The following Function with conditions 141.35/109.34 "absReal x|x >= 0x|otherwise`negate` x; 141.35/109.34 " 141.35/109.34 is transformed to 141.35/109.34 "absReal x = absReal2 x; 141.35/109.34 " 141.35/109.34 "absReal0 x True = `negate` x; 141.35/109.34 " 141.35/109.34 "absReal1 x True = x; 141.35/109.34 absReal1 x False = absReal0 x otherwise; 141.35/109.34 " 141.35/109.34 "absReal2 x = absReal1 x (x >= 0); 141.35/109.34 " 141.35/109.34 The following Function with conditions 141.35/109.34 "gcd' x 0 = x; 141.35/109.34 gcd' x y = gcd' y (x `rem` y); 141.35/109.34 " 141.35/109.34 is transformed to 141.35/109.34 "gcd' x wwu = gcd'2 x wwu; 141.35/109.34 gcd' x y = gcd'0 x y; 141.35/109.34 " 141.35/109.34 "gcd'0 x y = gcd' y (x `rem` y); 141.35/109.34 " 141.35/109.34 "gcd'1 True x wwu = x; 141.35/109.34 gcd'1 wwv www wwx = gcd'0 www wwx; 141.35/109.34 " 141.35/109.34 "gcd'2 x wwu = gcd'1 (wwu == 0) x wwu; 141.35/109.34 gcd'2 wwy wwz = gcd'0 wwy wwz; 141.35/109.34 " 141.35/109.34 The following Function with conditions 141.35/109.34 "gcd 0 0 = error []; 141.35/109.34 gcd x y = gcd' (abs x) (abs y) where { 141.35/109.34 gcd' x 0 = x; 141.35/109.34 gcd' x y = gcd' y (x `rem` y); 141.35/109.34 } 141.35/109.34 ; 141.35/109.34 " 141.35/109.34 is transformed to 141.35/109.34 "gcd wxu wxv = gcd3 wxu wxv; 141.35/109.34 gcd x y = gcd0 x y; 141.35/109.34 " 141.35/109.34 "gcd0 x y = gcd' (abs x) (abs y) where { 141.35/109.34 gcd' x wwu = gcd'2 x wwu; 141.35/109.34 gcd' x y = gcd'0 x y; 141.35/109.34 ; 141.35/109.34 gcd'0 x y = gcd' y (x `rem` y); 141.35/109.34 ; 141.35/109.34 gcd'1 True x wwu = x; 141.35/109.34 gcd'1 wwv www wwx = gcd'0 www wwx; 141.35/109.34 ; 141.35/109.34 gcd'2 x wwu = gcd'1 (wwu == 0) x wwu; 141.35/109.34 gcd'2 wwy wwz = gcd'0 wwy wwz; 141.35/109.34 } 141.35/109.34 ; 141.35/109.34 " 141.35/109.34 "gcd1 True wxu wxv = error []; 141.35/109.34 gcd1 wxw wxx wxy = gcd0 wxx wxy; 141.35/109.34 " 141.35/109.34 "gcd2 True wxu wxv = gcd1 (wxv == 0) wxu wxv; 141.35/109.34 gcd2 wxz wyu wyv = gcd0 wyu wyv; 141.35/109.34 " 141.35/109.34 "gcd3 wxu wxv = gcd2 (wxu == 0) wxu wxv; 141.35/109.34 gcd3 wyw wyx = gcd0 wyw wyx; 141.35/109.34 " 141.35/109.34 The following Function with conditions 141.35/109.34 "undefined |Falseundefined; 141.35/109.34 " 141.35/109.34 is transformed to 141.35/109.34 "undefined = undefined1; 141.35/109.34 " 141.35/109.34 "undefined0 True = undefined; 141.35/109.34 " 141.35/109.34 "undefined1 = undefined0 False; 141.35/109.34 " 141.35/109.34 The following Function with conditions 141.35/109.34 "reduce x y|y == 0error []|otherwisex `quot` d :% (y `quot` d) where { 141.35/109.34 d = gcd x y; 141.35/109.34 } 141.35/109.34 ; 141.35/109.34 " 141.35/109.34 is transformed to 141.35/109.34 "reduce x y = reduce2 x y; 141.35/109.34 " 141.35/109.34 "reduce2 x y = reduce1 x y (y == 0) where { 141.35/109.34 d = gcd x y; 141.35/109.34 ; 141.35/109.34 reduce0 x y True = x `quot` d :% (y `quot` d); 141.35/109.34 ; 141.35/109.34 reduce1 x y True = error []; 141.35/109.34 reduce1 x y False = reduce0 x y otherwise; 141.35/109.34 } 141.35/109.34 ; 141.35/109.34 " 141.35/109.34 The following Function with conditions 141.35/109.34 "addToFM_C combiner EmptyFM key elt = unitFM key elt; 141.35/109.34 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt|new_key < keymkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r|new_key > keymkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)|otherwiseBranch new_key (combiner elt new_elt) size fm_l fm_r; 141.35/109.34 " 141.35/109.34 is transformed to 141.35/109.34 "addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt; 141.35/109.34 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt; 141.35/109.34 " 141.35/109.34 "addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt); 141.35/109.34 addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise; 141.35/109.34 " 141.35/109.34 "addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r; 141.35/109.34 " 141.35/109.34 "addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r; 141.35/109.34 addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key); 141.35/109.34 " 141.35/109.34 "addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key); 141.35/109.34 " 141.35/109.34 "addToFM_C4 combiner EmptyFM key elt = unitFM key elt; 141.35/109.34 addToFM_C4 wzu wzv wzw wzx = addToFM_C3 wzu wzv wzw wzx; 141.35/109.34 " 141.35/109.34 The following Function with conditions 141.35/109.34 "mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; 141.35/109.34 mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; 141.35/109.34 mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz)|sIZE_RATIO * size_l < size_rmkBalBranch vvv vvw (mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) vvy) vvz|sIZE_RATIO * size_r < size_lmkBalBranch vuv vuw vuy (mkVBalBranch key elt vuz (Branch vvv vvw vvx vvy vvz))|otherwisemkBranch 13 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) where { 141.35/109.34 size_l = sizeFM (Branch vuv vuw vux vuy vuz); 141.35/109.34 ; 141.35/109.34 size_r = sizeFM (Branch vvv vvw vvx vvy vvz); 141.35/109.34 } 141.35/109.34 ; 141.35/109.34 " 141.35/109.34 is transformed to 141.35/109.34 "mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r; 141.35/109.34 mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM; 141.35/109.34 mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) = mkVBalBranch3 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); 141.35/109.34 " 141.35/109.34 "mkVBalBranch3 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) = mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * size_l < size_r) where { 141.35/109.34 mkVBalBranch0 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBranch 13 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); 141.35/109.34 ; 141.35/109.34 mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vuv vuw vuy (mkVBalBranch key elt vuz (Branch vvv vvw vvx vvy vvz)); 141.35/109.34 mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch0 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz otherwise; 141.35/109.34 ; 141.35/109.34 mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vvv vvw (mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) vvy) vvz; 141.35/109.34 mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * size_r < size_l); 141.35/109.34 ; 141.35/109.34 size_l = sizeFM (Branch vuv vuw vux vuy vuz); 141.35/109.34 ; 141.35/109.34 size_r = sizeFM (Branch vvv vvw vvx vvy vvz); 141.35/109.34 } 141.35/109.34 ; 141.35/109.34 " 141.35/109.34 "mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt; 141.35/109.34 mkVBalBranch4 xuv xuw xux xuy = mkVBalBranch3 xuv xuw xux xuy; 141.35/109.34 " 141.35/109.34 "mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt; 141.35/109.34 mkVBalBranch5 xvu xvv xvw xvx = mkVBalBranch4 xvu xvv xvw xvx; 141.35/109.34 " 141.35/109.34 The following Function with conditions 141.35/109.34 "splitGT EmptyFM split_key = emptyFM; 141.35/109.34 splitGT (Branch key elt vwu fm_l fm_r) split_key|split_key > keysplitGT fm_r split_key|split_key < keymkVBalBranch key elt (splitGT fm_l split_key) fm_r|otherwisefm_r; 141.35/109.34 " 141.35/109.34 is transformed to 141.35/109.34 "splitGT EmptyFM split_key = splitGT4 EmptyFM split_key; 141.35/109.34 splitGT (Branch key elt vwu fm_l fm_r) split_key = splitGT3 (Branch key elt vwu fm_l fm_r) split_key; 141.35/109.34 " 141.35/109.34 "splitGT1 key elt vwu fm_l fm_r split_key True = mkVBalBranch key elt (splitGT fm_l split_key) fm_r; 141.35/109.34 splitGT1 key elt vwu fm_l fm_r split_key False = splitGT0 key elt vwu fm_l fm_r split_key otherwise; 141.35/109.34 " 141.35/109.34 "splitGT0 key elt vwu fm_l fm_r split_key True = fm_r; 141.35/109.34 " 141.35/109.34 "splitGT2 key elt vwu fm_l fm_r split_key True = splitGT fm_r split_key; 141.35/109.34 splitGT2 key elt vwu fm_l fm_r split_key False = splitGT1 key elt vwu fm_l fm_r split_key (split_key < key); 141.35/109.34 " 141.35/109.34 "splitGT3 (Branch key elt vwu fm_l fm_r) split_key = splitGT2 key elt vwu fm_l fm_r split_key (split_key > key); 141.35/109.34 " 141.35/109.34 "splitGT4 EmptyFM split_key = emptyFM; 141.35/109.34 splitGT4 xwu xwv = splitGT3 xwu xwv; 141.35/109.34 " 141.35/109.34 The following Function with conditions 141.35/109.34 "splitLT EmptyFM split_key = emptyFM; 141.35/109.34 splitLT (Branch key elt vwv fm_l fm_r) split_key|split_key < keysplitLT fm_l split_key|split_key > keymkVBalBranch key elt fm_l (splitLT fm_r split_key)|otherwisefm_l; 141.35/109.34 " 141.35/109.34 is transformed to 141.35/109.34 "splitLT EmptyFM split_key = splitLT4 EmptyFM split_key; 141.35/109.34 splitLT (Branch key elt vwv fm_l fm_r) split_key = splitLT3 (Branch key elt vwv fm_l fm_r) split_key; 141.35/109.34 " 141.35/109.34 "splitLT2 key elt vwv fm_l fm_r split_key True = splitLT fm_l split_key; 141.35/109.34 splitLT2 key elt vwv fm_l fm_r split_key False = splitLT1 key elt vwv fm_l fm_r split_key (split_key > key); 141.35/109.34 " 141.35/109.34 "splitLT1 key elt vwv fm_l fm_r split_key True = mkVBalBranch key elt fm_l (splitLT fm_r split_key); 141.35/109.34 splitLT1 key elt vwv fm_l fm_r split_key False = splitLT0 key elt vwv fm_l fm_r split_key otherwise; 141.35/109.34 " 141.35/109.34 "splitLT0 key elt vwv fm_l fm_r split_key True = fm_l; 141.35/109.34 " 141.35/109.34 "splitLT3 (Branch key elt vwv fm_l fm_r) split_key = splitLT2 key elt vwv fm_l fm_r split_key (split_key < key); 141.35/109.34 " 141.35/109.34 "splitLT4 EmptyFM split_key = emptyFM; 141.35/109.34 splitLT4 xwy xwz = splitLT3 xwy xwz; 141.35/109.34 " 141.35/109.34 The following Function with conditions 141.35/109.34 "mkBalBranch1 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R; 141.35/109.34 " 141.35/109.34 is transformed to 141.35/109.34 "mkBalBranch1 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr); 141.35/109.34 " 141.35/109.34 "mkBalBranch10 fm_L fm_R vyz vzu vzv fm_ll fm_lr True = double_R fm_L fm_R; 141.35/109.34 " 141.35/109.34 "mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr True = single_R fm_L fm_R; 141.35/109.34 mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vyz vzu vzv fm_ll fm_lr otherwise; 141.35/109.34 " 141.35/109.34 "mkBalBranch12 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 141.35/109.34 " 141.35/109.34 The following Function with conditions 141.35/109.34 "mkBalBranch0 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R; 141.35/109.34 " 141.35/109.34 is transformed to 141.35/109.34 "mkBalBranch0 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr); 141.35/109.34 " 141.35/109.34 "mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr True = single_L fm_L fm_R; 141.35/109.34 mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vzy vzz wuu fm_rl fm_rr otherwise; 141.35/109.34 " 141.35/109.34 "mkBalBranch00 fm_L fm_R vzy vzz wuu fm_rl fm_rr True = double_L fm_L fm_R; 141.35/109.34 " 141.35/109.34 "mkBalBranch02 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 141.35/109.34 " 141.35/109.34 The following Function with conditions 141.35/109.34 "mkBalBranch key elt fm_L fm_R|size_l + size_r < 2mkBranch 1 key elt fm_L fm_R|size_r > sIZE_RATIO * size_lmkBalBranch0 fm_L fm_R fm_R|size_l > sIZE_RATIO * size_rmkBalBranch1 fm_L fm_R fm_L|otherwisemkBranch 2 key elt fm_L fm_R where { 141.35/109.34 double_L fm_l (Branch key_r elt_r vzw (Branch key_rl elt_rl vzx fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 141.35/109.34 ; 141.35/109.34 double_R (Branch key_l elt_l vyx fm_ll (Branch key_lr elt_lr vyy fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 141.35/109.34 ; 141.35/109.34 mkBalBranch0 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R; 141.35/109.34 ; 141.35/109.34 mkBalBranch1 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R; 141.35/109.34 ; 141.35/109.34 single_L fm_l (Branch key_r elt_r wuv fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 141.35/109.34 ; 141.35/109.34 single_R (Branch key_l elt_l vyw fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 141.35/109.34 ; 141.35/109.34 size_l = sizeFM fm_L; 141.35/109.34 ; 141.35/109.34 size_r = sizeFM fm_R; 141.35/109.34 } 141.35/109.34 ; 141.35/109.34 " 141.35/109.34 is transformed to 141.35/109.34 "mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R; 141.35/109.34 " 141.35/109.34 "mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { 141.35/109.34 double_L fm_l (Branch key_r elt_r vzw (Branch key_rl elt_rl vzx fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 141.35/109.34 ; 141.35/109.34 double_R (Branch key_l elt_l vyx fm_ll (Branch key_lr elt_lr vyy fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 141.35/109.34 ; 141.35/109.34 mkBalBranch0 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr); 141.35/109.34 ; 141.35/109.34 mkBalBranch00 fm_L fm_R vzy vzz wuu fm_rl fm_rr True = double_L fm_L fm_R; 141.35/109.34 ; 141.35/109.34 mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr True = single_L fm_L fm_R; 141.35/109.34 mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vzy vzz wuu fm_rl fm_rr otherwise; 141.35/109.34 ; 141.35/109.34 mkBalBranch02 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 141.35/109.34 ; 141.35/109.34 mkBalBranch1 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr); 141.35/109.34 ; 141.35/109.34 mkBalBranch10 fm_L fm_R vyz vzu vzv fm_ll fm_lr True = double_R fm_L fm_R; 141.35/109.34 ; 141.35/109.34 mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr True = single_R fm_L fm_R; 141.35/109.34 mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vyz vzu vzv fm_ll fm_lr otherwise; 141.35/109.34 ; 141.35/109.34 mkBalBranch12 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 141.35/109.34 ; 141.35/109.34 mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; 141.35/109.34 ; 141.35/109.34 mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L; 141.35/109.34 mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise; 141.35/109.34 ; 141.35/109.34 mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R; 141.35/109.34 mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r); 141.35/109.34 ; 141.35/109.34 mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; 141.35/109.34 mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l); 141.35/109.34 ; 141.35/109.34 single_L fm_l (Branch key_r elt_r wuv fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 141.35/109.34 ; 141.35/109.34 single_R (Branch key_l elt_l vyw fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 141.35/109.34 ; 141.35/109.34 size_l = sizeFM fm_L; 141.35/109.34 ; 141.35/109.34 size_r = sizeFM fm_R; 141.35/109.34 } 141.35/109.34 ; 141.35/109.34 " 141.35/109.34 The following Function with conditions 141.35/109.34 "lookupFM EmptyFM key = Nothing; 141.35/109.34 lookupFM (Branch key elt wvv fm_l fm_r) key_to_find|key_to_find < keylookupFM fm_l key_to_find|key_to_find > keylookupFM fm_r key_to_find|otherwiseJust elt; 141.35/109.34 " 141.35/109.34 is transformed to 141.35/109.34 "lookupFM EmptyFM key = lookupFM4 EmptyFM key; 141.35/109.34 lookupFM (Branch key elt wvv fm_l fm_r) key_to_find = lookupFM3 (Branch key elt wvv fm_l fm_r) key_to_find; 141.35/109.34 " 141.35/109.34 "lookupFM2 key elt wvv fm_l fm_r key_to_find True = lookupFM fm_l key_to_find; 141.35/109.34 lookupFM2 key elt wvv fm_l fm_r key_to_find False = lookupFM1 key elt wvv fm_l fm_r key_to_find (key_to_find > key); 141.35/109.34 " 141.35/109.34 "lookupFM0 key elt wvv fm_l fm_r key_to_find True = Just elt; 141.35/109.34 " 141.35/109.34 "lookupFM1 key elt wvv fm_l fm_r key_to_find True = lookupFM fm_r key_to_find; 141.35/109.34 lookupFM1 key elt wvv fm_l fm_r key_to_find False = lookupFM0 key elt wvv fm_l fm_r key_to_find otherwise; 141.35/109.34 " 141.35/109.34 "lookupFM3 (Branch key elt wvv fm_l fm_r) key_to_find = lookupFM2 key elt wvv fm_l fm_r key_to_find (key_to_find < key); 141.35/109.34 " 141.35/109.34 "lookupFM4 EmptyFM key = Nothing; 141.35/109.34 lookupFM4 xxy xxz = lookupFM3 xxy xxz; 141.35/109.34 " 141.35/109.34 141.35/109.34 ---------------------------------------- 141.35/109.34 141.35/109.34 (10) 141.35/109.34 Obligation: 141.35/109.34 mainModule Main 141.35/109.34 module FiniteMap where { 141.35/109.34 import qualified Main; 141.35/109.34 import qualified Maybe; 141.35/109.34 import qualified Prelude; 141.35/109.34 data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; 141.35/109.34 141.35/109.34 instance (Eq a, Eq b) => Eq FiniteMap b a where { 141.35/109.34 (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; 141.35/109.34 } 141.35/109.34 addToFM :: Ord a => FiniteMap a b -> a -> b -> FiniteMap a b; 141.35/109.34 addToFM fm key elt = addToFM_C addToFM0 fm key elt; 141.35/109.34 141.35/109.34 addToFM0 old new = new; 141.35/109.34 141.35/109.34 addToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> b -> a -> FiniteMap b a; 141.35/109.34 addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt; 141.35/109.34 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt; 141.35/109.34 141.35/109.34 addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r; 141.35/109.34 141.35/109.34 addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt); 141.35/109.34 addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise; 141.35/109.34 141.35/109.34 addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r; 141.35/109.34 addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key); 141.35/109.34 141.35/109.34 addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key); 141.35/109.34 141.35/109.34 addToFM_C4 combiner EmptyFM key elt = unitFM key elt; 141.35/109.34 addToFM_C4 wzu wzv wzw wzx = addToFM_C3 wzu wzv wzw wzx; 141.35/109.34 141.35/109.34 emptyFM :: FiniteMap a b; 141.35/109.34 emptyFM = EmptyFM; 141.35/109.34 141.35/109.34 findMax :: FiniteMap a b -> (a,b); 141.35/109.34 findMax (Branch key elt vxy vxz EmptyFM) = (key,elt); 141.35/109.34 findMax (Branch key elt vyu vyv fm_r) = findMax fm_r; 141.35/109.34 141.35/109.34 findMin :: FiniteMap a b -> (a,b); 141.35/109.34 findMin (Branch key elt wvw EmptyFM wvx) = (key,elt); 141.35/109.34 findMin (Branch key elt wvy fm_l wvz) = findMin fm_l; 141.35/109.34 141.35/109.34 fmToList :: FiniteMap b a -> [(b,a)]; 141.35/109.34 fmToList fm = foldFM fmToList0 [] fm; 141.35/109.34 141.35/109.34 fmToList0 key elt rest = (key,elt) : rest; 141.35/109.34 141.35/109.34 foldFM :: (c -> a -> b -> b) -> b -> FiniteMap c a -> b; 141.35/109.34 foldFM k z EmptyFM = z; 141.35/109.34 foldFM k z (Branch key elt wuw fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; 141.35/109.34 141.35/109.34 lookupFM :: Ord b => FiniteMap b a -> b -> Maybe a; 141.35/109.34 lookupFM EmptyFM key = lookupFM4 EmptyFM key; 141.35/109.34 lookupFM (Branch key elt wvv fm_l fm_r) key_to_find = lookupFM3 (Branch key elt wvv fm_l fm_r) key_to_find; 141.35/109.34 141.35/109.34 lookupFM0 key elt wvv fm_l fm_r key_to_find True = Just elt; 141.35/109.34 141.35/109.34 lookupFM1 key elt wvv fm_l fm_r key_to_find True = lookupFM fm_r key_to_find; 141.35/109.34 lookupFM1 key elt wvv fm_l fm_r key_to_find False = lookupFM0 key elt wvv fm_l fm_r key_to_find otherwise; 141.35/109.34 141.35/109.34 lookupFM2 key elt wvv fm_l fm_r key_to_find True = lookupFM fm_l key_to_find; 141.35/109.34 lookupFM2 key elt wvv fm_l fm_r key_to_find False = lookupFM1 key elt wvv fm_l fm_r key_to_find (key_to_find > key); 141.35/109.34 141.35/109.34 lookupFM3 (Branch key elt wvv fm_l fm_r) key_to_find = lookupFM2 key elt wvv fm_l fm_r key_to_find (key_to_find < key); 141.35/109.34 141.35/109.34 lookupFM4 EmptyFM key = Nothing; 141.35/109.34 lookupFM4 xxy xxz = lookupFM3 xxy xxz; 141.35/109.34 141.35/109.34 mkBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 141.35/109.34 mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R; 141.35/109.34 141.35/109.34 mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { 141.35/109.34 double_L fm_l (Branch key_r elt_r vzw (Branch key_rl elt_rl vzx fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 141.35/109.34 double_R (Branch key_l elt_l vyx fm_ll (Branch key_lr elt_lr vyy fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 141.35/109.34 mkBalBranch0 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr); 141.35/109.34 mkBalBranch00 fm_L fm_R vzy vzz wuu fm_rl fm_rr True = double_L fm_L fm_R; 141.35/109.34 mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr True = single_L fm_L fm_R; 141.35/109.34 mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vzy vzz wuu fm_rl fm_rr otherwise; 141.35/109.34 mkBalBranch02 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 141.35/109.34 mkBalBranch1 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr); 141.35/109.34 mkBalBranch10 fm_L fm_R vyz vzu vzv fm_ll fm_lr True = double_R fm_L fm_R; 141.35/109.34 mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr True = single_R fm_L fm_R; 141.35/109.34 mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vyz vzu vzv fm_ll fm_lr otherwise; 141.35/109.34 mkBalBranch12 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 141.35/109.34 mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; 141.35/109.34 mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L; 141.35/109.34 mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise; 141.35/109.34 mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R; 141.35/109.34 mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r); 141.35/109.34 mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; 141.35/109.34 mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l); 141.35/109.34 single_L fm_l (Branch key_r elt_r wuv fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 141.35/109.34 single_R (Branch key_l elt_l vyw fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 141.35/109.34 size_l = sizeFM fm_L; 141.35/109.34 size_r = sizeFM fm_R; 141.35/109.34 }; 141.35/109.34 141.35/109.34 mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 141.35/109.34 mkBranch which key elt fm_l fm_r = let { 141.35/109.34 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 141.35/109.34 } in result where { 141.35/109.34 balance_ok = True; 141.35/109.34 left_ok = left_ok0 fm_l key fm_l; 141.35/109.34 left_ok0 fm_l key EmptyFM = True; 141.35/109.34 left_ok0 fm_l key (Branch left_key vww vwx vwy vwz) = let { 141.35/109.34 biggest_left_key = fst (findMax fm_l); 141.35/109.34 } in biggest_left_key < key; 141.35/109.34 left_size = sizeFM fm_l; 141.35/109.34 right_ok = right_ok0 fm_r key fm_r; 141.35/109.34 right_ok0 fm_r key EmptyFM = True; 141.35/109.34 right_ok0 fm_r key (Branch right_key vxu vxv vxw vxx) = let { 141.35/109.34 smallest_right_key = fst (findMin fm_r); 141.35/109.34 } in key < smallest_right_key; 141.35/109.34 right_size = sizeFM fm_r; 141.35/109.34 unbox :: Int -> Int; 141.35/109.34 unbox x = x; 141.35/109.34 }; 141.35/109.34 141.35/109.34 mkVBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 141.35/109.34 mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r; 141.35/109.34 mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM; 141.35/109.34 mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) = mkVBalBranch3 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); 141.35/109.34 141.35/109.34 mkVBalBranch3 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) = mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * size_l < size_r) where { 141.35/109.34 mkVBalBranch0 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBranch 13 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); 141.35/109.34 mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vuv vuw vuy (mkVBalBranch key elt vuz (Branch vvv vvw vvx vvy vvz)); 141.35/109.34 mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch0 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz otherwise; 141.35/109.34 mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vvv vvw (mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) vvy) vvz; 141.35/109.34 mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * size_r < size_l); 141.35/109.34 size_l = sizeFM (Branch vuv vuw vux vuy vuz); 141.35/109.34 size_r = sizeFM (Branch vvv vvw vvx vvy vvz); 141.35/109.34 }; 141.35/109.34 141.35/109.34 mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt; 141.35/109.34 mkVBalBranch4 xuv xuw xux xuy = mkVBalBranch3 xuv xuw xux xuy; 141.35/109.34 141.35/109.34 mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt; 141.35/109.34 mkVBalBranch5 xvu xvv xvw xvx = mkVBalBranch4 xvu xvv xvw xvx; 141.35/109.34 141.35/109.34 plusFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 141.35/109.34 plusFM_C combiner EmptyFM fm2 = fm2; 141.35/109.34 plusFM_C combiner fm1 EmptyFM = fm1; 141.35/109.34 plusFM_C combiner fm1 (Branch split_key elt2 zz left right) = mkVBalBranch split_key new_elt (plusFM_C combiner lts left) (plusFM_C combiner gts right) where { 141.35/109.34 gts = splitGT fm1 split_key; 141.35/109.34 lts = splitLT fm1 split_key; 141.35/109.34 new_elt = new_elt0 elt2 combiner (lookupFM fm1 split_key); 141.35/109.34 new_elt0 elt2 combiner Nothing = elt2; 141.35/109.34 new_elt0 elt2 combiner (Just elt1) = combiner elt1 elt2; 141.35/109.34 }; 141.35/109.34 141.35/109.34 sIZE_RATIO :: Int; 141.35/109.34 sIZE_RATIO = 5; 141.35/109.34 141.35/109.34 sizeFM :: FiniteMap b a -> Int; 141.35/109.34 sizeFM EmptyFM = 0; 141.35/109.34 sizeFM (Branch wux wuy size wuz wvu) = size; 141.35/109.34 141.35/109.34 splitGT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 141.35/109.34 splitGT EmptyFM split_key = splitGT4 EmptyFM split_key; 141.35/109.34 splitGT (Branch key elt vwu fm_l fm_r) split_key = splitGT3 (Branch key elt vwu fm_l fm_r) split_key; 141.35/109.34 141.35/109.34 splitGT0 key elt vwu fm_l fm_r split_key True = fm_r; 141.35/109.34 141.35/109.34 splitGT1 key elt vwu fm_l fm_r split_key True = mkVBalBranch key elt (splitGT fm_l split_key) fm_r; 141.35/109.34 splitGT1 key elt vwu fm_l fm_r split_key False = splitGT0 key elt vwu fm_l fm_r split_key otherwise; 141.35/109.34 141.35/109.34 splitGT2 key elt vwu fm_l fm_r split_key True = splitGT fm_r split_key; 141.35/109.34 splitGT2 key elt vwu fm_l fm_r split_key False = splitGT1 key elt vwu fm_l fm_r split_key (split_key < key); 141.73/109.37 141.73/109.37 splitGT3 (Branch key elt vwu fm_l fm_r) split_key = splitGT2 key elt vwu fm_l fm_r split_key (split_key > key); 141.73/109.37 141.73/109.37 splitGT4 EmptyFM split_key = emptyFM; 141.73/109.37 splitGT4 xwu xwv = splitGT3 xwu xwv; 141.73/109.37 141.73/109.37 splitLT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; 141.73/109.37 splitLT EmptyFM split_key = splitLT4 EmptyFM split_key; 141.73/109.37 splitLT (Branch key elt vwv fm_l fm_r) split_key = splitLT3 (Branch key elt vwv fm_l fm_r) split_key; 141.73/109.37 141.73/109.37 splitLT0 key elt vwv fm_l fm_r split_key True = fm_l; 141.73/109.37 141.73/109.37 splitLT1 key elt vwv fm_l fm_r split_key True = mkVBalBranch key elt fm_l (splitLT fm_r split_key); 141.73/109.37 splitLT1 key elt vwv fm_l fm_r split_key False = splitLT0 key elt vwv fm_l fm_r split_key otherwise; 141.73/109.37 141.73/109.37 splitLT2 key elt vwv fm_l fm_r split_key True = splitLT fm_l split_key; 141.73/109.37 splitLT2 key elt vwv fm_l fm_r split_key False = splitLT1 key elt vwv fm_l fm_r split_key (split_key > key); 141.73/109.37 141.73/109.37 splitLT3 (Branch key elt vwv fm_l fm_r) split_key = splitLT2 key elt vwv fm_l fm_r split_key (split_key < key); 141.73/109.37 141.73/109.37 splitLT4 EmptyFM split_key = emptyFM; 141.73/109.37 splitLT4 xwy xwz = splitLT3 xwy xwz; 141.73/109.37 141.73/109.37 unitFM :: b -> a -> FiniteMap b a; 141.73/109.37 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 141.73/109.37 141.73/109.37 } 141.73/109.37 module Maybe where { 141.73/109.37 import qualified FiniteMap; 141.73/109.37 import qualified Main; 141.73/109.37 import qualified Prelude; 141.73/109.37 } 141.73/109.37 module Main where { 141.73/109.37 import qualified FiniteMap; 141.73/109.37 import qualified Maybe; 141.73/109.37 import qualified Prelude; 141.73/109.37 } 141.73/109.37 141.73/109.37 ---------------------------------------- 141.73/109.37 141.73/109.37 (11) LetRed (EQUIVALENT) 141.73/109.37 Let/Where Reductions: 141.73/109.37 The bindings of the following Let/Where expression 141.73/109.37 "gcd' (abs x) (abs y) where { 141.73/109.37 gcd' x wwu = gcd'2 x wwu; 141.73/109.37 gcd' x y = gcd'0 x y; 141.73/109.37 ; 141.73/109.37 gcd'0 x y = gcd' y (x `rem` y); 141.73/109.37 ; 141.73/109.37 gcd'1 True x wwu = x; 141.73/109.37 gcd'1 wwv www wwx = gcd'0 www wwx; 141.73/109.37 ; 141.73/109.37 gcd'2 x wwu = gcd'1 (wwu == 0) x wwu; 141.73/109.37 gcd'2 wwy wwz = gcd'0 wwy wwz; 141.73/109.37 } 141.73/109.37 " 141.73/109.37 are unpacked to the following functions on top level 141.73/109.37 "gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y); 141.73/109.37 " 141.73/109.37 "gcd0Gcd' x wwu = gcd0Gcd'2 x wwu; 141.73/109.37 gcd0Gcd' x y = gcd0Gcd'0 x y; 141.73/109.37 " 141.73/109.37 "gcd0Gcd'2 x wwu = gcd0Gcd'1 (wwu == 0) x wwu; 141.73/109.37 gcd0Gcd'2 wwy wwz = gcd0Gcd'0 wwy wwz; 141.73/109.37 " 141.73/109.37 "gcd0Gcd'1 True x wwu = x; 141.73/109.37 gcd0Gcd'1 wwv www wwx = gcd0Gcd'0 www wwx; 141.73/109.37 " 141.73/109.37 The bindings of the following Let/Where expression 141.73/109.37 "reduce1 x y (y == 0) where { 141.73/109.37 d = gcd x y; 141.73/109.37 ; 141.73/109.37 reduce0 x y True = x `quot` d :% (y `quot` d); 141.73/109.37 ; 141.73/109.37 reduce1 x y True = error []; 141.73/109.37 reduce1 x y False = reduce0 x y otherwise; 141.73/109.37 } 141.73/109.37 " 141.73/109.37 are unpacked to the following functions on top level 141.73/109.37 "reduce2D xyu xyv = gcd xyu xyv; 141.73/109.37 " 141.73/109.37 "reduce2Reduce1 xyu xyv x y True = error []; 141.73/109.37 reduce2Reduce1 xyu xyv x y False = reduce2Reduce0 xyu xyv x y otherwise; 141.73/109.37 " 141.73/109.37 "reduce2Reduce0 xyu xyv x y True = x `quot` reduce2D xyu xyv :% (y `quot` reduce2D xyu xyv); 141.73/109.37 " 141.73/109.37 The bindings of the following Let/Where expression 141.73/109.37 "mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { 141.73/109.37 double_L fm_l (Branch key_r elt_r vzw (Branch key_rl elt_rl vzx fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 141.73/109.37 ; 141.73/109.37 double_R (Branch key_l elt_l vyx fm_ll (Branch key_lr elt_lr vyy fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); 141.73/109.37 ; 141.73/109.37 mkBalBranch0 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr); 141.73/109.37 ; 141.73/109.37 mkBalBranch00 fm_L fm_R vzy vzz wuu fm_rl fm_rr True = double_L fm_L fm_R; 141.73/109.37 ; 141.73/109.37 mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr True = single_L fm_L fm_R; 141.73/109.37 mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vzy vzz wuu fm_rl fm_rr otherwise; 141.73/109.37 ; 141.73/109.37 mkBalBranch02 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 141.73/109.37 ; 141.73/109.37 mkBalBranch1 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr); 141.73/109.37 ; 141.73/109.37 mkBalBranch10 fm_L fm_R vyz vzu vzv fm_ll fm_lr True = double_R fm_L fm_R; 141.73/109.37 ; 141.73/109.37 mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr True = single_R fm_L fm_R; 141.73/109.37 mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vyz vzu vzv fm_ll fm_lr otherwise; 141.73/109.37 ; 141.73/109.37 mkBalBranch12 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 141.73/109.37 ; 141.73/109.37 mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; 141.73/109.37 ; 141.73/109.37 mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L; 141.73/109.37 mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise; 141.73/109.37 ; 141.73/109.37 mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R; 141.73/109.37 mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r); 141.73/109.37 ; 141.73/109.37 mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; 141.73/109.37 mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l); 141.73/109.37 ; 141.73/109.37 single_L fm_l (Branch key_r elt_r wuv fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 141.73/109.37 ; 141.73/109.37 single_R (Branch key_l elt_l vyw fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 141.73/109.37 ; 141.73/109.37 size_l = sizeFM fm_L; 141.73/109.37 ; 141.73/109.37 size_r = sizeFM fm_R; 141.73/109.37 } 141.73/109.37 " 141.73/109.37 are unpacked to the following functions on top level 141.73/109.37 "mkBalBranch6MkBalBranch0 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch6MkBalBranch02 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr); 141.73/109.37 " 141.73/109.37 "mkBalBranch6Single_R xyw xyx xyy xyz (Branch key_l elt_l vyw fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 xyw xyx fm_lr fm_r); 141.73/109.37 " 141.73/109.37 "mkBalBranch6MkBalBranch2 xyw xyx xyy xyz key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; 141.73/109.37 " 141.73/109.37 "mkBalBranch6Size_l xyw xyx xyy xyz = sizeFM xyy; 141.73/109.37 " 141.73/109.37 "mkBalBranch6MkBalBranch02 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 141.73/109.37 " 141.73/109.37 "mkBalBranch6MkBalBranch00 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr True = mkBalBranch6Double_L xyw xyx xyy xyz fm_L fm_R; 141.73/109.37 " 141.73/109.37 "mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 xyw xyx xyy xyz fm_L fm_R fm_R; 141.73/109.37 mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R (mkBalBranch6Size_l xyw xyx xyy xyz > sIZE_RATIO * mkBalBranch6Size_r xyw xyx xyy xyz); 141.73/109.37 " 141.73/109.37 "mkBalBranch6Double_L xyw xyx xyy xyz fm_l (Branch key_r elt_r vzw (Branch key_rl elt_rl vzx fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 xyw xyx fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 141.73/109.37 " 141.73/109.37 "mkBalBranch6MkBalBranch5 xyw xyx xyy xyz key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; 141.73/109.37 mkBalBranch6MkBalBranch5 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R (mkBalBranch6Size_r xyw xyx xyy xyz > sIZE_RATIO * mkBalBranch6Size_l xyw xyx xyy xyz); 141.73/109.37 " 141.73/109.37 "mkBalBranch6Single_L xyw xyx xyy xyz fm_l (Branch key_r elt_r wuv fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 xyw xyx fm_l fm_rl) fm_rr; 141.73/109.37 " 141.73/109.37 "mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr True = mkBalBranch6Single_R xyw xyx xyy xyz fm_L fm_R; 141.73/109.37 mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr False = mkBalBranch6MkBalBranch10 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr otherwise; 141.73/109.37 " 141.73/109.37 "mkBalBranch6MkBalBranch1 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch6MkBalBranch12 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr); 141.73/109.37 " 141.73/109.37 "mkBalBranch6MkBalBranch10 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr True = mkBalBranch6Double_R xyw xyx xyy xyz fm_L fm_R; 141.73/109.37 " 141.73/109.37 "mkBalBranch6Double_R xyw xyx xyy xyz (Branch key_l elt_l vyx fm_ll (Branch key_lr elt_lr vyy fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 xyw xyx fm_lrr fm_r); 141.73/109.37 " 141.73/109.37 "mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 xyw xyx xyy xyz fm_L fm_R fm_L; 141.73/109.37 mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 xyw xyx xyy xyz key elt fm_L fm_R otherwise; 141.73/109.37 " 141.73/109.37 "mkBalBranch6MkBalBranch12 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 141.73/109.37 " 141.73/109.37 "mkBalBranch6Size_r xyw xyx xyy xyz = sizeFM xyz; 141.73/109.37 " 141.73/109.37 "mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr True = mkBalBranch6Single_L xyw xyx xyy xyz fm_L fm_R; 141.73/109.37 mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr False = mkBalBranch6MkBalBranch00 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr otherwise; 141.73/109.37 " 141.73/109.37 The bindings of the following Let/Where expression 141.73/109.37 "let { 141.73/109.37 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 141.73/109.37 } in result where { 141.73/109.37 balance_ok = True; 141.73/109.37 ; 141.73/109.37 left_ok = left_ok0 fm_l key fm_l; 141.73/109.37 ; 141.73/109.37 left_ok0 fm_l key EmptyFM = True; 141.73/109.37 left_ok0 fm_l key (Branch left_key vww vwx vwy vwz) = let { 141.73/109.37 biggest_left_key = fst (findMax fm_l); 141.73/109.37 } in biggest_left_key < key; 141.73/109.37 ; 141.73/109.37 left_size = sizeFM fm_l; 141.73/109.37 ; 141.73/109.37 right_ok = right_ok0 fm_r key fm_r; 141.73/109.37 ; 141.73/109.37 right_ok0 fm_r key EmptyFM = True; 141.73/109.37 right_ok0 fm_r key (Branch right_key vxu vxv vxw vxx) = let { 141.73/109.37 smallest_right_key = fst (findMin fm_r); 141.73/109.37 } in key < smallest_right_key; 141.73/109.37 ; 141.73/109.37 right_size = sizeFM fm_r; 141.73/109.37 ; 141.73/109.37 unbox x = x; 141.73/109.37 } 141.73/109.37 " 141.73/109.37 are unpacked to the following functions on top level 141.73/109.37 "mkBranchLeft_size xzu xzv xzw = sizeFM xzu; 141.73/109.37 " 141.73/109.37 "mkBranchRight_size xzu xzv xzw = sizeFM xzv; 141.73/109.37 " 141.73/109.37 "mkBranchLeft_ok xzu xzv xzw = mkBranchLeft_ok0 xzu xzv xzw xzu xzw xzu; 141.73/109.37 " 141.73/109.37 "mkBranchUnbox xzu xzv xzw x = x; 141.73/109.37 " 141.73/109.37 "mkBranchLeft_ok0 xzu xzv xzw fm_l key EmptyFM = True; 141.73/109.37 mkBranchLeft_ok0 xzu xzv xzw fm_l key (Branch left_key vww vwx vwy vwz) = mkBranchLeft_ok0Biggest_left_key fm_l < key; 141.73/109.37 " 141.73/109.37 "mkBranchBalance_ok xzu xzv xzw = True; 141.73/109.37 " 141.73/109.37 "mkBranchRight_ok xzu xzv xzw = mkBranchRight_ok0 xzu xzv xzw xzv xzw xzv; 141.73/109.37 " 141.73/109.37 "mkBranchRight_ok0 xzu xzv xzw fm_r key EmptyFM = True; 141.73/109.37 mkBranchRight_ok0 xzu xzv xzw fm_r key (Branch right_key vxu vxv vxw vxx) = key < mkBranchRight_ok0Smallest_right_key fm_r; 141.73/109.37 " 141.73/109.37 The bindings of the following Let/Where expression 141.73/109.37 "let { 141.73/109.37 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 141.73/109.37 } in result" 141.73/109.37 are unpacked to the following functions on top level 141.73/109.37 "mkBranchResult xzx xzy xzz yuu = Branch xzx xzy (mkBranchUnbox xzz yuu xzx (1 + mkBranchLeft_size xzz yuu xzx + mkBranchRight_size xzz yuu xzx)) xzz yuu; 141.73/109.37 " 141.73/109.37 The bindings of the following Let/Where expression 141.73/109.37 "mkVBalBranch split_key new_elt (plusFM_C combiner lts left) (plusFM_C combiner gts right) where { 141.73/109.37 gts = splitGT fm1 split_key; 141.73/109.37 ; 141.73/109.37 lts = splitLT fm1 split_key; 141.73/109.37 ; 141.73/109.37 new_elt = new_elt0 elt2 combiner (lookupFM fm1 split_key); 141.73/109.37 ; 141.73/109.37 new_elt0 elt2 combiner Nothing = elt2; 141.73/109.37 new_elt0 elt2 combiner (Just elt1) = combiner elt1 elt2; 141.73/109.37 } 141.73/109.37 " 141.73/109.37 are unpacked to the following functions on top level 141.73/109.37 "plusFM_CLts yuv yuw yux yuy = splitLT yuv yuw; 141.73/109.37 " 141.73/109.37 "plusFM_CNew_elt0 yuv yuw yux yuy elt2 combiner Nothing = elt2; 141.73/109.37 plusFM_CNew_elt0 yuv yuw yux yuy elt2 combiner (Just elt1) = combiner elt1 elt2; 141.73/109.37 " 141.73/109.37 "plusFM_CGts yuv yuw yux yuy = splitGT yuv yuw; 141.73/109.37 " 141.73/109.37 "plusFM_CNew_elt yuv yuw yux yuy = plusFM_CNew_elt0 yuv yuw yux yuy yux yuy (lookupFM yuv yuw); 141.73/109.37 " 141.73/109.37 The bindings of the following Let/Where expression 141.73/109.37 "mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * size_l < size_r) where { 141.73/109.37 mkVBalBranch0 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBranch 13 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); 141.73/109.37 ; 141.73/109.37 mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vuv vuw vuy (mkVBalBranch key elt vuz (Branch vvv vvw vvx vvy vvz)); 141.73/109.37 mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch0 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz otherwise; 141.73/109.37 ; 141.73/109.37 mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vvv vvw (mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) vvy) vvz; 141.73/109.37 mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * size_r < size_l); 141.73/109.37 ; 141.73/109.37 size_l = sizeFM (Branch vuv vuw vux vuy vuz); 141.73/109.37 ; 141.73/109.37 size_r = sizeFM (Branch vvv vvw vvx vvy vvz); 141.73/109.37 } 141.73/109.37 " 141.73/109.37 are unpacked to the following functions on top level 141.73/109.37 "mkVBalBranch3Size_r yuz yvu yvv yvw yvx yvy yvz ywu ywv yww = sizeFM (Branch yuz yvu yvv yvw yvx); 141.73/109.37 " 141.73/109.37 "mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vuv vuw vuy (mkVBalBranch key elt vuz (Branch vvv vvw vvx vvy vvz)); 141.73/109.37 mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch3MkVBalBranch0 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz otherwise; 141.73/109.37 " 141.73/109.37 "mkVBalBranch3Size_l yuz yvu yvv yvw yvx yvy yvz ywu ywv yww = sizeFM (Branch yvy yvz ywu ywv yww); 141.73/109.37 " 141.73/109.37 "mkVBalBranch3MkVBalBranch0 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBranch 13 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); 141.73/109.37 " 141.73/109.37 "mkVBalBranch3MkVBalBranch2 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vvv vvw (mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) vvy) vvz; 141.73/109.37 mkVBalBranch3MkVBalBranch2 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * mkVBalBranch3Size_r yuz yvu yvv yvw yvx yvy yvz ywu ywv yww < mkVBalBranch3Size_l yuz yvu yvv yvw yvx yvy yvz ywu ywv yww); 141.73/109.37 " 141.73/109.37 The bindings of the following Let/Where expression 141.73/109.37 "let { 141.73/109.37 biggest_left_key = fst (findMax fm_l); 141.73/109.37 } in biggest_left_key < key" 141.73/109.37 are unpacked to the following functions on top level 141.73/109.37 "mkBranchLeft_ok0Biggest_left_key ywx = fst (findMax ywx); 141.73/109.37 " 141.73/109.37 The bindings of the following Let/Where expression 141.73/109.37 "let { 141.73/109.37 smallest_right_key = fst (findMin fm_r); 141.73/109.37 } in key < smallest_right_key" 141.73/109.37 are unpacked to the following functions on top level 141.73/109.37 "mkBranchRight_ok0Smallest_right_key ywy = fst (findMin ywy); 141.73/109.37 " 141.73/109.37 141.73/109.37 ---------------------------------------- 141.73/109.37 141.73/109.37 (12) 141.73/109.37 Obligation: 141.73/109.37 mainModule Main 141.73/109.37 module FiniteMap where { 141.73/109.37 import qualified Main; 141.73/109.37 import qualified Maybe; 141.73/109.37 import qualified Prelude; 141.73/109.37 data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; 141.73/109.37 141.73/109.37 instance (Eq a, Eq b) => Eq FiniteMap a b where { 141.73/109.37 (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; 141.73/109.37 } 141.73/109.37 addToFM :: Ord b => FiniteMap b a -> b -> a -> FiniteMap b a; 141.73/109.37 addToFM fm key elt = addToFM_C addToFM0 fm key elt; 141.73/109.37 141.73/109.37 addToFM0 old new = new; 141.73/109.37 141.73/109.37 addToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> b -> a -> FiniteMap b a; 141.73/109.37 addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt; 141.73/109.37 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt; 141.73/109.37 141.73/109.37 addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r; 141.73/109.37 141.73/109.37 addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt); 141.73/109.37 addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise; 141.73/109.37 141.73/109.37 addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r; 141.73/109.37 addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key); 141.73/109.37 141.73/109.37 addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key); 141.73/109.37 141.73/109.37 addToFM_C4 combiner EmptyFM key elt = unitFM key elt; 141.73/109.37 addToFM_C4 wzu wzv wzw wzx = addToFM_C3 wzu wzv wzw wzx; 141.73/109.37 141.73/109.37 emptyFM :: FiniteMap a b; 141.73/109.37 emptyFM = EmptyFM; 141.73/109.37 141.73/109.37 findMax :: FiniteMap a b -> (a,b); 141.73/109.37 findMax (Branch key elt vxy vxz EmptyFM) = (key,elt); 141.73/109.37 findMax (Branch key elt vyu vyv fm_r) = findMax fm_r; 141.73/109.37 141.73/109.37 findMin :: FiniteMap a b -> (a,b); 141.73/109.37 findMin (Branch key elt wvw EmptyFM wvx) = (key,elt); 141.73/109.37 findMin (Branch key elt wvy fm_l wvz) = findMin fm_l; 141.73/109.37 141.73/109.37 fmToList :: FiniteMap a b -> [(a,b)]; 141.73/109.37 fmToList fm = foldFM fmToList0 [] fm; 141.73/109.37 141.73/109.37 fmToList0 key elt rest = (key,elt) : rest; 141.73/109.37 141.73/109.37 foldFM :: (b -> c -> a -> a) -> a -> FiniteMap b c -> a; 141.73/109.37 foldFM k z EmptyFM = z; 141.73/109.37 foldFM k z (Branch key elt wuw fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; 141.73/109.37 141.73/109.37 lookupFM :: Ord a => FiniteMap a b -> a -> Maybe b; 141.73/109.37 lookupFM EmptyFM key = lookupFM4 EmptyFM key; 141.73/109.37 lookupFM (Branch key elt wvv fm_l fm_r) key_to_find = lookupFM3 (Branch key elt wvv fm_l fm_r) key_to_find; 141.73/109.37 141.73/109.37 lookupFM0 key elt wvv fm_l fm_r key_to_find True = Just elt; 141.73/109.37 141.73/109.37 lookupFM1 key elt wvv fm_l fm_r key_to_find True = lookupFM fm_r key_to_find; 141.73/109.37 lookupFM1 key elt wvv fm_l fm_r key_to_find False = lookupFM0 key elt wvv fm_l fm_r key_to_find otherwise; 141.73/109.37 141.73/109.37 lookupFM2 key elt wvv fm_l fm_r key_to_find True = lookupFM fm_l key_to_find; 141.73/109.37 lookupFM2 key elt wvv fm_l fm_r key_to_find False = lookupFM1 key elt wvv fm_l fm_r key_to_find (key_to_find > key); 141.73/109.37 141.73/109.37 lookupFM3 (Branch key elt wvv fm_l fm_r) key_to_find = lookupFM2 key elt wvv fm_l fm_r key_to_find (key_to_find < key); 141.73/109.37 141.73/109.37 lookupFM4 EmptyFM key = Nothing; 141.73/109.37 lookupFM4 xxy xxz = lookupFM3 xxy xxz; 141.73/109.37 141.73/109.37 mkBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 141.73/109.37 mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R; 141.73/109.37 141.73/109.37 mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 key elt fm_L fm_R key elt fm_L fm_R (mkBalBranch6Size_l key elt fm_L fm_R + mkBalBranch6Size_r key elt fm_L fm_R < 2); 141.73/109.37 141.73/109.37 mkBalBranch6Double_L xyw xyx xyy xyz fm_l (Branch key_r elt_r vzw (Branch key_rl elt_rl vzx fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 xyw xyx fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 141.73/109.37 141.73/109.37 mkBalBranch6Double_R xyw xyx xyy xyz (Branch key_l elt_l vyx fm_ll (Branch key_lr elt_lr vyy fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 xyw xyx fm_lrr fm_r); 141.73/109.37 141.73/109.37 mkBalBranch6MkBalBranch0 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch6MkBalBranch02 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr); 141.73/109.37 141.73/109.37 mkBalBranch6MkBalBranch00 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr True = mkBalBranch6Double_L xyw xyx xyy xyz fm_L fm_R; 141.73/109.37 141.73/109.37 mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr True = mkBalBranch6Single_L xyw xyx xyy xyz fm_L fm_R; 141.73/109.37 mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr False = mkBalBranch6MkBalBranch00 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr otherwise; 141.73/109.37 141.73/109.37 mkBalBranch6MkBalBranch02 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 141.73/109.37 141.73/109.37 mkBalBranch6MkBalBranch1 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch6MkBalBranch12 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr); 141.73/109.37 141.73/109.37 mkBalBranch6MkBalBranch10 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr True = mkBalBranch6Double_R xyw xyx xyy xyz fm_L fm_R; 141.73/109.37 141.73/109.37 mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr True = mkBalBranch6Single_R xyw xyx xyy xyz fm_L fm_R; 141.73/109.37 mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr False = mkBalBranch6MkBalBranch10 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr otherwise; 141.73/109.37 141.73/109.37 mkBalBranch6MkBalBranch12 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 141.73/109.37 141.73/109.37 mkBalBranch6MkBalBranch2 xyw xyx xyy xyz key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; 141.73/109.37 141.73/109.37 mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 xyw xyx xyy xyz fm_L fm_R fm_L; 141.73/109.37 mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 xyw xyx xyy xyz key elt fm_L fm_R otherwise; 141.73/109.37 141.73/109.37 mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 xyw xyx xyy xyz fm_L fm_R fm_R; 141.73/109.37 mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R (mkBalBranch6Size_l xyw xyx xyy xyz > sIZE_RATIO * mkBalBranch6Size_r xyw xyx xyy xyz); 141.73/109.37 141.73/109.37 mkBalBranch6MkBalBranch5 xyw xyx xyy xyz key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; 141.73/109.38 mkBalBranch6MkBalBranch5 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R (mkBalBranch6Size_r xyw xyx xyy xyz > sIZE_RATIO * mkBalBranch6Size_l xyw xyx xyy xyz); 141.73/109.38 141.73/109.38 mkBalBranch6Single_L xyw xyx xyy xyz fm_l (Branch key_r elt_r wuv fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 xyw xyx fm_l fm_rl) fm_rr; 141.73/109.38 141.73/109.38 mkBalBranch6Single_R xyw xyx xyy xyz (Branch key_l elt_l vyw fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 xyw xyx fm_lr fm_r); 141.73/109.38 141.73/109.38 mkBalBranch6Size_l xyw xyx xyy xyz = sizeFM xyy; 141.73/109.38 141.73/109.38 mkBalBranch6Size_r xyw xyx xyy xyz = sizeFM xyz; 141.73/109.38 141.73/109.38 mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 141.73/109.38 mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_l fm_r; 141.73/109.38 141.73/109.38 mkBranchBalance_ok xzu xzv xzw = True; 141.73/109.38 141.73/109.38 mkBranchLeft_ok xzu xzv xzw = mkBranchLeft_ok0 xzu xzv xzw xzu xzw xzu; 141.73/109.38 141.73/109.38 mkBranchLeft_ok0 xzu xzv xzw fm_l key EmptyFM = True; 141.73/109.38 mkBranchLeft_ok0 xzu xzv xzw fm_l key (Branch left_key vww vwx vwy vwz) = mkBranchLeft_ok0Biggest_left_key fm_l < key; 141.73/109.38 141.73/109.38 mkBranchLeft_ok0Biggest_left_key ywx = fst (findMax ywx); 141.73/109.38 141.73/109.38 mkBranchLeft_size xzu xzv xzw = sizeFM xzu; 141.73/109.38 141.73/109.38 mkBranchResult xzx xzy xzz yuu = Branch xzx xzy (mkBranchUnbox xzz yuu xzx (1 + mkBranchLeft_size xzz yuu xzx + mkBranchRight_size xzz yuu xzx)) xzz yuu; 141.73/109.38 141.73/109.38 mkBranchRight_ok xzu xzv xzw = mkBranchRight_ok0 xzu xzv xzw xzv xzw xzv; 141.73/109.38 141.73/109.38 mkBranchRight_ok0 xzu xzv xzw fm_r key EmptyFM = True; 141.73/109.38 mkBranchRight_ok0 xzu xzv xzw fm_r key (Branch right_key vxu vxv vxw vxx) = key < mkBranchRight_ok0Smallest_right_key fm_r; 141.73/109.38 141.73/109.38 mkBranchRight_ok0Smallest_right_key ywy = fst (findMin ywy); 141.73/109.38 141.73/109.38 mkBranchRight_size xzu xzv xzw = sizeFM xzv; 141.73/109.38 141.73/109.38 mkBranchUnbox :: Ord a => -> (FiniteMap a b) ( -> (FiniteMap a b) ( -> a (Int -> Int))); 141.73/109.38 mkBranchUnbox xzu xzv xzw x = x; 141.73/109.38 141.73/109.38 mkVBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 141.73/109.38 mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r; 141.73/109.38 mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM; 141.73/109.38 mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) = mkVBalBranch3 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); 141.73/109.38 141.73/109.38 mkVBalBranch3 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) = mkVBalBranch3MkVBalBranch2 vvv vvw vvx vvy vvz vuv vuw vux vuy vuz key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * mkVBalBranch3Size_l vvv vvw vvx vvy vvz vuv vuw vux vuy vuz < mkVBalBranch3Size_r vvv vvw vvx vvy vvz vuv vuw vux vuy vuz); 141.73/109.38 141.73/109.38 mkVBalBranch3MkVBalBranch0 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBranch 13 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); 141.73/109.38 141.73/109.38 mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vuv vuw vuy (mkVBalBranch key elt vuz (Branch vvv vvw vvx vvy vvz)); 141.73/109.38 mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch3MkVBalBranch0 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz otherwise; 141.73/109.38 141.73/109.38 mkVBalBranch3MkVBalBranch2 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vvv vvw (mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) vvy) vvz; 141.73/109.38 mkVBalBranch3MkVBalBranch2 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * mkVBalBranch3Size_r yuz yvu yvv yvw yvx yvy yvz ywu ywv yww < mkVBalBranch3Size_l yuz yvu yvv yvw yvx yvy yvz ywu ywv yww); 141.73/109.38 141.73/109.38 mkVBalBranch3Size_l yuz yvu yvv yvw yvx yvy yvz ywu ywv yww = sizeFM (Branch yvy yvz ywu ywv yww); 141.73/109.38 141.73/109.38 mkVBalBranch3Size_r yuz yvu yvv yvw yvx yvy yvz ywu ywv yww = sizeFM (Branch yuz yvu yvv yvw yvx); 141.73/109.38 141.73/109.38 mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt; 141.73/109.38 mkVBalBranch4 xuv xuw xux xuy = mkVBalBranch3 xuv xuw xux xuy; 141.73/109.38 141.73/109.38 mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt; 141.73/109.38 mkVBalBranch5 xvu xvv xvw xvx = mkVBalBranch4 xvu xvv xvw xvx; 141.73/109.38 141.73/109.38 plusFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 141.73/109.38 plusFM_C combiner EmptyFM fm2 = fm2; 141.73/109.38 plusFM_C combiner fm1 EmptyFM = fm1; 141.73/109.38 plusFM_C combiner fm1 (Branch split_key elt2 zz left right) = mkVBalBranch split_key (plusFM_CNew_elt fm1 split_key elt2 combiner) (plusFM_C combiner (plusFM_CLts fm1 split_key elt2 combiner) left) (plusFM_C combiner (plusFM_CGts fm1 split_key elt2 combiner) right); 141.73/109.38 141.73/109.38 plusFM_CGts yuv yuw yux yuy = splitGT yuv yuw; 141.73/109.38 141.73/109.38 plusFM_CLts yuv yuw yux yuy = splitLT yuv yuw; 141.73/109.38 141.73/109.38 plusFM_CNew_elt yuv yuw yux yuy = plusFM_CNew_elt0 yuv yuw yux yuy yux yuy (lookupFM yuv yuw); 141.73/109.38 141.73/109.38 plusFM_CNew_elt0 yuv yuw yux yuy elt2 combiner Nothing = elt2; 141.73/109.38 plusFM_CNew_elt0 yuv yuw yux yuy elt2 combiner (Just elt1) = combiner elt1 elt2; 141.73/109.38 141.73/109.38 sIZE_RATIO :: Int; 141.73/109.38 sIZE_RATIO = 5; 141.73/109.38 141.73/109.38 sizeFM :: FiniteMap a b -> Int; 141.73/109.38 sizeFM EmptyFM = 0; 141.73/109.38 sizeFM (Branch wux wuy size wuz wvu) = size; 141.73/109.38 141.73/109.38 splitGT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 141.73/109.38 splitGT EmptyFM split_key = splitGT4 EmptyFM split_key; 141.73/109.38 splitGT (Branch key elt vwu fm_l fm_r) split_key = splitGT3 (Branch key elt vwu fm_l fm_r) split_key; 141.73/109.38 141.73/109.38 splitGT0 key elt vwu fm_l fm_r split_key True = fm_r; 141.73/109.38 141.73/109.38 splitGT1 key elt vwu fm_l fm_r split_key True = mkVBalBranch key elt (splitGT fm_l split_key) fm_r; 141.73/109.38 splitGT1 key elt vwu fm_l fm_r split_key False = splitGT0 key elt vwu fm_l fm_r split_key otherwise; 141.73/109.38 141.73/109.38 splitGT2 key elt vwu fm_l fm_r split_key True = splitGT fm_r split_key; 141.73/109.38 splitGT2 key elt vwu fm_l fm_r split_key False = splitGT1 key elt vwu fm_l fm_r split_key (split_key < key); 141.73/109.38 141.73/109.38 splitGT3 (Branch key elt vwu fm_l fm_r) split_key = splitGT2 key elt vwu fm_l fm_r split_key (split_key > key); 141.73/109.38 141.73/109.38 splitGT4 EmptyFM split_key = emptyFM; 141.73/109.38 splitGT4 xwu xwv = splitGT3 xwu xwv; 141.73/109.38 141.73/109.38 splitLT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 141.73/109.38 splitLT EmptyFM split_key = splitLT4 EmptyFM split_key; 141.73/109.38 splitLT (Branch key elt vwv fm_l fm_r) split_key = splitLT3 (Branch key elt vwv fm_l fm_r) split_key; 141.73/109.38 141.73/109.38 splitLT0 key elt vwv fm_l fm_r split_key True = fm_l; 141.73/109.38 141.73/109.38 splitLT1 key elt vwv fm_l fm_r split_key True = mkVBalBranch key elt fm_l (splitLT fm_r split_key); 141.73/109.38 splitLT1 key elt vwv fm_l fm_r split_key False = splitLT0 key elt vwv fm_l fm_r split_key otherwise; 141.73/109.38 141.73/109.38 splitLT2 key elt vwv fm_l fm_r split_key True = splitLT fm_l split_key; 141.73/109.38 splitLT2 key elt vwv fm_l fm_r split_key False = splitLT1 key elt vwv fm_l fm_r split_key (split_key > key); 141.73/109.38 141.73/109.38 splitLT3 (Branch key elt vwv fm_l fm_r) split_key = splitLT2 key elt vwv fm_l fm_r split_key (split_key < key); 141.73/109.38 141.73/109.38 splitLT4 EmptyFM split_key = emptyFM; 141.73/109.38 splitLT4 xwy xwz = splitLT3 xwy xwz; 141.73/109.38 141.73/109.38 unitFM :: b -> a -> FiniteMap b a; 141.73/109.38 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 141.73/109.38 141.73/109.38 } 141.73/109.38 module Maybe where { 141.73/109.38 import qualified FiniteMap; 141.73/109.38 import qualified Main; 141.73/109.38 import qualified Prelude; 141.73/109.38 } 141.73/109.38 module Main where { 141.73/109.38 import qualified FiniteMap; 141.73/109.38 import qualified Maybe; 141.73/109.38 import qualified Prelude; 141.73/109.38 } 141.73/109.38 141.73/109.38 ---------------------------------------- 141.73/109.38 141.73/109.38 (13) NumRed (SOUND) 141.73/109.38 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 141.73/109.38 ---------------------------------------- 141.73/109.38 141.73/109.38 (14) 141.73/109.38 Obligation: 141.73/109.38 mainModule Main 141.73/109.38 module FiniteMap where { 141.73/109.38 import qualified Main; 141.73/109.38 import qualified Maybe; 141.73/109.38 import qualified Prelude; 141.73/109.38 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 141.73/109.38 141.73/109.38 instance (Eq a, Eq b) => Eq FiniteMap b a where { 141.73/109.38 (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; 141.73/109.38 } 141.73/109.38 addToFM :: Ord b => FiniteMap b a -> b -> a -> FiniteMap b a; 141.73/109.38 addToFM fm key elt = addToFM_C addToFM0 fm key elt; 141.73/109.38 141.73/109.38 addToFM0 old new = new; 141.73/109.38 141.73/109.38 addToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> b -> a -> FiniteMap b a; 141.73/109.38 addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt; 141.73/109.38 addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt; 141.73/109.38 141.73/109.38 addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r; 141.73/109.38 141.73/109.38 addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt); 141.73/109.38 addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise; 141.73/109.38 141.73/109.38 addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r; 141.73/109.38 addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key); 141.73/109.38 141.73/109.38 addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key); 141.73/109.38 141.73/109.38 addToFM_C4 combiner EmptyFM key elt = unitFM key elt; 141.73/109.38 addToFM_C4 wzu wzv wzw wzx = addToFM_C3 wzu wzv wzw wzx; 141.73/109.38 141.73/109.38 emptyFM :: FiniteMap b a; 141.73/109.38 emptyFM = EmptyFM; 141.73/109.38 141.73/109.38 findMax :: FiniteMap b a -> (b,a); 141.73/109.38 findMax (Branch key elt vxy vxz EmptyFM) = (key,elt); 141.73/109.38 findMax (Branch key elt vyu vyv fm_r) = findMax fm_r; 141.73/109.38 141.73/109.38 findMin :: FiniteMap b a -> (b,a); 141.73/109.38 findMin (Branch key elt wvw EmptyFM wvx) = (key,elt); 141.73/109.38 findMin (Branch key elt wvy fm_l wvz) = findMin fm_l; 141.73/109.38 141.73/109.38 fmToList :: FiniteMap b a -> [(b,a)]; 141.73/109.38 fmToList fm = foldFM fmToList0 [] fm; 141.73/109.38 141.73/109.38 fmToList0 key elt rest = (key,elt) : rest; 141.73/109.38 141.73/109.38 foldFM :: (a -> c -> b -> b) -> b -> FiniteMap a c -> b; 141.73/109.38 foldFM k z EmptyFM = z; 141.73/109.38 foldFM k z (Branch key elt wuw fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; 141.73/109.38 141.73/109.38 lookupFM :: Ord a => FiniteMap a b -> a -> Maybe b; 141.73/109.38 lookupFM EmptyFM key = lookupFM4 EmptyFM key; 141.73/109.38 lookupFM (Branch key elt wvv fm_l fm_r) key_to_find = lookupFM3 (Branch key elt wvv fm_l fm_r) key_to_find; 141.73/109.38 141.73/109.38 lookupFM0 key elt wvv fm_l fm_r key_to_find True = Just elt; 141.73/109.38 141.73/109.38 lookupFM1 key elt wvv fm_l fm_r key_to_find True = lookupFM fm_r key_to_find; 141.73/109.38 lookupFM1 key elt wvv fm_l fm_r key_to_find False = lookupFM0 key elt wvv fm_l fm_r key_to_find otherwise; 141.73/109.38 141.73/109.38 lookupFM2 key elt wvv fm_l fm_r key_to_find True = lookupFM fm_l key_to_find; 141.73/109.38 lookupFM2 key elt wvv fm_l fm_r key_to_find False = lookupFM1 key elt wvv fm_l fm_r key_to_find (key_to_find > key); 141.73/109.38 141.73/109.38 lookupFM3 (Branch key elt wvv fm_l fm_r) key_to_find = lookupFM2 key elt wvv fm_l fm_r key_to_find (key_to_find < key); 141.73/109.38 141.73/109.38 lookupFM4 EmptyFM key = Nothing; 141.73/109.38 lookupFM4 xxy xxz = lookupFM3 xxy xxz; 141.73/109.38 141.73/109.38 mkBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 141.73/109.38 mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R; 141.73/109.38 141.73/109.38 mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 key elt fm_L fm_R key elt fm_L fm_R (mkBalBranch6Size_l key elt fm_L fm_R + mkBalBranch6Size_r key elt fm_L fm_R < Pos (Succ (Succ Zero))); 141.73/109.38 141.73/109.38 mkBalBranch6Double_L xyw xyx xyy xyz fm_l (Branch key_r elt_r vzw (Branch key_rl elt_rl vzx fm_rll fm_rlr) fm_rr) = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) key_rl elt_rl (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) xyw xyx fm_l fm_rll) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) key_r elt_r fm_rlr fm_rr); 141.73/109.38 141.73/109.38 mkBalBranch6Double_R xyw xyx xyy xyz (Branch key_l elt_l vyx fm_ll (Branch key_lr elt_lr vyy fm_lrl fm_lrr)) fm_r = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) key_lr elt_lr (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))) key_l elt_l fm_ll fm_lrl) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) xyw xyx fm_lrr fm_r); 141.73/109.38 141.73/109.38 mkBalBranch6MkBalBranch0 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch6MkBalBranch02 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr); 141.73/109.38 141.73/109.38 mkBalBranch6MkBalBranch00 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr True = mkBalBranch6Double_L xyw xyx xyy xyz fm_L fm_R; 141.73/109.38 141.73/109.38 mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr True = mkBalBranch6Single_L xyw xyx xyy xyz fm_L fm_R; 141.73/109.38 mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr False = mkBalBranch6MkBalBranch00 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr otherwise; 141.73/109.38 141.73/109.38 mkBalBranch6MkBalBranch02 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr (sizeFM fm_rl < Pos (Succ (Succ Zero)) * sizeFM fm_rr); 141.73/109.38 141.73/109.38 mkBalBranch6MkBalBranch1 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch6MkBalBranch12 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr); 141.73/109.38 141.73/109.38 mkBalBranch6MkBalBranch10 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr True = mkBalBranch6Double_R xyw xyx xyy xyz fm_L fm_R; 141.73/109.38 141.73/109.38 mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr True = mkBalBranch6Single_R xyw xyx xyy xyz fm_L fm_R; 141.73/109.38 mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr False = mkBalBranch6MkBalBranch10 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr otherwise; 141.73/109.38 141.73/109.38 mkBalBranch6MkBalBranch12 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr (sizeFM fm_lr < Pos (Succ (Succ Zero)) * sizeFM fm_ll); 141.73/109.38 141.73/109.38 mkBalBranch6MkBalBranch2 xyw xyx xyy xyz key elt fm_L fm_R True = mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R; 141.73/109.38 141.73/109.38 mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 xyw xyx xyy xyz fm_L fm_R fm_L; 141.73/109.38 mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 xyw xyx xyy xyz key elt fm_L fm_R otherwise; 141.73/109.38 141.73/109.38 mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 xyw xyx xyy xyz fm_L fm_R fm_R; 141.73/109.38 mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R (mkBalBranch6Size_l xyw xyx xyy xyz > sIZE_RATIO * mkBalBranch6Size_r xyw xyx xyy xyz); 141.73/109.38 141.73/109.38 mkBalBranch6MkBalBranch5 xyw xyx xyy xyz key elt fm_L fm_R True = mkBranch (Pos (Succ Zero)) key elt fm_L fm_R; 141.73/109.38 mkBalBranch6MkBalBranch5 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R (mkBalBranch6Size_r xyw xyx xyy xyz > sIZE_RATIO * mkBalBranch6Size_l xyw xyx xyy xyz); 141.73/109.38 141.73/109.38 mkBalBranch6Single_L xyw xyx xyy xyz fm_l (Branch key_r elt_r wuv fm_rl fm_rr) = mkBranch (Pos (Succ (Succ (Succ Zero)))) key_r elt_r (mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) xyw xyx fm_l fm_rl) fm_rr; 141.73/109.38 141.73/109.38 mkBalBranch6Single_R xyw xyx xyy xyz (Branch key_l elt_l vyw fm_ll fm_lr) fm_r = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))) key_l elt_l fm_ll (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))) xyw xyx fm_lr fm_r); 141.73/109.38 141.73/109.38 mkBalBranch6Size_l xyw xyx xyy xyz = sizeFM xyy; 141.73/109.38 141.73/109.38 mkBalBranch6Size_r xyw xyx xyy xyz = sizeFM xyz; 141.73/109.38 141.73/109.38 mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 141.73/109.38 mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_l fm_r; 141.73/109.38 141.73/109.38 mkBranchBalance_ok xzu xzv xzw = True; 141.73/109.38 141.73/109.38 mkBranchLeft_ok xzu xzv xzw = mkBranchLeft_ok0 xzu xzv xzw xzu xzw xzu; 141.73/109.38 141.73/109.38 mkBranchLeft_ok0 xzu xzv xzw fm_l key EmptyFM = True; 141.73/109.38 mkBranchLeft_ok0 xzu xzv xzw fm_l key (Branch left_key vww vwx vwy vwz) = mkBranchLeft_ok0Biggest_left_key fm_l < key; 141.73/109.38 141.73/109.38 mkBranchLeft_ok0Biggest_left_key ywx = fst (findMax ywx); 141.73/109.38 141.73/109.38 mkBranchLeft_size xzu xzv xzw = sizeFM xzu; 141.73/109.38 141.73/109.38 mkBranchResult xzx xzy xzz yuu = Branch xzx xzy (mkBranchUnbox xzz yuu xzx (Pos (Succ Zero) + mkBranchLeft_size xzz yuu xzx + mkBranchRight_size xzz yuu xzx)) xzz yuu; 141.73/109.38 141.73/109.38 mkBranchRight_ok xzu xzv xzw = mkBranchRight_ok0 xzu xzv xzw xzv xzw xzv; 141.73/109.38 141.73/109.38 mkBranchRight_ok0 xzu xzv xzw fm_r key EmptyFM = True; 141.73/109.38 mkBranchRight_ok0 xzu xzv xzw fm_r key (Branch right_key vxu vxv vxw vxx) = key < mkBranchRight_ok0Smallest_right_key fm_r; 141.73/109.38 141.73/109.38 mkBranchRight_ok0Smallest_right_key ywy = fst (findMin ywy); 141.73/109.38 141.73/109.38 mkBranchRight_size xzu xzv xzw = sizeFM xzv; 141.73/109.38 141.73/109.38 mkBranchUnbox :: Ord a => -> (FiniteMap a b) ( -> (FiniteMap a b) ( -> a (Int -> Int))); 141.73/109.38 mkBranchUnbox xzu xzv xzw x = x; 141.73/109.38 141.73/109.38 mkVBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 141.73/109.38 mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r; 141.73/109.38 mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM; 141.73/109.38 mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) = mkVBalBranch3 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); 141.73/109.38 141.73/109.38 mkVBalBranch3 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) = mkVBalBranch3MkVBalBranch2 vvv vvw vvx vvy vvz vuv vuw vux vuy vuz key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * mkVBalBranch3Size_l vvv vvw vvx vvy vvz vuv vuw vux vuy vuz < mkVBalBranch3Size_r vvv vvw vvx vvy vvz vuv vuw vux vuy vuz); 141.73/109.38 141.73/109.38 mkVBalBranch3MkVBalBranch0 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); 141.73/109.38 141.73/109.38 mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vuv vuw vuy (mkVBalBranch key elt vuz (Branch vvv vvw vvx vvy vvz)); 141.73/109.38 mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch3MkVBalBranch0 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz otherwise; 141.73/109.38 141.73/109.38 mkVBalBranch3MkVBalBranch2 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vvv vvw (mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) vvy) vvz; 141.73/109.38 mkVBalBranch3MkVBalBranch2 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * mkVBalBranch3Size_r yuz yvu yvv yvw yvx yvy yvz ywu ywv yww < mkVBalBranch3Size_l yuz yvu yvv yvw yvx yvy yvz ywu ywv yww); 141.73/109.38 141.73/109.38 mkVBalBranch3Size_l yuz yvu yvv yvw yvx yvy yvz ywu ywv yww = sizeFM (Branch yvy yvz ywu ywv yww); 141.73/109.38 141.73/109.38 mkVBalBranch3Size_r yuz yvu yvv yvw yvx yvy yvz ywu ywv yww = sizeFM (Branch yuz yvu yvv yvw yvx); 141.73/109.38 141.73/109.38 mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt; 141.73/109.38 mkVBalBranch4 xuv xuw xux xuy = mkVBalBranch3 xuv xuw xux xuy; 141.73/109.38 141.73/109.38 mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt; 141.73/109.38 mkVBalBranch5 xvu xvv xvw xvx = mkVBalBranch4 xvu xvv xvw xvx; 141.73/109.38 141.73/109.38 plusFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 141.73/109.38 plusFM_C combiner EmptyFM fm2 = fm2; 141.73/109.38 plusFM_C combiner fm1 EmptyFM = fm1; 141.73/109.38 plusFM_C combiner fm1 (Branch split_key elt2 zz left right) = mkVBalBranch split_key (plusFM_CNew_elt fm1 split_key elt2 combiner) (plusFM_C combiner (plusFM_CLts fm1 split_key elt2 combiner) left) (plusFM_C combiner (plusFM_CGts fm1 split_key elt2 combiner) right); 141.73/109.38 141.73/109.38 plusFM_CGts yuv yuw yux yuy = splitGT yuv yuw; 141.73/109.38 141.73/109.38 plusFM_CLts yuv yuw yux yuy = splitLT yuv yuw; 141.73/109.38 141.73/109.38 plusFM_CNew_elt yuv yuw yux yuy = plusFM_CNew_elt0 yuv yuw yux yuy yux yuy (lookupFM yuv yuw); 141.73/109.38 141.73/109.38 plusFM_CNew_elt0 yuv yuw yux yuy elt2 combiner Nothing = elt2; 141.73/109.38 plusFM_CNew_elt0 yuv yuw yux yuy elt2 combiner (Just elt1) = combiner elt1 elt2; 141.73/109.38 141.73/109.38 sIZE_RATIO :: Int; 141.73/109.38 sIZE_RATIO = Pos (Succ (Succ (Succ (Succ (Succ Zero))))); 141.73/109.38 141.73/109.38 sizeFM :: FiniteMap a b -> Int; 141.73/109.38 sizeFM EmptyFM = Pos Zero; 141.73/109.38 sizeFM (Branch wux wuy size wuz wvu) = size; 141.73/109.38 141.73/109.38 splitGT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; 141.73/109.38 splitGT EmptyFM split_key = splitGT4 EmptyFM split_key; 141.73/109.38 splitGT (Branch key elt vwu fm_l fm_r) split_key = splitGT3 (Branch key elt vwu fm_l fm_r) split_key; 141.73/109.38 141.73/109.38 splitGT0 key elt vwu fm_l fm_r split_key True = fm_r; 141.73/109.38 141.73/109.38 splitGT1 key elt vwu fm_l fm_r split_key True = mkVBalBranch key elt (splitGT fm_l split_key) fm_r; 141.73/109.38 splitGT1 key elt vwu fm_l fm_r split_key False = splitGT0 key elt vwu fm_l fm_r split_key otherwise; 141.73/109.38 141.73/109.38 splitGT2 key elt vwu fm_l fm_r split_key True = splitGT fm_r split_key; 141.73/109.38 splitGT2 key elt vwu fm_l fm_r split_key False = splitGT1 key elt vwu fm_l fm_r split_key (split_key < key); 141.73/109.38 141.73/109.38 splitGT3 (Branch key elt vwu fm_l fm_r) split_key = splitGT2 key elt vwu fm_l fm_r split_key (split_key > key); 141.73/109.38 141.73/109.38 splitGT4 EmptyFM split_key = emptyFM; 141.73/109.38 splitGT4 xwu xwv = splitGT3 xwu xwv; 141.73/109.38 141.73/109.38 splitLT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; 141.73/109.38 splitLT EmptyFM split_key = splitLT4 EmptyFM split_key; 141.73/109.38 splitLT (Branch key elt vwv fm_l fm_r) split_key = splitLT3 (Branch key elt vwv fm_l fm_r) split_key; 141.73/109.38 141.73/109.38 splitLT0 key elt vwv fm_l fm_r split_key True = fm_l; 141.73/109.38 141.73/109.38 splitLT1 key elt vwv fm_l fm_r split_key True = mkVBalBranch key elt fm_l (splitLT fm_r split_key); 141.73/109.38 splitLT1 key elt vwv fm_l fm_r split_key False = splitLT0 key elt vwv fm_l fm_r split_key otherwise; 141.73/109.38 141.73/109.38 splitLT2 key elt vwv fm_l fm_r split_key True = splitLT fm_l split_key; 141.73/109.38 splitLT2 key elt vwv fm_l fm_r split_key False = splitLT1 key elt vwv fm_l fm_r split_key (split_key > key); 141.73/109.38 141.73/109.38 splitLT3 (Branch key elt vwv fm_l fm_r) split_key = splitLT2 key elt vwv fm_l fm_r split_key (split_key < key); 141.73/109.38 141.73/109.38 splitLT4 EmptyFM split_key = emptyFM; 141.73/109.38 splitLT4 xwy xwz = splitLT3 xwy xwz; 141.73/109.38 141.73/109.38 unitFM :: a -> b -> FiniteMap a b; 141.73/109.38 unitFM key elt = Branch key elt (Pos (Succ Zero)) emptyFM emptyFM; 141.73/109.38 141.73/109.38 } 141.73/109.38 module Maybe where { 141.73/109.38 import qualified FiniteMap; 141.73/109.38 import qualified Main; 141.73/109.38 import qualified Prelude; 141.73/109.38 } 141.73/109.38 module Main where { 141.73/109.38 import qualified FiniteMap; 141.73/109.38 import qualified Maybe; 141.73/109.38 import qualified Prelude; 141.73/109.38 } 141.73/109.42 EOF