106.30/73.66 MAYBE 108.59/74.35 proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs 108.59/74.35 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 108.59/74.35 108.59/74.35 108.59/74.35 H-Termination with start terms of the given HASKELL could not be shown: 108.59/74.35 108.59/74.35 (0) HASKELL 108.59/74.35 (1) CR [EQUIVALENT, 0 ms] 108.59/74.35 (2) HASKELL 108.59/74.35 (3) BR [EQUIVALENT, 0 ms] 108.59/74.35 (4) HASKELL 108.59/74.35 (5) COR [EQUIVALENT, 26 ms] 108.59/74.35 (6) HASKELL 108.59/74.35 (7) LetRed [EQUIVALENT, 0 ms] 108.59/74.35 (8) HASKELL 108.59/74.35 (9) NumRed [SOUND, 0 ms] 108.59/74.35 (10) HASKELL 108.59/74.35 108.59/74.35 108.59/74.35 ---------------------------------------- 108.59/74.35 108.59/74.35 (0) 108.59/74.35 Obligation: 108.59/74.35 mainModule Main 108.59/74.35 module FiniteMap where { 108.59/74.35 import qualified Main; 108.59/74.35 import qualified Maybe; 108.59/74.35 import qualified Prelude; 108.59/74.35 data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; 108.59/74.35 108.59/74.35 instance (Eq a, Eq b) => Eq FiniteMap b a where { 108.59/74.35 } 108.59/74.35 addListToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> [(b,a)] -> FiniteMap b a; 108.59/74.35 addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 108.59/74.35 add fmap (key,elt) = addToFM_C combiner fmap key elt; 108.59/74.35 }; 108.59/74.35 108.59/74.35 addToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> b -> a -> FiniteMap b a; 108.59/74.35 addToFM_C combiner EmptyFM key elt = unitFM key elt; 108.59/74.35 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 108.59/74.35 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) 108.59/74.35 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; 108.59/74.35 108.59/74.35 emptyFM :: FiniteMap a b; 108.59/74.35 emptyFM = EmptyFM; 108.59/74.35 108.59/74.35 findMax :: FiniteMap b a -> (b,a); 108.59/74.35 findMax (Branch key elt _ _ EmptyFM) = (key,elt); 108.59/74.35 findMax (Branch key elt _ _ fm_r) = findMax fm_r; 108.59/74.35 108.59/74.35 findMin :: FiniteMap a b -> (a,b); 108.59/74.35 findMin (Branch key elt _ EmptyFM _) = (key,elt); 108.59/74.35 findMin (Branch key elt _ fm_l _) = findMin fm_l; 108.59/74.35 108.59/74.35 mkBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 108.59/74.35 mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R 108.59/74.35 | size_r > sIZE_RATIO * size_l = case fm_R of { 108.59/74.35 Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R 108.59/74.35 | otherwise -> double_L fm_L fm_R; 108.59/74.35 } 108.59/74.35 | size_l > sIZE_RATIO * size_r = case fm_L of { 108.59/74.35 Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R 108.59/74.35 | otherwise -> double_R fm_L fm_R; 108.59/74.35 } 108.59/74.35 | otherwise = mkBranch 2 key elt fm_L fm_R where { 108.59/74.35 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); 108.59/74.35 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); 108.59/74.35 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; 108.59/74.35 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); 108.59/74.35 size_l = sizeFM fm_L; 108.59/74.35 size_r = sizeFM fm_R; 108.59/74.35 }; 108.59/74.35 108.59/74.35 mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 108.59/74.35 mkBranch which key elt fm_l fm_r = let { 108.59/74.35 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 108.59/74.35 } in result where { 108.59/74.35 balance_ok = True; 108.59/74.35 left_ok = case fm_l of { 108.59/74.35 EmptyFM-> True; 108.59/74.35 Branch left_key _ _ _ _-> let { 108.59/74.35 biggest_left_key = fst (findMax fm_l); 108.59/74.35 } in biggest_left_key < key; 108.59/74.35 } ; 108.59/74.35 left_size = sizeFM fm_l; 108.59/74.35 right_ok = case fm_r of { 108.59/74.35 EmptyFM-> True; 108.59/74.35 Branch right_key _ _ _ _-> let { 108.59/74.35 smallest_right_key = fst (findMin fm_r); 108.59/74.35 } in key < smallest_right_key; 108.59/74.35 } ; 108.59/74.35 right_size = sizeFM fm_r; 108.59/74.35 unbox :: Int -> Int; 108.59/74.35 unbox x = x; 108.59/74.35 }; 108.59/74.35 108.59/74.35 sIZE_RATIO :: Int; 108.59/74.35 sIZE_RATIO = 5; 108.59/74.35 108.59/74.35 sizeFM :: FiniteMap a b -> Int; 108.59/74.35 sizeFM EmptyFM = 0; 108.59/74.35 sizeFM (Branch _ _ size _ _) = size; 108.59/74.35 108.59/74.35 unitFM :: b -> a -> FiniteMap b a; 108.59/74.35 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 108.59/74.35 108.59/74.35 } 108.59/74.35 module Maybe where { 108.59/74.35 import qualified FiniteMap; 108.59/74.35 import qualified Main; 108.59/74.35 import qualified Prelude; 108.59/74.35 } 108.59/74.35 module Main where { 108.59/74.35 import qualified FiniteMap; 108.59/74.35 import qualified Maybe; 108.59/74.35 import qualified Prelude; 108.59/74.35 } 108.59/74.35 108.59/74.35 ---------------------------------------- 108.59/74.35 108.59/74.35 (1) CR (EQUIVALENT) 108.59/74.35 Case Reductions: 108.59/74.35 The following Case expression 108.59/74.35 "case fm_r of { 108.59/74.35 EmptyFM -> True; 108.59/74.35 Branch right_key _ _ _ _ -> let { 108.59/74.35 smallest_right_key = fst (findMin fm_r); 108.59/74.35 } in key < smallest_right_key} 108.59/74.35 " 108.59/74.35 is transformed to 108.59/74.35 "right_ok0 fm_r key EmptyFM = True; 108.59/74.35 right_ok0 fm_r key (Branch right_key _ _ _ _) = let { 108.59/74.35 smallest_right_key = fst (findMin fm_r); 108.59/74.35 } in key < smallest_right_key; 108.59/74.35 " 108.59/74.35 The following Case expression 108.59/74.35 "case fm_l of { 108.59/74.35 EmptyFM -> True; 108.59/74.35 Branch left_key _ _ _ _ -> let { 108.59/74.35 biggest_left_key = fst (findMax fm_l); 108.59/74.35 } in biggest_left_key < key} 108.59/74.35 " 108.59/74.35 is transformed to 108.59/74.35 "left_ok0 fm_l key EmptyFM = True; 108.59/74.35 left_ok0 fm_l key (Branch left_key _ _ _ _) = let { 108.59/74.35 biggest_left_key = fst (findMax fm_l); 108.59/74.35 } in biggest_left_key < key; 108.59/74.35 " 108.59/74.35 The following Case expression 108.59/74.35 "case fm_R of { 108.59/74.35 Branch _ _ _ fm_rl fm_rr |sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R} 108.59/74.35 " 108.59/74.35 is transformed to 108.59/74.35 "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; 108.59/74.35 " 108.59/74.35 The following Case expression 108.59/74.35 "case fm_L of { 108.59/74.35 Branch _ _ _ fm_ll fm_lr |sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R} 108.59/74.35 " 108.59/74.35 is transformed to 108.59/74.35 "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; 108.59/74.35 " 108.59/74.35 108.59/74.35 ---------------------------------------- 108.59/74.35 108.59/74.35 (2) 108.59/74.35 Obligation: 108.59/74.35 mainModule Main 108.59/74.35 module FiniteMap where { 108.59/74.35 import qualified Main; 108.59/74.35 import qualified Maybe; 108.59/74.35 import qualified Prelude; 108.59/74.35 data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; 108.59/74.35 108.59/74.35 instance (Eq a, Eq b) => Eq FiniteMap a b where { 108.59/74.35 } 108.59/74.35 addListToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> [(b,a)] -> FiniteMap b a; 108.59/74.35 addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 108.59/74.35 add fmap (key,elt) = addToFM_C combiner fmap key elt; 108.59/74.35 }; 108.59/74.35 108.59/74.35 addToFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> a -> b -> FiniteMap a b; 108.59/74.35 addToFM_C combiner EmptyFM key elt = unitFM key elt; 108.59/74.35 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 108.59/74.35 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) 108.59/74.35 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; 108.59/74.35 108.59/74.35 emptyFM :: FiniteMap b a; 108.59/74.35 emptyFM = EmptyFM; 108.59/74.35 108.59/74.35 findMax :: FiniteMap b a -> (b,a); 108.59/74.35 findMax (Branch key elt _ _ EmptyFM) = (key,elt); 108.59/74.35 findMax (Branch key elt _ _ fm_r) = findMax fm_r; 108.59/74.35 108.59/74.35 findMin :: FiniteMap a b -> (a,b); 108.59/74.35 findMin (Branch key elt _ EmptyFM _) = (key,elt); 108.59/74.35 findMin (Branch key elt _ fm_l _) = findMin fm_l; 108.59/74.35 108.59/74.35 mkBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 108.59/74.35 mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R 108.59/74.35 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R 108.59/74.35 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L 108.59/74.35 | otherwise = mkBranch 2 key elt fm_L fm_R where { 108.59/74.35 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); 108.59/74.35 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); 108.59/74.35 mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr) | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R 108.59/74.35 | otherwise = double_L fm_L fm_R; 108.59/74.35 mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr) | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R 108.59/74.35 | otherwise = double_R fm_L fm_R; 108.59/74.35 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; 108.59/74.35 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); 108.59/74.35 size_l = sizeFM fm_L; 108.59/74.35 size_r = sizeFM fm_R; 108.59/74.35 }; 108.59/74.35 108.59/74.35 mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 108.59/74.35 mkBranch which key elt fm_l fm_r = let { 108.59/74.35 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 108.59/74.35 } in result where { 108.59/74.35 balance_ok = True; 108.59/74.35 left_ok = left_ok0 fm_l key fm_l; 108.59/74.35 left_ok0 fm_l key EmptyFM = True; 108.59/74.35 left_ok0 fm_l key (Branch left_key _ _ _ _) = let { 108.59/74.35 biggest_left_key = fst (findMax fm_l); 108.59/74.35 } in biggest_left_key < key; 108.59/74.35 left_size = sizeFM fm_l; 108.59/74.35 right_ok = right_ok0 fm_r key fm_r; 108.59/74.35 right_ok0 fm_r key EmptyFM = True; 108.59/74.35 right_ok0 fm_r key (Branch right_key _ _ _ _) = let { 108.59/74.35 smallest_right_key = fst (findMin fm_r); 108.59/74.35 } in key < smallest_right_key; 108.59/74.35 right_size = sizeFM fm_r; 108.59/74.35 unbox :: Int -> Int; 108.59/74.35 unbox x = x; 108.59/74.35 }; 108.59/74.35 108.59/74.35 sIZE_RATIO :: Int; 108.59/74.35 sIZE_RATIO = 5; 108.59/74.35 108.59/74.35 sizeFM :: FiniteMap a b -> Int; 108.59/74.35 sizeFM EmptyFM = 0; 108.59/74.35 sizeFM (Branch _ _ size _ _) = size; 108.59/74.35 108.59/74.35 unitFM :: a -> b -> FiniteMap a b; 108.59/74.35 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 108.59/74.35 108.59/74.35 } 108.59/74.35 module Maybe where { 108.59/74.35 import qualified FiniteMap; 108.59/74.35 import qualified Main; 108.59/74.35 import qualified Prelude; 108.59/74.35 } 108.59/74.35 module Main where { 108.59/74.35 import qualified FiniteMap; 108.59/74.35 import qualified Maybe; 108.59/74.35 import qualified Prelude; 108.59/74.35 } 108.59/74.35 108.59/74.35 ---------------------------------------- 108.59/74.35 108.59/74.35 (3) BR (EQUIVALENT) 108.59/74.35 Replaced joker patterns by fresh variables and removed binding patterns. 108.59/74.35 ---------------------------------------- 108.59/74.35 108.59/74.35 (4) 108.59/74.35 Obligation: 108.59/74.35 mainModule Main 108.59/74.35 module FiniteMap where { 108.59/74.35 import qualified Main; 108.59/74.35 import qualified Maybe; 108.59/74.35 import qualified Prelude; 108.59/74.35 data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; 108.59/74.35 108.59/74.35 instance (Eq a, Eq b) => Eq FiniteMap b a where { 108.59/74.35 } 108.59/74.35 addListToFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> [(a,b)] -> FiniteMap a b; 108.59/74.35 addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 108.59/74.35 add fmap (key,elt) = addToFM_C combiner fmap key elt; 108.59/74.35 }; 108.59/74.35 108.59/74.35 addToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> b -> a -> FiniteMap b a; 108.59/74.35 addToFM_C combiner EmptyFM key elt = unitFM key elt; 108.59/74.35 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 108.59/74.35 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) 108.59/74.35 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; 108.59/74.35 108.59/74.35 emptyFM :: FiniteMap b a; 108.59/74.35 emptyFM = EmptyFM; 108.59/74.35 108.59/74.35 findMax :: FiniteMap b a -> (b,a); 108.59/74.35 findMax (Branch key elt yx yy EmptyFM) = (key,elt); 108.59/74.35 findMax (Branch key elt yz zu fm_r) = findMax fm_r; 108.59/74.35 108.59/74.35 findMin :: FiniteMap a b -> (a,b); 108.59/74.35 findMin (Branch key elt wx EmptyFM wy) = (key,elt); 108.59/74.35 findMin (Branch key elt wz fm_l xu) = findMin fm_l; 108.59/74.35 108.59/74.35 mkBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 108.59/74.35 mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R 108.59/74.35 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R 108.59/74.35 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L 108.59/74.35 | otherwise = mkBranch 2 key elt fm_L fm_R where { 108.59/74.35 double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw 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); 108.59/74.35 double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx 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); 108.59/74.35 mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R 108.59/74.35 | otherwise = double_L fm_L fm_R; 108.59/74.35 mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R 108.59/74.35 | otherwise = double_R fm_L fm_R; 108.59/74.35 single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 108.59/74.35 single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 108.59/74.35 size_l = sizeFM fm_L; 108.59/74.35 size_r = sizeFM fm_R; 108.59/74.35 }; 108.59/74.35 108.59/74.35 mkBranch :: Ord a => Int -> a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 108.59/74.35 mkBranch which key elt fm_l fm_r = let { 108.59/74.35 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 108.59/74.35 } in result where { 108.59/74.35 balance_ok = True; 108.59/74.35 left_ok = left_ok0 fm_l key fm_l; 108.59/74.35 left_ok0 fm_l key EmptyFM = True; 108.59/74.35 left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 108.59/74.35 biggest_left_key = fst (findMax fm_l); 108.59/74.35 } in biggest_left_key < key; 108.59/74.35 left_size = sizeFM fm_l; 108.59/74.35 right_ok = right_ok0 fm_r key fm_r; 108.59/74.35 right_ok0 fm_r key EmptyFM = True; 108.59/74.35 right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 108.59/74.35 smallest_right_key = fst (findMin fm_r); 108.59/74.35 } in key < smallest_right_key; 108.59/74.35 right_size = sizeFM fm_r; 108.59/74.35 unbox :: Int -> Int; 108.59/74.35 unbox x = x; 108.59/74.35 }; 108.59/74.35 108.59/74.35 sIZE_RATIO :: Int; 108.59/74.35 sIZE_RATIO = 5; 108.59/74.35 108.59/74.35 sizeFM :: FiniteMap b a -> Int; 108.59/74.35 sizeFM EmptyFM = 0; 108.59/74.35 sizeFM (Branch vz wu size wv ww) = size; 108.59/74.35 108.59/74.35 unitFM :: b -> a -> FiniteMap b a; 108.59/74.35 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 108.59/74.35 108.59/74.35 } 108.59/74.35 module Maybe where { 108.59/74.35 import qualified FiniteMap; 108.59/74.35 import qualified Main; 108.59/74.35 import qualified Prelude; 108.59/74.35 } 108.59/74.35 module Main where { 108.59/74.35 import qualified FiniteMap; 108.59/74.35 import qualified Maybe; 108.59/74.35 import qualified Prelude; 108.59/74.35 } 108.59/74.35 108.59/74.35 ---------------------------------------- 108.59/74.35 108.59/74.35 (5) COR (EQUIVALENT) 108.59/74.35 Cond Reductions: 108.59/74.35 The following Function with conditions 108.59/74.35 "compare x y|x == yEQ|x <= yLT|otherwiseGT; 108.59/74.35 " 108.59/74.35 is transformed to 108.59/74.35 "compare x y = compare3 x y; 108.59/74.35 " 108.59/74.35 "compare1 x y True = LT; 108.59/74.35 compare1 x y False = compare0 x y otherwise; 108.59/74.35 " 108.59/74.35 "compare2 x y True = EQ; 108.59/74.35 compare2 x y False = compare1 x y (x <= y); 108.59/74.35 " 108.59/74.35 "compare0 x y True = GT; 108.59/74.35 " 108.59/74.35 "compare3 x y = compare2 x y (x == y); 108.59/74.35 " 108.59/74.35 The following Function with conditions 108.59/74.35 "undefined |Falseundefined; 108.59/74.35 " 108.59/74.35 is transformed to 108.59/74.35 "undefined = undefined1; 108.59/74.35 " 108.59/74.35 "undefined0 True = undefined; 108.59/74.35 " 108.59/74.35 "undefined1 = undefined0 False; 108.59/74.35 " 108.59/74.35 The following Function with conditions 108.59/74.35 "addToFM_C combiner EmptyFM key elt = unitFM key elt; 108.59/74.35 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; 108.59/74.35 " 108.59/74.35 is transformed to 108.59/74.35 "addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt; 108.59/74.35 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; 108.59/74.35 " 108.59/74.35 "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; 108.59/74.35 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); 108.59/74.35 " 108.59/74.35 "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); 108.59/74.35 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; 108.59/74.35 " 108.59/74.35 "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; 108.59/74.35 " 108.59/74.35 "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); 108.59/74.35 " 108.59/74.35 "addToFM_C4 combiner EmptyFM key elt = unitFM key elt; 108.59/74.35 addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu; 108.59/74.35 " 108.59/74.35 The following Function with conditions 108.59/74.35 "mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R; 108.59/74.35 " 108.59/74.35 is transformed to 108.59/74.35 "mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr); 108.59/74.35 " 108.59/74.35 "mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R; 108.59/74.35 mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr otherwise; 108.59/74.35 " 108.59/74.35 "mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R; 108.59/74.35 " 108.59/74.35 "mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 108.59/74.35 " 108.59/74.35 The following Function with conditions 108.59/74.35 "mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R; 108.59/74.35 " 108.59/74.35 is transformed to 108.59/74.35 "mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr); 108.59/74.35 " 108.59/74.35 "mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R; 108.59/74.35 " 108.59/74.35 "mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R; 108.59/74.35 mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise; 108.59/74.35 " 108.59/74.35 "mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 108.59/74.35 " 108.59/74.35 The following Function with conditions 108.59/74.35 "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 { 108.59/74.35 double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw 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); 108.59/74.35 ; 108.59/74.35 double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx 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); 108.59/74.35 ; 108.59/74.35 mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R; 108.59/74.35 ; 108.59/74.35 mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R; 108.59/74.35 ; 108.59/74.35 single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 108.59/74.35 ; 108.59/74.35 single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 108.59/74.35 ; 108.59/74.35 size_l = sizeFM fm_L; 108.59/74.35 ; 108.59/74.35 size_r = sizeFM fm_R; 108.59/74.35 } 108.59/74.35 ; 108.59/74.35 " 108.59/74.35 is transformed to 108.59/74.35 "mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R; 108.59/74.35 " 108.59/74.35 "mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { 108.59/74.35 double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw 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); 108.59/74.35 ; 108.59/74.35 double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx 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); 108.59/74.35 ; 108.59/74.35 mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr); 108.59/74.35 ; 108.59/74.35 mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R; 108.59/74.35 ; 108.59/74.35 mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R; 108.59/74.35 mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise; 108.59/74.35 ; 108.59/74.35 mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 108.59/74.35 ; 108.59/74.35 mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr); 108.59/74.35 ; 108.59/74.35 mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R; 108.59/74.35 ; 108.59/74.35 mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R; 108.59/74.35 mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr otherwise; 108.59/74.35 ; 108.59/74.35 mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 108.59/74.35 ; 108.59/74.35 mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; 108.59/74.35 ; 108.59/74.35 mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L; 108.59/74.35 mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise; 108.59/74.35 ; 108.59/74.35 mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R; 108.59/74.35 mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r); 108.59/74.35 ; 108.59/74.35 mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; 108.59/74.35 mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l); 108.59/74.35 ; 108.59/74.35 single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 108.59/74.35 ; 108.59/74.35 single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 108.59/74.35 ; 108.59/74.35 size_l = sizeFM fm_L; 108.59/74.35 ; 108.59/74.35 size_r = sizeFM fm_R; 108.59/74.35 } 108.59/74.35 ; 108.59/74.35 " 108.59/74.35 108.59/74.35 ---------------------------------------- 108.59/74.35 108.59/74.35 (6) 108.59/74.35 Obligation: 108.59/74.35 mainModule Main 108.59/74.35 module FiniteMap where { 108.59/74.35 import qualified Main; 108.59/74.35 import qualified Maybe; 108.59/74.35 import qualified Prelude; 108.59/74.35 data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; 108.59/74.35 108.59/74.35 instance (Eq a, Eq b) => Eq FiniteMap a b where { 108.59/74.35 } 108.59/74.35 addListToFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> [(a,b)] -> FiniteMap a b; 108.59/74.35 addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 108.59/74.35 add fmap (key,elt) = addToFM_C combiner fmap key elt; 108.59/74.35 }; 108.59/74.35 108.59/74.35 addToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> b -> a -> FiniteMap b a; 108.59/74.35 addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt; 108.59/74.35 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; 108.59/74.35 108.59/74.35 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; 108.59/74.35 108.59/74.35 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); 108.59/74.35 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; 108.59/74.35 108.59/74.35 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; 108.59/74.35 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); 108.59/74.35 108.59/74.35 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); 108.59/74.35 108.59/74.35 addToFM_C4 combiner EmptyFM key elt = unitFM key elt; 108.59/74.35 addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu; 108.59/74.35 108.59/74.35 emptyFM :: FiniteMap a b; 108.59/74.35 emptyFM = EmptyFM; 108.59/74.35 108.59/74.35 findMax :: FiniteMap a b -> (a,b); 108.59/74.35 findMax (Branch key elt yx yy EmptyFM) = (key,elt); 108.59/74.35 findMax (Branch key elt yz zu fm_r) = findMax fm_r; 108.59/74.35 108.59/74.35 findMin :: FiniteMap b a -> (b,a); 108.59/74.35 findMin (Branch key elt wx EmptyFM wy) = (key,elt); 108.59/74.35 findMin (Branch key elt wz fm_l xu) = findMin fm_l; 108.59/74.35 108.59/74.35 mkBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 108.59/74.35 mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R; 108.59/74.35 108.59/74.35 mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { 108.59/74.35 double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw 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); 108.59/74.35 double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx 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); 108.59/74.35 mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr); 108.59/74.35 mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R; 108.59/74.35 mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R; 108.59/74.35 mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise; 108.59/74.35 mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 108.59/74.35 mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr); 108.59/74.35 mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R; 108.59/74.35 mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R; 108.59/74.35 mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr otherwise; 108.59/74.35 mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 108.59/74.35 mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; 108.59/74.35 mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L; 108.59/74.35 mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise; 108.59/74.35 mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R; 108.59/74.35 mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r); 108.59/74.35 mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; 108.59/74.35 mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l); 109.16/74.45 single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 109.16/74.45 single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 109.16/74.45 size_l = sizeFM fm_L; 109.16/74.45 size_r = sizeFM fm_R; 109.16/74.45 }; 109.16/74.45 109.16/74.45 mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 109.16/74.45 mkBranch which key elt fm_l fm_r = let { 109.16/74.45 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 109.16/74.45 } in result where { 109.16/74.45 balance_ok = True; 109.16/74.45 left_ok = left_ok0 fm_l key fm_l; 109.16/74.45 left_ok0 fm_l key EmptyFM = True; 109.16/74.45 left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 109.16/74.45 biggest_left_key = fst (findMax fm_l); 109.16/74.45 } in biggest_left_key < key; 109.16/74.45 left_size = sizeFM fm_l; 109.16/74.45 right_ok = right_ok0 fm_r key fm_r; 109.16/74.45 right_ok0 fm_r key EmptyFM = True; 109.16/74.45 right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 109.16/74.45 smallest_right_key = fst (findMin fm_r); 109.16/74.45 } in key < smallest_right_key; 109.16/74.45 right_size = sizeFM fm_r; 109.16/74.45 unbox :: Int -> Int; 109.16/74.45 unbox x = x; 109.16/74.45 }; 109.16/74.45 109.16/74.45 sIZE_RATIO :: Int; 109.16/74.45 sIZE_RATIO = 5; 109.16/74.45 109.16/74.45 sizeFM :: FiniteMap b a -> Int; 109.16/74.45 sizeFM EmptyFM = 0; 109.16/74.45 sizeFM (Branch vz wu size wv ww) = size; 109.16/74.45 109.16/74.45 unitFM :: b -> a -> FiniteMap b a; 109.16/74.45 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 109.16/74.45 109.16/74.45 } 109.16/74.45 module Maybe where { 109.16/74.45 import qualified FiniteMap; 109.16/74.45 import qualified Main; 109.16/74.45 import qualified Prelude; 109.16/74.45 } 109.16/74.45 module Main where { 109.16/74.45 import qualified FiniteMap; 109.16/74.45 import qualified Maybe; 109.16/74.45 import qualified Prelude; 109.16/74.45 } 109.16/74.45 109.16/74.45 ---------------------------------------- 109.16/74.45 109.16/74.45 (7) LetRed (EQUIVALENT) 109.16/74.45 Let/Where Reductions: 109.16/74.45 The bindings of the following Let/Where expression 109.16/74.45 "mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { 109.16/74.45 double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw 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); 109.16/74.45 ; 109.16/74.45 double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx 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); 109.16/74.45 ; 109.16/74.45 mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr); 109.16/74.45 ; 109.16/74.45 mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R; 109.16/74.45 ; 109.16/74.45 mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R; 109.16/74.45 mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise; 109.16/74.45 ; 109.16/74.45 mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 109.16/74.45 ; 109.16/74.45 mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr); 109.16/74.45 ; 109.16/74.45 mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R; 109.16/74.45 ; 109.16/74.45 mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R; 109.16/74.45 mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr otherwise; 109.16/74.45 ; 109.16/74.45 mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 109.16/74.45 ; 109.16/74.45 mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; 109.16/74.45 ; 109.16/74.45 mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L; 109.16/74.45 mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise; 109.16/74.45 ; 109.16/74.45 mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R; 109.16/74.45 mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r); 109.16/74.45 ; 109.16/74.45 mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; 109.16/74.45 mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l); 109.16/74.45 ; 109.16/74.45 single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; 109.16/74.45 ; 109.16/74.45 single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); 109.16/74.45 ; 109.16/74.45 size_l = sizeFM fm_L; 109.16/74.45 ; 109.16/74.45 size_r = sizeFM fm_R; 109.16/74.45 } 109.16/74.45 " 109.16/74.45 are unpacked to the following functions on top level 109.16/74.45 "mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; 109.16/74.45 mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_r vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_l vwx vwy vwz vxu); 109.16/74.45 " 109.16/74.45 "mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 109.16/74.45 " 109.16/74.45 "mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L; 109.16/74.45 mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise; 109.16/74.45 " 109.16/74.45 "mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr); 109.16/74.45 " 109.16/74.45 "mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Single_L vwx vwy vwz vxu fm_L fm_R; 109.16/74.45 mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise; 109.16/74.45 " 109.16/74.45 "mkBalBranch6Double_R vwx vwy vwz vxu (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 vwx vwy fm_lrr fm_r); 109.16/74.45 " 109.16/74.45 "mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R; 109.16/74.45 mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_l vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_r vwx vwy vwz vxu); 109.16/74.45 " 109.16/74.45 "mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vwz; 109.16/74.45 " 109.16/74.45 "mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Single_R vwx vwy vwz vxu fm_L fm_R; 109.16/74.45 mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr otherwise; 109.16/74.45 " 109.16/74.45 "mkBalBranch6Single_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 vwx vwy fm_l fm_rl) fm_rr; 109.16/74.45 " 109.16/74.45 "mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; 109.16/74.45 " 109.16/74.45 "mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr); 109.16/74.45 " 109.16/74.45 "mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Double_L vwx vwy vwz vxu fm_L fm_R; 109.16/74.45 " 109.16/74.45 "mkBalBranch6Double_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 vwx vwy fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 109.16/74.45 " 109.16/74.45 "mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Double_R vwx vwy vwz vxu fm_L fm_R; 109.16/74.45 " 109.16/74.45 "mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vxu; 109.16/74.45 " 109.16/74.45 "mkBalBranch6Single_R vwx vwy vwz vxu (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 vwx vwy fm_lr fm_r); 109.16/74.45 " 109.16/74.45 "mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 109.16/74.45 " 109.16/74.45 The bindings of the following Let/Where expression 109.16/74.45 "foldl add fm key_elt_pairs where { 109.16/74.45 add fmap (key,elt) = addToFM_C combiner fmap key elt; 109.16/74.45 } 109.16/74.45 " 109.16/74.45 are unpacked to the following functions on top level 109.16/74.45 "addListToFM_CAdd vxv fmap (key,elt) = addToFM_C vxv fmap key elt; 109.16/74.45 " 109.16/74.45 The bindings of the following Let/Where expression 109.16/74.45 "let { 109.16/74.45 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 109.16/74.45 } in result where { 109.16/74.45 balance_ok = True; 109.16/74.45 ; 109.16/74.45 left_ok = left_ok0 fm_l key fm_l; 109.16/74.45 ; 109.16/74.45 left_ok0 fm_l key EmptyFM = True; 109.16/74.45 left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 109.16/74.45 biggest_left_key = fst (findMax fm_l); 109.16/74.45 } in biggest_left_key < key; 109.16/74.45 ; 109.16/74.45 left_size = sizeFM fm_l; 109.16/74.45 ; 109.16/74.45 right_ok = right_ok0 fm_r key fm_r; 109.16/74.48 ; 109.16/74.48 right_ok0 fm_r key EmptyFM = True; 109.16/74.48 right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 109.16/74.48 smallest_right_key = fst (findMin fm_r); 109.16/74.48 } in key < smallest_right_key; 109.16/74.48 ; 109.16/74.48 right_size = sizeFM fm_r; 109.16/74.48 ; 109.16/74.48 unbox x = x; 109.16/74.48 } 109.16/74.48 " 109.16/74.48 are unpacked to the following functions on top level 109.16/74.48 "mkBranchLeft_ok vxw vxx vxy = mkBranchLeft_ok0 vxw vxx vxy vxw vxx vxw; 109.16/74.48 " 109.16/74.48 "mkBranchRight_size vxw vxx vxy = sizeFM vxy; 109.16/74.48 " 109.16/74.48 "mkBranchRight_ok vxw vxx vxy = mkBranchRight_ok0 vxw vxx vxy vxy vxx vxy; 109.16/74.48 " 109.16/74.48 "mkBranchBalance_ok vxw vxx vxy = True; 109.16/74.48 " 109.16/74.48 "mkBranchLeft_size vxw vxx vxy = sizeFM vxw; 109.16/74.48 " 109.16/74.48 "mkBranchUnbox vxw vxx vxy x = x; 109.16/74.48 " 109.16/74.48 "mkBranchLeft_ok0 vxw vxx vxy fm_l key EmptyFM = True; 109.16/74.48 mkBranchLeft_ok0 vxw vxx vxy fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key; 109.16/74.48 " 109.16/74.48 "mkBranchRight_ok0 vxw vxx vxy fm_r key EmptyFM = True; 109.16/74.48 mkBranchRight_ok0 vxw vxx vxy fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r; 109.16/74.48 " 109.16/74.48 The bindings of the following Let/Where expression 109.16/74.48 "let { 109.16/74.48 result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; 109.16/74.48 } in result" 109.16/74.48 are unpacked to the following functions on top level 109.16/74.48 "mkBranchResult vxz vyu vyv vyw = Branch vxz vyu (mkBranchUnbox vyv vxz vyw (1 + mkBranchLeft_size vyv vxz vyw + mkBranchRight_size vyv vxz vyw)) vyv vyw; 109.16/74.48 " 109.16/74.48 The bindings of the following Let/Where expression 109.16/74.48 "let { 109.16/74.48 biggest_left_key = fst (findMax fm_l); 109.16/74.48 } in biggest_left_key < key" 109.16/74.48 are unpacked to the following functions on top level 109.16/74.48 "mkBranchLeft_ok0Biggest_left_key vyx = fst (findMax vyx); 109.16/74.48 " 109.16/74.48 The bindings of the following Let/Where expression 109.16/74.48 "let { 109.16/74.48 smallest_right_key = fst (findMin fm_r); 109.16/74.48 } in key < smallest_right_key" 109.16/74.48 are unpacked to the following functions on top level 109.16/74.48 "mkBranchRight_ok0Smallest_right_key vyy = fst (findMin vyy); 109.16/74.48 " 109.16/74.48 109.16/74.48 ---------------------------------------- 109.16/74.48 109.16/74.48 (8) 109.16/74.48 Obligation: 109.16/74.48 mainModule Main 109.16/74.48 module FiniteMap where { 109.16/74.48 import qualified Main; 109.16/74.48 import qualified Maybe; 109.16/74.48 import qualified Prelude; 109.16/74.48 data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; 109.16/74.48 109.16/74.48 instance (Eq a, Eq b) => Eq FiniteMap a b where { 109.16/74.48 } 109.16/74.48 addListToFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> [(a,b)] -> FiniteMap a b; 109.16/74.48 addListToFM_C combiner fm key_elt_pairs = foldl (addListToFM_CAdd combiner) fm key_elt_pairs; 109.16/74.48 109.16/74.48 addListToFM_CAdd vxv fmap (key,elt) = addToFM_C vxv fmap key elt; 109.16/74.48 109.16/74.48 addToFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> a -> b -> FiniteMap a b; 109.16/74.48 addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt; 109.16/74.48 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; 109.16/74.48 109.16/74.48 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; 109.16/74.48 109.16/74.48 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); 109.16/74.48 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; 109.16/74.48 109.16/74.48 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; 109.16/74.48 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); 109.16/74.48 109.16/74.48 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); 109.16/74.48 109.16/74.48 addToFM_C4 combiner EmptyFM key elt = unitFM key elt; 109.16/74.48 addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu; 109.16/74.48 109.16/74.48 emptyFM :: FiniteMap b a; 109.16/74.48 emptyFM = EmptyFM; 109.16/74.48 109.16/74.48 findMax :: FiniteMap b a -> (b,a); 109.16/74.48 findMax (Branch key elt yx yy EmptyFM) = (key,elt); 109.16/74.48 findMax (Branch key elt yz zu fm_r) = findMax fm_r; 109.16/74.48 109.16/74.48 findMin :: FiniteMap a b -> (a,b); 109.16/74.48 findMin (Branch key elt wx EmptyFM wy) = (key,elt); 109.16/74.48 findMin (Branch key elt wz fm_l xu) = findMin fm_l; 109.16/74.48 109.16/74.48 mkBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 109.16/74.48 mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R; 109.16/74.48 109.16/74.48 mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 key elt fm_R fm_L key elt fm_L fm_R (mkBalBranch6Size_l key elt fm_R fm_L + mkBalBranch6Size_r key elt fm_R fm_L < 2); 109.16/74.48 109.16/74.48 mkBalBranch6Double_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 vwx vwy fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); 109.16/74.48 109.16/74.48 mkBalBranch6Double_R vwx vwy vwz vxu (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 vwx vwy fm_lrr fm_r); 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr); 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Double_L vwx vwy vwz vxu fm_L fm_R; 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Single_L vwx vwy vwz vxu fm_L fm_R; 109.16/74.48 mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise; 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr); 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Double_R vwx vwy vwz vxu fm_L fm_R; 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Single_R vwx vwy vwz vxu fm_L fm_R; 109.16/74.48 mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr otherwise; 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L; 109.16/74.48 mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise; 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R; 109.16/74.48 mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_l vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_r vwx vwy vwz vxu); 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; 109.16/74.48 mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_r vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_l vwx vwy vwz vxu); 109.16/74.48 109.16/74.48 mkBalBranch6Single_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 vwx vwy fm_l fm_rl) fm_rr; 109.16/74.48 109.16/74.48 mkBalBranch6Single_R vwx vwy vwz vxu (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 vwx vwy fm_lr fm_r); 109.16/74.48 109.16/74.48 mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vxu; 109.16/74.48 109.16/74.48 mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vwz; 109.16/74.48 109.16/74.48 mkBranch :: Ord a => Int -> a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 109.16/74.48 mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_l fm_r; 109.16/74.48 109.16/74.48 mkBranchBalance_ok vxw vxx vxy = True; 109.16/74.48 109.16/74.48 mkBranchLeft_ok vxw vxx vxy = mkBranchLeft_ok0 vxw vxx vxy vxw vxx vxw; 109.16/74.48 109.16/74.48 mkBranchLeft_ok0 vxw vxx vxy fm_l key EmptyFM = True; 109.16/74.48 mkBranchLeft_ok0 vxw vxx vxy fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key; 109.16/74.48 109.16/74.48 mkBranchLeft_ok0Biggest_left_key vyx = fst (findMax vyx); 109.16/74.48 109.16/74.48 mkBranchLeft_size vxw vxx vxy = sizeFM vxw; 109.16/74.48 109.16/74.48 mkBranchResult vxz vyu vyv vyw = Branch vxz vyu (mkBranchUnbox vyv vxz vyw (1 + mkBranchLeft_size vyv vxz vyw + mkBranchRight_size vyv vxz vyw)) vyv vyw; 109.16/74.48 109.16/74.48 mkBranchRight_ok vxw vxx vxy = mkBranchRight_ok0 vxw vxx vxy vxy vxx vxy; 109.16/74.48 109.16/74.48 mkBranchRight_ok0 vxw vxx vxy fm_r key EmptyFM = True; 109.16/74.48 mkBranchRight_ok0 vxw vxx vxy fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r; 109.16/74.48 109.16/74.48 mkBranchRight_ok0Smallest_right_key vyy = fst (findMin vyy); 109.16/74.48 109.16/74.48 mkBranchRight_size vxw vxx vxy = sizeFM vxy; 109.16/74.48 109.16/74.48 mkBranchUnbox :: Ord a => -> (FiniteMap a b) ( -> a ( -> (FiniteMap a b) (Int -> Int))); 109.16/74.48 mkBranchUnbox vxw vxx vxy x = x; 109.16/74.48 109.16/74.48 sIZE_RATIO :: Int; 109.16/74.48 sIZE_RATIO = 5; 109.16/74.48 109.16/74.48 sizeFM :: FiniteMap a b -> Int; 109.16/74.48 sizeFM EmptyFM = 0; 109.16/74.48 sizeFM (Branch vz wu size wv ww) = size; 109.16/74.48 109.16/74.48 unitFM :: b -> a -> FiniteMap b a; 109.16/74.48 unitFM key elt = Branch key elt 1 emptyFM emptyFM; 109.16/74.48 109.16/74.48 } 109.16/74.48 module Maybe where { 109.16/74.48 import qualified FiniteMap; 109.16/74.48 import qualified Main; 109.16/74.48 import qualified Prelude; 109.16/74.48 } 109.16/74.48 module Main where { 109.16/74.48 import qualified FiniteMap; 109.16/74.48 import qualified Maybe; 109.16/74.48 import qualified Prelude; 109.16/74.48 } 109.16/74.48 109.16/74.48 ---------------------------------------- 109.16/74.48 109.16/74.48 (9) NumRed (SOUND) 109.16/74.48 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 109.16/74.48 ---------------------------------------- 109.16/74.48 109.16/74.48 (10) 109.16/74.48 Obligation: 109.16/74.48 mainModule Main 109.16/74.48 module FiniteMap where { 109.16/74.48 import qualified Main; 109.16/74.48 import qualified Maybe; 109.16/74.48 import qualified Prelude; 109.16/74.48 data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; 109.16/74.48 109.16/74.48 instance (Eq a, Eq b) => Eq FiniteMap b a where { 109.16/74.48 } 109.16/74.48 addListToFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> [(a,b)] -> FiniteMap a b; 109.16/74.48 addListToFM_C combiner fm key_elt_pairs = foldl (addListToFM_CAdd combiner) fm key_elt_pairs; 109.16/74.48 109.16/74.48 addListToFM_CAdd vxv fmap (key,elt) = addToFM_C vxv fmap key elt; 109.16/74.48 109.16/74.48 addToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> b -> a -> FiniteMap b a; 109.16/74.48 addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt; 109.16/74.48 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; 109.16/74.48 109.16/74.48 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; 109.16/74.48 109.16/74.48 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); 109.16/74.48 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; 109.16/74.48 109.16/74.48 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; 109.16/74.48 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); 109.16/74.48 109.16/74.48 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); 109.16/74.48 109.16/74.48 addToFM_C4 combiner EmptyFM key elt = unitFM key elt; 109.16/74.48 addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu; 109.16/74.48 109.16/74.48 emptyFM :: FiniteMap a b; 109.16/74.48 emptyFM = EmptyFM; 109.16/74.48 109.16/74.48 findMax :: FiniteMap a b -> (a,b); 109.16/74.48 findMax (Branch key elt yx yy EmptyFM) = (key,elt); 109.16/74.48 findMax (Branch key elt yz zu fm_r) = findMax fm_r; 109.16/74.48 109.16/74.48 findMin :: FiniteMap b a -> (b,a); 109.16/74.48 findMin (Branch key elt wx EmptyFM wy) = (key,elt); 109.16/74.48 findMin (Branch key elt wz fm_l xu) = findMin fm_l; 109.16/74.48 109.16/74.48 mkBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; 109.16/74.48 mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R; 109.16/74.48 109.16/74.48 mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 key elt fm_R fm_L key elt fm_L fm_R (mkBalBranch6Size_l key elt fm_R fm_L + mkBalBranch6Size_r key elt fm_R fm_L < Pos (Succ (Succ Zero))); 109.16/74.48 109.16/74.48 mkBalBranch6Double_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw 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))))))) vwx vwy fm_l fm_rll) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) key_r elt_r fm_rlr fm_rr); 109.16/74.48 109.16/74.48 mkBalBranch6Double_R vwx vwy vwz vxu (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx 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))))))))))))) vwx vwy fm_lrr fm_r); 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr); 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Double_L vwx vwy vwz vxu fm_L fm_R; 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Single_L vwx vwy vwz vxu fm_L fm_R; 109.16/74.48 mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise; 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < Pos (Succ (Succ Zero)) * sizeFM fm_rr); 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr); 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Double_R vwx vwy vwz vxu fm_L fm_R; 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Single_R vwx vwy vwz vxu fm_L fm_R; 109.16/74.48 mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr otherwise; 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < Pos (Succ (Succ Zero)) * sizeFM fm_ll); 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R; 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L; 109.16/74.48 mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise; 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R; 109.16/74.48 mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_l vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_r vwx vwy vwz vxu); 109.16/74.48 109.16/74.48 mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ Zero)) key elt fm_L fm_R; 109.16/74.48 mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_r vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_l vwx vwy vwz vxu); 109.16/74.48 109.16/74.48 mkBalBranch6Single_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch (Pos (Succ (Succ (Succ Zero)))) key_r elt_r (mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) vwx vwy fm_l fm_rl) fm_rr; 109.16/74.48 109.16/74.48 mkBalBranch6Single_R vwx vwy vwz vxu (Branch key_l elt_l zv 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)))))))))) vwx vwy fm_lr fm_r); 109.16/74.48 109.16/74.48 mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vxu; 109.16/74.48 109.16/74.48 mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vwz; 109.16/74.48 109.16/74.48 mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; 109.16/74.48 mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_l fm_r; 109.16/74.48 109.16/74.48 mkBranchBalance_ok vxw vxx vxy = True; 109.16/74.48 109.16/74.48 mkBranchLeft_ok vxw vxx vxy = mkBranchLeft_ok0 vxw vxx vxy vxw vxx vxw; 109.16/74.48 109.16/74.48 mkBranchLeft_ok0 vxw vxx vxy fm_l key EmptyFM = True; 109.16/74.48 mkBranchLeft_ok0 vxw vxx vxy fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key; 109.16/74.48 109.16/74.48 mkBranchLeft_ok0Biggest_left_key vyx = fst (findMax vyx); 109.16/74.48 109.16/74.48 mkBranchLeft_size vxw vxx vxy = sizeFM vxw; 109.16/74.48 109.16/74.48 mkBranchResult vxz vyu vyv vyw = Branch vxz vyu (mkBranchUnbox vyv vxz vyw (Pos (Succ Zero) + mkBranchLeft_size vyv vxz vyw + mkBranchRight_size vyv vxz vyw)) vyv vyw; 109.16/74.48 109.16/74.48 mkBranchRight_ok vxw vxx vxy = mkBranchRight_ok0 vxw vxx vxy vxy vxx vxy; 109.16/74.48 109.16/74.48 mkBranchRight_ok0 vxw vxx vxy fm_r key EmptyFM = True; 109.16/74.48 mkBranchRight_ok0 vxw vxx vxy fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r; 109.16/74.48 109.16/74.48 mkBranchRight_ok0Smallest_right_key vyy = fst (findMin vyy); 109.16/74.48 109.16/74.48 mkBranchRight_size vxw vxx vxy = sizeFM vxy; 109.16/74.48 109.16/74.48 mkBranchUnbox :: Ord a => -> (FiniteMap a b) ( -> a ( -> (FiniteMap a b) (Int -> Int))); 109.16/74.48 mkBranchUnbox vxw vxx vxy x = x; 109.16/74.48 109.16/74.48 sIZE_RATIO :: Int; 109.16/74.48 sIZE_RATIO = Pos (Succ (Succ (Succ (Succ (Succ Zero))))); 109.16/74.48 109.16/74.48 sizeFM :: FiniteMap a b -> Int; 109.16/74.48 sizeFM EmptyFM = Pos Zero; 109.16/74.48 sizeFM (Branch vz wu size wv ww) = size; 109.16/74.48 109.16/74.48 unitFM :: b -> a -> FiniteMap b a; 109.16/74.48 unitFM key elt = Branch key elt (Pos (Succ Zero)) emptyFM emptyFM; 109.16/74.48 109.16/74.48 } 109.16/74.48 module Maybe where { 109.16/74.48 import qualified FiniteMap; 109.16/74.48 import qualified Main; 109.16/74.48 import qualified Prelude; 109.16/74.48 } 109.16/74.48 module Main where { 109.16/74.48 import qualified FiniteMap; 109.16/74.48 import qualified Maybe; 109.16/74.48 import qualified Prelude; 109.16/74.48 } 109.36/74.52 EOF