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code-conjure 0.7.4 → 0.7.6

raw patch · 186 files changed

+9053/−8392 lines, 186 filesPVP: major bump suggested

API removals or changes: PVP suggests a major version bump

API changes (from Hackage documentation)

- Conjure: omitEarlyTests :: Ingredient
- Conjure.Engine: omitEarlyTests :: Ingredient
- Conjure.Settings: earlyTestsI :: [Ingredient] -> Bool
- Conjure.Settings: omitEarlyTests :: Ingredient
- Conjure.Utils: sets :: [a] -> [[a]]
+ Conjure: maxEarlyTests :: Int -> Ingredient
+ Conjure.Conjurable: conjureResultHole :: Conjurable a => a -> Expr
+ Conjure.Engine: maxEarlyTests :: Int -> Ingredient
+ Conjure.Expr: mappArgs :: (Expr -> Expr) -> Expr -> Expr
+ Conjure.Expr: mappFun :: (Expr -> Expr) -> Expr -> Expr
+ Conjure.Settings: maxEarlyTests :: Int -> Ingredient
+ Conjure.Settings: maxEarlyTestsI :: [Ingredient] -> Int

Files

.gitignore view
@@ -60,21 +60,23 @@ eg/colin/*Funs eg/tri eg/bits+eg/digits eg/peano eg/these eg/tuple+eg/conditionals bench/carry-on bench/strategies bench/self bench/longshot bench/ill-hit-bench/p12-bench/p30+bench/i12+bench/i30 bench/candidates bench/redundants bench/erroneous bench/gps-bench/gps2+bench/psb2 bench/lowtests bench/terpret bench/weird
Makefile view
@@ -43,9 +43,11 @@   eg/bst \   eg/tri \   eg/bits \+  eg/digits \   eg/peano \   eg/these \   eg/tuple \+  eg/conditionals \   bench/candidates \   bench/redundants \   bench/erroneous \@@ -55,10 +57,10 @@   bench/strategies \   bench/self \   bench/carry-on \-  bench/p12 \-  bench/p30 \+  bench/i12 \+  bench/i30 \   bench/gps \-  bench/gps2 \+  bench/psb2 \   bench/terpret \   bench/unique \   bench/weird \
README.md view
@@ -64,8 +64,8 @@ addition, multiplication, subtraction and their neutral elements:  	ingredients :: [Ingredient]-	ingredients  =  [ unfun (0::Int)-	                , unfun (1::Int)+	ingredients  =  [ con (0::Int)+	                , con (1::Int) 	                , fun "+" ((+) :: Int -> Int -> Int) 	                , fun "*" ((*) :: Int -> Int -> Int) 	                , fun "-" ((-) :: Int -> Int -> Int)@@ -121,9 +121,9 @@ given list constructors, zero, one and subtraction:  	> conjure "take" (take' :: Int -> [A] -> [A])-	>   [ unfun (0 :: Int)-	>   , unfun (1 :: Int)-	>   , unfun ([] :: [A])+	>   [ con (0 :: Int)+	>   , con (1 :: Int)+	>   , con ([] :: [A]) 	>   , fun ":" ((:) :: A -> [A] -> [A]) 	>   , fun "-" ((-) :: Int -> Int -> Int) 	>   ]@@ -176,7 +176,7 @@ with the following call:  	conjureFromSpec "duplicates" duplicatesSpec-	  [ unfun ([] :: [Int])+	  [ con ([] :: [Int]) 	  , fun "not" not 	  , fun "&&" (&&) 	  , fun ":" ((:) :: Int -> [Int] -> [Int])
TODO.md view
@@ -7,14 +7,9 @@   constructors that are not recursive.   This change will need to be done in LeanCheck itself. -* Detail two new proposed pruning rules from Colin.-  (email from Feb 24 and follow-up in meeting)- * Allow timeout setting? -* Rethink Conjurable typeclass?--* Allow chains of guards (see below).+* Find most efficient of a given size (see below).  * Better error reporting when `Listable` is out-of-scope when using `deriveConjurable`.   This needs to be implemented on LeanCheck itself.@@ -25,36 +20,11 @@ 	(qsort example)  -## Allow chains of guards--With the use of `guard` right now,-Conjure can generate functions such as the following:--	function x y z-	  | x < 123    =  ...-	  | otherwise  =  ...--We should probably allow chains of guards such as the following:--	function x y z-	  | x < 123    =  ...-	  | x == 321   =  ...-	  | y == 12    =  ...-	  | otherwise  =  ...--Internally, these are just chains of if-then-else applications:--	function x y z  =  if x < 123-	                   then ...-					   else if x == 321-					   then ...-					   else if y == 12-					   then ...-					   else ...+## Find the most efficient of a given size -This change shouldn't be so complicated to introduce-requiring a change in `enumerateAppsFor` relaxing `ufor hx`-depending on what we have on the left...+While evaluating candidates, we can count the number of matches in order to+select the most efficient.  When actually conjuring, we always wait until the+end of the current size to select the candidate with least evaluations.   ## Forbid recursion into negatives@@ -78,6 +48,19 @@    This may require changing the format definitions themselves... 2. use this on `showDefn` somehow 3. use this on `toDynamicWithDefn` somehow++Alternative: include the guard as part of the pattern "internally".  As if we+had a n+k pattern.  Like so:++	tri 1  =  1+	tri x@(_ + 2)  =  x + tri (x - 1)++When displaying of course, we remove the n+k pattern.++This can be done as early as enumerating the possible patterns and should make+things easier in `keepB`.  The matching engine would have to be customized+somehow.  Maybe an `@`-named operator can adopt a special meaning in `Express`?+   This file is part of Conjure,
bench/candidates.hs view
@@ -40,43 +40,43 @@ main :: IO () main  =  do   printCandidates 9 6 "foo" (undefined :: Int -> Int)-    [ unfun (0 :: Int)-    , unfun (1 :: Int)+    [ con (0 :: Int)+    , con (1 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "*" ((*) :: Int -> Int -> Int)     , fun "-" ((-) :: Int -> Int -> Int)     ]    printCandidates 9 5 "?" (undefined :: Int -> Int -> Int)-    [ unfun (0 :: Int)+    [ con (0 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "*" ((*) :: Int -> Int -> Int)     , fun "dec" (subtract 1 :: Int -> Int)     ]    printCandidates 9 6 "goo" (undefined :: [Int] -> [Int])-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "++" ((++) :: [Int] -> [Int] -> [Int])     ]    printCandidates 9 6 "??" (undefined :: [Int] -> [Int] -> [Int])-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "++" ((++) :: [Int] -> [Int] -> [Int])     ]    printCandidates 9 6 "ton" (undefined :: Bool -> Bool)-    [ unfun False-    , unfun True+    [ con False+    , con True     , fun "&&" (&&)     , fun "||" (||)     , fun "not" not     ]    printCandidates 9 6 "&|" (undefined :: Bool -> Bool -> Bool)-    [ unfun False-    , unfun True+    [ con False+    , con True     , fun "&&" (&&)     , fun "||" (||)     , fun "not" not@@ -88,6 +88,6 @@   -- nevertheless useful for observing candidate filtering   -- through other means   printCandidates 9 6 "gcd" (undefined :: Int -> Int -> Int)-    [ unfun (0::Int)+    [ con (0::Int)     , fun "`mod`" (mod :: Int -> Int -> Int)     ]
bench/candidates.txt view
@@ -95,5420 +95,5420 @@  foo x  =  1 - x -foo x  =  x * x - 1--foo x  =  x + (x + x)--foo x  =  x + (x + 1)--foo x  =  x + (1 + 1)--foo x  =  x + x * x--foo x  =  x + (x - 1)--foo x  =  x + (0 - 1)--foo x  =  1 + (x + x)--foo x  =  1 + (x + 1)--foo x  =  1 + (1 + 1)--foo x  =  1 + x * x--foo x  =  1 + (0 - x)--foo x  =  1 + (1 - x)--foo x  =  x * (x + x)--foo x  =  x * (x * x)--foo x  =  x * (x - 1)--foo x  =  x * (0 - x)--foo x  =  x * (0 - 1)--foo x  =  x * (1 - x)--foo x  =  x - (x + x)--foo x  =  x - (x + 1)--foo x  =  x - (1 + 1)--foo x  =  x - x * x--foo x  =  0 - (x + x)--foo x  =  0 - (x + 1)--foo x  =  0 - (1 + 1)--foo x  =  1 - (x + x)--foo x  =  1 - (x + 1)--foo x  =  1 - (1 + 1)--foo x  =  1 - x * x---pattern candidates:--foo x  =  x--foo x  =  0--foo x  =  1--foo 0  =  0-foo x  =  1--foo 0  =  1-foo x  =  x--foo 0  =  1-foo x  =  0--foo x  =  x + x--foo x  =  x + 1--foo x  =  x * x--foo x  =  x - 1--foo x  =  0 - x--foo x  =  1 - x--foo 1  =  0-foo x  =  x--foo 1  =  0-foo x  =  1--foo 1  =  1-foo x  =  0--foo 0  =  0-foo x  =  x + 1--foo 0  =  0-foo x  =  x - 1--foo 0  =  0-foo x  =  1 - x--foo 0  =  1-foo x  =  x + x--foo 0  =  1-foo x  =  x * x--foo 0  =  1-foo x  =  x - 1--foo 0  =  1-foo x  =  0 - x--foo 0  =  0-foo 1  =  0-foo x  =  1--foo 0  =  1-foo 1  =  0-foo x  =  x--foo 0  =  1-foo 1  =  1-foo x  =  0--foo x  =  x * x - 1--foo x  =  x + (x + x)--foo x  =  x + (x + 1)--foo x  =  x + x * x--foo x  =  x + (x - 1)--foo x  =  1 + (x + x)--foo x  =  1 + (x + 1)--foo x  =  1 + x * x--foo x  =  1 + (0 - x)--foo x  =  1 + (1 - x)--foo x  =  x * (x + x)--foo x  =  x * (x * x)--foo x  =  x * (x - 1)--foo x  =  x * (0 - x)--foo x  =  x * (1 - x)--foo x  =  x - (x + x)--foo x  =  x - (x + 1)--foo x  =  x - x * x--foo x  =  0 - (x + x)--foo x  =  0 - (x + 1)--foo x  =  1 - (x + x)--foo x  =  1 - (x + 1)--foo x  =  1 - x * x--foo 1  =  0-foo x  =  x + x--foo 1  =  0-foo x  =  x + 1--foo 1  =  0-foo x  =  x * x--foo 1  =  0-foo x  =  0 - x--foo 1  =  1-foo x  =  x + x--foo 1  =  1-foo x  =  x + 1--foo 1  =  1-foo x  =  x - 1--foo 1  =  1-foo x  =  0 - x--foo 1  =  1-foo x  =  1 - x--foo 0  =  0-foo x  =  x * x - 1--foo 0  =  0-foo x  =  x + (x + 1)--foo 0  =  0-foo x  =  x + (x - 1)--foo 0  =  0-foo x  =  1 + (x + x)--foo 0  =  0-foo x  =  1 + (x + 1)--foo 0  =  0-foo x  =  1 + x * x--foo 0  =  0-foo x  =  1 + (0 - x)--foo 0  =  0-foo x  =  1 + (1 - x)--foo 0  =  0-foo x  =  x - (x + 1)--foo 0  =  0-foo x  =  0 - (x + 1)--foo 0  =  0-foo x  =  1 - (x + x)--foo 0  =  0-foo x  =  1 - x * x--foo 0  =  1-foo x  =  x * x - 1--foo 0  =  1-foo x  =  x + (x + x)--foo 0  =  1-foo x  =  x + x * x--foo 0  =  1-foo x  =  x + (x - 1)--foo 0  =  1-foo x  =  1 + (x + 1)--foo 0  =  1-foo x  =  1 + (1 - x)--foo 0  =  1-foo x  =  x * (x + x)--foo 0  =  1-foo x  =  x * (x * x)--foo 0  =  1-foo x  =  x * (x - 1)--foo 0  =  1-foo x  =  x * (0 - x)--foo 0  =  1-foo x  =  x * (1 - x)--foo 0  =  1-foo x  =  x - (x + x)--foo 0  =  1-foo x  =  x - (x + 1)--foo 0  =  1-foo x  =  x - x * x--foo 0  =  1-foo x  =  0 - (x + x)--foo 0  =  1-foo x  =  0 - (x + 1)--foo 0  =  1-foo x  =  1 - (x + 1)--foo 0  =  0-foo 1  =  0-foo x  =  x + 1--foo 0  =  0-foo 1  =  1-foo x  =  x + 1--foo 0  =  0-foo 1  =  1-foo x  =  x - 1--foo 0  =  0-foo 1  =  1-foo x  =  1 - x--foo 0  =  1-foo 1  =  0-foo x  =  x + x--foo 0  =  1-foo 1  =  0-foo x  =  x * x--foo 0  =  1-foo 1  =  0-foo x  =  0 - x--foo 0  =  1-foo 1  =  1-foo x  =  x + x--foo 0  =  1-foo 1  =  1-foo x  =  x - 1--foo 0  =  1-foo 1  =  1-foo x  =  0 - x----allowed patterns:--foo x  =  _---foo 0  =  _-foo x  =  _---foo 1  =  _-foo x  =  _---foo 0  =  _-foo 1  =  _-foo x  =  _-----allowed deconstructions:--_ - 1 :: Int--Candidates for: ? :: Int -> Int -> Int-  pruning with 13/34 rules-  [3,3,9,18,60,162,489,1475,4619] direct candidates, 0 duplicates-  [3,8,25,71,205,632,1957,5906,18303] pattern candidates, 0 duplicates--rules:-x * 0 == 0-0 * x == 0-x + 0 == x-0 + x == x-dec (x + y) == x + dec y-dec (x + y) == y + dec x-dec (x + y) == dec x + y-dec (x + y) == dec y + x-(x * y) * z == x * (y * z)-(x * y) * z == y * (x * z)-(x + y) + z == x + (y + z)-(x + y) + z == y + (x + z)-(x + x) * y == x * (y + y)-equations:-y * x == x * y-y + x == x + y-y + dec x == x + dec y-dec x + y == x + dec y-dec y + x == dec x + y-x + dec 0 == dec x-dec 0 + x == dec x-y * (x * z) == x * (y * z)-z * (x * y) == x * (y * z)-z * (y * x) == x * (y * z)-y + (x + z) == x + (y + z)-z + (x + y) == x + (y + z)-z + (y + x) == x + (y + z)-(z + y) * x == x * (y + z)-z * y + x == x + y * z-y * (x + x) == x * (y + y)-y + dec (dec x) == x + dec (dec y)-dec (dec x) + y == x + dec (dec y)-dec (dec y) + x == dec (dec x) + y-x + dec (dec 0) == dec (dec x)-dec (dec 0) + x == dec (dec x)--direct candidates:--x ? y  =  x--x ? y  =  y--x ? y  =  0--x ? y  =  dec x--x ? y  =  dec y--x ? y  =  dec 0--x ? y  =  x + x--x ? y  =  x + y--x ? y  =  y + y--x ? y  =  x * x--x ? y  =  x * y--x ? y  =  y * y--x ? y  =  dec (dec x)--x ? y  =  dec (dec y)--x ? y  =  dec (dec 0)--x ? y  =  dec (x * x)--x ? y  =  dec (x * y)--x ? y  =  dec (y * y)--x ? y  =  dec (dec (dec x))--x ? y  =  dec (dec (dec y))--x ? y  =  dec (dec (dec 0))--x ? y  =  x + dec x--x ? y  =  x + dec y--x ? y  =  x + dec 0--x ? y  =  y + dec x--x ? y  =  y + dec y--x ? y  =  y + dec 0--x ? y  =  x * dec x--x ? y  =  x * dec y--x ? y  =  x * dec 0--x ? y  =  y * dec x--x ? y  =  y * dec y--x ? y  =  y * dec 0--x ? y  =  dec (dec (x * x))--x ? y  =  dec (dec (x * y))--x ? y  =  dec (dec (y * y))--x ? y  =  dec (dec (dec (dec x)))--x ? y  =  dec (dec (dec (dec y)))--x ? y  =  dec (dec (dec (dec 0)))--x ? y  =  dec (x * dec x)--x ? y  =  dec (x * dec y)--x ? y  =  dec (x * dec 0)--x ? y  =  dec (y * dec x)--x ? y  =  dec (y * dec y)--x ? y  =  dec (y * dec 0)--x ? y  =  x + (x + x)--x ? y  =  x + (x + y)--x ? y  =  x + (y + y)--x ? y  =  x + x * x--x ? y  =  x + x * y--x ? y  =  x + y * y--x ? y  =  x + dec (dec x)--x ? y  =  x + dec (dec y)--x ? y  =  x + dec (dec 0)--x ? y  =  y + (x + x)--x ? y  =  y + (x + y)--x ? y  =  y + (y + y)--x ? y  =  y + x * x--x ? y  =  y + x * y--x ? y  =  y + y * y--x ? y  =  y + dec (dec x)--x ? y  =  y + dec (dec y)--x ? y  =  y + dec (dec 0)--x ? y  =  x * (x + x)--x ? y  =  x * (x + y)--x ? y  =  x * (y + y)--x ? y  =  x * (x * x)--x ? y  =  x * (x * y)--x ? y  =  x * (y * y)--x ? y  =  x * dec (dec x)--x ? y  =  x * dec (dec y)--x ? y  =  x * dec (dec 0)--x ? y  =  y * (x + x)--x ? y  =  y * (x + y)--x ? y  =  y * (y + y)--x ? y  =  y * (x * x)--x ? y  =  y * (x * y)--x ? y  =  y * (y * y)--x ? y  =  y * dec (dec x)--x ? y  =  y * dec (dec y)--x ? y  =  y * dec (dec 0)--x ? y  =  dec x + dec x--x ? y  =  dec x + dec y--x ? y  =  dec x + dec 0--x ? y  =  dec y + dec y--x ? y  =  dec y + dec 0--x ? y  =  dec 0 + dec 0--x ? y  =  dec x * dec x--x ? y  =  dec x * dec y--x ? y  =  dec x * dec 0--x ? y  =  dec y * dec y--x ? y  =  dec y * dec 0--x ? y  =  dec 0 * dec 0---pattern candidates:--x ? y  =  x--x ? y  =  y--x ? y  =  0--x ? y  =  dec x--x ? y  =  dec y--x ? 0  =  x-x ? y  =  y--x ? 0  =  x-x ? y  =  0--x ? 0  =  0-x ? y  =  x--0 ? x  =  x-x ? y  =  x--0 ? x  =  x-x ? y  =  0--0 ? x  =  0-x ? y  =  y--x ? y  =  x + x--x ? y  =  x + y--x ? y  =  y + y--x ? y  =  x * x--x ? y  =  x * y--x ? y  =  y * y--x ? y  =  dec (dec x)--x ? y  =  dec (dec y)--x ? 0  =  x-x ? y  =  dec x--x ? 0  =  x-x ? y  =  dec y--x ? 0  =  0-x ? y  =  dec x--x ? 0  =  0-x ? y  =  dec y--x ? 0  =  dec x-x ? y  =  x--x ? 0  =  dec x-x ? y  =  y--x ? 0  =  dec x-x ? y  =  0--0 ? x  =  x-x ? y  =  dec x--0 ? x  =  x-x ? y  =  dec y--0 ? x  =  0-x ? y  =  dec x--0 ? x  =  0-x ? y  =  dec y--0 ? x  =  dec x-x ? y  =  x--0 ? x  =  dec x-x ? y  =  y--0 ? x  =  dec x-x ? y  =  0--0 ? x  =  x-x ? 0  =  x-x ? y  =  0--0 ? x  =  x-x ? 0  =  0-x ? y  =  x--0 ? x  =  0-x ? 0  =  x-x ? y  =  y--x ? y  =  dec (x * x)--x ? y  =  dec (x * y)--x ? y  =  dec (y * y)--x ? y  =  dec (dec (dec x))--x ? y  =  dec (dec (dec y))--x ? y  =  x + dec x--x ? y  =  x + dec y--x ? y  =  y + dec x--x ? y  =  y + dec y--x ? y  =  x * dec x--x ? y  =  x * dec y--x ? y  =  y * dec x--x ? y  =  y * dec y--x ? 0  =  x-x ? y  =  x + x--x ? 0  =  x-x ? y  =  y + y--x ? 0  =  x-x ? y  =  x * x--x ? 0  =  x-x ? y  =  x * y--x ? 0  =  x-x ? y  =  y * y--x ? 0  =  x-x ? y  =  dec (dec x)--x ? 0  =  x-x ? y  =  dec (dec y)--x ? 0  =  0-x ? y  =  x + x--x ? 0  =  0-x ? y  =  x + y--x ? 0  =  0-x ? y  =  x * x--x ? 0  =  0-x ? y  =  dec (dec x)--x ? 0  =  0-x ? y  =  dec (dec y)--x ? 0  =  dec x-x ? y  =  dec y--x ? 0  =  x + x-x ? y  =  x--x ? 0  =  x + x-x ? y  =  y--x ? 0  =  x + x-x ? y  =  0--x ? 0  =  x * x-x ? y  =  x--x ? 0  =  x * x-x ? y  =  y--x ? 0  =  x * x-x ? y  =  0--x ? 0  =  dec (dec x)-x ? y  =  x--x ? 0  =  dec (dec x)-x ? y  =  y--x ? 0  =  dec (dec x)-x ? y  =  0--0 ? x  =  x-x ? y  =  x + x--0 ? x  =  x-x ? y  =  y + y--0 ? x  =  x-x ? y  =  x * x--0 ? x  =  x-x ? y  =  x * y--0 ? x  =  x-x ? y  =  y * y--0 ? x  =  x-x ? y  =  dec (dec x)--0 ? x  =  x-x ? y  =  dec (dec y)--0 ? x  =  0-x ? y  =  x + y--0 ? x  =  0-x ? y  =  y + y--0 ? x  =  0-x ? y  =  y * y--0 ? x  =  0-x ? y  =  dec (dec x)--0 ? x  =  0-x ? y  =  dec (dec y)--0 ? x  =  dec x-x ? y  =  dec x--0 ? x  =  x + x-x ? y  =  x--0 ? x  =  x + x-x ? y  =  y--0 ? x  =  x + x-x ? y  =  0--0 ? x  =  x * x-x ? y  =  x--0 ? x  =  x * x-x ? y  =  y--0 ? x  =  x * x-x ? y  =  0--0 ? x  =  dec (dec x)-x ? y  =  x--0 ? x  =  dec (dec x)-x ? y  =  y--0 ? x  =  dec (dec x)-x ? y  =  0--0 ? x  =  x-x ? 0  =  x-x ? y  =  dec x--0 ? x  =  x-x ? 0  =  x-x ? y  =  dec y--0 ? x  =  x-x ? 0  =  0-x ? y  =  dec x--0 ? x  =  x-x ? 0  =  0-x ? y  =  dec y--0 ? x  =  x-x ? 0  =  dec x-x ? y  =  x--0 ? x  =  x-x ? 0  =  dec x-x ? y  =  0--0 ? x  =  0-x ? 0  =  x-x ? y  =  dec x--0 ? x  =  0-x ? 0  =  x-x ? y  =  dec y--0 ? x  =  0-x ? 0  =  0-x ? y  =  dec x--0 ? x  =  0-x ? 0  =  0-x ? y  =  dec y--0 ? x  =  0-x ? 0  =  dec x-x ? y  =  y--0 ? x  =  dec x-x ? 0  =  x-x ? y  =  y--0 ? x  =  dec x-x ? 0  =  x-x ? y  =  0--0 ? x  =  dec x-x ? 0  =  0-x ? y  =  x--x ? 0  =  x-x ? y  =  x ? dec y--x ? 0  =  x-x ? y  =  y ? dec x--x ? 0  =  x-x ? y  =  y ? dec y--x ? 0  =  x-x ? y  =  0 ? dec y--x ? 0  =  x-x ? y  =  dec x ? x--x ? 0  =  x-x ? y  =  dec x ? y--x ? 0  =  x-x ? y  =  dec y ? x--0 ? x  =  x-x ? y  =  x ? dec y--0 ? x  =  x-x ? y  =  y ? dec x--0 ? x  =  x-x ? y  =  y ? dec y--0 ? x  =  x-x ? y  =  dec x ? x--0 ? x  =  x-x ? y  =  dec x ? y--0 ? x  =  x-x ? y  =  dec x ? 0--0 ? x  =  x-x ? y  =  dec y ? x--x ? y  =  dec (dec (x * x))--x ? y  =  dec (dec (x * y))--x ? y  =  dec (dec (y * y))--x ? y  =  dec (dec (dec (dec x)))--x ? y  =  dec (dec (dec (dec y)))--x ? y  =  dec (x * dec x)--x ? y  =  dec (x * dec y)--x ? y  =  dec (y * dec x)--x ? y  =  dec (y * dec y)--x ? y  =  x + (x + x)--x ? y  =  x + (x + y)--x ? y  =  x + (y + y)--x ? y  =  x + x * x--x ? y  =  x + x * y--x ? y  =  x + y * y--x ? y  =  x + dec (dec x)--x ? y  =  x + dec (dec y)--x ? y  =  y + (x + x)--x ? y  =  y + (x + y)--x ? y  =  y + (y + y)--x ? y  =  y + x * x--x ? y  =  y + x * y--x ? y  =  y + y * y--x ? y  =  y + dec (dec x)--x ? y  =  y + dec (dec y)--x ? y  =  x * (x + x)--x ? y  =  x * (x + y)--x ? y  =  x * (y + y)--x ? y  =  x * (x * x)--x ? y  =  x * (x * y)--x ? y  =  x * (y * y)--x ? y  =  x * dec (dec x)--x ? y  =  x * dec (dec y)--x ? y  =  y * (x + x)--x ? y  =  y * (x + y)--x ? y  =  y * (y + y)--x ? y  =  y * (x * x)--x ? y  =  y * (x * y)--x ? y  =  y * (y * y)--x ? y  =  y * dec (dec x)--x ? y  =  y * dec (dec y)--x ? y  =  dec x + dec x--x ? y  =  dec x + dec y--x ? y  =  dec y + dec y--x ? y  =  dec x * dec x--x ? y  =  dec x * dec y--x ? y  =  dec y * dec y--x ? 0  =  x-x ? y  =  dec (x * x)--x ? 0  =  x-x ? y  =  dec (x * y)--x ? 0  =  x-x ? y  =  dec (y * y)--x ? 0  =  x-x ? y  =  dec (dec (dec x))--x ? 0  =  x-x ? y  =  dec (dec (dec y))--x ? 0  =  x-x ? y  =  x + dec x--x ? 0  =  x-x ? y  =  x + dec y--x ? 0  =  x-x ? y  =  y + dec x--x ? 0  =  x-x ? y  =  y + dec y--x ? 0  =  x-x ? y  =  x * dec x--x ? 0  =  x-x ? y  =  x * dec y--x ? 0  =  x-x ? y  =  y * dec x--x ? 0  =  x-x ? y  =  y * dec y--x ? 0  =  0-x ? y  =  dec (x * x)--x ? 0  =  0-x ? y  =  dec (x * y)--x ? 0  =  0-x ? y  =  dec (y * y)--x ? 0  =  0-x ? y  =  dec (dec (dec x))--x ? 0  =  0-x ? y  =  dec (dec (dec y))--x ? 0  =  0-x ? y  =  x + dec x--x ? 0  =  0-x ? y  =  x + dec y--x ? 0  =  0-x ? y  =  y + dec x--x ? 0  =  0-x ? y  =  y + dec y--x ? 0  =  0-x ? y  =  x * dec x--x ? 0  =  0-x ? y  =  x * dec y--x ? 0  =  dec x-x ? y  =  x + x--x ? 0  =  dec x-x ? y  =  x + y--x ? 0  =  dec x-x ? y  =  y + y--x ? 0  =  dec x-x ? y  =  x * x--x ? 0  =  dec x-x ? y  =  x * y--x ? 0  =  dec x-x ? y  =  y * y--x ? 0  =  dec x-x ? y  =  dec (dec x)--x ? 0  =  dec x-x ? y  =  dec (dec y)--x ? 0  =  x + x-x ? y  =  dec x--x ? 0  =  x + x-x ? y  =  dec y--x ? 0  =  x * x-x ? y  =  dec x--x ? 0  =  x * x-x ? y  =  dec y--x ? 0  =  dec (dec x)-x ? y  =  dec x--x ? 0  =  dec (dec x)-x ? y  =  dec y--x ? 0  =  dec (x * x)-x ? y  =  x--x ? 0  =  dec (x * x)-x ? y  =  y--x ? 0  =  dec (x * x)-x ? y  =  0--x ? 0  =  dec (dec (dec x))-x ? y  =  x--x ? 0  =  dec (dec (dec x))-x ? y  =  y--x ? 0  =  dec (dec (dec x))-x ? y  =  0--x ? 0  =  x + dec x-x ? y  =  x--x ? 0  =  x + dec x-x ? y  =  y--x ? 0  =  x + dec x-x ? y  =  0--x ? 0  =  x * dec x-x ? y  =  x--x ? 0  =  x * dec x-x ? y  =  y--x ? 0  =  x * dec x-x ? y  =  0--0 ? x  =  x-x ? y  =  dec (x * x)--0 ? x  =  x-x ? y  =  dec (x * y)--0 ? x  =  x-x ? y  =  dec (y * y)--0 ? x  =  x-x ? y  =  dec (dec (dec x))--0 ? x  =  x-x ? y  =  dec (dec (dec y))--0 ? x  =  x-x ? y  =  x + dec x--0 ? x  =  x-x ? y  =  x + dec y--0 ? x  =  x-x ? y  =  y + dec x--0 ? x  =  x-x ? y  =  y + dec y--0 ? x  =  x-x ? y  =  x * dec x--0 ? x  =  x-x ? y  =  x * dec y--0 ? x  =  x-x ? y  =  y * dec x--0 ? x  =  x-x ? y  =  y * dec y--0 ? x  =  0-x ? y  =  dec (x * x)--0 ? x  =  0-x ? y  =  dec (x * y)--0 ? x  =  0-x ? y  =  dec (y * y)--0 ? x  =  0-x ? y  =  dec (dec (dec x))--0 ? x  =  0-x ? y  =  dec (dec (dec y))--0 ? x  =  0-x ? y  =  x + dec x--0 ? x  =  0-x ? y  =  x + dec y--0 ? x  =  0-x ? y  =  y + dec x--0 ? x  =  0-x ? y  =  y + dec y--0 ? x  =  0-x ? y  =  y * dec x--0 ? x  =  0-x ? y  =  y * dec y--0 ? x  =  dec x-x ? y  =  x + x--0 ? x  =  dec x-x ? y  =  x + y--0 ? x  =  dec x-x ? y  =  y + y--0 ? x  =  dec x-x ? y  =  x * x--0 ? x  =  dec x-x ? y  =  x * y--0 ? x  =  dec x-x ? y  =  y * y--0 ? x  =  dec x-x ? y  =  dec (dec x)--0 ? x  =  dec x-x ? y  =  dec (dec y)--0 ? x  =  x + x-x ? y  =  dec x--0 ? x  =  x + x-x ? y  =  dec y--0 ? x  =  x * x-x ? y  =  dec x--0 ? x  =  x * x-x ? y  =  dec y--0 ? x  =  dec (dec x)-x ? y  =  dec x--0 ? x  =  dec (dec x)-x ? y  =  dec y--0 ? x  =  dec (x * x)-x ? y  =  x--0 ? x  =  dec (x * x)-x ? y  =  y--0 ? x  =  dec (x * x)-x ? y  =  0--0 ? x  =  dec (dec (dec x))-x ? y  =  x--0 ? x  =  dec (dec (dec x))-x ? y  =  y--0 ? x  =  dec (dec (dec x))-x ? y  =  0--0 ? x  =  x + dec x-x ? y  =  x--0 ? x  =  x + dec x-x ? y  =  y--0 ? x  =  x + dec x-x ? y  =  0--0 ? x  =  x * dec x-x ? y  =  x--0 ? x  =  x * dec x-x ? y  =  y--0 ? x  =  x * dec x-x ? y  =  0--0 ? x  =  x-x ? 0  =  x-x ? y  =  x + x--0 ? x  =  x-x ? 0  =  x-x ? y  =  y + y--0 ? x  =  x-x ? 0  =  x-x ? y  =  x * x--0 ? x  =  x-x ? 0  =  x-x ? y  =  x * y--0 ? x  =  x-x ? 0  =  x-x ? y  =  y * y--0 ? x  =  x-x ? 0  =  x-x ? y  =  dec (dec x)--0 ? x  =  x-x ? 0  =  x-x ? y  =  dec (dec y)--0 ? x  =  x-x ? 0  =  0-x ? y  =  x + x--0 ? x  =  x-x ? 0  =  0-x ? y  =  x * x--0 ? x  =  x-x ? 0  =  0-x ? y  =  dec (dec x)--0 ? x  =  x-x ? 0  =  0-x ? y  =  dec (dec y)--0 ? x  =  x-x ? 0  =  dec x-x ? y  =  dec y--0 ? x  =  x-x ? 0  =  x + x-x ? y  =  x--0 ? x  =  x-x ? 0  =  x + x-x ? y  =  0--0 ? x  =  x-x ? 0  =  x * x-x ? y  =  x--0 ? x  =  x-x ? 0  =  x * x-x ? y  =  0--0 ? x  =  x-x ? 0  =  dec (dec x)-x ? y  =  x--0 ? x  =  x-x ? 0  =  dec (dec x)-x ? y  =  0--0 ? x  =  0-x ? 0  =  x-x ? y  =  y + y--0 ? x  =  0-x ? 0  =  x-x ? y  =  y * y--0 ? x  =  0-x ? 0  =  x-x ? y  =  dec (dec x)--0 ? x  =  0-x ? 0  =  x-x ? y  =  dec (dec y)--0 ? x  =  0-x ? 0  =  0-x ? y  =  x + y--0 ? x  =  0-x ? 0  =  0-x ? y  =  dec (dec x)--0 ? x  =  0-x ? 0  =  0-x ? y  =  dec (dec y)--0 ? x  =  0-x ? 0  =  dec x-x ? y  =  dec y--0 ? x  =  0-x ? 0  =  x + x-x ? y  =  y--0 ? x  =  0-x ? 0  =  x * x-x ? y  =  y--0 ? x  =  0-x ? 0  =  dec (dec x)-x ? y  =  y--0 ? x  =  dec x-x ? 0  =  x-x ? y  =  dec x--0 ? x  =  dec x-x ? 0  =  0-x ? y  =  dec x--0 ? x  =  dec x-x ? 0  =  dec x-x ? y  =  x--0 ? x  =  dec x-x ? 0  =  dec x-x ? y  =  y--0 ? x  =  dec x-x ? 0  =  dec x-x ? y  =  0--0 ? x  =  x + x-x ? 0  =  x-x ? y  =  y--0 ? x  =  x + x-x ? 0  =  x-x ? y  =  0--0 ? x  =  x + x-x ? 0  =  0-x ? y  =  x--0 ? x  =  x * x-x ? 0  =  x-x ? y  =  y--0 ? x  =  x * x-x ? 0  =  x-x ? y  =  0--0 ? x  =  x * x-x ? 0  =  0-x ? y  =  x--0 ? x  =  dec (dec x)-x ? 0  =  x-x ? y  =  y--0 ? x  =  dec (dec x)-x ? 0  =  x-x ? y  =  0--0 ? x  =  dec (dec x)-x ? 0  =  0-x ? y  =  x--0 ? 0  =  0-0 ? x  =  dec x-x ? y  =  dec x----allowed patterns:--x ? y  =  _---x ? 0  =  _-x ? y  =  _--0 ? x  =  _-x ? y  =  _---0 ? x  =  _-x ? 0  =  _-x ? y  =  _--0 ? 0  =  _-0 ? x  =  _-x ? y  =  _---0 ? 0  =  _-0 ? x  =  _-x ? 0  =  _-x ? y  =  _-----allowed deconstructions:--dec _ :: Int-dec (dec _) :: Int-dec (dec (dec _)) :: Int--Candidates for: goo :: [Int] -> [Int]-  pruning with 4/4 rules-  [2,0,1,0,1,0,1,0,1] direct candidates, 0 duplicates-  [2,1,1,3,4,7,10,17,26] pattern candidates, 0 duplicates--rules:-xs ++ [] == xs-[] ++ xs == xs-(xs ++ ys) ++ zs == xs ++ (ys ++ zs)-(x:xs) ++ ys == x:(xs ++ ys)--direct candidates:--goo xs  =  xs--goo xs  =  []--goo xs  =  xs ++ xs--goo xs  =  xs ++ (xs ++ xs)---pattern candidates:--goo xs  =  xs--goo xs  =  []--goo []  =  []-goo (x:xs)  =  xs--goo xs  =  xs ++ xs--goo []  =  []-goo (x:xs)  =  x:xs--goo []  =  []-goo (x:xs)  =  [x]--goo []  =  []-goo (x:xs)  =  xs ++ xs--goo []  =  []-goo (x:xs)  =  x:goo xs--goo []  =  []-goo (x:xs)  =  xs ++ goo xs--goo []  =  []-goo (x:xs)  =  goo xs ++ xs--goo xs  =  xs ++ (xs ++ xs)--goo []  =  []-goo (x:xs)  =  goo xs ++ goo xs--goo []  =  []-goo (x:xs)  =  x:x:xs--goo []  =  []-goo (x:xs)  =  [x,x]--goo []  =  []-goo (x:xs)  =  x:(xs ++ xs)--goo []  =  []-goo (x:xs)  =  xs ++ (x:xs)--goo []  =  []-goo (x:xs)  =  xs ++ [x]--goo []  =  []-goo (x:xs)  =  xs ++ (xs ++ xs)----allowed patterns:--goo xs  =  _---goo []  =  _-goo (x:xs)  =  _-----allowed deconstructions:---Candidates for: ?? :: [Int] -> [Int] -> [Int]-  pruning with 4/4 rules-  [3,0,4,0,8,0,16,0,32] direct candidates, 0 duplicates-  [3,8,15,45,127,268,845,1565,5692] pattern candidates, 0 duplicates--rules:-xs ++ [] == xs-[] ++ xs == xs-(xs ++ ys) ++ zs == xs ++ (ys ++ zs)-(x:xs) ++ ys == x:(xs ++ ys)--direct candidates:--xs ?? ys  =  xs--xs ?? ys  =  ys--xs ?? ys  =  []--xs ?? ys  =  xs ++ xs--xs ?? ys  =  xs ++ ys--xs ?? ys  =  ys ++ xs--xs ?? ys  =  ys ++ ys--xs ?? ys  =  xs ++ (xs ++ xs)--xs ?? ys  =  xs ++ (xs ++ ys)--xs ?? ys  =  xs ++ (ys ++ xs)--xs ?? ys  =  xs ++ (ys ++ ys)--xs ?? ys  =  ys ++ (xs ++ xs)--xs ?? ys  =  ys ++ (xs ++ ys)--xs ?? ys  =  ys ++ (ys ++ xs)--xs ?? ys  =  ys ++ (ys ++ ys)---pattern candidates:--xs ?? ys  =  xs--xs ?? ys  =  ys--xs ?? ys  =  []--xs ?? []  =  xs-xs ?? (x:ys)  =  ys--xs ?? []  =  xs-xs ?? (x:ys)  =  []--xs ?? []  =  []-xs ?? (x:ys)  =  xs--xs ?? []  =  []-xs ?? (x:ys)  =  ys--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  []--[] ?? xs  =  []-(x:xs) ?? ys  =  xs--[] ?? xs  =  []-(x:xs) ?? ys  =  ys--xs ?? ys  =  xs ++ xs--xs ?? ys  =  xs ++ ys--xs ?? ys  =  ys ++ xs--xs ?? ys  =  ys ++ ys--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  []--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  xs--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  ys--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  []--[] ?? xs  =  []-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  xs--[] ?? xs  =  []-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  []--xs ?? []  =  xs-xs ?? (x:ys)  =  xs ?? ys--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ?? xs--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ?? ys--xs ?? []  =  xs-xs ?? (x:ys)  =  [] ?? xs--xs ?? []  =  xs-xs ?? (x:ys)  =  [] ?? ys--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ?? xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ?? ys--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ?? []--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ?? xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ?? []--xs ?? []  =  xs-xs ?? (x:ys)  =  x:xs--xs ?? []  =  xs-xs ?? (x:ys)  =  x:ys--xs ?? []  =  xs-xs ?? (x:ys)  =  [x]--xs ?? []  =  xs-xs ?? (x:ys)  =  xs ++ xs--xs ?? []  =  xs-xs ?? (x:ys)  =  xs ++ ys--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ++ xs--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ++ ys--xs ?? []  =  []-xs ?? (x:ys)  =  x:xs--xs ?? []  =  []-xs ?? (x:ys)  =  x:ys--xs ?? []  =  []-xs ?? (x:ys)  =  [x]--xs ?? []  =  []-xs ?? (x:ys)  =  xs ++ xs--xs ?? []  =  []-xs ?? (x:ys)  =  xs ++ ys--xs ?? []  =  []-xs ?? (x:ys)  =  ys ++ xs--xs ?? []  =  []-xs ?? (x:ys)  =  ys ++ ys--xs ?? []  =  xs ++ xs-xs ?? (x:ys)  =  xs--xs ?? []  =  xs ++ xs-xs ?? (x:ys)  =  ys--xs ?? []  =  xs ++ xs-xs ?? (x:ys)  =  []--[] ?? xs  =  xs-(x:xs) ?? ys  =  x:xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  x:ys--[] ?? xs  =  xs-(x:xs) ?? ys  =  [x]--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ++ xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ++ ys--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ++ xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ++ ys--[] ?? xs  =  []-(x:xs) ?? ys  =  x:xs--[] ?? xs  =  []-(x:xs) ?? ys  =  x:ys--[] ?? xs  =  []-(x:xs) ?? ys  =  [x]--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ++ xs--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ++ ys--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ++ xs--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ++ ys--[] ?? xs  =  xs ++ xs-(x:xs) ?? ys  =  xs--[] ?? xs  =  xs ++ xs-(x:xs) ?? ys  =  ys--[] ?? xs  =  xs ++ xs-(x:xs) ?? ys  =  []--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  []--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  xs ?? xs--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  xs ?? ys--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  xs ?? []--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ?? xs--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ?? ys--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ?? []--[] ?? xs  =  xs-(x:xs) ?? []  =  xs ?? xs-(x:xs) ?? (y:ys)  =  xs--[] ?? xs  =  xs-(x:xs) ?? []  =  xs ?? []-(x:xs) ?? (y:ys)  =  xs--[] ?? xs  =  xs-(x:xs) ?? []  =  xs ?? xs-(x:xs) ?? (y:ys)  =  ys--[] ?? xs  =  xs-(x:xs) ?? []  =  xs ?? []-(x:xs) ?? (y:ys)  =  ys--[] ?? xs  =  xs-(x:xs) ?? []  =  xs ?? xs-(x:xs) ?? (y:ys)  =  []--[] ?? xs  =  xs-(x:xs) ?? []  =  xs ?? []-(x:xs) ?? (y:ys)  =  []--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  xs ?? xs--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  xs ?? ys--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  xs ?? []--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  ys ?? xs--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  ys ?? ys--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  ys ?? []--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  xs ?? xs--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  xs ?? ys--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  xs ?? []--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ?? xs--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ?? ys--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ?? []--[] ?? xs  =  []-(x:xs) ?? []  =  xs ?? xs-(x:xs) ?? (y:ys)  =  xs--[] ?? xs  =  []-(x:xs) ?? []  =  xs ?? []-(x:xs) ?? (y:ys)  =  xs--[] ?? xs  =  []-(x:xs) ?? []  =  xs ?? xs-(x:xs) ?? (y:ys)  =  ys--[] ?? xs  =  []-(x:xs) ?? []  =  xs ?? []-(x:xs) ?? (y:ys)  =  ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  xs ?? xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  xs ?? ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  xs ?? []--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  ys ?? xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  ys ?? []--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  [] ?? xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  [] ?? ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs ?? xs-(x:xs) ?? ys  =  xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs ?? []-(x:xs) ?? ys  =  xs--[] ?? []  =  []-[] ?? (x:xs)  =  [] ?? xs-(x:xs) ?? ys  =  xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs ?? xs-(x:xs) ?? ys  =  ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs ?? []-(x:xs) ?? ys  =  ys--[] ?? []  =  []-[] ?? (x:xs)  =  [] ?? xs-(x:xs) ?? ys  =  ys--xs ?? ys  =  xs ++ (xs ++ xs)--xs ?? ys  =  xs ++ (xs ++ ys)--xs ?? ys  =  xs ++ (ys ++ xs)--xs ?? ys  =  xs ++ (ys ++ ys)--xs ?? ys  =  ys ++ (xs ++ xs)--xs ?? ys  =  ys ++ (xs ++ ys)--xs ?? ys  =  ys ++ (ys ++ xs)--xs ?? ys  =  ys ++ (ys ++ ys)--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  x:xs--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  x:ys--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  [x]--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  y:xs--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  y:ys--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  [y]--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  xs ++ xs--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  xs ++ ys--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ++ xs--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ++ ys--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  x:xs--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  x:ys--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  [x]--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  y:xs--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  y:ys--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  [y]--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  xs ++ xs--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  xs ++ ys--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  ys ++ xs--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  ys ++ ys--[] ?? xs  =  xs-(x:xs) ?? []  =  x:xs-(x:xs) ?? (y:ys)  =  xs--[] ?? xs  =  xs-(x:xs) ?? []  =  x:xs-(x:xs) ?? (y:ys)  =  ys--[] ?? xs  =  xs-(x:xs) ?? []  =  x:xs-(x:xs) ?? (y:ys)  =  []--[] ?? xs  =  xs-(x:xs) ?? []  =  [x]-(x:xs) ?? (y:ys)  =  xs--[] ?? xs  =  xs-(x:xs) ?? []  =  [x]-(x:xs) ?? (y:ys)  =  ys--[] ?? xs  =  xs-(x:xs) ?? []  =  [x]-(x:xs) ?? (y:ys)  =  []--[] ?? xs  =  xs-(x:xs) ?? []  =  xs ++ xs-(x:xs) ?? (y:ys)  =  xs--[] ?? xs  =  xs-(x:xs) ?? []  =  xs ++ xs-(x:xs) ?? (y:ys)  =  ys--[] ?? xs  =  xs-(x:xs) ?? []  =  xs ++ xs-(x:xs) ?? (y:ys)  =  []--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  x:xs--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  x:ys--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  [x]--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  y:xs--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  y:ys--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  [y]--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  xs ++ xs--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  xs ++ ys--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ++ xs--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ++ ys--[] ?? xs  =  []-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  x:xs--[] ?? xs  =  []-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  x:ys--[] ?? xs  =  []-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  [x]--[] ?? xs  =  []-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  y:xs--[] ?? xs  =  []-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  y:ys--[] ?? xs  =  []-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  [y]--[] ?? xs  =  []-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  xs ++ xs--[] ?? xs  =  []-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  xs ++ ys--[] ?? xs  =  []-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  ys ++ xs--[] ?? xs  =  []-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  ys ++ ys--[] ?? xs  =  []-(x:xs) ?? []  =  x:xs-(x:xs) ?? (y:ys)  =  xs--[] ?? xs  =  []-(x:xs) ?? []  =  x:xs-(x:xs) ?? (y:ys)  =  ys--[] ?? xs  =  []-(x:xs) ?? []  =  x:xs-(x:xs) ?? (y:ys)  =  []--[] ?? xs  =  []-(x:xs) ?? []  =  [x]-(x:xs) ?? (y:ys)  =  xs--[] ?? xs  =  []-(x:xs) ?? []  =  [x]-(x:xs) ?? (y:ys)  =  ys--[] ?? xs  =  []-(x:xs) ?? []  =  [x]-(x:xs) ?? (y:ys)  =  []--[] ?? xs  =  []-(x:xs) ?? []  =  xs ++ xs-(x:xs) ?? (y:ys)  =  xs--[] ?? xs  =  []-(x:xs) ?? []  =  xs ++ xs-(x:xs) ?? (y:ys)  =  ys--[] ?? xs  =  []-(x:xs) ?? []  =  xs ++ xs-(x:xs) ?? (y:ys)  =  []--[] ?? xs  =  xs ++ xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys--[] ?? xs  =  xs ++ xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  []--[] ?? xs  =  xs ++ xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  xs--[] ?? xs  =  xs ++ xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  x:xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  x:ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  [x]--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  xs ++ xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  xs ++ ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  ys ++ xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  ys ++ ys--[] ?? []  =  []-[] ?? (x:xs)  =  x:xs-(x:xs) ?? ys  =  xs--[] ?? []  =  []-[] ?? (x:xs)  =  x:xs-(x:xs) ?? ys  =  ys--[] ?? []  =  []-[] ?? (x:xs)  =  x:xs-(x:xs) ?? ys  =  []--[] ?? []  =  []-[] ?? (x:xs)  =  [x]-(x:xs) ?? ys  =  xs--[] ?? []  =  []-[] ?? (x:xs)  =  [x]-(x:xs) ?? ys  =  ys--[] ?? []  =  []-[] ?? (x:xs)  =  [x]-(x:xs) ?? ys  =  []--[] ?? []  =  []-[] ?? (x:xs)  =  xs ++ xs-(x:xs) ?? ys  =  xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs ++ xs-(x:xs) ?? ys  =  ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs ++ xs-(x:xs) ?? ys  =  []--xs ?? []  =  xs-xs ?? (x:ys)  =  (x:xs) ?? ys--xs ?? []  =  xs-xs ?? (x:ys)  =  (x:ys) ?? ys--xs ?? []  =  xs-xs ?? (x:ys)  =  [x] ?? ys--xs ?? []  =  xs-xs ?? (x:ys)  =  (xs ++ xs) ?? ys--xs ?? []  =  xs-xs ?? (x:ys)  =  (xs ++ ys) ?? ys--xs ?? []  =  xs-xs ?? (x:ys)  =  (ys ++ xs) ?? ys--xs ?? []  =  xs-xs ?? (x:ys)  =  (ys ++ ys) ?? ys--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ?? (x:xs)--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ?? (x:ys)--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ?? [x]--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ?? (xs ++ xs)--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ?? (xs ++ ys)--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ?? (ys ++ xs)--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ?? (ys ++ ys)--xs ?? []  =  xs-xs ?? (x:ys)  =  x:xs ?? ys--xs ?? []  =  xs-xs ?? (x:ys)  =  x:ys ?? xs--xs ?? []  =  xs-xs ?? (x:ys)  =  x:ys ?? ys--xs ?? []  =  xs-xs ?? (x:ys)  =  x:[] ?? xs--xs ?? []  =  xs-xs ?? (x:ys)  =  x:[] ?? ys--xs ?? []  =  xs-xs ?? (x:ys)  =  xs ++ xs ?? ys--xs ?? []  =  xs-xs ?? (x:ys)  =  xs ++ ys ?? xs--xs ?? []  =  xs-xs ?? (x:ys)  =  xs ++ ys ?? ys--xs ?? []  =  xs-xs ?? (x:ys)  =  xs ++ [] ?? xs--xs ?? []  =  xs-xs ?? (x:ys)  =  xs ++ [] ?? ys--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ++ xs ?? ys--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ++ ys ?? xs--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ++ ys ?? ys--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ++ [] ?? xs--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ++ [] ?? ys--xs ?? []  =  xs-xs ?? (x:ys)  =  xs ?? ys ++ xs--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ?? xs ++ xs--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ?? ys ++ xs--xs ?? []  =  xs-xs ?? (x:ys)  =  [] ?? xs ++ xs--xs ?? []  =  xs-xs ?? (x:ys)  =  [] ?? ys ++ xs--xs ?? []  =  xs-xs ?? (x:ys)  =  xs ?? ys ++ ys--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ?? xs ++ ys--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ?? ys ++ ys--xs ?? []  =  xs-xs ?? (x:ys)  =  [] ?? xs ++ ys--xs ?? []  =  xs-xs ?? (x:ys)  =  [] ?? ys ++ ys--xs ?? []  =  []-xs ?? (x:ys)  =  x:xs ?? ys--xs ?? []  =  []-xs ?? (x:ys)  =  x:ys ?? xs--xs ?? []  =  []-xs ?? (x:ys)  =  x:ys ?? ys--xs ?? []  =  []-xs ?? (x:ys)  =  x:[] ?? xs--xs ?? []  =  []-xs ?? (x:ys)  =  x:[] ?? ys--xs ?? []  =  []-xs ?? (x:ys)  =  xs ++ xs ?? ys--xs ?? []  =  []-xs ?? (x:ys)  =  xs ++ ys ?? xs--xs ?? []  =  []-xs ?? (x:ys)  =  xs ++ ys ?? ys--xs ?? []  =  []-xs ?? (x:ys)  =  xs ++ [] ?? xs--xs ?? []  =  []-xs ?? (x:ys)  =  xs ++ [] ?? ys--xs ?? []  =  []-xs ?? (x:ys)  =  ys ++ xs ?? ys--xs ?? []  =  []-xs ?? (x:ys)  =  ys ++ ys ?? xs--xs ?? []  =  []-xs ?? (x:ys)  =  ys ++ ys ?? ys--xs ?? []  =  []-xs ?? (x:ys)  =  ys ++ [] ?? xs--xs ?? []  =  []-xs ?? (x:ys)  =  ys ++ [] ?? ys--xs ?? []  =  []-xs ?? (x:ys)  =  xs ?? ys ++ xs--xs ?? []  =  []-xs ?? (x:ys)  =  ys ?? xs ++ xs--xs ?? []  =  []-xs ?? (x:ys)  =  ys ?? ys ++ xs--xs ?? []  =  []-xs ?? (x:ys)  =  [] ?? xs ++ xs--xs ?? []  =  []-xs ?? (x:ys)  =  [] ?? ys ++ xs--xs ?? []  =  []-xs ?? (x:ys)  =  xs ?? ys ++ ys--xs ?? []  =  []-xs ?? (x:ys)  =  ys ?? xs ++ ys--xs ?? []  =  []-xs ?? (x:ys)  =  ys ?? ys ++ ys--xs ?? []  =  []-xs ?? (x:ys)  =  [] ?? xs ++ ys--xs ?? []  =  []-xs ?? (x:ys)  =  [] ?? ys ++ ys--xs ?? []  =  xs ++ xs-xs ?? (x:ys)  =  xs ?? ys--xs ?? []  =  xs ++ xs-xs ?? (x:ys)  =  ys ?? xs--xs ?? []  =  xs ++ xs-xs ?? (x:ys)  =  ys ?? ys--xs ?? []  =  xs ++ xs-xs ?? (x:ys)  =  [] ?? xs--xs ?? []  =  xs ++ xs-xs ?? (x:ys)  =  [] ?? ys--[] ?? xs  =  xs-(x:xs) ?? ys  =  x:xs ?? xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  x:xs ?? ys--[] ?? xs  =  xs-(x:xs) ?? ys  =  x:xs ?? []--[] ?? xs  =  xs-(x:xs) ?? ys  =  x:ys ?? xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  x:ys ?? []--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ++ xs ?? xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ++ xs ?? ys--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ++ xs ?? []--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ++ ys ?? xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ++ ys ?? []--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ++ xs ?? xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ++ xs ?? ys--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ++ xs ?? []--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ++ ys ?? xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ++ ys ?? []--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ?? xs ++ xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ?? ys ++ xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ?? [] ++ xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ?? xs ++ xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ?? [] ++ xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ?? xs ++ ys--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ?? ys ++ ys--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ?? [] ++ ys--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ?? xs ++ ys--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ?? [] ++ ys--[] ?? xs  =  []-(x:xs) ?? ys  =  x:xs ?? xs--[] ?? xs  =  []-(x:xs) ?? ys  =  x:xs ?? ys--[] ?? xs  =  []-(x:xs) ?? ys  =  x:xs ?? []--[] ?? xs  =  []-(x:xs) ?? ys  =  x:ys ?? xs--[] ?? xs  =  []-(x:xs) ?? ys  =  x:ys ?? []--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ++ xs ?? xs--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ++ xs ?? ys--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ++ xs ?? []--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ++ ys ?? xs--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ++ ys ?? []--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ++ xs ?? xs--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ++ xs ?? ys--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ++ xs ?? []--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ++ ys ?? xs--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ++ ys ?? []--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ?? xs ++ xs--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ?? ys ++ xs--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ?? [] ++ xs--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ?? xs ++ xs--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ?? [] ++ xs--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ?? xs ++ ys--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ?? ys ++ ys--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ?? [] ++ ys--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ?? xs ++ ys--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ?? [] ++ ys--[] ?? xs  =  xs ++ xs-(x:xs) ?? ys  =  xs ?? xs--[] ?? xs  =  xs ++ xs-(x:xs) ?? ys  =  xs ?? ys--[] ?? xs  =  xs ++ xs-(x:xs) ?? ys  =  xs ?? []--[] ?? xs  =  xs ++ xs-(x:xs) ?? ys  =  ys ?? xs--[] ?? xs  =  xs ++ xs-(x:xs) ?? ys  =  ys ?? []--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  xs ?? xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  xs ?? ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  xs ?? []--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ?? xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ?? ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ?? []--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  [] ?? xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  [] ?? ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs ?? xs-(x:xs) ?? (y:ys)  =  xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs ?? []-(x:xs) ?? (y:ys)  =  xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  [] ?? xs-(x:xs) ?? (y:ys)  =  xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs ?? xs-(x:xs) ?? (y:ys)  =  []--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs ?? []-(x:xs) ?? (y:ys)  =  []--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  [] ?? xs-(x:xs) ?? (y:ys)  =  []--[] ?? []  =  []-[] ?? (x:xs)  =  xs ?? xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs ?? []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys--[] ?? []  =  []-[] ?? (x:xs)  =  [] ?? xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs ?? xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  []--[] ?? []  =  []-[] ?? (x:xs)  =  xs ?? []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  []--[] ?? []  =  []-[] ?? (x:xs)  =  [] ?? xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  []--xs ?? []  =  xs-xs ?? (x:ys)  =  x:x:xs--xs ?? []  =  xs-xs ?? (x:ys)  =  x:x:ys--xs ?? []  =  xs-xs ?? (x:ys)  =  [x,x]--xs ?? []  =  xs-xs ?? (x:ys)  =  x:(xs ++ xs)--xs ?? []  =  xs-xs ?? (x:ys)  =  x:(xs ++ ys)--xs ?? []  =  xs-xs ?? (x:ys)  =  x:(ys ++ xs)--xs ?? []  =  xs-xs ?? (x:ys)  =  x:(ys ++ ys)--xs ?? []  =  xs-xs ?? (x:ys)  =  xs ++ (x:xs)--xs ?? []  =  xs-xs ?? (x:ys)  =  xs ++ (x:ys)--xs ?? []  =  xs-xs ?? (x:ys)  =  xs ++ [x]--xs ?? []  =  xs-xs ?? (x:ys)  =  xs ++ (xs ++ xs)--xs ?? []  =  xs-xs ?? (x:ys)  =  xs ++ (xs ++ ys)--xs ?? []  =  xs-xs ?? (x:ys)  =  xs ++ (ys ++ xs)--xs ?? []  =  xs-xs ?? (x:ys)  =  xs ++ (ys ++ ys)--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ++ (x:xs)--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ++ (x:ys)--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ++ [x]--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ++ (xs ++ xs)--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ++ (xs ++ ys)--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ++ (ys ++ xs)--xs ?? []  =  xs-xs ?? (x:ys)  =  ys ++ (ys ++ ys)--xs ?? []  =  []-xs ?? (x:ys)  =  x:x:xs--xs ?? []  =  []-xs ?? (x:ys)  =  x:x:ys--xs ?? []  =  []-xs ?? (x:ys)  =  [x,x]--xs ?? []  =  []-xs ?? (x:ys)  =  x:(xs ++ xs)--xs ?? []  =  []-xs ?? (x:ys)  =  x:(xs ++ ys)--xs ?? []  =  []-xs ?? (x:ys)  =  x:(ys ++ xs)--xs ?? []  =  []-xs ?? (x:ys)  =  x:(ys ++ ys)--xs ?? []  =  []-xs ?? (x:ys)  =  xs ++ (x:xs)--xs ?? []  =  []-xs ?? (x:ys)  =  xs ++ (x:ys)--xs ?? []  =  []-xs ?? (x:ys)  =  xs ++ [x]--xs ?? []  =  []-xs ?? (x:ys)  =  xs ++ (xs ++ xs)--xs ?? []  =  []-xs ?? (x:ys)  =  xs ++ (xs ++ ys)--xs ?? []  =  []-xs ?? (x:ys)  =  xs ++ (ys ++ xs)--xs ?? []  =  []-xs ?? (x:ys)  =  xs ++ (ys ++ ys)--xs ?? []  =  []-xs ?? (x:ys)  =  ys ++ (x:xs)--xs ?? []  =  []-xs ?? (x:ys)  =  ys ++ (x:ys)--xs ?? []  =  []-xs ?? (x:ys)  =  ys ++ [x]--xs ?? []  =  []-xs ?? (x:ys)  =  ys ++ (xs ++ xs)--xs ?? []  =  []-xs ?? (x:ys)  =  ys ++ (xs ++ ys)--xs ?? []  =  []-xs ?? (x:ys)  =  ys ++ (ys ++ xs)--xs ?? []  =  []-xs ?? (x:ys)  =  ys ++ (ys ++ ys)--xs ?? []  =  xs ++ xs-xs ?? (x:ys)  =  x:xs--xs ?? []  =  xs ++ xs-xs ?? (x:ys)  =  x:ys--xs ?? []  =  xs ++ xs-xs ?? (x:ys)  =  [x]--xs ?? []  =  xs ++ xs-xs ?? (x:ys)  =  xs ++ ys--xs ?? []  =  xs ++ xs-xs ?? (x:ys)  =  ys ++ xs--xs ?? []  =  xs ++ xs-xs ?? (x:ys)  =  ys ++ ys--xs ?? []  =  xs ++ (xs ++ xs)-xs ?? (x:ys)  =  xs--xs ?? []  =  xs ++ (xs ++ xs)-xs ?? (x:ys)  =  ys--xs ?? []  =  xs ++ (xs ++ xs)-xs ?? (x:ys)  =  []--[] ?? xs  =  xs-(x:xs) ?? ys  =  x:x:xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  x:x:ys--[] ?? xs  =  xs-(x:xs) ?? ys  =  [x,x]--[] ?? xs  =  xs-(x:xs) ?? ys  =  x:(xs ++ xs)--[] ?? xs  =  xs-(x:xs) ?? ys  =  x:(xs ++ ys)--[] ?? xs  =  xs-(x:xs) ?? ys  =  x:(ys ++ xs)--[] ?? xs  =  xs-(x:xs) ?? ys  =  x:(ys ++ ys)--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ++ (x:xs)--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ++ (x:ys)--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ++ [x]--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ++ (xs ++ xs)--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ++ (xs ++ ys)--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ++ (ys ++ xs)--[] ?? xs  =  xs-(x:xs) ?? ys  =  xs ++ (ys ++ ys)--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ++ (x:xs)--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ++ (x:ys)--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ++ [x]--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ++ (xs ++ xs)--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ++ (xs ++ ys)--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ++ (ys ++ xs)--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ++ (ys ++ ys)--[] ?? xs  =  []-(x:xs) ?? ys  =  x:x:xs--[] ?? xs  =  []-(x:xs) ?? ys  =  x:x:ys--[] ?? xs  =  []-(x:xs) ?? ys  =  [x,x]--[] ?? xs  =  []-(x:xs) ?? ys  =  x:(xs ++ xs)--[] ?? xs  =  []-(x:xs) ?? ys  =  x:(xs ++ ys)--[] ?? xs  =  []-(x:xs) ?? ys  =  x:(ys ++ xs)--[] ?? xs  =  []-(x:xs) ?? ys  =  x:(ys ++ ys)--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ++ (x:xs)--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ++ (x:ys)--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ++ [x]--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ++ (xs ++ xs)--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ++ (xs ++ ys)--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ++ (ys ++ xs)--[] ?? xs  =  []-(x:xs) ?? ys  =  xs ++ (ys ++ ys)--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ++ (x:xs)--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ++ (x:ys)--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ++ [x]--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ++ (xs ++ xs)--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ++ (xs ++ ys)--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ++ (ys ++ xs)--[] ?? xs  =  []-(x:xs) ?? ys  =  ys ++ (ys ++ ys)--[] ?? xs  =  xs ++ xs-(x:xs) ?? ys  =  x:xs--[] ?? xs  =  xs ++ xs-(x:xs) ?? ys  =  x:ys--[] ?? xs  =  xs ++ xs-(x:xs) ?? ys  =  [x]--[] ?? xs  =  xs ++ xs-(x:xs) ?? ys  =  xs ++ xs--[] ?? xs  =  xs ++ xs-(x:xs) ?? ys  =  xs ++ ys--[] ?? xs  =  xs ++ xs-(x:xs) ?? ys  =  ys ++ xs--[] ?? xs  =  xs ++ (xs ++ xs)-(x:xs) ?? ys  =  xs--[] ?? xs  =  xs ++ (xs ++ xs)-(x:xs) ?? ys  =  ys--[] ?? xs  =  xs ++ (xs ++ xs)-(x:xs) ?? ys  =  []--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  x:xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  x:ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  [x]--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  y:xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  y:ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  [y]--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  xs ++ xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  xs ++ ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ++ xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ++ ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  x:xs-(x:xs) ?? (y:ys)  =  xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  x:xs-(x:xs) ?? (y:ys)  =  []--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  [x]-(x:xs) ?? (y:ys)  =  xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  [x]-(x:xs) ?? (y:ys)  =  []--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs ++ xs-(x:xs) ?? (y:ys)  =  xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? []  =  xs ++ xs-(x:xs) ?? (y:ys)  =  []--[] ?? []  =  []-[] ?? (x:xs)  =  x:xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys--[] ?? []  =  []-[] ?? (x:xs)  =  x:xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  []--[] ?? []  =  []-[] ?? (x:xs)  =  [x]-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys--[] ?? []  =  []-[] ?? (x:xs)  =  [x]-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  []--[] ?? []  =  []-[] ?? (x:xs)  =  xs ++ xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs ++ xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  []----allowed patterns:--xs ?? ys  =  _---xs ?? []  =  _-xs ?? (x:ys)  =  _--[] ?? xs  =  _-(x:xs) ?? ys  =  _---[] ?? xs  =  _-(x:xs) ?? []  =  _-(x:xs) ?? (y:ys)  =  _--[] ?? []  =  _-[] ?? (x:xs)  =  _-(x:xs) ?? ys  =  _---[] ?? []  =  _-[] ?? (x:xs)  =  _-(x:xs) ?? []  =  _-(x:xs) ?? (y:ys)  =  _-----allowed deconstructions:---Candidates for: ton :: Bool -> Bool-  pruning with 39/49 rules-  [3,1,0,0,0,0,0,0,0] direct candidates, 0 duplicates-  [3,3,0,0,0,0,0,0,0] pattern candidates, 0 duplicates--rules:-not False == True-not True == False-p && p == p-p || p == p-not (not p) == p-p && False == False-p && True == p-False && p == False-True && p == p-p || False == p-p || True == True-False || p == p-True || p == True-not (p && q) == not p || not q-not (p && q) == not q || not p-not (p || q) == not p && not q-not (p || q) == not q && not p-p && not p == False-not p && p == False-p || not p == True-not p || p == True-(p && q) && r == p && (q && r)-(p && q) && r == q && (p && r)-(p || q) || r == p || (q || r)-(p || q) || r == q || (p || r)-p && (p && q) == p && q-p && (q && p) == p && q-p && (q && p) == q && p-p || (p || q) == p || q-p || (q || p) == p || q-p || (q || p) == q || p-p && (p || q) == p-p && (q || p) == p-(p || q) && p == p-(p || q) && q == q-p || p && q == p-p || q && p == p-p && q || p == p-p && q || q == q-equations:-q && p == p && q-q || p == p || q-q && (p && r) == p && (q && r)-r && (p && q) == p && (q && r)-r && (q && p) == p && (q && r)-q || (p || r) == p || (q || r)-r || (p || q) == p || (q || r)-r || (q || p) == p || (q || r)-(r || q) && p == p && (q || r)-r && q || p == p || q && r--direct candidates:--ton p  =  p--ton p  =  False--ton p  =  True--ton p  =  not p---pattern candidates:--ton p  =  p--ton p  =  False--ton p  =  True--ton p  =  not p--ton False  =  False-ton True  =  True--ton False  =  True-ton True  =  False----allowed patterns:--ton p  =  _---ton False  =  _-ton True  =  _-----allowed deconstructions:---Candidates for: &| :: Bool -> Bool -> Bool-  pruning with 39/49 rules-  [4,2,2,4,2,16,17,56,110] direct candidates, 0 duplicates-  [4,14,26,10,2,16,17,56,110] pattern candidates, 0 duplicates--rules:-not False == True-not True == False-p && p == p-p || p == p-not (not p) == p-p && False == False-p && True == p-False && p == False-True && p == p-p || False == p-p || True == True-False || p == p-True || p == True-not (p && q) == not p || not q-not (p && q) == not q || not p-not (p || q) == not p && not q-not (p || q) == not q && not p-p && not p == False-not p && p == False-p || not p == True-not p || p == True-(p && q) && r == p && (q && r)-(p && q) && r == q && (p && r)-(p || q) || r == p || (q || r)-(p || q) || r == q || (p || r)-p && (p && q) == p && q-p && (q && p) == p && q-p && (q && p) == q && p-p || (p || q) == p || q-p || (q || p) == p || q-p || (q || p) == q || p-p && (p || q) == p-p && (q || p) == p-(p || q) && p == p-(p || q) && q == q-p || p && q == p-p || q && p == p-p && q || p == p-p && q || q == q-equations:-q && p == p && q-q || p == p || q-q && (p && r) == p && (q && r)-r && (p && q) == p && (q && r)-r && (q && p) == p && (q && r)-q || (p || r) == p || (q || r)-r || (p || q) == p || (q || r)-r || (q || p) == p || (q || r)-(r || q) && p == p && (q || r)-r && q || p == p || q && r--direct candidates:--p &| q  =  p--p &| q  =  q--p &| q  =  False--p &| q  =  True--p &| q  =  not p--p &| q  =  not q--p &| q  =  p && q--p &| q  =  p || q--p &| q  =  p && not q--p &| q  =  q && not p--p &| q  =  p || not q--p &| q  =  q || not p--p &| q  =  not p && not q--p &| q  =  not p || not q--p &| q  =  p && (q && not p)--p &| q  =  p && (q || not p)--p &| q  =  q && (p && not q)--p &| q  =  q && (p || not q)--p &| q  =  p || q && not p--p &| q  =  p || (q || not p)--p &| q  =  q || p && not q--p &| q  =  q || (p || not q)--p &| q  =  not p && (p && q)--p &| q  =  not p && (p || q)--p &| q  =  not q && (p && q)--p &| q  =  not q && (p || q)--p &| q  =  not p || p && q--p &| q  =  not p || (p || q)--p &| q  =  not q || p && q--p &| q  =  not q || (p || q)---pattern candidates:--p &| q  =  p--p &| q  =  q--p &| q  =  False--p &| q  =  True--p &| q  =  not p--p &| q  =  not q--p &| False  =  p-p &| True  =  False--p &| False  =  p-p &| True  =  True--p &| False  =  False-p &| True  =  p--p &| False  =  False-p &| True  =  True--p &| False  =  True-p &| True  =  p--p &| False  =  True-p &| True  =  False--False &| p  =  p-True &| p  =  False--False &| p  =  p-True &| p  =  True--False &| p  =  False-True &| p  =  p--False &| p  =  False-True &| p  =  True--False &| p  =  True-True &| p  =  p--False &| p  =  True-True &| p  =  False--p &| q  =  p && q--p &| q  =  p || q--p &| False  =  p-p &| True  =  not p--p &| False  =  False-p &| True  =  not p--p &| False  =  True-p &| True  =  not p--p &| False  =  not p-p &| True  =  p--p &| False  =  not p-p &| True  =  False--p &| False  =  not p-p &| True  =  True--False &| p  =  p-True &| p  =  not p--False &| p  =  False-True &| p  =  not p--False &| p  =  True-True &| p  =  not p--False &| p  =  not p-True &| p  =  p--False &| p  =  not p-True &| p  =  False--False &| p  =  not p-True &| p  =  True--False &| p  =  p-True &| False  =  False-True &| True  =  True--False &| p  =  p-True &| False  =  True-True &| True  =  False--False &| p  =  False-True &| False  =  False-True &| True  =  True--False &| p  =  False-True &| False  =  True-True &| True  =  False--False &| p  =  True-True &| False  =  False-True &| True  =  True--False &| p  =  True-True &| False  =  True-True &| True  =  False--False &| False  =  False-False &| True  =  True-True &| p  =  p--False &| False  =  False-False &| True  =  True-True &| p  =  False--False &| False  =  False-False &| True  =  True-True &| p  =  True--False &| False  =  True-False &| True  =  False-True &| p  =  p--False &| False  =  True-False &| True  =  False-True &| p  =  False--False &| False  =  True-False &| True  =  False-True &| p  =  True--p &| q  =  p && not q--p &| q  =  q && not p--p &| q  =  p || not q--p &| q  =  q || not p--False &| p  =  not p-True &| False  =  False-True &| True  =  True--False &| p  =  not p-True &| False  =  True-True &| True  =  False--False &| False  =  False-False &| True  =  True-True &| p  =  not p--False &| False  =  True-False &| True  =  False-True &| p  =  not p--False &| False  =  False-False &| True  =  True-True &| False  =  True-True &| True  =  False--False &| False  =  True-False &| True  =  False-True &| False  =  False-True &| True  =  True--p &| q  =  not p && not q--p &| q  =  not p || not q--p &| q  =  p && (q && not p)--p &| q  =  p && (q || not p)--p &| q  =  q && (p && not q)--p &| q  =  q && (p || not q)--p &| q  =  p || q && not p--p &| q  =  p || (q || not p)--p &| q  =  q || p && not q--p &| q  =  q || (p || not q)--p &| q  =  not p && (p && q)--p &| q  =  not p && (p || q)--p &| q  =  not q && (p && q)--p &| q  =  not q && (p || q)--p &| q  =  not p || p && q--p &| q  =  not p || (p || q)--p &| q  =  not q || p && q--p &| q  =  not q || (p || q)----allowed patterns:--p &| q  =  _---p &| False  =  _-p &| True  =  _--False &| p  =  _-True &| p  =  _---False &| p  =  _-True &| False  =  _-True &| True  =  _--False &| False  =  _-False &| True  =  _-True &| p  =  _---False &| False  =  _-False &| True  =  _-True &| False  =  _-True &| True  =  _-----allowed deconstructions:---Candidates for: gcd :: Int -> Int -> Int-  pruning with 0/0 rules-  [3,0,9,0,54,0,405,0,3402] direct candidates, 0 duplicates-  [3,6,11,50,98,330,774,2714,6660] pattern candidates, 0 duplicates--no rules.--direct candidates:--gcd x y  =  x--gcd x y  =  y--gcd x y  =  0--gcd x y  =  x `mod` x--gcd x y  =  x `mod` y--gcd x y  =  x `mod` 0--gcd x y  =  y `mod` x--gcd x y  =  y `mod` y--gcd x y  =  y `mod` 0--gcd x y  =  0 `mod` x--gcd x y  =  0 `mod` y--gcd x y  =  0 `mod` 0--gcd x y  =  (x `mod` x) `mod` x--gcd x y  =  (x `mod` x) `mod` y--gcd x y  =  (x `mod` x) `mod` 0--gcd x y  =  (x `mod` y) `mod` x--gcd x y  =  (x `mod` y) `mod` y--gcd x y  =  (x `mod` y) `mod` 0--gcd x y  =  (x `mod` 0) `mod` x--gcd x y  =  (x `mod` 0) `mod` y--gcd x y  =  (x `mod` 0) `mod` 0--gcd x y  =  (y `mod` x) `mod` x--gcd x y  =  (y `mod` x) `mod` y--gcd x y  =  (y `mod` x) `mod` 0--gcd x y  =  (y `mod` y) `mod` x--gcd x y  =  (y `mod` y) `mod` y--gcd x y  =  (y `mod` y) `mod` 0--gcd x y  =  (y `mod` 0) `mod` x--gcd x y  =  (y `mod` 0) `mod` y--gcd x y  =  (y `mod` 0) `mod` 0--gcd x y  =  (0 `mod` x) `mod` x--gcd x y  =  (0 `mod` x) `mod` y--gcd x y  =  (0 `mod` x) `mod` 0--gcd x y  =  (0 `mod` y) `mod` x--gcd x y  =  (0 `mod` y) `mod` y--gcd x y  =  (0 `mod` y) `mod` 0--gcd x y  =  (0 `mod` 0) `mod` x--gcd x y  =  (0 `mod` 0) `mod` y--gcd x y  =  (0 `mod` 0) `mod` 0--gcd x y  =  x `mod` (x `mod` x)--gcd x y  =  x `mod` (x `mod` y)--gcd x y  =  x `mod` (x `mod` 0)--gcd x y  =  x `mod` (y `mod` x)--gcd x y  =  x `mod` (y `mod` y)--gcd x y  =  x `mod` (y `mod` 0)--gcd x y  =  x `mod` (0 `mod` x)--gcd x y  =  x `mod` (0 `mod` y)--gcd x y  =  x `mod` (0 `mod` 0)--gcd x y  =  y `mod` (x `mod` x)--gcd x y  =  y `mod` (x `mod` y)--gcd x y  =  y `mod` (x `mod` 0)--gcd x y  =  y `mod` (y `mod` x)--gcd x y  =  y `mod` (y `mod` y)--gcd x y  =  y `mod` (y `mod` 0)--gcd x y  =  y `mod` (0 `mod` x)--gcd x y  =  y `mod` (0 `mod` y)--gcd x y  =  y `mod` (0 `mod` 0)--gcd x y  =  0 `mod` (x `mod` x)--gcd x y  =  0 `mod` (x `mod` y)--gcd x y  =  0 `mod` (x `mod` 0)--gcd x y  =  0 `mod` (y `mod` x)--gcd x y  =  0 `mod` (y `mod` y)--gcd x y  =  0 `mod` (y `mod` 0)--gcd x y  =  0 `mod` (0 `mod` x)--gcd x y  =  0 `mod` (0 `mod` y)--gcd x y  =  0 `mod` (0 `mod` 0)---pattern candidates:--gcd x y  =  x--gcd x y  =  y--gcd x y  =  0--gcd x 0  =  x-gcd x y  =  y--gcd x 0  =  x-gcd x y  =  0--gcd x 0  =  0-gcd x y  =  x--gcd 0 x  =  x-gcd x y  =  x--gcd 0 x  =  x-gcd x y  =  0--gcd 0 x  =  0-gcd x y  =  y--gcd x y  =  x `mod` x--gcd x y  =  x `mod` y--gcd x y  =  x `mod` 0--gcd x y  =  y `mod` x--gcd x y  =  y `mod` y--gcd x y  =  y `mod` 0--gcd x y  =  0 `mod` x--gcd x y  =  0 `mod` y--gcd 0 x  =  x-gcd x 0  =  x-gcd x y  =  0--gcd 0 x  =  x-gcd x 0  =  0-gcd x y  =  x--gcd 0 x  =  0-gcd x 0  =  x-gcd x y  =  y--gcd x 0  =  x-gcd x y  =  x `mod` x--gcd x 0  =  x-gcd x y  =  x `mod` y--gcd x 0  =  x-gcd x y  =  x `mod` 0--gcd x 0  =  x-gcd x y  =  y `mod` x--gcd x 0  =  x-gcd x y  =  y `mod` y--gcd x 0  =  x-gcd x y  =  y `mod` 0--gcd x 0  =  x-gcd x y  =  0 `mod` x--gcd x 0  =  x-gcd x y  =  0 `mod` y--gcd x 0  =  0-gcd x y  =  x `mod` x--gcd x 0  =  0-gcd x y  =  x `mod` y--gcd x 0  =  0-gcd x y  =  x `mod` 0--gcd x 0  =  0-gcd x y  =  y `mod` x--gcd x 0  =  0-gcd x y  =  y `mod` y--gcd x 0  =  0-gcd x y  =  y `mod` 0--gcd x 0  =  0-gcd x y  =  0 `mod` x--gcd x 0  =  0-gcd x y  =  0 `mod` y--gcd x 0  =  x `mod` x-gcd x y  =  x--gcd x 0  =  x `mod` x-gcd x y  =  y--gcd x 0  =  x `mod` x-gcd x y  =  0--gcd x 0  =  x `mod` 0-gcd x y  =  x--gcd x 0  =  x `mod` 0-gcd x y  =  y--gcd x 0  =  x `mod` 0-gcd x y  =  0--gcd x 0  =  0 `mod` x-gcd x y  =  x--gcd x 0  =  0 `mod` x-gcd x y  =  y--gcd x 0  =  0 `mod` x-gcd x y  =  0--gcd 0 x  =  x-gcd x y  =  x `mod` x--gcd 0 x  =  x-gcd x y  =  x `mod` y--gcd 0 x  =  x-gcd x y  =  x `mod` 0--gcd 0 x  =  x-gcd x y  =  y `mod` x--gcd 0 x  =  x-gcd x y  =  y `mod` y--gcd 0 x  =  x-gcd x y  =  y `mod` 0--gcd 0 x  =  x-gcd x y  =  0 `mod` x--gcd 0 x  =  x-gcd x y  =  0 `mod` y--gcd 0 x  =  0-gcd x y  =  x `mod` x--gcd 0 x  =  0-gcd x y  =  x `mod` y--gcd 0 x  =  0-gcd x y  =  x `mod` 0--gcd 0 x  =  0-gcd x y  =  y `mod` x--gcd 0 x  =  0-gcd x y  =  y `mod` y--gcd 0 x  =  0-gcd x y  =  y `mod` 0--gcd 0 x  =  0-gcd x y  =  0 `mod` x--gcd 0 x  =  0-gcd x y  =  0 `mod` y--gcd 0 x  =  x `mod` x-gcd x y  =  x--gcd 0 x  =  x `mod` x-gcd x y  =  y--gcd 0 x  =  x `mod` x-gcd x y  =  0--gcd 0 x  =  x `mod` 0-gcd x y  =  x--gcd 0 x  =  x `mod` 0-gcd x y  =  y--gcd 0 x  =  x `mod` 0-gcd x y  =  0--gcd 0 x  =  0 `mod` x-gcd x y  =  x--gcd 0 x  =  0 `mod` x-gcd x y  =  y--gcd 0 x  =  0 `mod` x-gcd x y  =  0--gcd x y  =  (x `mod` x) `mod` x--gcd x y  =  (x `mod` x) `mod` y--gcd x y  =  (x `mod` x) `mod` 0--gcd x y  =  (x `mod` y) `mod` x--gcd x y  =  (x `mod` y) `mod` y--gcd x y  =  (x `mod` y) `mod` 0--gcd x y  =  (x `mod` 0) `mod` x--gcd x y  =  (x `mod` 0) `mod` y--gcd x y  =  (x `mod` 0) `mod` 0--gcd x y  =  (y `mod` x) `mod` x--gcd x y  =  (y `mod` x) `mod` y--gcd x y  =  (y `mod` x) `mod` 0--gcd x y  =  (y `mod` y) `mod` x--gcd x y  =  (y `mod` y) `mod` y--gcd x y  =  (y `mod` y) `mod` 0--gcd x y  =  (y `mod` 0) `mod` x--gcd x y  =  (y `mod` 0) `mod` y--gcd x y  =  (y `mod` 0) `mod` 0--gcd x y  =  (0 `mod` x) `mod` x--gcd x y  =  (0 `mod` x) `mod` y--gcd x y  =  (0 `mod` x) `mod` 0--gcd x y  =  (0 `mod` y) `mod` x--gcd x y  =  (0 `mod` y) `mod` y--gcd x y  =  (0 `mod` y) `mod` 0--gcd x y  =  x `mod` (x `mod` x)--gcd x y  =  x `mod` (x `mod` y)--gcd x y  =  x `mod` (x `mod` 0)--gcd x y  =  x `mod` (y `mod` x)--gcd x y  =  x `mod` (y `mod` y)--gcd x y  =  x `mod` (y `mod` 0)--gcd x y  =  x `mod` (0 `mod` x)--gcd x y  =  x `mod` (0 `mod` y)--gcd x y  =  y `mod` (x `mod` x)--gcd x y  =  y `mod` (x `mod` y)--gcd x y  =  y `mod` (x `mod` 0)--gcd x y  =  y `mod` (y `mod` x)--gcd x y  =  y `mod` (y `mod` y)--gcd x y  =  y `mod` (y `mod` 0)--gcd x y  =  y `mod` (0 `mod` x)--gcd x y  =  y `mod` (0 `mod` y)--gcd x y  =  0 `mod` (x `mod` x)--gcd x y  =  0 `mod` (x `mod` y)--gcd x y  =  0 `mod` (x `mod` 0)--gcd x y  =  0 `mod` (y `mod` x)--gcd x y  =  0 `mod` (y `mod` y)--gcd x y  =  0 `mod` (y `mod` 0)--gcd x y  =  0 `mod` (0 `mod` x)--gcd x y  =  0 `mod` (0 `mod` y)--gcd 0 x  =  x-gcd x 0  =  x-gcd x y  =  x `mod` x--gcd 0 x  =  x-gcd x 0  =  x-gcd x y  =  x `mod` y--gcd 0 x  =  x-gcd x 0  =  x-gcd x y  =  x `mod` 0--gcd 0 x  =  x-gcd x 0  =  x-gcd x y  =  y `mod` x--gcd 0 x  =  x-gcd x 0  =  x-gcd x y  =  y `mod` y--gcd 0 x  =  x-gcd x 0  =  x-gcd x y  =  y `mod` 0--gcd 0 x  =  x-gcd x 0  =  x-gcd x y  =  0 `mod` x--gcd 0 x  =  x-gcd x 0  =  x-gcd x y  =  0 `mod` y--gcd 0 x  =  x-gcd x 0  =  0-gcd x y  =  x `mod` x--gcd 0 x  =  x-gcd x 0  =  0-gcd x y  =  x `mod` y--gcd 0 x  =  x-gcd x 0  =  0-gcd x y  =  x `mod` 0--gcd 0 x  =  x-gcd x 0  =  0-gcd x y  =  y `mod` x--gcd 0 x  =  x-gcd x 0  =  0-gcd x y  =  y `mod` y--gcd 0 x  =  x-gcd x 0  =  0-gcd x y  =  y `mod` 0--gcd 0 x  =  x-gcd x 0  =  0-gcd x y  =  0 `mod` x--gcd 0 x  =  x-gcd x 0  =  0-gcd x y  =  0 `mod` y--gcd 0 x  =  x-gcd x 0  =  x `mod` x-gcd x y  =  x--gcd 0 x  =  x-gcd x 0  =  x `mod` x-gcd x y  =  0--gcd 0 x  =  x-gcd x 0  =  x `mod` 0-gcd x y  =  x--gcd 0 x  =  x-gcd x 0  =  x `mod` 0-gcd x y  =  0--gcd 0 x  =  x-gcd x 0  =  0 `mod` x-gcd x y  =  x--gcd 0 x  =  x-gcd x 0  =  0 `mod` x-gcd x y  =  0--gcd 0 x  =  0-gcd x 0  =  x-gcd x y  =  x `mod` x--gcd 0 x  =  0-gcd x 0  =  x-gcd x y  =  x `mod` y--gcd 0 x  =  0-gcd x 0  =  x-gcd x y  =  x `mod` 0--gcd 0 x  =  0-gcd x 0  =  x-gcd x y  =  y `mod` x--gcd 0 x  =  0-gcd x 0  =  x-gcd x y  =  y `mod` y--gcd 0 x  =  0-gcd x 0  =  x-gcd x y  =  y `mod` 0--gcd 0 x  =  0-gcd x 0  =  x-gcd x y  =  0 `mod` x--gcd 0 x  =  0-gcd x 0  =  x-gcd x y  =  0 `mod` y--gcd 0 x  =  0-gcd x 0  =  0-gcd x y  =  x `mod` x--gcd 0 x  =  0-gcd x 0  =  0-gcd x y  =  x `mod` y--gcd 0 x  =  0-gcd x 0  =  0-gcd x y  =  x `mod` 0--gcd 0 x  =  0-gcd x 0  =  0-gcd x y  =  y `mod` x--gcd 0 x  =  0-gcd x 0  =  0-gcd x y  =  y `mod` y--gcd 0 x  =  0-gcd x 0  =  0-gcd x y  =  y `mod` 0--gcd 0 x  =  0-gcd x 0  =  0-gcd x y  =  0 `mod` x--gcd 0 x  =  0-gcd x 0  =  0-gcd x y  =  0 `mod` y--gcd 0 x  =  0-gcd x 0  =  x `mod` x-gcd x y  =  y--gcd 0 x  =  0-gcd x 0  =  x `mod` 0-gcd x y  =  y--gcd 0 x  =  0-gcd x 0  =  0 `mod` x-gcd x y  =  y--gcd 0 x  =  x `mod` x-gcd x 0  =  x-gcd x y  =  y--gcd 0 x  =  x `mod` x-gcd x 0  =  x-gcd x y  =  0--gcd 0 x  =  x `mod` x-gcd x 0  =  0-gcd x y  =  x--gcd 0 x  =  x `mod` 0-gcd x 0  =  x-gcd x y  =  y--gcd 0 x  =  x `mod` 0-gcd x 0  =  x-gcd x y  =  0--gcd 0 x  =  x `mod` 0-gcd x 0  =  0-gcd x y  =  x--gcd 0 x  =  0 `mod` x-gcd x 0  =  x-gcd x y  =  y--gcd 0 x  =  0 `mod` x-gcd x 0  =  x-gcd x y  =  0--gcd 0 x  =  0 `mod` x-gcd x 0  =  0-gcd x y  =  x--gcd x 0  =  x-gcd x y  =  gcd x (x `mod` y)--gcd x 0  =  x-gcd x y  =  gcd x (y `mod` y)--gcd x 0  =  x-gcd x y  =  gcd y (x `mod` x)--gcd x 0  =  x-gcd x y  =  gcd y (x `mod` y)--gcd x 0  =  x-gcd x y  =  gcd y (y `mod` x)--gcd x 0  =  x-gcd x y  =  gcd y (y `mod` y)--gcd x 0  =  x-gcd x y  =  gcd 0 (x `mod` y)--gcd x 0  =  x-gcd x y  =  gcd 0 (y `mod` y)--gcd x 0  =  x-gcd x y  =  gcd (x `mod` x) x--gcd x 0  =  x-gcd x y  =  gcd (x `mod` x) y--gcd x 0  =  x-gcd x y  =  gcd (x `mod` y) x--gcd x 0  =  x-gcd x y  =  gcd (y `mod` x) x--gcd x 0  =  x-gcd x y  =  gcd (y `mod` x) y--gcd x 0  =  x-gcd x y  =  gcd (y `mod` y) x--gcd 0 x  =  x-gcd x y  =  gcd x (x `mod` y)--gcd 0 x  =  x-gcd x y  =  gcd x (y `mod` y)--gcd 0 x  =  x-gcd x y  =  gcd y (x `mod` x)--gcd 0 x  =  x-gcd x y  =  gcd y (x `mod` y)--gcd 0 x  =  x-gcd x y  =  gcd y (y `mod` x)--gcd 0 x  =  x-gcd x y  =  gcd y (y `mod` y)--gcd 0 x  =  x-gcd x y  =  gcd (x `mod` x) x--gcd 0 x  =  x-gcd x y  =  gcd (x `mod` x) y--gcd 0 x  =  x-gcd x y  =  gcd (x `mod` x) 0--gcd 0 x  =  x-gcd x y  =  gcd (x `mod` y) x--gcd 0 x  =  x-gcd x y  =  gcd (y `mod` x) x--gcd 0 x  =  x-gcd x y  =  gcd (y `mod` x) y--gcd 0 x  =  x-gcd x y  =  gcd (y `mod` x) 0--gcd 0 x  =  x-gcd x y  =  gcd (y `mod` y) x--gcd x 0  =  x-gcd x y  =  (x `mod` x) `mod` x--gcd x 0  =  x-gcd x y  =  (x `mod` x) `mod` y--gcd x 0  =  x-gcd x y  =  (x `mod` x) `mod` 0--gcd x 0  =  x-gcd x y  =  (x `mod` y) `mod` x--gcd x 0  =  x-gcd x y  =  (x `mod` y) `mod` y--gcd x 0  =  x-gcd x y  =  (x `mod` y) `mod` 0--gcd x 0  =  x-gcd x y  =  (x `mod` 0) `mod` x--gcd x 0  =  x-gcd x y  =  (x `mod` 0) `mod` y--gcd x 0  =  x-gcd x y  =  (x `mod` 0) `mod` 0--gcd x 0  =  x-gcd x y  =  (y `mod` x) `mod` x--gcd x 0  =  x-gcd x y  =  (y `mod` x) `mod` y--gcd x 0  =  x-gcd x y  =  (y `mod` x) `mod` 0--gcd x 0  =  x-gcd x y  =  (y `mod` y) `mod` x--gcd x 0  =  x-gcd x y  =  (y `mod` y) `mod` y--gcd x 0  =  x-gcd x y  =  (y `mod` y) `mod` 0--gcd x 0  =  x-gcd x y  =  (y `mod` 0) `mod` x--gcd x 0  =  x-gcd x y  =  (y `mod` 0) `mod` y--gcd x 0  =  x-gcd x y  =  (y `mod` 0) `mod` 0--gcd x 0  =  x-gcd x y  =  (0 `mod` x) `mod` x--gcd x 0  =  x-gcd x y  =  (0 `mod` x) `mod` y--gcd x 0  =  x-gcd x y  =  (0 `mod` x) `mod` 0--gcd x 0  =  x-gcd x y  =  (0 `mod` y) `mod` x--gcd x 0  =  x-gcd x y  =  (0 `mod` y) `mod` y--gcd x 0  =  x-gcd x y  =  (0 `mod` y) `mod` 0--gcd x 0  =  x-gcd x y  =  x `mod` (x `mod` x)--gcd x 0  =  x-gcd x y  =  x `mod` (x `mod` y)--gcd x 0  =  x-gcd x y  =  x `mod` (x `mod` 0)--gcd x 0  =  x-gcd x y  =  x `mod` (y `mod` x)--gcd x 0  =  x-gcd x y  =  x `mod` (y `mod` y)--gcd x 0  =  x-gcd x y  =  x `mod` (y `mod` 0)--gcd x 0  =  x-gcd x y  =  x `mod` (0 `mod` x)--gcd x 0  =  x-gcd x y  =  x `mod` (0 `mod` y)--gcd x 0  =  x-gcd x y  =  y `mod` (x `mod` x)--gcd x 0  =  x-gcd x y  =  y `mod` (x `mod` y)--gcd x 0  =  x-gcd x y  =  y `mod` (x `mod` 0)--gcd x 0  =  x-gcd x y  =  y `mod` (y `mod` x)--gcd x 0  =  x-gcd x y  =  y `mod` (y `mod` y)--gcd x 0  =  x-gcd x y  =  y `mod` (y `mod` 0)--gcd x 0  =  x-gcd x y  =  y `mod` (0 `mod` x)--gcd x 0  =  x-gcd x y  =  y `mod` (0 `mod` y)--gcd x 0  =  x-gcd x y  =  0 `mod` (x `mod` x)--gcd x 0  =  x-gcd x y  =  0 `mod` (x `mod` y)--gcd x 0  =  x-gcd x y  =  0 `mod` (x `mod` 0)--gcd x 0  =  x-gcd x y  =  0 `mod` (y `mod` x)--gcd x 0  =  x-gcd x y  =  0 `mod` (y `mod` y)--gcd x 0  =  x-gcd x y  =  0 `mod` (y `mod` 0)--gcd x 0  =  x-gcd x y  =  0 `mod` (0 `mod` x)--gcd x 0  =  x-gcd x y  =  0 `mod` (0 `mod` y)--gcd x 0  =  0-gcd x y  =  (x `mod` x) `mod` x--gcd x 0  =  0-gcd x y  =  (x `mod` x) `mod` y--gcd x 0  =  0-gcd x y  =  (x `mod` x) `mod` 0--gcd x 0  =  0-gcd x y  =  (x `mod` y) `mod` x--gcd x 0  =  0-gcd x y  =  (x `mod` y) `mod` y--gcd x 0  =  0-gcd x y  =  (x `mod` y) `mod` 0--gcd x 0  =  0-gcd x y  =  (x `mod` 0) `mod` x--gcd x 0  =  0-gcd x y  =  (x `mod` 0) `mod` y--gcd x 0  =  0-gcd x y  =  (x `mod` 0) `mod` 0--gcd x 0  =  0-gcd x y  =  (y `mod` x) `mod` x--gcd x 0  =  0-gcd x y  =  (y `mod` x) `mod` y--gcd x 0  =  0-gcd x y  =  (y `mod` x) `mod` 0--gcd x 0  =  0-gcd x y  =  (y `mod` y) `mod` x--gcd x 0  =  0-gcd x y  =  (y `mod` y) `mod` y--gcd x 0  =  0-gcd x y  =  (y `mod` y) `mod` 0--gcd x 0  =  0-gcd x y  =  (y `mod` 0) `mod` x--gcd x 0  =  0-gcd x y  =  (y `mod` 0) `mod` y--gcd x 0  =  0-gcd x y  =  (y `mod` 0) `mod` 0--gcd x 0  =  0-gcd x y  =  (0 `mod` x) `mod` x--gcd x 0  =  0-gcd x y  =  (0 `mod` x) `mod` y--gcd x 0  =  0-gcd x y  =  (0 `mod` x) `mod` 0--gcd x 0  =  0-gcd x y  =  (0 `mod` y) `mod` x--gcd x 0  =  0-gcd x y  =  (0 `mod` y) `mod` y--gcd x 0  =  0-gcd x y  =  (0 `mod` y) `mod` 0--gcd x 0  =  0-gcd x y  =  x `mod` (x `mod` x)--gcd x 0  =  0-gcd x y  =  x `mod` (x `mod` y)--gcd x 0  =  0-gcd x y  =  x `mod` (x `mod` 0)--gcd x 0  =  0-gcd x y  =  x `mod` (y `mod` x)--gcd x 0  =  0-gcd x y  =  x `mod` (y `mod` y)--gcd x 0  =  0-gcd x y  =  x `mod` (y `mod` 0)--gcd x 0  =  0-gcd x y  =  x `mod` (0 `mod` x)--gcd x 0  =  0-gcd x y  =  x `mod` (0 `mod` y)--gcd x 0  =  0-gcd x y  =  y `mod` (x `mod` x)--gcd x 0  =  0-gcd x y  =  y `mod` (x `mod` y)--gcd x 0  =  0-gcd x y  =  y `mod` (x `mod` 0)--gcd x 0  =  0-gcd x y  =  y `mod` (y `mod` x)--gcd x 0  =  0-gcd x y  =  y `mod` (y `mod` y)--gcd x 0  =  0-gcd x y  =  y `mod` (y `mod` 0)--gcd x 0  =  0-gcd x y  =  y `mod` (0 `mod` x)--gcd x 0  =  0-gcd x y  =  y `mod` (0 `mod` y)--gcd x 0  =  0-gcd x y  =  0 `mod` (x `mod` x)--gcd x 0  =  0-gcd x y  =  0 `mod` (x `mod` y)--gcd x 0  =  0-gcd x y  =  0 `mod` (x `mod` 0)--gcd x 0  =  0-gcd x y  =  0 `mod` (y `mod` x)--gcd x 0  =  0-gcd x y  =  0 `mod` (y `mod` y)--gcd x 0  =  0-gcd x y  =  0 `mod` (y `mod` 0)--gcd x 0  =  0-gcd x y  =  0 `mod` (0 `mod` x)--gcd x 0  =  0-gcd x y  =  0 `mod` (0 `mod` y)--gcd x 0  =  x `mod` x-gcd x y  =  x `mod` y--gcd x 0  =  x `mod` x-gcd x y  =  x `mod` 0--gcd x 0  =  x `mod` x-gcd x y  =  y `mod` x--gcd x 0  =  x `mod` x-gcd x y  =  y `mod` y--gcd x 0  =  x `mod` x-gcd x y  =  y `mod` 0--gcd x 0  =  x `mod` x-gcd x y  =  0 `mod` x--gcd x 0  =  x `mod` x-gcd x y  =  0 `mod` y--gcd x 0  =  x `mod` 0-gcd x y  =  x `mod` x--gcd x 0  =  x `mod` 0-gcd x y  =  y `mod` x--gcd x 0  =  x `mod` 0-gcd x y  =  y `mod` y--gcd x 0  =  x `mod` 0-gcd x y  =  y `mod` 0--gcd x 0  =  x `mod` 0-gcd x y  =  0 `mod` x--gcd x 0  =  x `mod` 0-gcd x y  =  0 `mod` y--gcd x 0  =  0 `mod` x-gcd x y  =  x `mod` x--gcd x 0  =  0 `mod` x-gcd x y  =  x `mod` y--gcd x 0  =  0 `mod` x-gcd x y  =  x `mod` 0--gcd x 0  =  0 `mod` x-gcd x y  =  y `mod` y--gcd x 0  =  0 `mod` x-gcd x y  =  y `mod` 0--gcd x 0  =  0 `mod` x-gcd x y  =  0 `mod` y--gcd x 0  =  (x `mod` x) `mod` x-gcd x y  =  x--gcd x 0  =  (x `mod` x) `mod` x-gcd x y  =  y--gcd x 0  =  (x `mod` x) `mod` x-gcd x y  =  0--gcd x 0  =  (x `mod` x) `mod` 0-gcd x y  =  x--gcd x 0  =  (x `mod` x) `mod` 0-gcd x y  =  y--gcd x 0  =  (x `mod` x) `mod` 0-gcd x y  =  0--gcd x 0  =  (x `mod` 0) `mod` x-gcd x y  =  x--gcd x 0  =  (x `mod` 0) `mod` x-gcd x y  =  y--gcd x 0  =  (x `mod` 0) `mod` x-gcd x y  =  0--gcd x 0  =  (x `mod` 0) `mod` 0-gcd x y  =  x--gcd x 0  =  (x `mod` 0) `mod` 0-gcd x y  =  y--gcd x 0  =  (x `mod` 0) `mod` 0-gcd x y  =  0--gcd x 0  =  (0 `mod` x) `mod` x-gcd x y  =  x--gcd x 0  =  (0 `mod` x) `mod` x-gcd x y  =  y--gcd x 0  =  (0 `mod` x) `mod` x-gcd x y  =  0--gcd x 0  =  (0 `mod` x) `mod` 0-gcd x y  =  x--gcd x 0  =  (0 `mod` x) `mod` 0-gcd x y  =  y--gcd x 0  =  (0 `mod` x) `mod` 0-gcd x y  =  0--gcd x 0  =  x `mod` (x `mod` x)-gcd x y  =  x--gcd x 0  =  x `mod` (x `mod` x)-gcd x y  =  y--gcd x 0  =  x `mod` (x `mod` x)-gcd x y  =  0--gcd x 0  =  x `mod` (x `mod` 0)-gcd x y  =  x--gcd x 0  =  x `mod` (x `mod` 0)-gcd x y  =  y--gcd x 0  =  x `mod` (x `mod` 0)-gcd x y  =  0--gcd x 0  =  x `mod` (0 `mod` x)-gcd x y  =  x--gcd x 0  =  x `mod` (0 `mod` x)-gcd x y  =  y--gcd x 0  =  x `mod` (0 `mod` x)-gcd x y  =  0--gcd x 0  =  0 `mod` (x `mod` x)-gcd x y  =  x--gcd x 0  =  0 `mod` (x `mod` x)-gcd x y  =  y--gcd x 0  =  0 `mod` (x `mod` x)-gcd x y  =  0--gcd x 0  =  0 `mod` (x `mod` 0)-gcd x y  =  x--gcd x 0  =  0 `mod` (x `mod` 0)-gcd x y  =  y--gcd x 0  =  0 `mod` (x `mod` 0)-gcd x y  =  0--gcd x 0  =  0 `mod` (0 `mod` x)-gcd x y  =  x--gcd x 0  =  0 `mod` (0 `mod` x)-gcd x y  =  y--gcd x 0  =  0 `mod` (0 `mod` x)-gcd x y  =  0--gcd 0 x  =  x-gcd x y  =  (x `mod` x) `mod` x--gcd 0 x  =  x-gcd x y  =  (x `mod` x) `mod` y--gcd 0 x  =  x-gcd x y  =  (x `mod` x) `mod` 0--gcd 0 x  =  x-gcd x y  =  (x `mod` y) `mod` x--gcd 0 x  =  x-gcd x y  =  (x `mod` y) `mod` y--gcd 0 x  =  x-gcd x y  =  (x `mod` y) `mod` 0--gcd 0 x  =  x-gcd x y  =  (x `mod` 0) `mod` x--gcd 0 x  =  x-gcd x y  =  (x `mod` 0) `mod` y--gcd 0 x  =  x-gcd x y  =  (x `mod` 0) `mod` 0--gcd 0 x  =  x-gcd x y  =  (y `mod` x) `mod` x--gcd 0 x  =  x-gcd x y  =  (y `mod` x) `mod` y--gcd 0 x  =  x-gcd x y  =  (y `mod` x) `mod` 0--gcd 0 x  =  x-gcd x y  =  (y `mod` y) `mod` x--gcd 0 x  =  x-gcd x y  =  (y `mod` y) `mod` y--gcd 0 x  =  x-gcd x y  =  (y `mod` y) `mod` 0--gcd 0 x  =  x-gcd x y  =  (y `mod` 0) `mod` x--gcd 0 x  =  x-gcd x y  =  (y `mod` 0) `mod` y--gcd 0 x  =  x-gcd x y  =  (y `mod` 0) `mod` 0--gcd 0 x  =  x-gcd x y  =  (0 `mod` x) `mod` x--gcd 0 x  =  x-gcd x y  =  (0 `mod` x) `mod` y--gcd 0 x  =  x-gcd x y  =  (0 `mod` x) `mod` 0--gcd 0 x  =  x-gcd x y  =  (0 `mod` y) `mod` x--gcd 0 x  =  x-gcd x y  =  (0 `mod` y) `mod` y--gcd 0 x  =  x-gcd x y  =  (0 `mod` y) `mod` 0--gcd 0 x  =  x-gcd x y  =  x `mod` (x `mod` x)--gcd 0 x  =  x-gcd x y  =  x `mod` (x `mod` y)--gcd 0 x  =  x-gcd x y  =  x `mod` (x `mod` 0)--gcd 0 x  =  x-gcd x y  =  x `mod` (y `mod` x)--gcd 0 x  =  x-gcd x y  =  x `mod` (y `mod` y)--gcd 0 x  =  x-gcd x y  =  x `mod` (y `mod` 0)--gcd 0 x  =  x-gcd x y  =  x `mod` (0 `mod` x)--gcd 0 x  =  x-gcd x y  =  x `mod` (0 `mod` y)--gcd 0 x  =  x-gcd x y  =  y `mod` (x `mod` x)--gcd 0 x  =  x-gcd x y  =  y `mod` (x `mod` y)--gcd 0 x  =  x-gcd x y  =  y `mod` (x `mod` 0)--gcd 0 x  =  x-gcd x y  =  y `mod` (y `mod` x)--gcd 0 x  =  x-gcd x y  =  y `mod` (y `mod` y)--gcd 0 x  =  x-gcd x y  =  y `mod` (y `mod` 0)--gcd 0 x  =  x-gcd x y  =  y `mod` (0 `mod` x)--gcd 0 x  =  x-gcd x y  =  y `mod` (0 `mod` y)--gcd 0 x  =  x-gcd x y  =  0 `mod` (x `mod` x)--gcd 0 x  =  x-gcd x y  =  0 `mod` (x `mod` y)--gcd 0 x  =  x-gcd x y  =  0 `mod` (x `mod` 0)--gcd 0 x  =  x-gcd x y  =  0 `mod` (y `mod` x)--gcd 0 x  =  x-gcd x y  =  0 `mod` (y `mod` y)--gcd 0 x  =  x-gcd x y  =  0 `mod` (y `mod` 0)--gcd 0 x  =  x-gcd x y  =  0 `mod` (0 `mod` x)--gcd 0 x  =  x-gcd x y  =  0 `mod` (0 `mod` y)--gcd 0 x  =  0-gcd x y  =  (x `mod` x) `mod` x--gcd 0 x  =  0-gcd x y  =  (x `mod` x) `mod` y--gcd 0 x  =  0-gcd x y  =  (x `mod` x) `mod` 0--gcd 0 x  =  0-gcd x y  =  (x `mod` y) `mod` x--gcd 0 x  =  0-gcd x y  =  (x `mod` y) `mod` y--gcd 0 x  =  0-gcd x y  =  (x `mod` y) `mod` 0--gcd 0 x  =  0-gcd x y  =  (x `mod` 0) `mod` x--gcd 0 x  =  0-gcd x y  =  (x `mod` 0) `mod` y--gcd 0 x  =  0-gcd x y  =  (x `mod` 0) `mod` 0--gcd 0 x  =  0-gcd x y  =  (y `mod` x) `mod` x--gcd 0 x  =  0-gcd x y  =  (y `mod` x) `mod` y--gcd 0 x  =  0-gcd x y  =  (y `mod` x) `mod` 0--gcd 0 x  =  0-gcd x y  =  (y `mod` y) `mod` x--gcd 0 x  =  0-gcd x y  =  (y `mod` y) `mod` y--gcd 0 x  =  0-gcd x y  =  (y `mod` y) `mod` 0--gcd 0 x  =  0-gcd x y  =  (y `mod` 0) `mod` x--gcd 0 x  =  0-gcd x y  =  (y `mod` 0) `mod` y--gcd 0 x  =  0-gcd x y  =  (y `mod` 0) `mod` 0--gcd 0 x  =  0-gcd x y  =  (0 `mod` x) `mod` x--gcd 0 x  =  0-gcd x y  =  (0 `mod` x) `mod` y--gcd 0 x  =  0-gcd x y  =  (0 `mod` x) `mod` 0--gcd 0 x  =  0-gcd x y  =  (0 `mod` y) `mod` x--gcd 0 x  =  0-gcd x y  =  (0 `mod` y) `mod` y--gcd 0 x  =  0-gcd x y  =  (0 `mod` y) `mod` 0--gcd 0 x  =  0-gcd x y  =  x `mod` (x `mod` x)--gcd 0 x  =  0-gcd x y  =  x `mod` (x `mod` y)--gcd 0 x  =  0-gcd x y  =  x `mod` (x `mod` 0)--gcd 0 x  =  0-gcd x y  =  x `mod` (y `mod` x)--gcd 0 x  =  0-gcd x y  =  x `mod` (y `mod` y)--gcd 0 x  =  0-gcd x y  =  x `mod` (y `mod` 0)--gcd 0 x  =  0-gcd x y  =  x `mod` (0 `mod` x)--gcd 0 x  =  0-gcd x y  =  x `mod` (0 `mod` y)--gcd 0 x  =  0-gcd x y  =  y `mod` (x `mod` x)--gcd 0 x  =  0-gcd x y  =  y `mod` (x `mod` y)--gcd 0 x  =  0-gcd x y  =  y `mod` (x `mod` 0)--gcd 0 x  =  0-gcd x y  =  y `mod` (y `mod` x)--gcd 0 x  =  0-gcd x y  =  y `mod` (y `mod` y)--gcd 0 x  =  0-gcd x y  =  y `mod` (y `mod` 0)--gcd 0 x  =  0-gcd x y  =  y `mod` (0 `mod` x)--gcd 0 x  =  0-gcd x y  =  y `mod` (0 `mod` y)--gcd 0 x  =  0-gcd x y  =  0 `mod` (x `mod` x)--gcd 0 x  =  0-gcd x y  =  0 `mod` (x `mod` y)--gcd 0 x  =  0-gcd x y  =  0 `mod` (x `mod` 0)--gcd 0 x  =  0-gcd x y  =  0 `mod` (y `mod` x)--gcd 0 x  =  0-gcd x y  =  0 `mod` (y `mod` y)--gcd 0 x  =  0-gcd x y  =  0 `mod` (y `mod` 0)--gcd 0 x  =  0-gcd x y  =  0 `mod` (0 `mod` x)--gcd 0 x  =  0-gcd x y  =  0 `mod` (0 `mod` y)--gcd 0 x  =  x `mod` x-gcd x y  =  x `mod` x--gcd 0 x  =  x `mod` x-gcd x y  =  x `mod` y--gcd 0 x  =  x `mod` x-gcd x y  =  x `mod` 0--gcd 0 x  =  x `mod` x-gcd x y  =  y `mod` x--gcd 0 x  =  x `mod` x-gcd x y  =  y `mod` 0--gcd 0 x  =  x `mod` x-gcd x y  =  0 `mod` x--gcd 0 x  =  x `mod` x-gcd x y  =  0 `mod` y--gcd 0 x  =  x `mod` 0-gcd x y  =  x `mod` x--gcd 0 x  =  x `mod` 0-gcd x y  =  x `mod` y--gcd 0 x  =  x `mod` 0-gcd x y  =  x `mod` 0--gcd 0 x  =  x `mod` 0-gcd x y  =  y `mod` y--gcd 0 x  =  x `mod` 0-gcd x y  =  0 `mod` x--gcd 0 x  =  x `mod` 0-gcd x y  =  0 `mod` y--gcd 0 x  =  0 `mod` x-gcd x y  =  x `mod` x--gcd 0 x  =  0 `mod` x-gcd x y  =  x `mod` 0--gcd 0 x  =  0 `mod` x-gcd x y  =  y `mod` x--gcd 0 x  =  0 `mod` x-gcd x y  =  y `mod` y--gcd 0 x  =  0 `mod` x-gcd x y  =  y `mod` 0--gcd 0 x  =  0 `mod` x-gcd x y  =  0 `mod` x--gcd 0 x  =  (x `mod` x) `mod` x-gcd x y  =  x--gcd 0 x  =  (x `mod` x) `mod` x-gcd x y  =  y--gcd 0 x  =  (x `mod` x) `mod` x-gcd x y  =  0--gcd 0 x  =  (x `mod` x) `mod` 0-gcd x y  =  x--gcd 0 x  =  (x `mod` x) `mod` 0-gcd x y  =  y--gcd 0 x  =  (x `mod` x) `mod` 0-gcd x y  =  0--gcd 0 x  =  (x `mod` 0) `mod` x-gcd x y  =  x--gcd 0 x  =  (x `mod` 0) `mod` x-gcd x y  =  y--gcd 0 x  =  (x `mod` 0) `mod` x-gcd x y  =  0--gcd 0 x  =  (x `mod` 0) `mod` 0-gcd x y  =  x--gcd 0 x  =  (x `mod` 0) `mod` 0-gcd x y  =  y--gcd 0 x  =  (x `mod` 0) `mod` 0-gcd x y  =  0--gcd 0 x  =  (0 `mod` x) `mod` x-gcd x y  =  x--gcd 0 x  =  (0 `mod` x) `mod` x-gcd x y  =  y--gcd 0 x  =  (0 `mod` x) `mod` x-gcd x y  =  0--gcd 0 x  =  (0 `mod` x) `mod` 0-gcd x y  =  x--gcd 0 x  =  (0 `mod` x) `mod` 0-gcd x y  =  y--gcd 0 x  =  (0 `mod` x) `mod` 0-gcd x y  =  0--gcd 0 x  =  x `mod` (x `mod` x)-gcd x y  =  x--gcd 0 x  =  x `mod` (x `mod` x)-gcd x y  =  y--gcd 0 x  =  x `mod` (x `mod` x)-gcd x y  =  0--gcd 0 x  =  x `mod` (x `mod` 0)-gcd x y  =  x--gcd 0 x  =  x `mod` (x `mod` 0)-gcd x y  =  y--gcd 0 x  =  x `mod` (x `mod` 0)-gcd x y  =  0--gcd 0 x  =  x `mod` (0 `mod` x)-gcd x y  =  x--gcd 0 x  =  x `mod` (0 `mod` x)-gcd x y  =  y--gcd 0 x  =  x `mod` (0 `mod` x)-gcd x y  =  0--gcd 0 x  =  0 `mod` (x `mod` x)-gcd x y  =  x--gcd 0 x  =  0 `mod` (x `mod` x)-gcd x y  =  y--gcd 0 x  =  0 `mod` (x `mod` x)-gcd x y  =  0--gcd 0 x  =  0 `mod` (x `mod` 0)-gcd x y  =  x--gcd 0 x  =  0 `mod` (x `mod` 0)-gcd x y  =  y--gcd 0 x  =  0 `mod` (x `mod` 0)-gcd x y  =  0--gcd 0 x  =  0 `mod` (0 `mod` x)-gcd x y  =  x--gcd 0 x  =  0 `mod` (0 `mod` x)-gcd x y  =  y--gcd 0 x  =  0 `mod` (0 `mod` x)-gcd x y  =  0+foo x  =  x + (x + x)++foo x  =  x + (x + 1)++foo x  =  x + (1 + 1)++foo x  =  x + x * x++foo x  =  x + (x - 1)++foo x  =  x + (0 - 1)++foo x  =  1 + (x + x)++foo x  =  1 + (x + 1)++foo x  =  1 + (1 + 1)++foo x  =  1 + x * x++foo x  =  1 + (0 - x)++foo x  =  1 + (1 - x)++foo x  =  x * (x + x)++foo x  =  x * (x * x)++foo x  =  x * (x - 1)++foo x  =  x * (0 - x)++foo x  =  x * (0 - 1)++foo x  =  x * (1 - x)++foo x  =  x - (x + x)++foo x  =  x - (x + 1)++foo x  =  x - (1 + 1)++foo x  =  x - x * x++foo x  =  0 - (x + x)++foo x  =  0 - (x + 1)++foo x  =  0 - (1 + 1)++foo x  =  1 - (x + x)++foo x  =  1 - (x + 1)++foo x  =  1 - (1 + 1)++foo x  =  1 - x * x++foo x  =  x * x - 1+++pattern candidates:++foo x  =  x++foo x  =  0++foo x  =  1++foo 0  =  0+foo x  =  1++foo 0  =  1+foo x  =  x++foo 0  =  1+foo x  =  0++foo x  =  x + x++foo x  =  x + 1++foo x  =  x * x++foo x  =  x - 1++foo x  =  0 - x++foo x  =  1 - x++foo 1  =  0+foo x  =  x++foo 1  =  0+foo x  =  1++foo 1  =  1+foo x  =  0++foo 0  =  0+foo x  =  x + 1++foo 0  =  0+foo x  =  x - 1++foo 0  =  0+foo x  =  1 - x++foo 0  =  1+foo x  =  x + x++foo 0  =  1+foo x  =  x * x++foo 0  =  1+foo x  =  x - 1++foo 0  =  1+foo x  =  0 - x++foo 0  =  0+foo 1  =  0+foo x  =  1++foo 0  =  1+foo 1  =  0+foo x  =  x++foo 0  =  1+foo 1  =  1+foo x  =  0++foo x  =  x + (x + x)++foo x  =  x + (x + 1)++foo x  =  x + x * x++foo x  =  x + (x - 1)++foo x  =  1 + (x + x)++foo x  =  1 + (x + 1)++foo x  =  1 + x * x++foo x  =  1 + (0 - x)++foo x  =  1 + (1 - x)++foo x  =  x * (x + x)++foo x  =  x * (x * x)++foo x  =  x * (x - 1)++foo x  =  x * (0 - x)++foo x  =  x * (1 - x)++foo x  =  x - (x + x)++foo x  =  x - (x + 1)++foo x  =  x - x * x++foo x  =  0 - (x + x)++foo x  =  0 - (x + 1)++foo x  =  1 - (x + x)++foo x  =  1 - (x + 1)++foo x  =  1 - x * x++foo x  =  x * x - 1++foo 1  =  0+foo x  =  x + x++foo 1  =  0+foo x  =  x + 1++foo 1  =  0+foo x  =  x * x++foo 1  =  0+foo x  =  0 - x++foo 1  =  1+foo x  =  x + x++foo 1  =  1+foo x  =  x + 1++foo 1  =  1+foo x  =  x - 1++foo 1  =  1+foo x  =  0 - x++foo 1  =  1+foo x  =  1 - x++foo 0  =  0+foo x  =  x + (x + 1)++foo 0  =  0+foo x  =  x + (x - 1)++foo 0  =  0+foo x  =  1 + (x + x)++foo 0  =  0+foo x  =  1 + (x + 1)++foo 0  =  0+foo x  =  1 + x * x++foo 0  =  0+foo x  =  1 + (0 - x)++foo 0  =  0+foo x  =  1 + (1 - x)++foo 0  =  0+foo x  =  x - (x + 1)++foo 0  =  0+foo x  =  0 - (x + 1)++foo 0  =  0+foo x  =  1 - (x + x)++foo 0  =  0+foo x  =  1 - x * x++foo 0  =  0+foo x  =  x * x - 1++foo 0  =  1+foo x  =  x + (x + x)++foo 0  =  1+foo x  =  x + x * x++foo 0  =  1+foo x  =  x + (x - 1)++foo 0  =  1+foo x  =  1 + (x + 1)++foo 0  =  1+foo x  =  1 + (1 - x)++foo 0  =  1+foo x  =  x * (x + x)++foo 0  =  1+foo x  =  x * (x * x)++foo 0  =  1+foo x  =  x * (x - 1)++foo 0  =  1+foo x  =  x * (0 - x)++foo 0  =  1+foo x  =  x * (1 - x)++foo 0  =  1+foo x  =  x - (x + x)++foo 0  =  1+foo x  =  x - (x + 1)++foo 0  =  1+foo x  =  x - x * x++foo 0  =  1+foo x  =  0 - (x + x)++foo 0  =  1+foo x  =  0 - (x + 1)++foo 0  =  1+foo x  =  1 - (x + 1)++foo 0  =  1+foo x  =  x * x - 1++foo 0  =  0+foo 1  =  0+foo x  =  x + 1++foo 0  =  0+foo 1  =  1+foo x  =  x + 1++foo 0  =  0+foo 1  =  1+foo x  =  x - 1++foo 0  =  0+foo 1  =  1+foo x  =  1 - x++foo 0  =  1+foo 1  =  0+foo x  =  x + x++foo 0  =  1+foo 1  =  0+foo x  =  x * x++foo 0  =  1+foo 1  =  0+foo x  =  0 - x++foo 0  =  1+foo 1  =  1+foo x  =  x + x++foo 0  =  1+foo 1  =  1+foo x  =  x - 1++foo 0  =  1+foo 1  =  1+foo x  =  0 - x++++allowed patterns:++foo x  =  _+++foo 0  =  _+foo x  =  _+++foo 1  =  _+foo x  =  _+++foo 0  =  _+foo 1  =  _+foo x  =  _+++++allowed deconstructions:++_ - 1 :: Int++Candidates for: ? :: Int -> Int -> Int+  pruning with 13/34 rules+  [3,3,9,18,60,162,489,1475,4619] direct candidates, 0 duplicates+  [3,8,25,71,205,632,1957,5906,18303] pattern candidates, 0 duplicates++rules:+x * 0 == 0+0 * x == 0+x + 0 == x+0 + x == x+dec (x + y) == x + dec y+dec (x + y) == y + dec x+dec (x + y) == dec x + y+dec (x + y) == dec y + x+(x * y) * z == x * (y * z)+(x * y) * z == y * (x * z)+(x + y) + z == x + (y + z)+(x + y) + z == y + (x + z)+(x + x) * y == x * (y + y)+equations:+y * x == x * y+y + x == x + y+y + dec x == x + dec y+dec x + y == x + dec y+dec y + x == dec x + y+x + dec 0 == dec x+dec 0 + x == dec x+y * (x * z) == x * (y * z)+z * (x * y) == x * (y * z)+z * (y * x) == x * (y * z)+y + (x + z) == x + (y + z)+z + (x + y) == x + (y + z)+z + (y + x) == x + (y + z)+(z + y) * x == x * (y + z)+z * y + x == x + y * z+y * (x + x) == x * (y + y)+y + dec (dec x) == x + dec (dec y)+dec (dec x) + y == x + dec (dec y)+dec (dec y) + x == dec (dec x) + y+x + dec (dec 0) == dec (dec x)+dec (dec 0) + x == dec (dec x)++direct candidates:++x ? y  =  x++x ? y  =  y++x ? y  =  0++x ? y  =  dec x++x ? y  =  dec y++x ? y  =  dec 0++x ? y  =  dec (dec x)++x ? y  =  dec (dec y)++x ? y  =  dec (dec 0)++x ? y  =  x + x++x ? y  =  x + y++x ? y  =  y + y++x ? y  =  x * x++x ? y  =  x * y++x ? y  =  y * y++x ? y  =  dec (dec (dec x))++x ? y  =  dec (dec (dec y))++x ? y  =  dec (dec (dec 0))++x ? y  =  dec (x * x)++x ? y  =  dec (x * y)++x ? y  =  dec (y * y)++x ? y  =  x + dec x++x ? y  =  x + dec y++x ? y  =  x + dec 0++x ? y  =  y + dec x++x ? y  =  y + dec y++x ? y  =  y + dec 0++x ? y  =  x * dec x++x ? y  =  x * dec y++x ? y  =  x * dec 0++x ? y  =  y * dec x++x ? y  =  y * dec y++x ? y  =  y * dec 0++x ? y  =  dec (dec (dec (dec x)))++x ? y  =  dec (dec (dec (dec y)))++x ? y  =  dec (dec (dec (dec 0)))++x ? y  =  dec (dec (x * x))++x ? y  =  dec (dec (x * y))++x ? y  =  dec (dec (y * y))++x ? y  =  dec (x * dec x)++x ? y  =  dec (x * dec y)++x ? y  =  dec (x * dec 0)++x ? y  =  dec (y * dec x)++x ? y  =  dec (y * dec y)++x ? y  =  dec (y * dec 0)++x ? y  =  x + dec (dec x)++x ? y  =  x + dec (dec y)++x ? y  =  x + dec (dec 0)++x ? y  =  x + (x + x)++x ? y  =  x + (x + y)++x ? y  =  x + (y + y)++x ? y  =  x + x * x++x ? y  =  x + x * y++x ? y  =  x + y * y++x ? y  =  y + dec (dec x)++x ? y  =  y + dec (dec y)++x ? y  =  y + dec (dec 0)++x ? y  =  y + (x + x)++x ? y  =  y + (x + y)++x ? y  =  y + (y + y)++x ? y  =  y + x * x++x ? y  =  y + x * y++x ? y  =  y + y * y++x ? y  =  x * dec (dec x)++x ? y  =  x * dec (dec y)++x ? y  =  x * dec (dec 0)++x ? y  =  x * (x + x)++x ? y  =  x * (x + y)++x ? y  =  x * (y + y)++x ? y  =  x * (x * x)++x ? y  =  x * (x * y)++x ? y  =  x * (y * y)++x ? y  =  y * dec (dec x)++x ? y  =  y * dec (dec y)++x ? y  =  y * dec (dec 0)++x ? y  =  y * (x + x)++x ? y  =  y * (x + y)++x ? y  =  y * (y + y)++x ? y  =  y * (x * x)++x ? y  =  y * (x * y)++x ? y  =  y * (y * y)++x ? y  =  dec x + dec x++x ? y  =  dec x + dec y++x ? y  =  dec x + dec 0++x ? y  =  dec y + dec y++x ? y  =  dec y + dec 0++x ? y  =  dec 0 + dec 0++x ? y  =  dec x * dec x++x ? y  =  dec x * dec y++x ? y  =  dec x * dec 0++x ? y  =  dec y * dec y++x ? y  =  dec y * dec 0++x ? y  =  dec 0 * dec 0+++pattern candidates:++x ? y  =  x++x ? y  =  y++x ? y  =  0++x ? y  =  dec x++x ? y  =  dec y++x ? 0  =  x+x ? y  =  y++x ? 0  =  x+x ? y  =  0++x ? 0  =  0+x ? y  =  x++0 ? x  =  x+x ? y  =  x++0 ? x  =  x+x ? y  =  0++0 ? x  =  0+x ? y  =  y++x ? y  =  dec (dec x)++x ? y  =  dec (dec y)++x ? y  =  x + x++x ? y  =  x + y++x ? y  =  y + y++x ? y  =  x * x++x ? y  =  x * y++x ? y  =  y * y++x ? 0  =  x+x ? y  =  dec x++x ? 0  =  x+x ? y  =  dec y++x ? 0  =  0+x ? y  =  dec x++x ? 0  =  0+x ? y  =  dec y++x ? 0  =  dec x+x ? y  =  x++x ? 0  =  dec x+x ? y  =  y++x ? 0  =  dec x+x ? y  =  0++0 ? x  =  x+x ? y  =  dec x++0 ? x  =  x+x ? y  =  dec y++0 ? x  =  0+x ? y  =  dec x++0 ? x  =  0+x ? y  =  dec y++0 ? x  =  dec x+x ? y  =  x++0 ? x  =  dec x+x ? y  =  y++0 ? x  =  dec x+x ? y  =  0++0 ? x  =  x+x ? 0  =  x+x ? y  =  0++0 ? x  =  x+x ? 0  =  0+x ? y  =  x++0 ? x  =  0+x ? 0  =  x+x ? y  =  y++x ? y  =  dec (dec (dec x))++x ? y  =  dec (dec (dec y))++x ? y  =  dec (x * x)++x ? y  =  dec (x * y)++x ? y  =  dec (y * y)++x ? y  =  x + dec x++x ? y  =  x + dec y++x ? y  =  y + dec x++x ? y  =  y + dec y++x ? y  =  x * dec x++x ? y  =  x * dec y++x ? y  =  y * dec x++x ? y  =  y * dec y++x ? 0  =  x+x ? y  =  dec (dec x)++x ? 0  =  x+x ? y  =  dec (dec y)++x ? 0  =  x+x ? y  =  x + x++x ? 0  =  x+x ? y  =  y + y++x ? 0  =  x+x ? y  =  x * x++x ? 0  =  x+x ? y  =  x * y++x ? 0  =  x+x ? y  =  y * y++x ? 0  =  0+x ? y  =  dec (dec x)++x ? 0  =  0+x ? y  =  dec (dec y)++x ? 0  =  0+x ? y  =  x + x++x ? 0  =  0+x ? y  =  x + y++x ? 0  =  0+x ? y  =  x * x++x ? 0  =  dec x+x ? y  =  dec y++x ? 0  =  dec (dec x)+x ? y  =  x++x ? 0  =  dec (dec x)+x ? y  =  y++x ? 0  =  dec (dec x)+x ? y  =  0++x ? 0  =  x + x+x ? y  =  x++x ? 0  =  x + x+x ? y  =  y++x ? 0  =  x + x+x ? y  =  0++x ? 0  =  x * x+x ? y  =  x++x ? 0  =  x * x+x ? y  =  y++x ? 0  =  x * x+x ? y  =  0++0 ? x  =  x+x ? y  =  dec (dec x)++0 ? x  =  x+x ? y  =  dec (dec y)++0 ? x  =  x+x ? y  =  x + x++0 ? x  =  x+x ? y  =  y + y++0 ? x  =  x+x ? y  =  x * x++0 ? x  =  x+x ? y  =  x * y++0 ? x  =  x+x ? y  =  y * y++0 ? x  =  0+x ? y  =  dec (dec x)++0 ? x  =  0+x ? y  =  dec (dec y)++0 ? x  =  0+x ? y  =  x + y++0 ? x  =  0+x ? y  =  y + y++0 ? x  =  0+x ? y  =  y * y++0 ? x  =  dec x+x ? y  =  dec x++0 ? x  =  dec (dec x)+x ? y  =  x++0 ? x  =  dec (dec x)+x ? y  =  y++0 ? x  =  dec (dec x)+x ? y  =  0++0 ? x  =  x + x+x ? y  =  x++0 ? x  =  x + x+x ? y  =  y++0 ? x  =  x + x+x ? y  =  0++0 ? x  =  x * x+x ? y  =  x++0 ? x  =  x * x+x ? y  =  y++0 ? x  =  x * x+x ? y  =  0++0 ? x  =  x+x ? 0  =  x+x ? y  =  dec x++0 ? x  =  x+x ? 0  =  x+x ? y  =  dec y++0 ? x  =  x+x ? 0  =  0+x ? y  =  dec x++0 ? x  =  x+x ? 0  =  0+x ? y  =  dec y++0 ? x  =  x+x ? 0  =  dec x+x ? y  =  x++0 ? x  =  x+x ? 0  =  dec x+x ? y  =  0++0 ? x  =  0+x ? 0  =  x+x ? y  =  dec x++0 ? x  =  0+x ? 0  =  x+x ? y  =  dec y++0 ? x  =  0+x ? 0  =  0+x ? y  =  dec x++0 ? x  =  0+x ? 0  =  0+x ? y  =  dec y++0 ? x  =  0+x ? 0  =  dec x+x ? y  =  y++0 ? x  =  dec x+x ? 0  =  x+x ? y  =  y++0 ? x  =  dec x+x ? 0  =  x+x ? y  =  0++0 ? x  =  dec x+x ? 0  =  0+x ? y  =  x++x ? y  =  dec (dec (dec (dec x)))++x ? y  =  dec (dec (dec (dec y)))++x ? y  =  dec (dec (x * x))++x ? y  =  dec (dec (x * y))++x ? y  =  dec (dec (y * y))++x ? y  =  dec (x * dec x)++x ? y  =  dec (x * dec y)++x ? y  =  dec (y * dec x)++x ? y  =  dec (y * dec y)++x ? y  =  x + dec (dec x)++x ? y  =  x + dec (dec y)++x ? y  =  x + (x + x)++x ? y  =  x + (x + y)++x ? y  =  x + (y + y)++x ? y  =  x + x * x++x ? y  =  x + x * y++x ? y  =  x + y * y++x ? y  =  y + dec (dec x)++x ? y  =  y + dec (dec y)++x ? y  =  y + (x + x)++x ? y  =  y + (x + y)++x ? y  =  y + (y + y)++x ? y  =  y + x * x++x ? y  =  y + x * y++x ? y  =  y + y * y++x ? y  =  x * dec (dec x)++x ? y  =  x * dec (dec y)++x ? y  =  x * (x + x)++x ? y  =  x * (x + y)++x ? y  =  x * (y + y)++x ? y  =  x * (x * x)++x ? y  =  x * (x * y)++x ? y  =  x * (y * y)++x ? y  =  y * dec (dec x)++x ? y  =  y * dec (dec y)++x ? y  =  y * (x + x)++x ? y  =  y * (x + y)++x ? y  =  y * (y + y)++x ? y  =  y * (x * x)++x ? y  =  y * (x * y)++x ? y  =  y * (y * y)++x ? y  =  dec x + dec x++x ? y  =  dec x + dec y++x ? y  =  dec y + dec y++x ? y  =  dec x * dec x++x ? y  =  dec x * dec y++x ? y  =  dec y * dec y++x ? 0  =  x+x ? y  =  dec (dec (dec x))++x ? 0  =  x+x ? y  =  dec (dec (dec y))++x ? 0  =  x+x ? y  =  dec (x * x)++x ? 0  =  x+x ? y  =  dec (x * y)++x ? 0  =  x+x ? y  =  dec (y * y)++x ? 0  =  x+x ? y  =  x + dec x++x ? 0  =  x+x ? y  =  x + dec y++x ? 0  =  x+x ? y  =  y + dec x++x ? 0  =  x+x ? y  =  y + dec y++x ? 0  =  x+x ? y  =  x * dec x++x ? 0  =  x+x ? y  =  x * dec y++x ? 0  =  x+x ? y  =  y * dec x++x ? 0  =  x+x ? y  =  y * dec y++x ? 0  =  0+x ? y  =  dec (dec (dec x))++x ? 0  =  0+x ? y  =  dec (dec (dec y))++x ? 0  =  0+x ? y  =  dec (x * x)++x ? 0  =  0+x ? y  =  dec (x * y)++x ? 0  =  0+x ? y  =  dec (y * y)++x ? 0  =  0+x ? y  =  x + dec x++x ? 0  =  0+x ? y  =  x + dec y++x ? 0  =  0+x ? y  =  y + dec x++x ? 0  =  0+x ? y  =  y + dec y++x ? 0  =  0+x ? y  =  x * dec x++x ? 0  =  0+x ? y  =  x * dec y++x ? 0  =  dec x+x ? y  =  dec (dec x)++x ? 0  =  dec x+x ? y  =  dec (dec y)++x ? 0  =  dec x+x ? y  =  x + x++x ? 0  =  dec x+x ? y  =  x + y++x ? 0  =  dec x+x ? y  =  y + y++x ? 0  =  dec x+x ? y  =  x * x++x ? 0  =  dec x+x ? y  =  x * y++x ? 0  =  dec x+x ? y  =  y * y++x ? 0  =  dec (dec x)+x ? y  =  dec x++x ? 0  =  dec (dec x)+x ? y  =  dec y++x ? 0  =  x + x+x ? y  =  dec x++x ? 0  =  x + x+x ? y  =  dec y++x ? 0  =  x * x+x ? y  =  dec x++x ? 0  =  x * x+x ? y  =  dec y++x ? 0  =  dec (dec (dec x))+x ? y  =  x++x ? 0  =  dec (dec (dec x))+x ? y  =  y++x ? 0  =  dec (dec (dec x))+x ? y  =  0++x ? 0  =  dec (x * x)+x ? y  =  x++x ? 0  =  dec (x * x)+x ? y  =  y++x ? 0  =  dec (x * x)+x ? y  =  0++x ? 0  =  x + dec x+x ? y  =  x++x ? 0  =  x + dec x+x ? y  =  y++x ? 0  =  x + dec x+x ? y  =  0++x ? 0  =  x * dec x+x ? y  =  x++x ? 0  =  x * dec x+x ? y  =  y++x ? 0  =  x * dec x+x ? y  =  0++0 ? x  =  x+x ? y  =  dec (dec (dec x))++0 ? x  =  x+x ? y  =  dec (dec (dec y))++0 ? x  =  x+x ? y  =  dec (x * x)++0 ? x  =  x+x ? y  =  dec (x * y)++0 ? x  =  x+x ? y  =  dec (y * y)++0 ? x  =  x+x ? y  =  x + dec x++0 ? x  =  x+x ? y  =  x + dec y++0 ? x  =  x+x ? y  =  y + dec x++0 ? x  =  x+x ? y  =  y + dec y++0 ? x  =  x+x ? y  =  x * dec x++0 ? x  =  x+x ? y  =  x * dec y++0 ? x  =  x+x ? y  =  y * dec x++0 ? x  =  x+x ? y  =  y * dec y++0 ? x  =  0+x ? y  =  dec (dec (dec x))++0 ? x  =  0+x ? y  =  dec (dec (dec y))++0 ? x  =  0+x ? y  =  dec (x * x)++0 ? x  =  0+x ? y  =  dec (x * y)++0 ? x  =  0+x ? y  =  dec (y * y)++0 ? x  =  0+x ? y  =  x + dec x++0 ? x  =  0+x ? y  =  x + dec y++0 ? x  =  0+x ? y  =  y + dec x++0 ? x  =  0+x ? y  =  y + dec y++0 ? x  =  0+x ? y  =  y * dec x++0 ? x  =  0+x ? y  =  y * dec y++0 ? x  =  dec x+x ? y  =  dec (dec x)++0 ? x  =  dec x+x ? y  =  dec (dec y)++0 ? x  =  dec x+x ? y  =  x + x++0 ? x  =  dec x+x ? y  =  x + y++0 ? x  =  dec x+x ? y  =  y + y++0 ? x  =  dec x+x ? y  =  x * x++0 ? x  =  dec x+x ? y  =  x * y++0 ? x  =  dec x+x ? y  =  y * y++0 ? x  =  dec (dec x)+x ? y  =  dec x++0 ? x  =  dec (dec x)+x ? y  =  dec y++0 ? x  =  x + x+x ? y  =  dec x++0 ? x  =  x + x+x ? y  =  dec y++0 ? x  =  x * x+x ? y  =  dec x++0 ? x  =  x * x+x ? y  =  dec y++0 ? x  =  dec (dec (dec x))+x ? y  =  x++0 ? x  =  dec (dec (dec x))+x ? y  =  y++0 ? x  =  dec (dec (dec x))+x ? y  =  0++0 ? x  =  dec (x * x)+x ? y  =  x++0 ? x  =  dec (x * x)+x ? y  =  y++0 ? x  =  dec (x * x)+x ? y  =  0++0 ? x  =  x + dec x+x ? y  =  x++0 ? x  =  x + dec x+x ? y  =  y++0 ? x  =  x + dec x+x ? y  =  0++0 ? x  =  x * dec x+x ? y  =  x++0 ? x  =  x * dec x+x ? y  =  y++0 ? x  =  x * dec x+x ? y  =  0++0 ? x  =  x+x ? 0  =  x+x ? y  =  dec (dec x)++0 ? x  =  x+x ? 0  =  x+x ? y  =  dec (dec y)++0 ? x  =  x+x ? 0  =  x+x ? y  =  x + x++0 ? x  =  x+x ? 0  =  x+x ? y  =  y + y++0 ? x  =  x+x ? 0  =  x+x ? y  =  x * x++0 ? x  =  x+x ? 0  =  x+x ? y  =  x * y++0 ? x  =  x+x ? 0  =  x+x ? y  =  y * y++0 ? x  =  x+x ? 0  =  0+x ? y  =  dec (dec x)++0 ? x  =  x+x ? 0  =  0+x ? y  =  dec (dec y)++0 ? x  =  x+x ? 0  =  0+x ? y  =  x + x++0 ? x  =  x+x ? 0  =  0+x ? y  =  x * x++0 ? x  =  x+x ? 0  =  dec x+x ? y  =  dec y++0 ? x  =  x+x ? 0  =  dec (dec x)+x ? y  =  x++0 ? x  =  x+x ? 0  =  dec (dec x)+x ? y  =  0++0 ? x  =  x+x ? 0  =  x + x+x ? y  =  x++0 ? x  =  x+x ? 0  =  x + x+x ? y  =  0++0 ? x  =  x+x ? 0  =  x * x+x ? y  =  x++0 ? x  =  x+x ? 0  =  x * x+x ? y  =  0++0 ? x  =  0+x ? 0  =  x+x ? y  =  dec (dec x)++0 ? x  =  0+x ? 0  =  x+x ? y  =  dec (dec y)++0 ? x  =  0+x ? 0  =  x+x ? y  =  y + y++0 ? x  =  0+x ? 0  =  x+x ? y  =  y * y++0 ? x  =  0+x ? 0  =  0+x ? y  =  dec (dec x)++0 ? x  =  0+x ? 0  =  0+x ? y  =  dec (dec y)++0 ? x  =  0+x ? 0  =  0+x ? y  =  x + y++0 ? x  =  0+x ? 0  =  dec x+x ? y  =  dec y++0 ? x  =  0+x ? 0  =  dec (dec x)+x ? y  =  y++0 ? x  =  0+x ? 0  =  x + x+x ? y  =  y++0 ? x  =  0+x ? 0  =  x * x+x ? y  =  y++0 ? x  =  dec x+x ? 0  =  x+x ? y  =  dec x++0 ? x  =  dec x+x ? 0  =  0+x ? y  =  dec x++0 ? x  =  dec x+x ? 0  =  dec x+x ? y  =  x++0 ? x  =  dec x+x ? 0  =  dec x+x ? y  =  y++0 ? x  =  dec x+x ? 0  =  dec x+x ? y  =  0++0 ? x  =  dec (dec x)+x ? 0  =  x+x ? y  =  y++0 ? x  =  dec (dec x)+x ? 0  =  x+x ? y  =  0++0 ? x  =  dec (dec x)+x ? 0  =  0+x ? y  =  x++0 ? x  =  x + x+x ? 0  =  x+x ? y  =  y++0 ? x  =  x + x+x ? 0  =  x+x ? y  =  0++0 ? x  =  x + x+x ? 0  =  0+x ? y  =  x++0 ? x  =  x * x+x ? 0  =  x+x ? y  =  y++0 ? x  =  x * x+x ? 0  =  x+x ? y  =  0++0 ? x  =  x * x+x ? 0  =  0+x ? y  =  x++0 ? 0  =  0+0 ? x  =  dec x+x ? y  =  dec x++x ? 0  =  x+x ? y  =  x ? dec y++x ? 0  =  x+x ? y  =  y ? dec x++x ? 0  =  x+x ? y  =  y ? dec y++x ? 0  =  x+x ? y  =  0 ? dec y++x ? 0  =  x+x ? y  =  dec x ? x++x ? 0  =  x+x ? y  =  dec x ? y++x ? 0  =  x+x ? y  =  dec y ? x++0 ? x  =  x+x ? y  =  x ? dec y++0 ? x  =  x+x ? y  =  y ? dec x++0 ? x  =  x+x ? y  =  y ? dec y++0 ? x  =  x+x ? y  =  dec x ? x++0 ? x  =  x+x ? y  =  dec x ? y++0 ? x  =  x+x ? y  =  dec x ? 0++0 ? x  =  x+x ? y  =  dec y ? x++++allowed patterns:++x ? y  =  _+++x ? 0  =  _+x ? y  =  _++0 ? x  =  _+x ? y  =  _+++0 ? x  =  _+x ? 0  =  _+x ? y  =  _++0 ? 0  =  _+0 ? x  =  _+x ? y  =  _+++0 ? 0  =  _+0 ? x  =  _+x ? 0  =  _+x ? y  =  _+++++allowed deconstructions:++dec _ :: Int+dec (dec _) :: Int+dec (dec (dec _)) :: Int++Candidates for: goo :: [Int] -> [Int]+  pruning with 4/4 rules+  [2,0,1,0,1,0,1,0,1] direct candidates, 0 duplicates+  [2,1,1,3,4,7,10,17,26] pattern candidates, 0 duplicates++rules:+xs ++ [] == xs+[] ++ xs == xs+(xs ++ ys) ++ zs == xs ++ (ys ++ zs)+(x:xs) ++ ys == x:(xs ++ ys)++direct candidates:++goo xs  =  xs++goo xs  =  []++goo xs  =  xs ++ xs++goo xs  =  xs ++ (xs ++ xs)+++pattern candidates:++goo xs  =  xs++goo xs  =  []++goo []  =  []+goo (x:xs)  =  xs++goo xs  =  xs ++ xs++goo []  =  []+goo (x:xs)  =  x:xs++goo []  =  []+goo (x:xs)  =  [x]++goo []  =  []+goo (x:xs)  =  xs ++ xs++goo xs  =  xs ++ (xs ++ xs)++goo []  =  []+goo (x:xs)  =  x:goo xs++goo []  =  []+goo (x:xs)  =  xs ++ goo xs++goo []  =  []+goo (x:xs)  =  goo xs ++ xs++goo []  =  []+goo (x:xs)  =  x:x:xs++goo []  =  []+goo (x:xs)  =  [x,x]++goo []  =  []+goo (x:xs)  =  x:(xs ++ xs)++goo []  =  []+goo (x:xs)  =  xs ++ (x:xs)++goo []  =  []+goo (x:xs)  =  xs ++ [x]++goo []  =  []+goo (x:xs)  =  xs ++ (xs ++ xs)++goo []  =  []+goo (x:xs)  =  goo xs ++ goo xs++++allowed patterns:++goo xs  =  _+++goo []  =  _+goo (x:xs)  =  _+++++allowed deconstructions:+++Candidates for: ?? :: [Int] -> [Int] -> [Int]+  pruning with 4/4 rules+  [3,0,4,0,8,0,16,0,32] direct candidates, 0 duplicates+  [3,8,15,45,127,268,845,1565,5692] pattern candidates, 0 duplicates++rules:+xs ++ [] == xs+[] ++ xs == xs+(xs ++ ys) ++ zs == xs ++ (ys ++ zs)+(x:xs) ++ ys == x:(xs ++ ys)++direct candidates:++xs ?? ys  =  xs++xs ?? ys  =  ys++xs ?? ys  =  []++xs ?? ys  =  xs ++ xs++xs ?? ys  =  xs ++ ys++xs ?? ys  =  ys ++ xs++xs ?? ys  =  ys ++ ys++xs ?? ys  =  xs ++ (xs ++ xs)++xs ?? ys  =  xs ++ (xs ++ ys)++xs ?? ys  =  xs ++ (ys ++ xs)++xs ?? ys  =  xs ++ (ys ++ ys)++xs ?? ys  =  ys ++ (xs ++ xs)++xs ?? ys  =  ys ++ (xs ++ ys)++xs ?? ys  =  ys ++ (ys ++ xs)++xs ?? ys  =  ys ++ (ys ++ ys)+++pattern candidates:++xs ?? ys  =  xs++xs ?? ys  =  ys++xs ?? ys  =  []++xs ?? []  =  xs+xs ?? (x:ys)  =  ys++xs ?? []  =  xs+xs ?? (x:ys)  =  []++xs ?? []  =  []+xs ?? (x:ys)  =  xs++xs ?? []  =  []+xs ?? (x:ys)  =  ys++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs++[] ?? xs  =  xs+(x:xs) ?? ys  =  []++[] ?? xs  =  []+(x:xs) ?? ys  =  xs++[] ?? xs  =  []+(x:xs) ?? ys  =  ys++xs ?? ys  =  xs ++ xs++xs ?? ys  =  xs ++ ys++xs ?? ys  =  ys ++ xs++xs ?? ys  =  ys ++ ys++[] ?? xs  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  ys++[] ?? xs  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  []++[] ?? xs  =  xs+(x:xs) ?? []  =  []+(x:xs) ?? (y:ys)  =  xs++[] ?? xs  =  xs+(x:xs) ?? []  =  []+(x:xs) ?? (y:ys)  =  ys++[] ?? xs  =  []+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  ys++[] ?? xs  =  []+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  []++[] ?? xs  =  []+(x:xs) ?? []  =  []+(x:xs) ?? (y:ys)  =  xs++[] ?? xs  =  []+(x:xs) ?? []  =  []+(x:xs) ?? (y:ys)  =  ys++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? ys  =  xs++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? ys  =  ys++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? ys  =  []++xs ?? []  =  xs+xs ?? (x:ys)  =  x:xs++xs ?? []  =  xs+xs ?? (x:ys)  =  x:ys++xs ?? []  =  xs+xs ?? (x:ys)  =  [x]++xs ?? []  =  xs+xs ?? (x:ys)  =  xs ++ xs++xs ?? []  =  xs+xs ?? (x:ys)  =  xs ++ ys++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ++ xs++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ++ ys++xs ?? []  =  []+xs ?? (x:ys)  =  x:xs++xs ?? []  =  []+xs ?? (x:ys)  =  x:ys++xs ?? []  =  []+xs ?? (x:ys)  =  [x]++xs ?? []  =  []+xs ?? (x:ys)  =  xs ++ xs++xs ?? []  =  []+xs ?? (x:ys)  =  xs ++ ys++xs ?? []  =  []+xs ?? (x:ys)  =  ys ++ xs++xs ?? []  =  []+xs ?? (x:ys)  =  ys ++ ys++xs ?? []  =  xs ++ xs+xs ?? (x:ys)  =  xs++xs ?? []  =  xs ++ xs+xs ?? (x:ys)  =  ys++xs ?? []  =  xs ++ xs+xs ?? (x:ys)  =  []++[] ?? xs  =  xs+(x:xs) ?? ys  =  x:xs++[] ?? xs  =  xs+(x:xs) ?? ys  =  x:ys++[] ?? xs  =  xs+(x:xs) ?? ys  =  [x]++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ++ xs++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ++ ys++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ++ xs++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ++ ys++[] ?? xs  =  []+(x:xs) ?? ys  =  x:xs++[] ?? xs  =  []+(x:xs) ?? ys  =  x:ys++[] ?? xs  =  []+(x:xs) ?? ys  =  [x]++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ++ xs++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ++ ys++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ++ xs++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ++ ys++[] ?? xs  =  xs ++ xs+(x:xs) ?? ys  =  xs++[] ?? xs  =  xs ++ xs+(x:xs) ?? ys  =  ys++[] ?? xs  =  xs ++ xs+(x:xs) ?? ys  =  []++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  []++xs ?? []  =  xs+xs ?? (x:ys)  =  xs ?? ys++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ?? xs++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ?? ys++xs ?? []  =  xs+xs ?? (x:ys)  =  [] ?? xs++xs ?? []  =  xs+xs ?? 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[]  =  []+[] ?? (x:xs)  =  xs ?? []+(x:xs) ?? ys  =  xs++[] ?? []  =  []+[] ?? (x:xs)  =  [] ?? xs+(x:xs) ?? ys  =  xs++[] ?? []  =  []+[] ?? (x:xs)  =  xs ?? xs+(x:xs) ?? ys  =  ys++[] ?? []  =  []+[] ?? (x:xs)  =  xs ?? []+(x:xs) ?? ys  =  ys++[] ?? []  =  []+[] ?? (x:xs)  =  [] ?? xs+(x:xs) ?? ys  =  ys++xs ?? []  =  xs+xs ?? (x:ys)  =  x:x:xs++xs ?? []  =  xs+xs ?? (x:ys)  =  x:x:ys++xs ?? []  =  xs+xs ?? (x:ys)  =  [x,x]++xs ?? []  =  xs+xs ?? (x:ys)  =  x:(xs ++ xs)++xs ?? []  =  xs+xs ?? (x:ys)  =  x:(xs ++ ys)++xs ?? []  =  xs+xs ?? (x:ys)  =  x:(ys ++ xs)++xs ?? []  =  xs+xs ?? (x:ys)  =  x:(ys ++ ys)++xs ?? []  =  xs+xs ?? (x:ys)  =  xs ++ (x:xs)++xs ?? []  =  xs+xs ?? (x:ys)  =  xs ++ (x:ys)++xs ?? []  =  xs+xs ?? (x:ys)  =  xs ++ [x]++xs ?? []  =  xs+xs ?? (x:ys)  =  xs ++ (xs ++ xs)++xs ?? []  =  xs+xs ?? (x:ys)  =  xs ++ (xs ++ ys)++xs ?? []  =  xs+xs ?? (x:ys)  =  xs ++ (ys ++ xs)++xs ?? []  =  xs+xs ?? (x:ys)  =  xs ++ (ys ++ ys)++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ++ (x:xs)++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ++ (x:ys)++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ++ [x]++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ++ (xs ++ xs)++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ++ (xs ++ ys)++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ++ (ys ++ xs)++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ++ (ys ++ ys)++xs ?? []  =  []+xs ?? (x:ys)  =  x:x:xs++xs ?? []  =  []+xs ?? (x:ys)  =  x:x:ys++xs ?? []  =  []+xs ?? (x:ys)  =  [x,x]++xs ?? []  =  []+xs ?? (x:ys)  =  x:(xs ++ xs)++xs ?? []  =  []+xs ?? (x:ys)  =  x:(xs ++ ys)++xs ?? []  =  []+xs ?? (x:ys)  =  x:(ys ++ xs)++xs ?? []  =  []+xs ?? (x:ys)  =  x:(ys ++ ys)++xs ?? []  =  []+xs ?? (x:ys)  =  xs ++ (x:xs)++xs ?? []  =  []+xs ?? (x:ys)  =  xs ++ (x:ys)++xs ?? []  =  []+xs ?? (x:ys)  =  xs ++ [x]++xs ?? []  =  []+xs ?? (x:ys)  =  xs ++ (xs ++ xs)++xs ?? []  =  []+xs ?? (x:ys)  =  xs ++ (xs ++ ys)++xs ?? []  =  []+xs ?? (x:ys)  =  xs ++ (ys ++ xs)++xs ?? []  =  []+xs ?? (x:ys)  =  xs ++ (ys ++ ys)++xs ?? []  =  []+xs ?? (x:ys)  =  ys ++ (x:xs)++xs ?? []  =  []+xs ?? (x:ys)  =  ys ++ (x:ys)++xs ?? []  =  []+xs ?? (x:ys)  =  ys ++ [x]++xs ?? []  =  []+xs ?? (x:ys)  =  ys ++ (xs ++ xs)++xs ?? []  =  []+xs ?? (x:ys)  =  ys ++ (xs ++ ys)++xs ?? []  =  []+xs ?? (x:ys)  =  ys ++ (ys ++ xs)++xs ?? []  =  []+xs ?? (x:ys)  =  ys ++ (ys ++ ys)++xs ?? []  =  xs ++ xs+xs ?? (x:ys)  =  x:xs++xs ?? []  =  xs ++ xs+xs ?? (x:ys)  =  x:ys++xs ?? []  =  xs ++ xs+xs ?? (x:ys)  =  [x]++xs ?? []  =  xs ++ xs+xs ?? (x:ys)  =  xs ++ ys++xs ?? []  =  xs ++ xs+xs ?? (x:ys)  =  ys ++ xs++xs ?? []  =  xs ++ xs+xs ?? (x:ys)  =  ys ++ ys++xs ?? []  =  xs ++ (xs ++ xs)+xs ?? (x:ys)  =  xs++xs ?? []  =  xs ++ (xs ++ xs)+xs ?? (x:ys)  =  ys++xs ?? []  =  xs ++ (xs ++ xs)+xs ?? (x:ys)  =  []++[] ?? xs  =  xs+(x:xs) ?? ys  =  x:x:xs++[] ?? xs  =  xs+(x:xs) ?? ys  =  x:x:ys++[] ?? xs  =  xs+(x:xs) ?? ys  =  [x,x]++[] ?? xs  =  xs+(x:xs) ?? ys  =  x:(xs ++ xs)++[] ?? xs  =  xs+(x:xs) ?? ys  =  x:(xs ++ ys)++[] ?? xs  =  xs+(x:xs) ?? ys  =  x:(ys ++ xs)++[] ?? xs  =  xs+(x:xs) ?? ys  =  x:(ys ++ ys)++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ++ (x:xs)++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ++ (x:ys)++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ++ [x]++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ++ (xs ++ xs)++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ++ (xs ++ ys)++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ++ (ys ++ xs)++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ++ (ys ++ ys)++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ++ (x:xs)++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ++ (x:ys)++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ++ [x]++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ++ (xs ++ xs)++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ++ (xs ++ ys)++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ++ (ys ++ xs)++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ++ (ys ++ ys)++[] ?? xs  =  []+(x:xs) ?? ys  =  x:x:xs++[] ?? xs  =  []+(x:xs) ?? ys  =  x:x:ys++[] ?? xs  =  []+(x:xs) ?? ys  =  [x,x]++[] ?? xs  =  []+(x:xs) ?? ys  =  x:(xs ++ xs)++[] ?? xs  =  []+(x:xs) ?? ys  =  x:(xs ++ ys)++[] ?? xs  =  []+(x:xs) ?? ys  =  x:(ys ++ xs)++[] ?? xs  =  []+(x:xs) ?? ys  =  x:(ys ++ ys)++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ++ (x:xs)++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ++ (x:ys)++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ++ [x]++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ++ (xs ++ xs)++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ++ (xs ++ ys)++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ++ (ys ++ xs)++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ++ (ys ++ ys)++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ++ (x:xs)++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ++ (x:ys)++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ++ [x]++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ++ (xs ++ xs)++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ++ (xs ++ ys)++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ++ (ys ++ xs)++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ++ (ys ++ ys)++[] ?? xs  =  xs ++ xs+(x:xs) ?? ys  =  x:xs++[] ?? xs  =  xs ++ xs+(x:xs) ?? ys  =  x:ys++[] ?? xs  =  xs ++ xs+(x:xs) ?? ys  =  [x]++[] ?? xs  =  xs ++ xs+(x:xs) ?? ys  =  xs ++ xs++[] ?? xs  =  xs ++ xs+(x:xs) ?? ys  =  xs ++ ys++[] ?? xs  =  xs ++ xs+(x:xs) ?? ys  =  ys ++ xs++[] ?? xs  =  xs ++ (xs ++ xs)+(x:xs) ?? ys  =  xs++[] ?? xs  =  xs ++ (xs ++ xs)+(x:xs) ?? ys  =  ys++[] ?? xs  =  xs ++ (xs ++ xs)+(x:xs) ?? ys  =  []++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  x:xs++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  x:ys++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  [x]++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  y:xs++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  y:ys++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  [y]++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  xs ++ xs++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  xs ++ ys++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  ys ++ xs++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  ys ++ ys++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  x:xs+(x:xs) ?? (y:ys)  =  xs++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  x:xs+(x:xs) ?? (y:ys)  =  []++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  [x]+(x:xs) ?? (y:ys)  =  xs++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  [x]+(x:xs) ?? (y:ys)  =  []++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs ++ xs+(x:xs) ?? (y:ys)  =  xs++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs ++ xs+(x:xs) ?? (y:ys)  =  []++[] ?? []  =  []+[] ?? (x:xs)  =  x:xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  ys++[] ?? []  =  []+[] ?? (x:xs)  =  x:xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  []++[] ?? []  =  []+[] ?? (x:xs)  =  [x]+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  ys++[] ?? []  =  []+[] ?? (x:xs)  =  [x]+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  []++[] ?? []  =  []+[] ?? (x:xs)  =  xs ++ xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  ys++[] ?? []  =  []+[] ?? (x:xs)  =  xs ++ xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  []++xs ?? []  =  xs+xs ?? (x:ys)  =  x:xs ?? ys++xs ?? []  =  xs+xs ?? (x:ys)  =  x:ys ?? xs++xs ?? []  =  xs+xs ?? (x:ys)  =  x:ys ?? ys++xs ?? []  =  xs+xs ?? (x:ys)  =  x:[] ?? xs++xs ?? []  =  xs+xs ?? (x:ys)  =  x:[] ?? ys++xs ?? []  =  xs+xs ?? (x:ys)  =  xs ++ xs ?? ys++xs ?? []  =  xs+xs ?? (x:ys)  =  xs ++ ys ?? xs++xs ?? []  =  xs+xs ?? (x:ys)  =  xs ++ ys ?? ys++xs ?? []  =  xs+xs ?? (x:ys)  =  xs ++ [] ?? xs++xs ?? []  =  xs+xs ?? (x:ys)  =  xs ++ [] ?? ys++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ++ xs ?? ys++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ++ ys ?? xs++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ++ ys ?? ys++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ++ [] ?? xs++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ++ [] ?? ys++xs ?? []  =  xs+xs ?? (x:ys)  =  xs ?? ys ++ xs++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ?? xs ++ xs++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ?? ys ++ xs++xs ?? []  =  xs+xs ?? (x:ys)  =  [] ?? xs ++ xs++xs ?? []  =  xs+xs ?? (x:ys)  =  [] ?? ys ++ xs++xs ?? []  =  xs+xs ?? (x:ys)  =  xs ?? ys ++ ys++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ?? xs ++ ys++xs ?? []  =  xs+xs ?? (x:ys)  =  ys ?? ys ++ ys++xs ?? []  =  xs+xs ?? (x:ys)  =  [] ?? xs ++ ys++xs ?? []  =  xs+xs ?? (x:ys)  =  [] ?? ys ++ ys++xs ?? []  =  []+xs ?? (x:ys)  =  x:xs ?? ys++xs ?? []  =  []+xs ?? (x:ys)  =  x:ys ?? xs++xs ?? []  =  []+xs ?? (x:ys)  =  x:ys ?? ys++xs ?? []  =  []+xs ?? (x:ys)  =  x:[] ?? xs++xs ?? []  =  []+xs ?? (x:ys)  =  x:[] ?? ys++xs ?? []  =  []+xs ?? (x:ys)  =  xs ++ xs ?? ys++xs ?? []  =  []+xs ?? (x:ys)  =  xs ++ ys ?? xs++xs ?? []  =  []+xs ?? (x:ys)  =  xs ++ ys ?? ys++xs ?? []  =  []+xs ?? (x:ys)  =  xs ++ [] ?? xs++xs ?? []  =  []+xs ?? (x:ys)  =  xs ++ [] ?? ys++xs ?? []  =  []+xs ?? (x:ys)  =  ys ++ xs ?? ys++xs ?? []  =  []+xs ?? (x:ys)  =  ys ++ ys ?? xs++xs ?? []  =  []+xs ?? (x:ys)  =  ys ++ ys ?? ys++xs ?? []  =  []+xs ?? (x:ys)  =  ys ++ [] ?? xs++xs ?? []  =  []+xs ?? (x:ys)  =  ys ++ [] ?? ys++xs ?? []  =  []+xs ?? (x:ys)  =  xs ?? ys ++ xs++xs ?? []  =  []+xs ?? (x:ys)  =  ys ?? xs ++ xs++xs ?? []  =  []+xs ?? (x:ys)  =  ys ?? ys ++ xs++xs ?? []  =  []+xs ?? (x:ys)  =  [] ?? xs ++ xs++xs ?? []  =  []+xs ?? (x:ys)  =  [] ?? ys ++ xs++xs ?? []  =  []+xs ?? (x:ys)  =  xs ?? ys ++ ys++xs ?? []  =  []+xs ?? (x:ys)  =  ys ?? xs ++ ys++xs ?? []  =  []+xs ?? (x:ys)  =  ys ?? ys ++ ys++xs ?? []  =  []+xs ?? (x:ys)  =  [] ?? xs ++ ys++xs ?? []  =  []+xs ?? (x:ys)  =  [] ?? ys ++ ys++xs ?? []  =  xs ++ xs+xs ?? (x:ys)  =  xs ?? ys++xs ?? []  =  xs ++ xs+xs ?? (x:ys)  =  ys ?? xs++xs ?? []  =  xs ++ xs+xs ?? (x:ys)  =  ys ?? ys++xs ?? []  =  xs ++ xs+xs ?? (x:ys)  =  [] ?? xs++xs ?? []  =  xs ++ xs+xs ?? (x:ys)  =  [] ?? ys++[] ?? xs  =  xs+(x:xs) ?? ys  =  x:xs ?? xs++[] ?? xs  =  xs+(x:xs) ?? ys  =  x:xs ?? ys++[] ?? xs  =  xs+(x:xs) ?? ys  =  x:xs ?? []++[] ?? xs  =  xs+(x:xs) ?? ys  =  x:ys ?? xs++[] ?? xs  =  xs+(x:xs) ?? ys  =  x:ys ?? []++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ++ xs ?? xs++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ++ xs ?? ys++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ++ xs ?? []++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ++ ys ?? xs++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ++ ys ?? []++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ++ xs ?? xs++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ++ xs ?? ys++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ++ xs ?? []++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ++ ys ?? xs++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ++ ys ?? []++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ?? xs ++ xs++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ?? ys ++ xs++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ?? [] ++ xs++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ?? xs ++ xs++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ?? [] ++ xs++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ?? xs ++ ys++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ?? ys ++ ys++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ?? [] ++ ys++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ?? xs ++ ys++[] ?? xs  =  xs+(x:xs) ?? ys  =  ys ?? [] ++ ys++[] ?? xs  =  []+(x:xs) ?? ys  =  x:xs ?? xs++[] ?? xs  =  []+(x:xs) ?? ys  =  x:xs ?? ys++[] ?? xs  =  []+(x:xs) ?? ys  =  x:xs ?? []++[] ?? xs  =  []+(x:xs) ?? ys  =  x:ys ?? xs++[] ?? xs  =  []+(x:xs) ?? ys  =  x:ys ?? []++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ++ xs ?? xs++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ++ xs ?? ys++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ++ xs ?? []++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ++ ys ?? xs++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ++ ys ?? []++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ++ xs ?? xs++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ++ xs ?? ys++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ++ xs ?? []++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ++ ys ?? xs++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ++ ys ?? []++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ?? xs ++ xs++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ?? ys ++ xs++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ?? [] ++ xs++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ?? xs ++ xs++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ?? [] ++ xs++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ?? xs ++ ys++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ?? ys ++ ys++[] ?? xs  =  []+(x:xs) ?? ys  =  xs ?? [] ++ ys++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ?? xs ++ ys++[] ?? xs  =  []+(x:xs) ?? ys  =  ys ?? [] ++ ys++[] ?? xs  =  xs ++ xs+(x:xs) ?? ys  =  xs ?? xs++[] ?? xs  =  xs ++ xs+(x:xs) ?? ys  =  xs ?? ys++[] ?? xs  =  xs ++ xs+(x:xs) ?? ys  =  xs ?? []++[] ?? xs  =  xs ++ xs+(x:xs) ?? ys  =  ys ?? xs++[] ?? xs  =  xs ++ xs+(x:xs) ?? ys  =  ys ?? []++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  xs ?? xs++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  xs ?? ys++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  xs ?? []++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  ys ?? xs++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  ys ?? ys++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  ys ?? []++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  [] ?? xs++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  [] ?? ys++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs ?? xs+(x:xs) ?? (y:ys)  =  xs++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs ?? []+(x:xs) ?? (y:ys)  =  xs++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  [] ?? xs+(x:xs) ?? (y:ys)  =  xs++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs ?? xs+(x:xs) ?? (y:ys)  =  []++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  xs ?? []+(x:xs) ?? (y:ys)  =  []++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? []  =  [] ?? xs+(x:xs) ?? (y:ys)  =  []++[] ?? []  =  []+[] ?? (x:xs)  =  xs ?? xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  ys++[] ?? []  =  []+[] ?? (x:xs)  =  xs ?? []+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  ys++[] ?? []  =  []+[] ?? (x:xs)  =  [] ?? xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  ys++[] ?? []  =  []+[] ?? (x:xs)  =  xs ?? xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  []++[] ?? []  =  []+[] ?? (x:xs)  =  xs ?? []+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  []++[] ?? []  =  []+[] ?? (x:xs)  =  [] ?? xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  []++xs ?? []  =  xs+xs ?? (x:ys)  =  (x:xs) ?? ys++xs ?? []  =  xs+xs ?? (x:ys)  =  (x:ys) ?? ys++xs ?? []  =  xs+xs ?? (x:ys)  =  [x] ?? ys++xs ?? []  =  xs+xs ?? (x:ys)  =  (xs ++ xs) ?? ys++xs ?? []  =  xs+xs ?? (x:ys)  =  (xs ++ ys) ?? ys++xs ?? []  =  xs+xs ?? (x:ys)  =  (ys ++ xs) ?? ys++xs ?? []  =  xs+xs ?? (x:ys)  =  (ys ++ ys) ?? ys++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ?? (x:xs)++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ?? (x:ys)++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ?? [x]++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ?? (xs ++ xs)++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ?? (xs ++ ys)++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ?? (ys ++ xs)++[] ?? xs  =  xs+(x:xs) ?? ys  =  xs ?? (ys ++ ys)++++allowed patterns:++xs ?? ys  =  _+++xs ?? []  =  _+xs ?? (x:ys)  =  _++[] ?? xs  =  _+(x:xs) ?? ys  =  _+++[] ?? xs  =  _+(x:xs) ?? []  =  _+(x:xs) ?? (y:ys)  =  _++[] ?? []  =  _+[] ?? (x:xs)  =  _+(x:xs) ?? ys  =  _+++[] ?? []  =  _+[] ?? (x:xs)  =  _+(x:xs) ?? []  =  _+(x:xs) ?? (y:ys)  =  _+++++allowed deconstructions:+++Candidates for: ton :: Bool -> Bool+  pruning with 39/49 rules+  [3,1,0,0,0,0,0,0,0] direct candidates, 0 duplicates+  [3,3,0,0,0,0,0,0,0] pattern candidates, 0 duplicates++rules:+not False == True+not True == False+p && p == p+p || p == p+not (not p) == p+p && False == False+p && True == p+False && p == False+True && p == p+p || False == p+p || True == True+False || p == p+True || p == True+not (p && q) == not p || not q+not (p && q) == not q || not p+not (p || q) == not p && not q+not (p || q) == not q && not p+p && not p == False+not p && p == False+p || not p == True+not p || p == True+(p && q) && r == p && (q && r)+(p && q) && r == q && (p && r)+(p || q) || r == p || (q || r)+(p || q) || r == q || (p || r)+p && (p && q) == p && q+p && (q && p) == p && q+p && (q && p) == q && p+p || (p || q) == p || q+p || (q || p) == p || q+p || (q || p) == q || p+p && (p || q) == p+p && (q || p) == p+(p || q) && p == p+(p || q) && q == q+p || p && q == p+p || q && p == p+p && q || p == p+p && q || q == q+equations:+q && p == p && q+q || p == p || q+q && (p && r) == p && (q && r)+r && (p && q) == p && (q && r)+r && (q && p) == p && (q && r)+q || (p || r) == p || (q || r)+r || (p || q) == p || (q || r)+r || (q || p) == p || (q || r)+(r || q) && p == p && (q || r)+r && q || p == p || q && r++direct candidates:++ton p  =  p++ton p  =  False++ton p  =  True++ton p  =  not p+++pattern candidates:++ton p  =  p++ton p  =  False++ton p  =  True++ton p  =  not p++ton False  =  False+ton True  =  True++ton False  =  True+ton True  =  False++++allowed patterns:++ton p  =  _+++ton False  =  _+ton True  =  _+++++allowed deconstructions:+++Candidates for: &| :: Bool -> Bool -> Bool+  pruning with 39/49 rules+  [4,2,2,4,2,16,17,56,110] direct candidates, 0 duplicates+  [4,14,26,10,2,16,17,56,110] pattern candidates, 0 duplicates++rules:+not False == True+not True == False+p && p == p+p || p == p+not (not p) == p+p && False == False+p && True == p+False && p == False+True && p == p+p || False == p+p || True == True+False || p == p+True || p == True+not (p && q) == not p || not q+not (p && q) == not q || not p+not (p || q) == not p && not q+not (p || q) == not q && not p+p && not p == False+not p && p == False+p || not p == True+not p || p == True+(p && q) && r == p && (q && r)+(p && q) && r == q && (p && r)+(p || q) || r == p || (q || r)+(p || q) || r == q || (p || r)+p && (p && q) == p && q+p && (q && p) == p && q+p && (q && p) == q && p+p || (p || q) == p || q+p || (q || p) == p || q+p || (q || p) == q || p+p && (p || q) == p+p && (q || p) == p+(p || q) && p == p+(p || q) && q == q+p || p && q == p+p || q && p == p+p && q || p == p+p && q || q == q+equations:+q && p == p && q+q || p == p || q+q && (p && r) == p && (q && r)+r && (p && q) == p && (q && r)+r && (q && p) == p && (q && r)+q || (p || r) == p || (q || r)+r || (p || q) == p || (q || r)+r || (q || p) == p || (q || r)+(r || q) && p == p && (q || r)+r && q || p == p || q && r++direct candidates:++p &| q  =  p++p &| q  =  q++p &| q  =  False++p &| q  =  True++p &| q  =  not p++p &| q  =  not q++p &| q  =  p && q++p &| q  =  p || q++p &| q  =  p && not q++p &| q  =  q && not p++p &| q  =  p || not q++p &| q  =  q || not p++p &| q  =  not p && not q++p &| q  =  not p || not q++p &| q  =  p && (q && not p)++p &| q  =  p && (q || not p)++p &| q  =  q && (p && not q)++p &| q  =  q && (p || not q)++p &| q  =  p || q && not p++p &| q  =  p || (q || not p)++p &| q  =  q || p && not q++p &| q  =  q || (p || not q)++p &| q  =  not p && (p && q)++p &| q  =  not p && (p || q)++p &| q  =  not q && (p && q)++p &| q  =  not q && (p || q)++p &| q  =  not p || p && q++p &| q  =  not p || (p || q)++p &| q  =  not q || p && q++p &| q  =  not q || (p || q)+++pattern candidates:++p &| q  =  p++p &| q  =  q++p &| q  =  False++p &| q  =  True++p &| q  =  not p++p &| q  =  not q++p &| False  =  p+p &| True  =  False++p &| False  =  p+p &| True  =  True++p &| False  =  False+p &| True  =  p++p &| False  =  False+p &| True  =  True++p &| False  =  True+p &| True  =  p++p &| False  =  True+p &| True  =  False++False &| p  =  p+True &| p  =  False++False &| p  =  p+True &| p  =  True++False &| p  =  False+True &| p  =  p++False &| p  =  False+True &| p  =  True++False &| p  =  True+True &| p  =  p++False &| p  =  True+True &| p  =  False++p &| q  =  p && q++p &| q  =  p || q++p &| False  =  p+p &| True  =  not p++p &| False  =  False+p &| True  =  not p++p &| False  =  True+p &| True  =  not p++p &| False  =  not p+p &| True  =  p++p &| False  =  not p+p &| True  =  False++p &| False  =  not p+p &| True  =  True++False &| p  =  p+True &| p  =  not p++False &| p  =  False+True &| p  =  not p++False &| p  =  True+True &| p  =  not p++False &| p  =  not p+True &| p  =  p++False &| p  =  not p+True &| p  =  False++False &| p  =  not p+True &| p  =  True++False &| p  =  p+True &| False  =  False+True &| True  =  True++False &| p  =  p+True &| False  =  True+True &| True  =  False++False &| p  =  False+True &| False  =  False+True &| True  =  True++False &| p  =  False+True &| False  =  True+True &| True  =  False++False &| p  =  True+True &| False  =  False+True &| True  =  True++False &| p  =  True+True &| False  =  True+True &| True  =  False++False &| False  =  False+False &| True  =  True+True &| p  =  p++False &| False  =  False+False &| True  =  True+True &| p  =  False++False &| False  =  False+False &| True  =  True+True &| p  =  True++False &| False  =  True+False &| True  =  False+True &| p  =  p++False &| False  =  True+False &| True  =  False+True &| p  =  False++False &| False  =  True+False &| True  =  False+True &| p  =  True++p &| q  =  p && not q++p &| q  =  q && not p++p &| q  =  p || not q++p &| q  =  q || not p++False &| p  =  not p+True &| False  =  False+True &| True  =  True++False &| p  =  not p+True &| False  =  True+True &| True  =  False++False &| False  =  False+False &| True  =  True+True &| p  =  not p++False &| False  =  True+False &| True  =  False+True &| p  =  not p++False &| False  =  False+False &| True  =  True+True &| False  =  True+True &| True  =  False++False &| False  =  True+False &| True  =  False+True &| False  =  False+True &| True  =  True++p &| q  =  not p && not q++p &| q  =  not p || not q++p &| q  =  p && (q && not p)++p &| q  =  p && (q || not p)++p &| q  =  q && (p && not q)++p &| q  =  q && (p || not q)++p &| q  =  p || q && not p++p &| q  =  p || (q || not p)++p &| q  =  q || p && not q++p &| q  =  q || (p || not q)++p &| q  =  not p && (p && q)++p &| q  =  not p && (p || q)++p &| q  =  not q && (p && q)++p &| q  =  not q && (p || q)++p &| q  =  not p || p && q++p &| q  =  not p || (p || q)++p &| q  =  not q || p && q++p &| q  =  not q || (p || q)++++allowed patterns:++p &| q  =  _+++p &| False  =  _+p &| True  =  _++False &| p  =  _+True &| p  =  _+++False &| p  =  _+True &| False  =  _+True &| True  =  _++False &| False  =  _+False &| True  =  _+True &| p  =  _+++False &| False  =  _+False &| True  =  _+True &| False  =  _+True &| True  =  _+++++allowed deconstructions:+++Candidates for: gcd :: Int -> Int -> Int+  pruning with 0/0 rules+  [3,0,9,0,54,0,405,0,3402] direct candidates, 0 duplicates+  [3,6,11,50,98,330,774,2714,6660] pattern candidates, 0 duplicates++no rules.++direct candidates:++gcd x y  =  x++gcd x y  =  y++gcd x y  =  0++gcd x y  =  x `mod` x++gcd x y  =  x `mod` y++gcd x y  =  x `mod` 0++gcd x y  =  y `mod` x++gcd x y  =  y `mod` y++gcd x y  =  y `mod` 0++gcd x y  =  0 `mod` x++gcd x y  =  0 `mod` y++gcd x y  =  0 `mod` 0++gcd x y  =  x `mod` (x `mod` x)++gcd x y  =  x `mod` (x `mod` y)++gcd x y  =  x `mod` (x `mod` 0)++gcd x y  =  x `mod` (y `mod` x)++gcd x y  =  x `mod` (y `mod` y)++gcd x y  =  x `mod` (y `mod` 0)++gcd x y  =  x `mod` (0 `mod` x)++gcd x y  =  x `mod` (0 `mod` y)++gcd x y  =  x `mod` (0 `mod` 0)++gcd x y  =  y `mod` (x `mod` x)++gcd x y  =  y `mod` (x `mod` y)++gcd x y  =  y `mod` (x `mod` 0)++gcd x y  =  y `mod` (y `mod` x)++gcd x y  =  y `mod` (y `mod` y)++gcd x y  =  y `mod` (y `mod` 0)++gcd x y  =  y `mod` (0 `mod` x)++gcd x y  =  y `mod` (0 `mod` y)++gcd x y  =  y `mod` (0 `mod` 0)++gcd x y  =  0 `mod` (x `mod` x)++gcd x y  =  0 `mod` (x `mod` y)++gcd x y  =  0 `mod` (x `mod` 0)++gcd x y  =  0 `mod` (y `mod` x)++gcd x y  =  0 `mod` (y `mod` y)++gcd x y  =  0 `mod` (y `mod` 0)++gcd x y  =  0 `mod` (0 `mod` x)++gcd x y  =  0 `mod` (0 `mod` y)++gcd x y  =  0 `mod` (0 `mod` 0)++gcd x y  =  (x `mod` x) `mod` x++gcd x y  =  (x `mod` x) `mod` y++gcd x y  =  (x `mod` x) `mod` 0++gcd x y  =  (x `mod` y) `mod` x++gcd x y  =  (x `mod` y) `mod` y++gcd x y  =  (x `mod` y) `mod` 0++gcd x y  =  (x `mod` 0) `mod` x++gcd x y  =  (x `mod` 0) `mod` y++gcd x y  =  (x `mod` 0) `mod` 0++gcd x y  =  (y `mod` x) `mod` x++gcd x y  =  (y `mod` x) `mod` y++gcd x y  =  (y `mod` x) `mod` 0++gcd x y  =  (y `mod` y) `mod` x++gcd x y  =  (y `mod` y) `mod` y++gcd x y  =  (y `mod` y) `mod` 0++gcd x y  =  (y `mod` 0) `mod` x++gcd x y  =  (y `mod` 0) `mod` y++gcd x y  =  (y `mod` 0) `mod` 0++gcd x y  =  (0 `mod` x) `mod` x++gcd x y  =  (0 `mod` x) `mod` y++gcd x y  =  (0 `mod` x) `mod` 0++gcd x y  =  (0 `mod` y) `mod` x++gcd x y  =  (0 `mod` y) `mod` y++gcd x y  =  (0 `mod` y) `mod` 0++gcd x y  =  (0 `mod` 0) `mod` x++gcd x y  =  (0 `mod` 0) `mod` y++gcd x y  =  (0 `mod` 0) `mod` 0+++pattern candidates:++gcd x y  =  x++gcd x y  =  y++gcd x y  =  0++gcd x 0  =  x+gcd x y  =  y++gcd x 0  =  x+gcd x y  =  0++gcd x 0  =  0+gcd x y  =  x++gcd 0 x  =  x+gcd x y  =  x++gcd 0 x  =  x+gcd x y  =  0++gcd 0 x  =  0+gcd x y  =  y++gcd x y  =  x `mod` x++gcd x y  =  x `mod` y++gcd x y  =  x `mod` 0++gcd x y  =  y `mod` x++gcd x y  =  y `mod` y++gcd x y  =  y `mod` 0++gcd x y  =  0 `mod` x++gcd x y  =  0 `mod` y++gcd 0 x  =  x+gcd x 0  =  x+gcd x y  =  0++gcd 0 x  =  x+gcd x 0  =  0+gcd x y  =  x++gcd 0 x  =  0+gcd x 0  =  x+gcd x y  =  y++gcd x 0  =  x+gcd x y  =  x `mod` x++gcd x 0  =  x+gcd x y  =  x `mod` y++gcd x 0  =  x+gcd x y  =  x `mod` 0++gcd x 0  =  x+gcd x y  =  y `mod` x++gcd x 0  =  x+gcd x y  =  y `mod` y++gcd x 0  =  x+gcd x y  =  y `mod` 0++gcd x 0  =  x+gcd x y  =  0 `mod` x++gcd x 0  =  x+gcd x y  =  0 `mod` y++gcd x 0  =  0+gcd x y  =  x `mod` x++gcd x 0  =  0+gcd x y  =  x `mod` y++gcd x 0  =  0+gcd x y  =  x `mod` 0++gcd x 0  =  0+gcd x y  =  y `mod` x++gcd x 0  =  0+gcd x y  =  y `mod` y++gcd x 0  =  0+gcd x y  =  y `mod` 0++gcd x 0  =  0+gcd x y  =  0 `mod` x++gcd x 0  =  0+gcd x y  =  0 `mod` y++gcd x 0  =  x `mod` x+gcd x y  =  x++gcd x 0  =  x `mod` x+gcd x y  =  y++gcd x 0  =  x `mod` x+gcd x y  =  0++gcd x 0  =  x `mod` 0+gcd x y  =  x++gcd x 0  =  x `mod` 0+gcd x y  =  y++gcd x 0  =  x `mod` 0+gcd x y  =  0++gcd x 0  =  0 `mod` x+gcd x y  =  x++gcd x 0  =  0 `mod` x+gcd x y  =  y++gcd x 0  =  0 `mod` x+gcd x y  =  0++gcd 0 x  =  x+gcd x y  =  x `mod` x++gcd 0 x  =  x+gcd x y  =  x `mod` y++gcd 0 x  =  x+gcd x y  =  x `mod` 0++gcd 0 x  =  x+gcd x y  =  y `mod` x++gcd 0 x  =  x+gcd x y  =  y `mod` y++gcd 0 x  =  x+gcd x y  =  y `mod` 0++gcd 0 x  =  x+gcd x y  =  0 `mod` x++gcd 0 x  =  x+gcd x y  =  0 `mod` y++gcd 0 x  =  0+gcd x y  =  x `mod` x++gcd 0 x  =  0+gcd x y  =  x `mod` y++gcd 0 x  =  0+gcd x y  =  x `mod` 0++gcd 0 x  =  0+gcd x y  =  y `mod` x++gcd 0 x  =  0+gcd x y  =  y `mod` y++gcd 0 x  =  0+gcd x y  =  y `mod` 0++gcd 0 x  =  0+gcd x y  =  0 `mod` x++gcd 0 x  =  0+gcd x y  =  0 `mod` y++gcd 0 x  =  x `mod` x+gcd x y  =  x++gcd 0 x  =  x `mod` x+gcd x y  =  y++gcd 0 x  =  x `mod` x+gcd x y  =  0++gcd 0 x  =  x `mod` 0+gcd x y  =  x++gcd 0 x  =  x `mod` 0+gcd x y  =  y++gcd 0 x  =  x `mod` 0+gcd x y  =  0++gcd 0 x  =  0 `mod` x+gcd x y  =  x++gcd 0 x  =  0 `mod` x+gcd x y  =  y++gcd 0 x  =  0 `mod` x+gcd x y  =  0++gcd x y  =  x `mod` (x `mod` x)++gcd x y  =  x `mod` (x `mod` y)++gcd x y  =  x `mod` (x `mod` 0)++gcd x y  =  x `mod` (y `mod` x)++gcd x y  =  x `mod` (y `mod` y)++gcd x y  =  x `mod` (y `mod` 0)++gcd x y  =  x `mod` (0 `mod` x)++gcd x y  =  x `mod` (0 `mod` y)++gcd x y  =  y `mod` (x `mod` x)++gcd x y  =  y `mod` (x `mod` y)++gcd x y  =  y `mod` (x `mod` 0)++gcd x y  =  y `mod` (y `mod` x)++gcd x y  =  y `mod` (y `mod` y)++gcd x y  =  y `mod` (y `mod` 0)++gcd x y  =  y `mod` (0 `mod` x)++gcd x y  =  y `mod` (0 `mod` y)++gcd x y  =  0 `mod` (x `mod` x)++gcd x y  =  0 `mod` (x `mod` y)++gcd x y  =  0 `mod` (x `mod` 0)++gcd x y  =  0 `mod` (y `mod` x)++gcd x y  =  0 `mod` (y `mod` y)++gcd x y  =  0 `mod` (y `mod` 0)++gcd x y  =  0 `mod` (0 `mod` x)++gcd x y  =  0 `mod` (0 `mod` y)++gcd x y  =  (x `mod` x) `mod` x++gcd x y  =  (x `mod` x) `mod` y++gcd x y  =  (x `mod` x) `mod` 0++gcd x y  =  (x `mod` y) `mod` x++gcd x y  =  (x `mod` y) `mod` y++gcd x y  =  (x `mod` y) `mod` 0++gcd x y  =  (x `mod` 0) `mod` x++gcd x y  =  (x `mod` 0) `mod` y++gcd x y  =  (x `mod` 0) `mod` 0++gcd x y  =  (y `mod` x) `mod` x++gcd x y  =  (y `mod` x) `mod` y++gcd x y  =  (y `mod` x) `mod` 0++gcd x y  =  (y `mod` y) `mod` x++gcd x y  =  (y `mod` y) `mod` y++gcd x y  =  (y `mod` y) `mod` 0++gcd x y  =  (y `mod` 0) `mod` x++gcd x y  =  (y `mod` 0) `mod` y++gcd x y  =  (y `mod` 0) `mod` 0++gcd x y  =  (0 `mod` x) `mod` x++gcd x y  =  (0 `mod` x) `mod` y++gcd x y  =  (0 `mod` x) `mod` 0++gcd x y  =  (0 `mod` y) `mod` x++gcd x y  =  (0 `mod` y) `mod` y++gcd x y  =  (0 `mod` y) `mod` 0++gcd 0 x  =  x+gcd x 0  =  x+gcd x y  =  x `mod` x++gcd 0 x  =  x+gcd x 0  =  x+gcd x y  =  x `mod` y++gcd 0 x  =  x+gcd x 0  =  x+gcd x y  =  x `mod` 0++gcd 0 x  =  x+gcd x 0  =  x+gcd x y  =  y `mod` x++gcd 0 x  =  x+gcd x 0  =  x+gcd x y  =  y `mod` y++gcd 0 x  =  x+gcd x 0  =  x+gcd x y  =  y `mod` 0++gcd 0 x  =  x+gcd x 0  =  x+gcd x y  =  0 `mod` x++gcd 0 x  =  x+gcd x 0  =  x+gcd x y  =  0 `mod` y++gcd 0 x  =  x+gcd x 0  =  0+gcd x y  =  x `mod` x++gcd 0 x  =  x+gcd x 0  =  0+gcd x y  =  x `mod` y++gcd 0 x  =  x+gcd x 0  =  0+gcd x y  =  x `mod` 0++gcd 0 x  =  x+gcd x 0  =  0+gcd x y  =  y `mod` x++gcd 0 x  =  x+gcd x 0  =  0+gcd x y  =  y `mod` y++gcd 0 x  =  x+gcd x 0  =  0+gcd x y  =  y `mod` 0++gcd 0 x  =  x+gcd x 0  =  0+gcd x y  =  0 `mod` x++gcd 0 x  =  x+gcd x 0  =  0+gcd x y  =  0 `mod` y++gcd 0 x  =  x+gcd x 0  =  x `mod` x+gcd x y  =  x++gcd 0 x  =  x+gcd x 0  =  x `mod` x+gcd x y  =  0++gcd 0 x  =  x+gcd x 0  =  x `mod` 0+gcd x y  =  x++gcd 0 x  =  x+gcd x 0  =  x `mod` 0+gcd x y  =  0++gcd 0 x  =  x+gcd x 0  =  0 `mod` x+gcd x y  =  x++gcd 0 x  =  x+gcd x 0  =  0 `mod` x+gcd x y  =  0++gcd 0 x  =  0+gcd x 0  =  x+gcd x y  =  x `mod` x++gcd 0 x  =  0+gcd x 0  =  x+gcd x y  =  x `mod` y++gcd 0 x  =  0+gcd x 0  =  x+gcd x y  =  x `mod` 0++gcd 0 x  =  0+gcd x 0  =  x+gcd x y  =  y `mod` x++gcd 0 x  =  0+gcd x 0  =  x+gcd x y  =  y `mod` y++gcd 0 x  =  0+gcd x 0  =  x+gcd x y  =  y `mod` 0++gcd 0 x  =  0+gcd x 0  =  x+gcd x y  =  0 `mod` x++gcd 0 x  =  0+gcd x 0  =  x+gcd x y  =  0 `mod` y++gcd 0 x  =  0+gcd x 0  =  0+gcd x y  =  x `mod` x++gcd 0 x  =  0+gcd x 0  =  0+gcd x y  =  x `mod` y++gcd 0 x  =  0+gcd x 0  =  0+gcd x y  =  x `mod` 0++gcd 0 x  =  0+gcd x 0  =  0+gcd x y  =  y `mod` x++gcd 0 x  =  0+gcd x 0  =  0+gcd x y  =  y `mod` y++gcd 0 x  =  0+gcd x 0  =  0+gcd x y  =  y `mod` 0++gcd 0 x  =  0+gcd x 0  =  0+gcd x y  =  0 `mod` x++gcd 0 x  =  0+gcd x 0  =  0+gcd x y  =  0 `mod` y++gcd 0 x  =  0+gcd x 0  =  x `mod` x+gcd x y  =  y++gcd 0 x  =  0+gcd x 0  =  x `mod` 0+gcd x y  =  y++gcd 0 x  =  0+gcd x 0  =  0 `mod` x+gcd x y  =  y++gcd 0 x  =  x `mod` x+gcd x 0  =  x+gcd x y  =  y++gcd 0 x  =  x `mod` x+gcd x 0  =  x+gcd x y  =  0++gcd 0 x  =  x `mod` x+gcd x 0  =  0+gcd x y  =  x++gcd 0 x  =  x `mod` 0+gcd x 0  =  x+gcd x y  =  y++gcd 0 x  =  x `mod` 0+gcd x 0  =  x+gcd x y  =  0++gcd 0 x  =  x `mod` 0+gcd x 0  =  0+gcd x y  =  x++gcd 0 x  =  0 `mod` x+gcd x 0  =  x+gcd x y  =  y++gcd 0 x  =  0 `mod` x+gcd x 0  =  x+gcd x y  =  0++gcd 0 x  =  0 `mod` x+gcd x 0  =  0+gcd x y  =  x++gcd x 0  =  x+gcd x y  =  x `mod` (x `mod` x)++gcd x 0  =  x+gcd x y  =  x `mod` (x `mod` y)++gcd x 0  =  x+gcd x y  =  x `mod` (x `mod` 0)++gcd x 0  =  x+gcd x y  =  x `mod` (y `mod` x)++gcd x 0  =  x+gcd x y  =  x `mod` (y `mod` y)++gcd x 0  =  x+gcd x y  =  x `mod` (y `mod` 0)++gcd x 0  =  x+gcd x y  =  x `mod` (0 `mod` x)++gcd x 0  =  x+gcd x y  =  x `mod` (0 `mod` y)++gcd x 0  =  x+gcd x y  =  y `mod` (x `mod` x)++gcd x 0  =  x+gcd x y  =  y `mod` (x `mod` y)++gcd x 0  =  x+gcd x y  =  y `mod` (x `mod` 0)++gcd x 0  =  x+gcd x y  =  y `mod` (y `mod` x)++gcd x 0  =  x+gcd x y  =  y `mod` (y `mod` y)++gcd x 0  =  x+gcd x y  =  y `mod` (y `mod` 0)++gcd x 0  =  x+gcd x y  =  y `mod` (0 `mod` x)++gcd x 0  =  x+gcd x y  =  y `mod` (0 `mod` y)++gcd x 0  =  x+gcd x y  =  0 `mod` (x `mod` x)++gcd x 0  =  x+gcd x y  =  0 `mod` (x `mod` y)++gcd x 0  =  x+gcd x y  =  0 `mod` (x `mod` 0)++gcd x 0  =  x+gcd x y  =  0 `mod` (y `mod` x)++gcd x 0  =  x+gcd x y  =  0 `mod` (y `mod` y)++gcd x 0  =  x+gcd x y  =  0 `mod` (y `mod` 0)++gcd x 0  =  x+gcd x y  =  0 `mod` (0 `mod` x)++gcd x 0  =  x+gcd x y  =  0 `mod` (0 `mod` y)++gcd x 0  =  x+gcd x y  =  (x `mod` x) `mod` x++gcd x 0  =  x+gcd x y  =  (x `mod` x) `mod` y++gcd x 0  =  x+gcd x y  =  (x `mod` x) `mod` 0++gcd x 0  =  x+gcd x y  =  (x `mod` y) `mod` x++gcd x 0  =  x+gcd x y  =  (x `mod` y) `mod` y++gcd x 0  =  x+gcd x y  =  (x `mod` y) `mod` 0++gcd x 0  =  x+gcd x y  =  (x `mod` 0) `mod` x++gcd x 0  =  x+gcd x y  =  (x `mod` 0) `mod` y++gcd x 0  =  x+gcd x y  =  (x `mod` 0) `mod` 0++gcd x 0  =  x+gcd x y  =  (y `mod` x) `mod` x++gcd x 0  =  x+gcd x y  =  (y `mod` x) `mod` y++gcd x 0  =  x+gcd x y  =  (y `mod` x) `mod` 0++gcd x 0  =  x+gcd x y  =  (y `mod` y) `mod` x++gcd x 0  =  x+gcd x y  =  (y `mod` y) `mod` y++gcd x 0  =  x+gcd x y  =  (y `mod` y) `mod` 0++gcd x 0  =  x+gcd x y  =  (y `mod` 0) `mod` x++gcd x 0  =  x+gcd x y  =  (y `mod` 0) `mod` y++gcd x 0  =  x+gcd x y  =  (y `mod` 0) `mod` 0++gcd x 0  =  x+gcd x y  =  (0 `mod` x) `mod` x++gcd x 0  =  x+gcd x y  =  (0 `mod` x) `mod` y++gcd x 0  =  x+gcd x y  =  (0 `mod` x) `mod` 0++gcd x 0  =  x+gcd x y  =  (0 `mod` y) `mod` x++gcd x 0  =  x+gcd x y  =  (0 `mod` y) `mod` y++gcd x 0  =  x+gcd x y  =  (0 `mod` y) `mod` 0++gcd x 0  =  0+gcd x y  =  x `mod` (x `mod` x)++gcd x 0  =  0+gcd x y  =  x `mod` (x `mod` y)++gcd x 0  =  0+gcd x y  =  x `mod` (x `mod` 0)++gcd x 0  =  0+gcd x y  =  x `mod` (y `mod` x)++gcd x 0  =  0+gcd x y  =  x `mod` (y `mod` y)++gcd x 0  =  0+gcd x y  =  x `mod` (y `mod` 0)++gcd x 0  =  0+gcd x y  =  x `mod` (0 `mod` x)++gcd x 0  =  0+gcd x y  =  x `mod` (0 `mod` y)++gcd x 0  =  0+gcd x y  =  y `mod` (x `mod` x)++gcd x 0  =  0+gcd x y  =  y `mod` (x `mod` y)++gcd x 0  =  0+gcd x y  =  y `mod` (x `mod` 0)++gcd x 0  =  0+gcd x y  =  y `mod` (y `mod` x)++gcd x 0  =  0+gcd x y  =  y `mod` (y `mod` y)++gcd x 0  =  0+gcd x y  =  y `mod` (y `mod` 0)++gcd x 0  =  0+gcd x y  =  y `mod` (0 `mod` x)++gcd x 0  =  0+gcd x y  =  y `mod` (0 `mod` y)++gcd x 0  =  0+gcd x y  =  0 `mod` (x `mod` x)++gcd x 0  =  0+gcd x y  =  0 `mod` (x `mod` y)++gcd x 0  =  0+gcd x y  =  0 `mod` (x `mod` 0)++gcd x 0  =  0+gcd x y  =  0 `mod` (y `mod` x)++gcd x 0  =  0+gcd x y  =  0 `mod` (y `mod` y)++gcd x 0  =  0+gcd x y  =  0 `mod` (y `mod` 0)++gcd x 0  =  0+gcd x y  =  0 `mod` (0 `mod` x)++gcd x 0  =  0+gcd x y  =  0 `mod` (0 `mod` y)++gcd x 0  =  0+gcd x y  =  (x `mod` x) `mod` x++gcd x 0  =  0+gcd x y  =  (x `mod` x) `mod` y++gcd x 0  =  0+gcd x y  =  (x `mod` x) `mod` 0++gcd x 0  =  0+gcd x y  =  (x `mod` y) `mod` x++gcd x 0  =  0+gcd x y  =  (x `mod` y) `mod` y++gcd x 0  =  0+gcd x y  =  (x `mod` y) `mod` 0++gcd x 0  =  0+gcd x y  =  (x `mod` 0) `mod` x++gcd x 0  =  0+gcd x y  =  (x `mod` 0) `mod` y++gcd x 0  =  0+gcd x y  =  (x `mod` 0) `mod` 0++gcd x 0  =  0+gcd x y  =  (y `mod` x) `mod` x++gcd x 0  =  0+gcd x y  =  (y `mod` x) `mod` y++gcd x 0  =  0+gcd x y  =  (y `mod` x) `mod` 0++gcd x 0  =  0+gcd x y  =  (y `mod` y) `mod` x++gcd x 0  =  0+gcd x y  =  (y `mod` y) `mod` y++gcd x 0  =  0+gcd x y  =  (y `mod` y) `mod` 0++gcd x 0  =  0+gcd x y  =  (y `mod` 0) `mod` x++gcd x 0  =  0+gcd x y  =  (y `mod` 0) `mod` y++gcd x 0  =  0+gcd x y  =  (y `mod` 0) `mod` 0++gcd x 0  =  0+gcd x y  =  (0 `mod` x) `mod` x++gcd x 0  =  0+gcd x y  =  (0 `mod` x) `mod` y++gcd x 0  =  0+gcd x y  =  (0 `mod` x) `mod` 0++gcd x 0  =  0+gcd x y  =  (0 `mod` y) `mod` x++gcd x 0  =  0+gcd x y  =  (0 `mod` y) `mod` y++gcd x 0  =  0+gcd x y  =  (0 `mod` y) `mod` 0++gcd x 0  =  x `mod` x+gcd x y  =  x `mod` y++gcd x 0  =  x `mod` x+gcd x y  =  x `mod` 0++gcd x 0  =  x `mod` x+gcd x y  =  y `mod` x++gcd x 0  =  x `mod` x+gcd x y  =  y `mod` y++gcd x 0  =  x `mod` x+gcd x y  =  y `mod` 0++gcd x 0  =  x `mod` x+gcd x y  =  0 `mod` x++gcd x 0  =  x `mod` x+gcd x y  =  0 `mod` y++gcd x 0  =  x `mod` 0+gcd x y  =  x `mod` x++gcd x 0  =  x `mod` 0+gcd x y  =  y `mod` x++gcd x 0  =  x `mod` 0+gcd x y  =  y `mod` y++gcd x 0  =  x `mod` 0+gcd x y  =  y `mod` 0++gcd x 0  =  x `mod` 0+gcd x y  =  0 `mod` x++gcd x 0  =  x `mod` 0+gcd x y  =  0 `mod` y++gcd x 0  =  0 `mod` x+gcd x y  =  x `mod` x++gcd x 0  =  0 `mod` x+gcd x y  =  x `mod` y++gcd x 0  =  0 `mod` x+gcd x y  =  x `mod` 0++gcd x 0  =  0 `mod` x+gcd x y  =  y `mod` y++gcd x 0  =  0 `mod` x+gcd x y  =  y `mod` 0++gcd x 0  =  0 `mod` x+gcd x y  =  0 `mod` y++gcd x 0  =  x `mod` (x `mod` x)+gcd x y  =  x++gcd x 0  =  x `mod` (x `mod` x)+gcd x y  =  y++gcd x 0  =  x `mod` (x `mod` x)+gcd x y  =  0++gcd x 0  =  x `mod` (x `mod` 0)+gcd x y  =  x++gcd x 0  =  x `mod` (x `mod` 0)+gcd x y  =  y++gcd x 0  =  x `mod` (x `mod` 0)+gcd x y  =  0++gcd x 0  =  x `mod` (0 `mod` x)+gcd x y  =  x++gcd x 0  =  x `mod` (0 `mod` x)+gcd x y  =  y++gcd x 0  =  x `mod` (0 `mod` x)+gcd x y  =  0++gcd x 0  =  0 `mod` (x `mod` x)+gcd x y  =  x++gcd x 0  =  0 `mod` (x `mod` x)+gcd x y  =  y++gcd x 0  =  0 `mod` (x `mod` x)+gcd x y  =  0++gcd x 0  =  0 `mod` (x `mod` 0)+gcd x y  =  x++gcd x 0  =  0 `mod` (x `mod` 0)+gcd x y  =  y++gcd x 0  =  0 `mod` (x `mod` 0)+gcd x y  =  0++gcd x 0  =  0 `mod` (0 `mod` x)+gcd x y  =  x++gcd x 0  =  0 `mod` (0 `mod` x)+gcd x y  =  y++gcd x 0  =  0 `mod` (0 `mod` x)+gcd x y  =  0++gcd x 0  =  (x `mod` x) `mod` x+gcd x y  =  x++gcd x 0  =  (x `mod` x) `mod` x+gcd x y  =  y++gcd x 0  =  (x `mod` x) `mod` x+gcd x y  =  0++gcd x 0  =  (x `mod` x) `mod` 0+gcd x y  =  x++gcd x 0  =  (x `mod` x) `mod` 0+gcd x y  =  y++gcd x 0  =  (x `mod` x) `mod` 0+gcd x y  =  0++gcd x 0  =  (x `mod` 0) `mod` x+gcd x y  =  x++gcd x 0  =  (x `mod` 0) `mod` x+gcd x y  =  y++gcd x 0  =  (x `mod` 0) `mod` x+gcd x y  =  0++gcd x 0  =  (x `mod` 0) `mod` 0+gcd x y  =  x++gcd x 0  =  (x `mod` 0) `mod` 0+gcd x y  =  y++gcd x 0  =  (x `mod` 0) `mod` 0+gcd x y  =  0++gcd x 0  =  (0 `mod` x) `mod` x+gcd x y  =  x++gcd x 0  =  (0 `mod` x) `mod` x+gcd x y  =  y++gcd x 0  =  (0 `mod` x) `mod` x+gcd x y  =  0++gcd x 0  =  (0 `mod` x) `mod` 0+gcd x y  =  x++gcd x 0  =  (0 `mod` x) `mod` 0+gcd x y  =  y++gcd x 0  =  (0 `mod` x) `mod` 0+gcd x y  =  0++gcd 0 x  =  x+gcd x y  =  x `mod` (x `mod` x)++gcd 0 x  =  x+gcd x y  =  x `mod` (x `mod` y)++gcd 0 x  =  x+gcd x y  =  x `mod` (x `mod` 0)++gcd 0 x  =  x+gcd x y  =  x `mod` (y `mod` x)++gcd 0 x  =  x+gcd x y  =  x `mod` (y `mod` y)++gcd 0 x  =  x+gcd x y  =  x `mod` (y `mod` 0)++gcd 0 x  =  x+gcd x y  =  x `mod` (0 `mod` x)++gcd 0 x  =  x+gcd x y  =  x `mod` (0 `mod` y)++gcd 0 x  =  x+gcd x y  =  y `mod` (x `mod` x)++gcd 0 x  =  x+gcd x y  =  y `mod` (x `mod` y)++gcd 0 x  =  x+gcd x y  =  y `mod` (x `mod` 0)++gcd 0 x  =  x+gcd x y  =  y `mod` (y `mod` x)++gcd 0 x  =  x+gcd x y  =  y `mod` (y `mod` y)++gcd 0 x  =  x+gcd x y  =  y `mod` (y `mod` 0)++gcd 0 x  =  x+gcd x y  =  y `mod` (0 `mod` x)++gcd 0 x  =  x+gcd x y  =  y `mod` (0 `mod` y)++gcd 0 x  =  x+gcd x y  =  0 `mod` (x `mod` x)++gcd 0 x  =  x+gcd x y  =  0 `mod` (x `mod` y)++gcd 0 x  =  x+gcd x y  =  0 `mod` (x `mod` 0)++gcd 0 x  =  x+gcd x y  =  0 `mod` (y `mod` x)++gcd 0 x  =  x+gcd x y  =  0 `mod` (y `mod` y)++gcd 0 x  =  x+gcd x y  =  0 `mod` (y `mod` 0)++gcd 0 x  =  x+gcd x y  =  0 `mod` (0 `mod` x)++gcd 0 x  =  x+gcd x y  =  0 `mod` (0 `mod` y)++gcd 0 x  =  x+gcd x y  =  (x `mod` x) `mod` x++gcd 0 x  =  x+gcd x y  =  (x `mod` x) `mod` y++gcd 0 x  =  x+gcd x y  =  (x `mod` x) `mod` 0++gcd 0 x  =  x+gcd x y  =  (x `mod` y) `mod` x++gcd 0 x  =  x+gcd x y  =  (x `mod` y) `mod` y++gcd 0 x  =  x+gcd x y  =  (x `mod` y) `mod` 0++gcd 0 x  =  x+gcd x y  =  (x `mod` 0) `mod` x++gcd 0 x  =  x+gcd x y  =  (x `mod` 0) `mod` y++gcd 0 x  =  x+gcd x y  =  (x `mod` 0) `mod` 0++gcd 0 x  =  x+gcd x y  =  (y `mod` x) `mod` x++gcd 0 x  =  x+gcd x y  =  (y `mod` x) `mod` y++gcd 0 x  =  x+gcd x y  =  (y `mod` x) `mod` 0++gcd 0 x  =  x+gcd x y  =  (y `mod` y) `mod` x++gcd 0 x  =  x+gcd x y  =  (y `mod` y) `mod` y++gcd 0 x  =  x+gcd x y  =  (y `mod` y) `mod` 0++gcd 0 x  =  x+gcd x y  =  (y `mod` 0) `mod` x++gcd 0 x  =  x+gcd x y  =  (y `mod` 0) `mod` y++gcd 0 x  =  x+gcd x y  =  (y `mod` 0) `mod` 0++gcd 0 x  =  x+gcd x y  =  (0 `mod` x) `mod` x++gcd 0 x  =  x+gcd x y  =  (0 `mod` x) `mod` y++gcd 0 x  =  x+gcd x y  =  (0 `mod` x) `mod` 0++gcd 0 x  =  x+gcd x y  =  (0 `mod` y) `mod` x++gcd 0 x  =  x+gcd x y  =  (0 `mod` y) `mod` y++gcd 0 x  =  x+gcd x y  =  (0 `mod` y) `mod` 0++gcd 0 x  =  0+gcd x y  =  x `mod` (x `mod` x)++gcd 0 x  =  0+gcd x y  =  x `mod` (x `mod` y)++gcd 0 x  =  0+gcd x y  =  x `mod` (x `mod` 0)++gcd 0 x  =  0+gcd x y  =  x `mod` (y `mod` x)++gcd 0 x  =  0+gcd x y  =  x `mod` (y `mod` y)++gcd 0 x  =  0+gcd x y  =  x `mod` (y `mod` 0)++gcd 0 x  =  0+gcd x y  =  x `mod` (0 `mod` x)++gcd 0 x  =  0+gcd x y  =  x `mod` (0 `mod` y)++gcd 0 x  =  0+gcd x y  =  y `mod` (x `mod` x)++gcd 0 x  =  0+gcd x y  =  y `mod` (x `mod` y)++gcd 0 x  =  0+gcd x y  =  y `mod` (x `mod` 0)++gcd 0 x  =  0+gcd x y  =  y `mod` (y `mod` x)++gcd 0 x  =  0+gcd x y  =  y `mod` (y `mod` y)++gcd 0 x  =  0+gcd x y  =  y `mod` (y `mod` 0)++gcd 0 x  =  0+gcd x y  =  y `mod` (0 `mod` x)++gcd 0 x  =  0+gcd x y  =  y `mod` (0 `mod` y)++gcd 0 x  =  0+gcd x y  =  0 `mod` (x `mod` x)++gcd 0 x  =  0+gcd x y  =  0 `mod` (x `mod` y)++gcd 0 x  =  0+gcd x y  =  0 `mod` (x `mod` 0)++gcd 0 x  =  0+gcd x y  =  0 `mod` (y `mod` x)++gcd 0 x  =  0+gcd x y  =  0 `mod` (y `mod` y)++gcd 0 x  =  0+gcd x y  =  0 `mod` (y `mod` 0)++gcd 0 x  =  0+gcd x y  =  0 `mod` (0 `mod` x)++gcd 0 x  =  0+gcd x y  =  0 `mod` (0 `mod` y)++gcd 0 x  =  0+gcd x y  =  (x `mod` x) `mod` x++gcd 0 x  =  0+gcd x y  =  (x `mod` x) `mod` y++gcd 0 x  =  0+gcd x y  =  (x `mod` x) `mod` 0++gcd 0 x  =  0+gcd x y  =  (x `mod` y) `mod` x++gcd 0 x  =  0+gcd x y  =  (x `mod` y) `mod` y++gcd 0 x  =  0+gcd x y  =  (x `mod` y) `mod` 0++gcd 0 x  =  0+gcd x y  =  (x `mod` 0) `mod` x++gcd 0 x  =  0+gcd x y  =  (x `mod` 0) `mod` y++gcd 0 x  =  0+gcd x y  =  (x `mod` 0) `mod` 0++gcd 0 x  =  0+gcd x y  =  (y `mod` x) `mod` x++gcd 0 x  =  0+gcd x y  =  (y `mod` x) `mod` y++gcd 0 x  =  0+gcd x y  =  (y `mod` x) `mod` 0++gcd 0 x  =  0+gcd x y  =  (y `mod` y) `mod` x++gcd 0 x  =  0+gcd x y  =  (y `mod` y) `mod` y++gcd 0 x  =  0+gcd x y  =  (y `mod` y) `mod` 0++gcd 0 x  =  0+gcd x y  =  (y `mod` 0) `mod` x++gcd 0 x  =  0+gcd x y  =  (y `mod` 0) `mod` y++gcd 0 x  =  0+gcd x y  =  (y `mod` 0) `mod` 0++gcd 0 x  =  0+gcd x y  =  (0 `mod` x) `mod` x++gcd 0 x  =  0+gcd x y  =  (0 `mod` x) `mod` y++gcd 0 x  =  0+gcd x y  =  (0 `mod` x) `mod` 0++gcd 0 x  =  0+gcd x y  =  (0 `mod` y) `mod` x++gcd 0 x  =  0+gcd x y  =  (0 `mod` y) `mod` y++gcd 0 x  =  0+gcd x y  =  (0 `mod` y) `mod` 0++gcd 0 x  =  x `mod` x+gcd x y  =  x `mod` x++gcd 0 x  =  x `mod` x+gcd x y  =  x `mod` y++gcd 0 x  =  x `mod` x+gcd x y  =  x `mod` 0++gcd 0 x  =  x `mod` x+gcd x y  =  y `mod` x++gcd 0 x  =  x `mod` x+gcd x y  =  y `mod` 0++gcd 0 x  =  x `mod` x+gcd x y  =  0 `mod` x++gcd 0 x  =  x `mod` x+gcd x y  =  0 `mod` y++gcd 0 x  =  x `mod` 0+gcd x y  =  x `mod` x++gcd 0 x  =  x `mod` 0+gcd x y  =  x `mod` y++gcd 0 x  =  x `mod` 0+gcd x y  =  x `mod` 0++gcd 0 x  =  x `mod` 0+gcd x y  =  y `mod` y++gcd 0 x  =  x `mod` 0+gcd x y  =  0 `mod` x++gcd 0 x  =  x `mod` 0+gcd x y  =  0 `mod` y++gcd 0 x  =  0 `mod` x+gcd x y  =  x `mod` x++gcd 0 x  =  0 `mod` x+gcd x y  =  x `mod` 0++gcd 0 x  =  0 `mod` x+gcd x y  =  y `mod` x++gcd 0 x  =  0 `mod` x+gcd x y  =  y `mod` y++gcd 0 x  =  0 `mod` x+gcd x y  =  y `mod` 0++gcd 0 x  =  0 `mod` x+gcd x y  =  0 `mod` x++gcd 0 x  =  x `mod` (x `mod` x)+gcd x y  =  x++gcd 0 x  =  x `mod` (x `mod` x)+gcd x y  =  y++gcd 0 x  =  x `mod` (x `mod` x)+gcd x y  =  0++gcd 0 x  =  x `mod` (x `mod` 0)+gcd x y  =  x++gcd 0 x  =  x `mod` (x `mod` 0)+gcd x y  =  y++gcd 0 x  =  x `mod` (x `mod` 0)+gcd x y  =  0++gcd 0 x  =  x `mod` (0 `mod` x)+gcd x y  =  x++gcd 0 x  =  x `mod` (0 `mod` x)+gcd x y  =  y++gcd 0 x  =  x `mod` (0 `mod` x)+gcd x y  =  0++gcd 0 x  =  0 `mod` (x `mod` x)+gcd x y  =  x++gcd 0 x  =  0 `mod` (x `mod` x)+gcd x y  =  y++gcd 0 x  =  0 `mod` (x `mod` x)+gcd x y  =  0++gcd 0 x  =  0 `mod` (x `mod` 0)+gcd x y  =  x++gcd 0 x  =  0 `mod` (x `mod` 0)+gcd x y  =  y++gcd 0 x  =  0 `mod` (x `mod` 0)+gcd x y  =  0++gcd 0 x  =  0 `mod` (0 `mod` x)+gcd x y  =  x++gcd 0 x  =  0 `mod` (0 `mod` x)+gcd x y  =  y++gcd 0 x  =  0 `mod` (0 `mod` x)+gcd x y  =  0++gcd 0 x  =  (x `mod` x) `mod` x+gcd x y  =  x++gcd 0 x  =  (x `mod` x) `mod` x+gcd x y  =  y++gcd 0 x  =  (x `mod` x) `mod` x+gcd x y  =  0++gcd 0 x  =  (x `mod` x) `mod` 0+gcd x y  =  x++gcd 0 x  =  (x `mod` x) `mod` 0+gcd x y  =  y++gcd 0 x  =  (x `mod` x) `mod` 0+gcd x y  =  0++gcd 0 x  =  (x `mod` 0) `mod` x+gcd x y  =  x++gcd 0 x  =  (x `mod` 0) `mod` x+gcd x y  =  y++gcd 0 x  =  (x `mod` 0) `mod` x+gcd x y  =  0++gcd 0 x  =  (x `mod` 0) `mod` 0+gcd x y  =  x++gcd 0 x  =  (x `mod` 0) `mod` 0+gcd x y  =  y++gcd 0 x  =  (x `mod` 0) `mod` 0+gcd x y  =  0++gcd 0 x  =  (0 `mod` x) `mod` x+gcd x y  =  x++gcd 0 x  =  (0 `mod` x) `mod` x+gcd x y  =  y++gcd 0 x  =  (0 `mod` x) `mod` x+gcd x y  =  0++gcd 0 x  =  (0 `mod` x) `mod` 0+gcd x y  =  x++gcd 0 x  =  (0 `mod` x) `mod` 0+gcd x y  =  y++gcd 0 x  =  (0 `mod` x) `mod` 0+gcd x y  =  0++gcd x 0  =  x+gcd x y  =  gcd x (x `mod` y)++gcd x 0  =  x+gcd x y  =  gcd x (y `mod` y)++gcd x 0  =  x+gcd x y  =  gcd y (x `mod` x)++gcd x 0  =  x+gcd x y  =  gcd y (x `mod` y)++gcd x 0  =  x+gcd x y  =  gcd y (y `mod` x)++gcd x 0  =  x+gcd x y  =  gcd y (y `mod` y)++gcd x 0  =  x+gcd x y  =  gcd 0 (x `mod` y)++gcd x 0  =  x+gcd x y  =  gcd 0 (y `mod` y)++gcd x 0  =  x+gcd x y  =  gcd (x `mod` x) x++gcd x 0  =  x+gcd x y  =  gcd (x `mod` x) y++gcd x 0  =  x+gcd x y  =  gcd (x `mod` y) x++gcd x 0  =  x+gcd x y  =  gcd (y `mod` x) x++gcd x 0  =  x+gcd x y  =  gcd (y `mod` x) y++gcd x 0  =  x+gcd x y  =  gcd (y `mod` y) x++gcd 0 x  =  x+gcd x y  =  gcd x (x `mod` y)++gcd 0 x  =  x+gcd x y  =  gcd x (y `mod` y)++gcd 0 x  =  x+gcd x y  =  gcd y (x `mod` x)++gcd 0 x  =  x+gcd x y  =  gcd y (x `mod` y)++gcd 0 x  =  x+gcd x y  =  gcd y (y `mod` x)++gcd 0 x  =  x+gcd x y  =  gcd y (y `mod` y)++gcd 0 x  =  x+gcd x y  =  gcd (x `mod` x) x++gcd 0 x  =  x+gcd x y  =  gcd (x `mod` x) y++gcd 0 x  =  x+gcd x y  =  gcd (x `mod` x) 0++gcd 0 x  =  x+gcd x y  =  gcd (x `mod` y) x++gcd 0 x  =  x+gcd x y  =  gcd (y `mod` x) x++gcd 0 x  =  x+gcd x y  =  gcd (y `mod` x) y++gcd 0 x  =  x+gcd x y  =  gcd (y `mod` x) 0++gcd 0 x  =  x+gcd x y  =  gcd (y `mod` y) x
bench/carry-on.hs view
@@ -15,8 +15,8 @@ main  =  do   -- carry on Conjuring larger implementations   conjure "factorial n" factorial-    [ unfun (0::Int)-    , unfun (1::Int)+    [ con (0::Int)+    , con (1::Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "*" ((*) :: Int -> Int -> Int)     , fun "-" ((-) :: Int -> Int -> Int)
bench/carry-on.txt view
@@ -2,46 +2,46 @@ -- testing 4 combinations of argument values -- pruning with 27/65 rules -- 3 candidates of size 1--- 3 candidates of size 2--- 7 candidates of size 3--- 8 candidates of size 4--- 28 candidates of size 5--- 35 candidates of size 6--- 167 candidates of size 7--- tested 95 candidates+-- 0 candidates of size 2+-- 6 candidates of size 3+-- 0 candidates of size 4+-- 23 candidates of size 5+-- 0 candidates of size 6+-- 147 candidates of size 7+-- tested 173 candidates factorial 0  =  1 factorial x  =  x * factorial (x - 1) --- 203 candidates of size 8--- tested 254 candidates+-- 8 candidates of size 8+-- tested 182 candidates factorial 1  =  1 factorial x  =  x * factorial (x - 1) --- 1048 candidates of size 9--- tested 547 candidates+-- 941 candidates of size 9+-- tested 1115 candidates factorial 0  =  0 factorial 1  =  1 factorial x  =  x * factorial (x - 1) --- tested 555 candidates+-- tested 1123 candidates factorial 0  =  1 factorial 1  =  1 factorial x  =  x * factorial (x - 1) --- 1299 candidates of size 10--- 7200 candidates of size 11--- tested 3213 candidates+-- 49 candidates of size 10+-- 6490 candidates of size 11+-- tested 7239 candidates factorial 0  =  1 factorial x  =  x + x * (factorial (x - 1) - 1) --- tested 3393 candidates+-- tested 7421 candidates factorial 0  =  1 factorial x  =  x - x * (1 - factorial (x - 1)) --- tested 3516 candidates+-- tested 7544 candidates factorial 0  =  1 factorial x  =  (0 - x) * (0 - factorial (x - 1)) --- tested 10001 candidates+-- tested 7667 candidates factorial n  =  undefined  -- search exhausted
bench/erroneous.hs view
@@ -58,44 +58,44 @@   let n = 6    printErroneousCandidates (n+1) "foo" (undefined :: Int -> Int)-    [ unfun (0 :: Int)-    , unfun (1 :: Int)-    , unfun (2 :: Int)+    [ con (0 :: Int)+    , con (1 :: Int)+    , con (2 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "*" ((*) :: Int -> Int -> Int)     , fun "-" ((-) :: Int -> Int -> Int)     ]    printErroneousCandidates n "?" (undefined :: Int -> Int -> Int)-    [ unfun (0 :: Int)+    [ con (0 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "*" ((*) :: Int -> Int -> Int)     , fun "dec" (subtract 1 :: Int -> Int)     ]    printErroneousCandidates (n+1) "goo" (undefined :: [Int] -> [Int])-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "++" ((++) :: [Int] -> [Int] -> [Int])     ]    printErroneousCandidates n "??" (undefined :: [Int] -> [Int] -> [Int])-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "++" ((++) :: [Int] -> [Int] -> [Int])     ]    printErroneousCandidates n "ton" (undefined :: Bool -> Bool)-    [ unfun False-    , unfun True+    [ con False+    , con True     , fun "&&" (&&)     , fun "||" (||)     , fun "not" not     ]    printErroneousCandidates n "&|" (undefined :: Bool -> Bool -> Bool)-    [ unfun False-    , unfun True+    [ con False+    , con True     , fun "&&" (&&)     , fun "||" (||)     , fun "not" not
bench/erroneous.txt view
@@ -138,6 +138,30 @@ -- 1 ? 0  =  bottom  -- and 16 other errors  x ? 0  =  x+x ? y  =  dec (dec x ? y)+-- 0 ? 1  =  bottom  -- and 16 other errors++x ? 0  =  0+x ? y  =  dec (dec x ? y)+-- 0 ? 1  =  bottom  -- and 16 other errors++x ? 0  =  dec x+x ? y  =  dec x ? y+-- 0 ? 1  =  bottom  -- and 16 other errors++0 ? x  =  x+x ? y  =  dec (x ? dec y)+-- 1 ? 0  =  bottom  -- and 16 other errors++0 ? x  =  0+x ? y  =  dec (x ? dec y)+-- 1 ? 0  =  bottom  -- and 16 other errors++0 ? x  =  dec x+x ? y  =  x ? dec y+-- 1 ? 0  =  bottom  -- and 16 other errors++x ? 0  =  x x ? y  =  x ? dec (dec y) -- 0 ? 1  =  bottom  -- and 9 other errors @@ -208,30 +232,6 @@ 0 ? x  =  x x ? y  =  dec (dec y) ? x -- 1 ? 0  =  bottom  -- and 6 other errors--x ? 0  =  x-x ? y  =  dec (dec x ? y)--- 0 ? 1  =  bottom  -- and 16 other errors--x ? 0  =  0-x ? y  =  dec (dec x ? y)--- 0 ? 1  =  bottom  -- and 16 other errors--x ? 0  =  dec x-x ? y  =  dec x ? y--- 0 ? 1  =  bottom  -- and 16 other errors--0 ? x  =  x-x ? y  =  dec (x ? dec y)--- 1 ? 0  =  bottom  -- and 16 other errors--0 ? x  =  0-x ? y  =  dec (x ? dec y)--- 1 ? 0  =  bottom  -- and 16 other errors--0 ? x  =  dec x-x ? y  =  x ? dec y--- 1 ? 0  =  bottom  -- and 16 other errors   Erroneous candidates for: goo :: [Int] -> [Int]
bench/gps.hs view
@@ -44,10 +44,10 @@  gps1c30p :: IO () gps1c30p  =  conjure "gps1" gps1p-  [ unfun (0 :: Float)-  , unfun (1 :: Float)-  , unfun (1/2 :: Float)-  , unfun (-1 :: Float)+  [ con (0 :: Float)+  , con (1 :: Float)+  , con (1/2 :: Float)+  , con (-1 :: Float)   , fun "+" ((+) :: Float -> Float -> Float)   , fun "*" ((*) :: Float -> Float -> Float)   , fun "-" ((-) :: Float -> Float -> Float)@@ -56,9 +56,9 @@   , fun "id" (id :: Float -> Float)   , fun "fromIntegral" (fromIntegral :: Int -> Float) -  , unfun (0 :: Int)-  , unfun (1 :: Int)-  , unfun (-1 :: Int)+  , con (0 :: Int)+  , con (1 :: Int)+  , con (-1 :: Int)   , fun "+" ((+) :: Int -> Int -> Int)   , fun "*" ((*) :: Int -> Int -> Int)   , fun "-" ((-) :: Int -> Int -> Int)@@ -71,8 +71,8 @@   , fun "round" (round :: Float -> Int)   , fun "truncate" (truncate :: Float -> Int) -  , unfun False-  , unfun True+  , con False+  , con True   , fun "&&" (&&)   , fun "||" (||)   , fun "not" not@@ -95,17 +95,16 @@  gps2c :: IO () gps2c  =  conjure "gps2" gps2p-  [ unfun "small"-  , unfun "large"-  , unfun (1000 :: Int)-  , unfun (2000 :: Int)+  [ con "small"+  , con "large"+  , con (1000 :: Int)+  , con (2000 :: Int)   , fun "Just" (Just :: String -> Maybe String)   , fun "Nothing" (Nothing :: Maybe String)   , fun "<=" ((<=) :: Int -> Int -> Bool)   , fun "<" ((<) :: Int -> Int -> Bool)-  , iif (undefined :: Maybe String)+  , guard   , maxTests 5040-  , maxSize 30   ]  @@ -117,27 +116,28 @@ gps3g1 start end step  =  enumFromThenTo start (step+start) (end-1)  gps3g2 :: Int -> Int -> Int -> [Int]-gps3g2 start end step  =  if start < end-                          then start : gps3g2 (start+step) end step-                          else []+gps3g2 start end step+  | start < end  =  start : gps3g2 (start+step) end step -- 11+  | otherwise    =  [] -- 12  gps3c :: IO () gps3c  =  do   conjure "gps3" gps3p-    [ unfun (1 :: Int)+    [ con (1 :: Int)     , fun "enumFromThenTo" ((\x y z -> take 720 $ enumFromThenTo x y z) :: Int -> Int -> Int -> [Int])     , fun "+" ((+) :: Int -> Int -> Int)     , fun "-" ((-) :: Int -> Int -> Int)     ]    -- not possible, no recursive descent-  conjure "gps3" gps3p-    [ unfun ([] :: [Int])+  conjure "gps3_alt" gps3p+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "+" ((+) :: Int -> Int -> Int)     , fun "<" ((<) :: Int -> Int -> Bool)-    , iif (undefined :: [Int])-    , maxSize 8+    , guard+    , dontRequireDescent+    -- TODO: shouldn't a solution appear here?     ]  @@ -170,27 +170,43 @@ gps5p " "  =  " " gps5p "!"  =  "!!!" gps5p "aa"  =  "aaaa"+gps5p " a"  =  " aa"+gps5p "!a"  =  "!!!aa"  gps5g :: String -> String-gps5g []  =  []+gps5g ""  =  "" gps5g (c:cs)   | isLetter c  =  c:c:gps5g cs   | c == '!'    =  c:c:c:gps5g cs   | otherwise   =  c:gps5g cs  gps5c :: IO ()-gps5c  =  conjure "gps5" gps5p -- can't find-  [ unfun ""+gps5c  =  conjure "gps5" gps5p+  [ con ""   , fun ":" ((:) :: Char -> String -> String)-  , unfun '!'+  , con '!'   , fun "==" ((==) :: Char -> Char -> Bool)   , fun "isLetter" (isLetter :: Char -> Bool)-  , iif (undefined :: String -> String)-  , maxSize 6+  , guard+  -- BENCHMARK: increase to 26 to find+  , maxSize 12 -- 26   ]+  -- found (lapmatrud unplugged):+  -- -- 65.5s, 10856 candidates of size 26+  -- -- 65.5s, tested 20317 candidates+  -- gps5 ""  =  ""+  -- gps5 (c:cs)+  --   | isLetter c  =  c:c:gps5 cs+  --   | c == '!'  =  c:c:c:gps5 cs+  --   | otherwise  =  c:gps5 cs  + -- GPS Benchmark #6 -- Collatz/Hailstone numbers --+-- Given an integer, find the number of terms in the Collatz (hailstone)+-- sequence starting from that integer.+-- NOTE: The sequence is actually always infinite,+-- so I assume it is the count until reaching 1.  gps6p :: Int -> Int gps6p 1  =  1@@ -212,26 +228,71 @@                         then n `div` 2  -- 10                         else 3*n + 1)   -- 15 --- This one is out of reach performance wise:--- Speculate hangs with this background.--- Removing three or setting maxEqSize to 4 makes it unhang.--- But a size of 15 or 17 is simplyl out of our reach.+nextCollatz' :: Int -> Int+nextCollatz' 1  =  4+nextCollatz' 2  =  1+nextCollatz' 3  =  10+nextCollatz' 4  =  2+nextCollatz' 5  =  16+nextCollatz' 6  =  3++nextCollatz :: Int -> Int+nextCollatz n+  | even n     =  n `div` 2+  | otherwise  =  3*n + 1+ gps6c :: IO ()-gps6c  =  conjure "gps6" gps6p-  [ unfun (1 :: Int)-  , unfun (2 :: Int)-  , unfun (3 :: Int)-  , fun "+" ((+) :: Int -> Int -> Int)-  , fun "*" ((*) :: Int -> Int -> Int)-  , fun "`div`" (div :: Int -> Int -> Int)-  , fun "even" (even :: Int -> Bool)-  , iif (undefined :: Int)-  , maxSize 6-  , maxEquationSize 3-  ]+gps6c  =  do+  -- This one is out of reach performance wise:+  -- Speculate hangs with this background.+  -- Removing three or setting maxEqSize to 4 makes it unhang.+  -- But a size of 15 or 17 is simplyl out of our reach.+  conjure "gps6direct" gps6p+    [ con (1 :: Int)+    , con (2 :: Int)+    , con (3 :: Int)+    , fun "+" ((+) :: Int -> Int -> Int)+    , fun "*" ((*) :: Int -> Int -> Int)+    , fun "`div`" (div :: Int -> Int -> Int)+    , fun "even" (even :: Int -> Bool)+    , iif (undefined :: Int)+    , maxSize 6+    , maxEquationSize 3  -- degenerate case in Speculate+    ] +  conjure "gps6step" gps6p+    [ con (1 :: Int)+    , fun "+" ((+) :: Int -> Int -> Int)+    , fun "nextCollatz" nextCollatz+    , dontRequireDescent+    ] +  conjure "nextCollatz" nextCollatz+    [ con (1 :: Int)+    , con (2 :: Int)+    , con (3 :: Int)+    , fun "+" ((+) :: Int -> Int -> Int)+    , fun "*" ((*) :: Int -> Int -> Int)+    , fun "`div`" (div :: Int -> Int -> Int)+    , fun "even" (even :: Int -> Bool)+    , guard+    , target 720720+    , maxEquationSize 3  -- degenerate case in Speculate+    -- BENCHMARK: set maxSize 11+    , maxSize 6 -- 11+    ]+  -- -- on lapmatrud (2025-08), found after+  -- -- 18.5s, 754952 candidates of size 11+  -- -- 19.4s, tested 568616 candidates+  -- nextCollatz x+  --   | even x  =  x `div` 2+  --   | otherwise  =  1 + x * 3++ -- GPS Benchmark #7 -- Replace Space with Newline (P 4.3)+-- Given a string input, print the string, replacing spaces with newlines.+-- Also, return the integer count of the non-whitespace characters.+-- The input string will not have tabs or newlines.  gps7p :: String -> (String, Int) gps7p "a"  =  ("a", 1)@@ -301,7 +362,7 @@  gps9c :: IO () gps9c  =  conjure "gps9" gps9p-  [ unfun (1 :: Int)+  [ con (1 :: Int)   , fun "map" (map :: (Int -> Int) -> [Int] -> [Int])   , fun "filter" (filter :: (Int -> Bool) -> [Int] -> [Int])   , fun ".." (enumFromTo :: Int -> Int -> [Int])@@ -353,31 +414,31 @@ gps10c :: IO () gps10c  =  do   conjure "wallisNext" wallisNextP-    [ unfun (1 :: Integer)-    , unfun (2 :: Integer)+    [ con (1 :: Integer)+    , con (2 :: Integer)     , fun "+" ((+) :: Integer -> Integer -> Integer)     , fun "*" ((*) :: Integer -> Integer -> Integer)     , fun "%" ((%) :: Integer -> Integer -> Rational)     , fun "<" ((<) :: Integer -> Integer -> Bool) --  , fun "numerator" (numerator :: Rational -> Integer) --  , fun "denominator" (denominator :: Rational -> Integer)-    , iif (undefined :: Rational)+    , guard     ]    -- simplified background   conjure "wallisNext" wallisNextP-    [ unfun (0 :: Integer)-    , unfun (1 :: Integer)+    [ con (0 :: Integer)+    , con (1 :: Integer)     , fun "+" ((+) :: Integer -> Integer -> Integer)     , fun "*" ((*) :: Integer -> Integer -> Integer)     , fun "%" ((%) :: Integer -> Integer -> Rational)     ]    conjure "gps10" gps10p-    [ unfun (2 :: Integer)-    , unfun (3 :: Integer)+    [ con (2 :: Integer)+    , con (3 :: Integer)     , fun "%" ((%) :: Integer -> Integer -> Rational)---  , unfun (2/3 :: Rational)+--  , con (2/3 :: Rational)     , fun "product"    (product :: [Rational] -> Rational)     , fun "take"       (take :: Int -> [Rational] -> [Rational])     , fun "iterate"    ((\f -> take 720 . iterate f) :: (Rational -> Rational) -> Rational -> [Rational])@@ -409,7 +470,7 @@     ]    conjure "gps11" gps11p-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "++" ((++) :: [Int] -> [Int] -> [Int])     , fun "length"  (length :: String -> Int)@@ -438,8 +499,8 @@     , fun "fromJust"  (fromJust :: Maybe Int -> Int)     , fun "-"         ((-) :: Int -> Int -> Int)     , fun "=="        ((==) :: Int -> Int -> Bool)-    , unfun (0 :: Int)-    , unfun (1 :: Int)+    , con (0 :: Int)+    , con (1 :: Int)     , maxSize 11     ] @@ -496,9 +557,9 @@ gps14c :: IO () gps14c  =  do   conjure "odd" odd'-    [ unfun (0 :: Int)-    , unfun (1 :: Int)-    , unfun (2 :: Int)+    [ con (0 :: Int)+    , con (1 :: Int)+    , con (2 :: Int)     , fun "`mod`" (mod :: Int -> Int -> Int)     , fun "/=" ((/=) :: Int -> Int -> Bool)     ]@@ -513,13 +574,13 @@   -- gps14 []  =  0   -- gps14 (x:xs)  =  x `mod` 2 + gps14 xs   conjure "gps14" gps14p-    [ unfun (0 :: Int)-    , unfun (1 :: Int)-    , unfun (2 :: Int)+    [ con (0 :: Int)+    , con (1 :: Int)+    , con (2 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "`mod`" (mod :: Int -> Int -> Int)     , fun "==" ((==) :: Int -> Int -> Bool)-    , iif (undefined :: Int)+    , guard     ]  @@ -577,8 +638,8 @@  gps17c :: IO () gps17c  =  conjure "gps17" gps17p-  [ unfun (0 :: Int)-  , unfun (1 :: Int)+  [ con (0 :: Int)+  , con (1 :: Int)   , fun "+" ((+) :: Int -> Int -> Int)   , fun "*" ((*) :: Int -> Int -> Int)   , fun "-" ((-) :: Int -> Int -> Int)@@ -602,7 +663,7 @@ gps18c :: IO () gps18c  =  do   conjure "gps18" gps18p-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun "+" ((+) :: Int -> Int -> Int)     , fun ":" ((:) :: Int -> [Int] -> [Int])     ]@@ -692,19 +753,19 @@ gps20c :: IO () gps20c  =  do   conjure "isVowel" isVowel'-    [ unfun 'a'-    , unfun 'e'-    , unfun 'i'-    , unfun 'o'-    , unfun 'u'-    , unfun 'y'-    , unfun True-    , unfun False+    [ con 'a'+    , con 'e'+    , con 'i'+    , con 'o'+    , con 'u'+    , con 'y'+    , con True+    , con False     ]    conjureFromSpec "pig1" pig1Spec-    [ unfun "ay"-    , iif (undefined :: String)+    [ con "ay"+    , guard     , fun "isVowel" isVowel     , fun "++" ((++) :: String -> String -> String)     , fun ":" ((:) :: Char -> String -> String)@@ -727,6 +788,7 @@ gps21p [-1]  =  [0] gps21p [1,-1]  =  [1,0] gps21p [-1,1]  =  [0,1]+gps21p [-1,-1]  =  [0,0]  gps21g :: [Int] -> [Int] gps21g []  =  []@@ -734,11 +796,11 @@  gps21c :: IO () gps21c  =  conjure "gps21" gps21p-  [ unfun ([] :: [Int])-  , unfun (0 :: Int)+  [ con ([] :: [Int])+  , con (0 :: Int)   , fun ":" ((:) :: Int -> [Int] -> [Int])   , fun "<" ((<) :: Int -> Int -> Bool)-  , iif (undefined :: Int)+  , guard   ]  @@ -778,8 +840,16 @@  gps22c :: IO () gps22c  =  do+  conjure "scrabble1" scrabble1 $+    [ con (1 :: Int)+    -- comment-out the following to find function+    -- at size 137 after 1025 candidates in 6.0s+    -- limited here for faster runtimes+    , maxSize 13+    ] ++ map con "dgbcmpfhvwykjxqz"+   conjureFromSpec "gps22" gps22s-    [ unfun (0 :: Int)+    [ con (0 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "map" (map :: (Int -> Int) -> [Int] -> [Int])     , fun "scrabble1" scrabble1@@ -808,14 +878,19 @@  gps24c :: IO () gps24c  =  conjure "gps24" gps24p-  [ unfun ' '-  , unfun (64 :: Int)+  [ con ' '+  , con (64 :: Int)   , fun "+" ((+) :: Int -> Int -> Int)   , fun "`mod`" (mod :: Int -> Int -> Int)   , fun "sum" (sum :: [Int] -> Int)   , fun "ord" ord   , fun "chr" chr   , fun "map" (map :: (Char -> Int) -> String -> [Int])++  -- The following flag is here so behaviour is consistent between different+  -- GHC versions (8.8 and later).  It makes no significant difference in+  -- runtime for this example.+  , maxEarlyTests 0   ]  @@ -834,12 +909,12 @@  -- out of reach performance-wise gps25c :: IO ()-gps25c  =  conjure "gps25" gps25p $ take 0-  [ unfun (0 :: Int)-  , unfun (10 :: Int)-  , unfun ([] :: [Int])+gps25c  =  conjure "gps25" gps25p+  [ con (0 :: Int)+  , con (10 :: Int)+  , con ([] :: [Int])   , fun ":" ((:) :: Int -> [Int] -> [Int])-  , iif (undefined :: [Int])+  , guard   , fun "abs" (abs :: Int -> Int)   , fun "<" ((<) :: Int -> Int -> Bool)   , fun "rem" (rem :: Int -> Int -> Int)@@ -858,48 +933,57 @@  gps26g :: Int -> Int -> Int -> Int -> Int -> Char gps26g a b c d x-  | x >= a     =  'A'-  | x >= b     =  'B'-  | x >= c     =  'C'-  | x >= d     =  'D'-  | otherwise  =  'F'+  | x >= a     =  'A'  -- 5+  | x >= b     =  'B'  -- 10+  | x >= c     =  'C'  -- 15+  | x >= d     =  'D'  -- 20+  | otherwise  =  'F'  -- 21 --- out of reach performance-wise+-- out of reach performance-wise, OOM at size 21, see:+-- -- 20.6s, 4000000 candidates of size 16+-- -- 38.2s, 0 candidates of size 20+-- gps: out of memory+ gps26c :: IO () gps26c  =  conjure "gps26" gps26p-  [ unfun 'A'-  , unfun 'B'-  , unfun 'C'-  , unfun 'D'-  , unfun 'F'-  , iif (undefined :: Char)+  [ con 'A'+  , con 'B'+  , con 'C'+  , con 'D'+  , con 'F'+  , guard   , fun ">=" ((>=) :: Int -> Int -> Bool)-  , maxSize 2   ]   -- GPS Benchmark #27 -- Median --+-- Given three integers, print their median. gps27p :: Int -> Int -> Int -> Int gps27p 0 1 2  =  1+gps27p 0 2 1  =  1+gps27p 2 3 1  =  2 gps27p 1 0 2  =  1-gps27p (-1) 1 0  =  0+gps27p 4 3 1  =  3+gps27p 4 1 3  =  3  gps27g :: Int -> Int -> Int -> Int gps27g x y z-  | y < x && x < z  =  x  -- 8-  | x < y && y < z  =  y  -- 16-  | otherwise       =  z  -- 17--- Conjure found a smaller implementation!+  | y <= x && x <= z || z <= x && x <= y  =  x  -- 16+  | x <= y && y <= z || z <= y && y <= x  =  y  -- 32+  | otherwise                             =  z  -- 33  gps27c :: IO () gps27c  =  do-  conjure "gps27" gps27p-    [ fun "<" ((<) :: Int -> Int -> Bool)+  -- simply unreachable performance-wise+  -- it gets OOM at size 25 after >83s.+  conjure "gps27_median" gps27p+    [ fun "<=" ((<=) :: Int -> Int -> Bool)     , fun "&&" (&&)-    , iif (undefined :: Int)+    , fun "||" (||)+    , guard     ] -  conjure "gps27b" gps27p+  conjure "gps27b_median" gps27p     [ fun "min" (min :: Int -> Int -> Int)     , fun "max" (max :: Int -> Int -> Int)     ]@@ -938,10 +1022,10 @@  gps29c :: IO () gps29c  =  conjureFromSpec "gps29" gps29s-  [ unfun (0 :: Int)-  , unfun (1 :: Int)+  [ con (0 :: Int)+  , con (1 :: Int)   , fun "+" ((+) :: Int->Int->Int)-  , iif (undefined :: Int)+  , guard   , fun "isVowel" isVowel   ]
bench/gps.txt view
@@ -6,28 +6,29 @@ -- 1 candidates of size 3 -- 2 candidates of size 4 -- tested 4 candidates-gps1 x y  =  fromIntegral x + y+gps1 x y  =  y + fromIntegral x  gps2 :: Int -> Maybe [Char] -- testing 6 combinations of argument values -- pruning with 9/17 rules -- 1 candidates of size 1 -- 2 candidates of size 2--- 3 candidates of size 3--- 2 candidates of size 4--- 2 candidates of size 5+-- 0 candidates of size 3+-- 0 candidates of size 4+-- 0 candidates of size 5 -- 0 candidates of size 6 -- 32 candidates of size 7--- 32 candidates of size 8--- 48 candidates of size 9--- 32 candidates of size 10--- 16 candidates of size 11--- 512 candidates of size 12--- 1408 candidates of size 13--- tested 1171 candidates-gps2 x  =  if 2000 <= x-           then Just "large"-           else if x < 1000 then Just "small" else Nothing+-- 16 candidates of size 8+-- 0 candidates of size 9+-- 0 candidates of size 10+-- 0 candidates of size 11+-- 256 candidates of size 12+-- 640 candidates of size 13+-- tested 664 candidates+gps2 x+  | 2000 <= x  =  Just "large"+  | 1000 <= x  =  Nothing+  | otherwise  =  Just "small"  gps3 :: Int -> Int -> Int -> [Int] -- testing 2 combinations of argument values@@ -39,11 +40,11 @@ -- 0 candidates of size 5 -- 1248 candidates of size 6 -- 0 candidates of size 7--- 17008 candidates of size 8--- tested 12358 candidates+-- 13680 candidates of size 8+-- tested 3238 candidates gps3 x y z  =  enumFromThenTo x (x + z) (y - 1) -gps3 :: Int -> Int -> Int -> [Int]+gps3_alt :: Int -> Int -> Int -> [Int] -- testing 2 combinations of argument values -- pruning with 6/18 rules -- 1 candidates of size 1@@ -54,8 +55,13 @@ -- 0 candidates of size 6 -- 81 candidates of size 7 -- 36 candidates of size 8--- tested 136 candidates-gps3  =  undefined  -- search exhausted+-- 441 candidates of size 9+-- 432 candidates of size 10+-- 2403 candidates of size 11+-- 3636 candidates of size 12+-- 13311 candidates of size 13+-- tested 20359 candidates+gps3_alt  =  undefined  -- search exhausted  gps4 :: [Char] -> [Char] -> [Char] -> Bool -- testing 9 combinations of argument values@@ -75,29 +81,60 @@ gps4 cs ds es  =  length cs < length ds && length ds < length es  gps5 :: [Char] -> [Char]--- testing 5 combinations of argument values--- pruning with 2/3 rules+-- testing 7 combinations of argument values+-- pruning with 5/6 rules -- 2 candidates of size 1 -- 0 candidates of size 2 -- 2 candidates of size 3 -- 0 candidates of size 4--- 4 candidates of size 5+-- 3 candidates of size 5 -- 0 candidates of size 6--- tested 8 candidates+-- 3 candidates of size 7+-- 0 candidates of size 8+-- 3 candidates of size 9+-- 2 candidates of size 10+-- 6 candidates of size 11+-- 5 candidates of size 12+-- tested 26 candidates gps5  =  undefined  -- search exhausted -gps6 :: Int -> Int+gps6direct :: Int -> Int -- testing 9 combinations of argument values -- pruning with 16/18 rules -- 4 candidates of size 1--- 2 candidates of size 2--- 14 candidates of size 3--- 14 candidates of size 4--- 186 candidates of size 5--- 165 candidates of size 6--- tested 385 candidates-gps6  =  undefined  -- search exhausted+-- 0 candidates of size 2+-- 12 candidates of size 3+-- 0 candidates of size 4+-- 172 candidates of size 5+-- 0 candidates of size 6+-- tested 188 candidates+gps6direct  =  undefined  -- search exhausted +gps6step :: Int -> Int+-- testing 9 combinations of argument values+-- pruning with 4/8 rules+-- 2 candidates of size 1+-- 1 candidates of size 2+-- 3 candidates of size 3+-- 4 candidates of size 4+-- 12 candidates of size 5+-- 27 candidates of size 6+-- tested 46 candidates+gps6step 1  =  1+gps6step x  =  1 + gps6step (nextCollatz x)++nextCollatz :: Int -> Int+-- testing 360 combinations of argument values+-- pruning with 16/18 rules+-- 4 candidates of size 1+-- 0 candidates of size 2+-- 12 candidates of size 3+-- 0 candidates of size 4+-- 172 candidates of size 5+-- 0 candidates of size 6+-- tested 188 candidates+nextCollatz  =  undefined  -- search exhausted+ gps7 :: [Char] -> ([Char],Int) -- testing 4 combinations of argument values -- pruning with 5/10 rules@@ -112,7 +149,7 @@ -- 88 candidates of size 9 -- 201 candidates of size 10 -- 442 candidates of size 11--- tested 546 candidates+-- tested 553 candidates gps7 cs  =  (init (unlines (words cs)),length (filter (not . isSpace) cs))  gps8 :: [Char] -> [Char] -> [(Int,Char,Char)]@@ -135,10 +172,10 @@ -- 10 candidates of size 5 -- 21 candidates of size 6 -- 30 candidates of size 7--- 77 candidates of size 8--- 134 candidates of size 9--- 245 candidates of size 10--- tested 306 candidates+-- 69 candidates of size 8+-- 114 candidates of size 9+-- 212 candidates of size 10+-- tested 278 candidates gps9 x  =  filter even (filter (x >) (map sq [1..x]))  wallisNext :: Ratio Integer -> Ratio Integer@@ -147,12 +184,12 @@ -- 1 candidates of size 1 -- 0 candidates of size 2 -- 3 candidates of size 3--- 0 candidates of size 4+-- 15 candidates of size 4 -- 4 candidates of size 5--- 0 candidates of size 6+-- 86 candidates of size 6 -- 5 candidates of size 7--- 1 candidates of size 8--- tested 14 candidates+-- 513 candidates of size 8+-- tested 368 candidates wallisNext (x % y)  =  (y + 1) % (x + 1)  wallisNext :: Ratio Integer -> Ratio Integer@@ -161,12 +198,12 @@ -- 1 candidates of size 1 -- 0 candidates of size 2 -- 4 candidates of size 3--- 0 candidates of size 4+-- 16 candidates of size 4 -- 3 candidates of size 5--- 0 candidates of size 6+-- 71 candidates of size 6 -- 5 candidates of size 7--- 1 candidates of size 8--- tested 14 candidates+-- 393 candidates of size 8+-- tested 295 candidates wallisNext (x % y)  =  (y + 1) % (x + 1)  gps10 :: Int -> Ratio Integer@@ -201,10 +238,10 @@ -- 0 candidates of size 3 -- 0 candidates of size 4 -- 0 candidates of size 5--- 2 candidates of size 6+-- 1 candidates of size 6 -- 0 candidates of size 7 -- 1 candidates of size 8--- tested 4 candidates+-- tested 3 candidates gps11 []  =  [] gps11 (cs:css)  =  gps11 css ++ [length cs] @@ -222,8 +259,8 @@ -- 416 candidates of size 9 -- 956 candidates of size 10 -- 3073 candidates of size 11--- tested 4404 candidates-gps12 xs  =  (length xs - fromJust (findIndex (0 ==) (reverse xs))) - 1+-- tested 1713 candidates+gps12 xs  =  (length xs - 1) - fromJust (findIndex (0 ==) (reverse xs))  gps13 :: [Ratio Integer] -> Ratio Integer -- testing 3 combinations of argument values@@ -234,9 +271,9 @@ -- 2 candidates of size 4 -- 9 candidates of size 5 -- 12 candidates of size 6--- 67 candidates of size 7--- 97 candidates of size 8--- tested 179 candidates+-- 63 candidates of size 7+-- 95 candidates of size 8+-- tested 106 candidates gps13 qs  =  foldr (+) 0 qs / fromIntegral (length qs)  odd :: Int -> Bool@@ -245,9 +282,9 @@ -- 0 candidates of size 1 -- 0 candidates of size 2 -- 3 candidates of size 3--- 2 candidates of size 4--- 37 candidates of size 5--- tested 17 candidates+-- 0 candidates of size 4+-- 35 candidates of size 5+-- tested 15 candidates odd x  =  0 /= x `mod` 2  gps14 :: [Int] -> Int@@ -270,7 +307,7 @@ -- 30 candidates of size 5 -- 6 candidates of size 6 -- 345 candidates of size 7--- tested 83 candidates+-- tested 46 candidates gps14 []  =  0 gps14 (x:xs)  =  x + gps14 xs `mod` 2 @@ -299,15 +336,15 @@ -- testing 4 combinations of argument values -- pruning with 27/65 rules -- 3 candidates of size 1--- 3 candidates of size 2--- 7 candidates of size 3--- 8 candidates of size 4--- 28 candidates of size 5--- 35 candidates of size 6--- 167 candidates of size 7--- 203 candidates of size 8--- 1048 candidates of size 9--- tested 466 candidates+-- 0 candidates of size 2+-- 6 candidates of size 3+-- 0 candidates of size 4+-- 23 candidates of size 5+-- 0 candidates of size 6+-- 147 candidates of size 7+-- 8 candidates of size 8+-- 941 candidates of size 9+-- tested 1032 candidates gps17 0  =  0 gps17 x  =  x * x + gps17 (x - 1) @@ -319,11 +356,11 @@ -- 0 candidates of size 3 -- 10 candidates of size 4 -- 25 candidates of size 5--- 34 candidates of size 6--- 138 candidates of size 7--- 126 candidates of size 8--- 743 candidates of size 9--- tested 767 candidates+-- 24 candidates of size 6+-- 114 candidates of size 7+-- 72 candidates of size 8+-- 481 candidates of size 9+-- tested 250 candidates gps18 [] xs  =  xs gps18 (x:xs) []  =  xs gps18 (x:xs) (y:ys)  =  x + y:gps18 xs ys@@ -335,7 +372,7 @@ -- 0 candidates of size 2 -- 0 candidates of size 3 -- 10 candidates of size 4--- tested 10 candidates+-- tested 4 candidates gps18  =  zipWith (+)  gps19 :: Int -> [Char] -> [Char]@@ -350,28 +387,28 @@ -- testing 12 combinations of argument values -- pruning with 0/0 rules -- 2 candidates of size 1--- 1 candidates of size 2--- 1 candidates of size 3--- 2 candidates of size 4--- 2 candidates of size 5--- 3 candidates of size 6--- 4 candidates of size 7--- 4 candidates of size 8--- 4 candidates of size 9--- 5 candidates of size 10--- 5 candidates of size 11--- 5 candidates of size 12--- 5 candidates of size 13--- 4 candidates of size 14--- 4 candidates of size 15--- 4 candidates of size 16--- 3 candidates of size 17--- 2 candidates of size 18--- 2 candidates of size 19--- 1 candidates of size 20--- 1 candidates of size 21+-- 0 candidates of size 2+-- 0 candidates of size 3+-- 0 candidates of size 4+-- 0 candidates of size 5+-- 0 candidates of size 6+-- 0 candidates of size 7+-- 0 candidates of size 8+-- 0 candidates of size 9+-- 0 candidates of size 10+-- 0 candidates of size 11+-- 0 candidates of size 12+-- 0 candidates of size 13+-- 0 candidates of size 14+-- 0 candidates of size 15+-- 0 candidates of size 16+-- 0 candidates of size 17+-- 0 candidates of size 18+-- 0 candidates of size 19+-- 0 candidates of size 20+-- 0 candidates of size 21 -- 1 candidates of size 22--- tested 65 candidates+-- tested 3 candidates isVowel 'a'  =  True isVowel 'e'  =  True isVowel 'i'  =  True@@ -389,18 +426,18 @@ -- 13 candidates of size 5 -- 28 candidates of size 6 -- 46 candidates of size 7--- 125 candidates of size 8--- 200 candidates of size 9--- 625 candidates of size 10--- 1066 candidates of size 11--- 3459 candidates of size 12--- 6361 candidates of size 13--- 20207 candidates of size 14--- tested 27628 candidates+-- 115 candidates of size 8+-- 176 candidates of size 9+-- 441 candidates of size 10+-- 708 candidates of size 11+-- 1747 candidates of size 12+-- 2919 candidates of size 13+-- 6925 candidates of size 14+-- tested 8943 candidates pig1 ""  =  "ay"-pig1 (c:cs)  =  if isVowel c-                then (c:cs) ++ "ay"-                else cs ++ (c:"ay")+pig1 (c:cs)+  | isVowel c  =  (c:cs) ++ "ay"+  | otherwise  =  cs ++ (c:"ay")  gps20c :: [Char] -> [Char] -- pruning with 1/1 rules@@ -413,22 +450,46 @@ gps20c cs  =  unwords (map pig1 (words cs))  gps21 :: [Int] -> [Int]--- testing 4 combinations of argument values+-- testing 5 combinations of argument values -- pruning with 4/4 rules -- 2 candidates of size 1 -- 0 candidates of size 2 -- 2 candidates of size 3 -- 0 candidates of size 4--- 4 candidates of size 5+-- 2 candidates of size 5 -- 0 candidates of size 6--- 8 candidates of size 7+-- 2 candidates of size 7 -- 0 candidates of size 8--- 16 candidates of size 9--- 4 candidates of size 10--- tested 34 candidates+-- 2 candidates of size 9+-- 0 candidates of size 10+-- 6 candidates of size 11+-- 0 candidates of size 12+-- 8 candidates of size 13+-- tested 19 candidates gps21 []  =  []-gps21 (x:xs)  =  (if x < 0 then 0 else x):gps21 xs+gps21 (x:xs)+  | x < 0  =  0:gps21 xs+  | otherwise  =  x:gps21 xs +scrabble1 :: Char -> Int+-- testing 97 combinations of argument values+-- pruning with 0/0 rules+-- 1 candidates of size 1+-- 0 candidates of size 2+-- 0 candidates of size 3+-- 0 candidates of size 4+-- 0 candidates of size 5+-- 0 candidates of size 6+-- 0 candidates of size 7+-- 0 candidates of size 8+-- 0 candidates of size 9+-- 0 candidates of size 10+-- 0 candidates of size 11+-- 0 candidates of size 12+-- 0 candidates of size 13+-- tested 1 candidates+scrabble1  =  undefined  -- search exhausted+ gps22 :: [Char] -> Int -- pruning with 5/9 rules -- 1 candidates of size 1@@ -448,23 +509,33 @@ -- testing 4 combinations of argument values -- pruning with 15/19 rules -- 1 candidates of size 1--- 1 candidates of size 2--- 0 candidates of size 3+-- 2 candidates of size 2+-- 3 candidates of size 3 -- 2 candidates of size 4--- 2 candidates of size 5--- 2 candidates of size 6--- 14 candidates of size 7--- 25 candidates of size 8--- 71 candidates of size 9--- 176 candidates of size 10--- tested 245 candidates+-- 8 candidates of size 5+-- 13 candidates of size 6+-- 30 candidates of size 7+-- 75 candidates of size 8+-- 193 candidates of size 9+-- 469 candidates of size 10+-- tested 376 candidates gps24 cs  =  chr (ord ' ' + sum (map ord cs) `mod` 64)  gps25 :: Int -> [Int] -- testing 4 combinations of argument values--- pruning with 0/0 rules--- 0 candidates of size 1--- tested 0 candidates+-- pruning with 32/37 rules+-- reasoning produced 1 incorrect properties, please re-run with more tests for faster results+-- 1 candidates of size 1+-- 0 candidates of size 2+-- 3 candidates of size 3+-- 1 candidates of size 4+-- 21 candidates of size 5+-- 30 candidates of size 6+-- 259 candidates of size 7+-- 695 candidates of size 8+-- 4225 candidates of size 9+-- 15042 candidates of size 10+-- tested 20277 candidates gps25  =  undefined  -- search exhausted  gps26 :: Int -> Int -> Int -> Int -> Int -> Char@@ -472,12 +543,21 @@ -- pruning with 4/4 rules -- 5 candidates of size 1 -- 0 candidates of size 2--- tested 5 candidates+-- 0 candidates of size 3+-- 0 candidates of size 4+-- 0 candidates of size 5+-- 400 candidates of size 6+-- 0 candidates of size 7+-- 0 candidates of size 8+-- 0 candidates of size 9+-- 0 candidates of size 10+-- 40000 candidates of size 11+-- tested 40405 candidates gps26  =  undefined  -- search exhausted -gps27 :: Int -> Int -> Int -> Int--- testing 3 combinations of argument values--- pruning with 14/18 rules+gps27_median :: Int -> Int -> Int -> Int+-- testing 6 combinations of argument values+-- pruning with 32/42 rules -- 3 candidates of size 1 -- 0 candidates of size 2 -- 0 candidates of size 3@@ -487,23 +567,30 @@ -- 0 candidates of size 7 -- 0 candidates of size 8 -- 0 candidates of size 9--- 90 candidates of size 10--- 2592 candidates of size 11--- tested 1489 candidates-gps27 x y z  =  if x < y-                then if y < z then y else z-                else x+-- 180 candidates of size 10+-- 648 candidates of size 11+-- 0 candidates of size 12+-- 0 candidates of size 13+-- 1440 candidates of size 14+-- 6480 candidates of size 15+-- 11664 candidates of size 16+-- tested 20451 candidates+gps27_median  =  undefined  -- search exhausted -gps27b :: Int -> Int -> Int -> Int--- testing 3 combinations of argument values+gps27b_median :: Int -> Int -> Int -> Int+-- testing 6 combinations of argument values -- pruning with 20/30 rules -- 3 candidates of size 1 -- 0 candidates of size 2 -- 6 candidates of size 3 -- 0 candidates of size 4 -- 12 candidates of size 5--- tested 15 candidates-gps27b x y z  =  min z (max x y)+-- 0 candidates of size 6+-- 63 candidates of size 7+-- 0 candidates of size 8+-- 342 candidates of size 9+-- tested 376 candidates+gps27b_median x y z  =  min (max x y) (max z (min x y))  gps28 :: Int -> Int -> Int -> Int -> Int -- testing 5 combinations of argument values@@ -527,9 +614,12 @@ -- 2 candidates of size 5 -- 6 candidates of size 6 -- 10 candidates of size 7--- 8 candidates of size 8--- 24 candidates of size 9--- tested 36 candidates+-- 4 candidates of size 8+-- 12 candidates of size 9+-- 26 candidates of size 10+-- tested 55 candidates gps29 ""  =  0-gps29 (c:cs)  =  (if isVowel c then 1 else 0) + gps29 cs+gps29 (c:cs)+  | isVowel c  =  1 + gps29 cs+  | otherwise  =  gps29 cs
− bench/gps2.hs 
@@ -1,784 +0,0 @@--- gps2.hs: General Program Synthesis Benchmark Suite II------ Copyright (C) 2021-2025 Rudy Matela--- Distributed under the 3-Clause BSD licence (see the file LICENSE).-{-# LANGUAGE CPP, TemplateHaskell #-}-import Conjure-import System.Environment (getArgs)--import Data.List (findIndex, inits)               -- for  #1-import Data.Char (toUpper)                        -- for  #4-import Data.Ratio ((%))                           -- for  #7-import Data.List (findIndices, tails, isPrefixOf) -- for #12-import Data.Maybe (fromJust)                      -- for #23-import Test.LeanCheck                             -- for #24-import Data.Express                               -- for #24---gps1p :: [Int] -> Maybe Int-gps1p [0,-1,2]   =  Just 1-gps1p [-1,0,1]   =  Just 0-gps1p [0,-1]     =  Just 1-gps1p [1,-1,-1]  =  Just 2--gps1g :: [Int] -> Maybe Int-gps1g xs  =  findIndex (0 >) (map sum (tail (inits xs)))--gps1p2 :: Int -> [Int] -> Int-gps1p2 0 [0,-1,2]   =  1-gps1p2 0 [-1,0,1]   =  0-gps1p2 0 [0,-1]     =  1-gps1p2 0 [1,-1,-1]  =  2-gps1p2 0 [0,0,0,-1]  =  3-gps1p2 0 [1,0,0,-2]  =  3---- efficient gps1, unreachable performance-wise-gps1g2 :: Int -> [Int] -> Int-gps1g2 t []  =  undefined -- 1-gps1g2 t (x:xs)  =  if t + x < 0 -- 7-                    then 0 -- 8-                    else 1 + gps1g2 (t + x) xs -- 15--gps1c :: IO ()-gps1c  =  do-  conjure "gps1" gps1p-    [ unfun (0 :: Int)-    , fun "+" ((+) :: Int -> Int -> Int)-    , fun ">" ((>) :: Int -> Int -> Bool)-    , fun "foldr" (foldr :: (Int -> Int -> Int) -> Int -> [Int] -> Int)-    , fun "sum" (sum :: [Int] -> Int)-    , fun "findIndex" (findIndex :: (Int -> Bool) -> [Int] -> Maybe Int)-    , fun "map" (map :: ([Int] -> Int) -> [[Int]] -> [Int])-    , fun "inits" (inits :: [Int] -> [[Int]])-    , fun "tail" (tail :: [[Int]] -> [[Int]])-    ]--  conjure "gps1" gps1p-    [ unfun (0 :: Int)-    , fun "+" ((+) :: Int -> Int -> Int)-    , fun ">" ((>) :: Int -> Int -> Bool)-    , fun "sum" (sum :: [Int] -> Int)-    , fun "foldr" (foldr :: (Int -> Int -> Int) -> Int -> [Int] -> Int)-    , fun "findIndex" (findIndex :: (Int -> Bool) -> [Int] -> Maybe Int)-    , fun "map" (map :: ([Int] -> Int) -> [[Int]] -> [Int])-    , fun "inits" (inits :: [Int] -> [[Int]])-    , fun "tail" (tail :: [[Int]] -> [[Int]])-    ]--  conjure "gps1" gps1p2-    [ unfun (0 :: Int)-    , unfun (1 :: Int)-    , fun "+" ((+) :: Int -> Int -> Int)-    , fun "<" ((<) :: Int -> Int -> Bool)-    , iif (undefined :: Int)-    , fun "undefined" (undefined :: Int)-    , maxSize 4-    , maxEquationSize 4-    ]---gps2p :: Double -> Double -> Int -> Double-gps2p 2 1 1  =  2 + 1-gps2p 2 1 2  =  2 + 1 + 1 + 0.5-gps2p 2 1 3  =  2 + 1 + 1 + 0.5 + 0.5 + 0.25-gps2p 3 1 1  =  3 + 1-gps2p 3 1 2  =  3 + 1 + 1/3---- apex to apex-gps2g :: Double -> Double -> Int -> Double-gps2g h0 h1 0  =  h0 + h1-gps2g h0 h1 n  =  h0 + h1 + gps2g h1 (h1 * (h1 / h0)) (n - 1)--- size 17, out of reach performance-wise--gps2c :: IO ()-gps2c  =  do-  conjure "gps2" gps2p-    [ unfun (0 :: Int)-    , unfun (1 :: Int)-    , fun "*" ((*) :: Double -> Double -> Double)-    , fun "/" ((/) :: Double -> Double -> Double)-    , fun "+" ((+) :: Double -> Double -> Double)-    , fun "-" ((-) :: Double -> Double -> Double)-    , maxSize 6-    ]---gps3p :: String -> Int-gps3p "X X X X X X X X X XXX"  =  300-gps3p "11 11 11 11 11 11 11 11 11 11"  =  20---- unreachable performance wise--- I presume a correct solution would need around 30 symbols-gps3c :: IO ()-gps3c  =  conjure "gps3" gps3p []------ GPS #4: https://www.codewars.com/kata/517abf86da9663f1d2000003--- Here we're using the problem description as in the GPS2 paper--- considering we're getting input as kebab-case.--- Nevertheless, this one is out of reach performance-wise (and OOM-wise)--gps4s :: (String -> String) -> [Property]-gps4s g  =-  [ property $ g "the-stealth-warrior" == "theStealthWarrior"-  , property $ g "camel-case" == "camelCase"-  , property $ g "Kebab-Case" == "KebabCase"-  ]--gps4g :: String -> String-gps4g ""  =  ""--- gps4g ('-':c:cs)  =  toUpper c : gps4g cs--- gps4g ('_':c:cs)  =  toUpper c : gps4g cs-gps4g (c:cs)  =  if c == '-'                                   --  5-                 then if null cs                               --  8-                      then ""                                  --  9-                      else toUpper (head cs) : gps4g (tail cs) -- 16-                 else c : gps4g cs                             -- 19--gps4c :: IO ()-gps4c  =  do-  conjureFromSpec "gps4" gps4s-    [ unfun '-'-    , unfun ("" :: String)-    , fun ":" ((:) :: Char -> String -> String)-    , fun "==" ((==) :: Char -> Char -> Bool)-    , fun "head" (head :: String -> Char)-    , fun "tail" (tail :: String -> String)-    , iif (undefined :: Char)-    , iif (undefined :: String)-    , fun "toUpper" (toUpper :: Char -> Char)-    , maxSize 6-    ]----- GPS #5: Coin Sums--- https://projecteuler.net/problem=31------ The problem description is inconsistent with the one given in the paper.------ Paper: change-making problem in USD--- Euler: How many different ways can £2 be made using any number of coins?------ I'm considering the Paper to be canonical, as the one in Project Euler can be solved by a constant function:------ solution :: Int--- solution  =  6378216738  -- <-- arbitrary example here, I didn't run the numbers-gps5p :: Int -> [Int]-gps5p 100  =  [4, 0, 0, 0]-gps5p  50  =  [2, 0, 0, 0]-gps5p  25  =  [1, 0, 0, 0]-gps5p  30  =  [1, 0, 1, 0]-gps5p  20  =  [0, 2, 0, 0]-gps5p   3  =  [0, 0, 0, 3]--gps5s :: ([Int] -> Int -> [Int]) -> [Property]-gps5s t  =-  [ property $ t [25, 10, 5, 1] 100 == [4, 0, 0, 0]-  , property $ t [25, 10, 5, 1]  50 == [2, 0, 0, 0]-  , property $ t [25, 10, 5, 1]  25 == [1, 0, 0, 0]-  , property $ t [25, 10, 5, 1]  30 == [1, 0, 1, 0]-  , property $ t [25, 10, 5, 1]  20 == [0, 2, 0, 0]-  , property $ t [25, 10, 5, 1]   3 == [0, 0, 0, 3]-  ]--coins :: [Int]-coins  =  [25, 10, 5, 1]--gps5g :: Int -> [Int]-gps5g  =  tell coins--tell :: [Int] -> Int -> [Int]-tell []     a  =  []-tell (n:ns) a  =  a `div` n : tell ns (a `mod` n)--gps5c :: IO ()-gps5c  =  do-  -- cannot conjure directly due to needing to introduce a local definition-  conjure "gps5" gps5p-    [-    ]--  conjureFromSpec "tell" gps5s-    [ unfun ([] :: [Int])-    , fun ":" ((:) :: Int -> [Int] -> [Int])-    , fun "`div`" (div :: Int -> Int -> Int)-    , fun "`mod`" (mod :: Int -> Int -> Int)-    ]--  conjure "gps5" gps5p-    [ unfun coins-    , fun "tell" tell-    ]--  conjure "gps5" gps5p-    [ unfun (1 :: Int)-    , unfun (5 :: Int)-    , unfun (10 :: Int)-    , unfun (25 :: Int)-    , unfun ([] :: [Int])-    , fun ":" ((:) :: Int -> [Int] -> [Int])-    , fun "tell" tell-    , target 50400-    ]----- GPS2#6: Cut Vector-gps6g :: [Int] -> Int-gps6g xs  =  snd-          $  minimum-          [  (abs (sum xs0 - sum xs1), i)-          |  i <- [0 .. length xs]-          ,  let (xs0, xs1) = splitAt i xs-          ]---- not Conjurable due to needing local definition--- I conjecture it _perhaps-maybe_ this could be done in 3 steps,--- but I'll leave this as-is for now.-gps6c :: IO ()-gps6c  =-  conjure "gps6" gps6g []----- GPS2#7: Dice Game--- https://projecteuler.net/problem=31--- https://github.com/thelmuth/Clojush/blob/psb2-v1.0/src/clojush/problems/psb2/dice_game.clj--- again, paper and problem are inconsistent, going with paper-gps7p :: Integer -> Integer -> Rational-gps7p 4 6  =  1 % 4-gps7p 6 4  =  7 % 12-gps7p 2 4  =  1 % 8-gps7p 4 2  =  5 % 8-gps7p 2 6  =  1 % 12-gps7p 6 2  =  3 % 4--gps7g :: Integer -> Integer -> Rational-gps7g peter colin  =  sum (map (min colin) [0 .. (peter-1)]) % (colin*peter)---- out of reach performance-wise-gps7c :: IO ()-gps7c  =  do-  conjure "gps7" gps7p $ take 0-    [ unfun (0 :: Integer)-    , unfun (1 :: Integer)-    , fun "%" ((%) :: Integer -> Integer -> Rational)-    , fun "+" ((+) :: Integer -> Integer -> Integer)-    , fun "-" ((-) :: Integer -> Integer -> Integer)-    , fun "*" ((*) :: Integer -> Integer -> Integer)-    , fun "min" (min :: Integer -> Integer -> Integer)-    , fun ".." (enumFromTo :: Integer -> Integer -> [Integer])-    , fun "map" (map :: (Integer -> Integer) -> [Integer] -> [Integer])-    , fun "sum" (sum :: [Integer] -> Integer)-    , maxSize 6-    ]---gps8p :: Int -> [Int] -> (Int,Int)-gps8p 2 [1,1,2]  =  (1,1)-gps8p 3 [1,1,2]  =  (1,2)-gps8p 2 [0,1,0,2]  =  (0,2)--gps8g :: Int -> [Int] -> (Int,Int)-gps8g x xs  =  head [(y,z) | y <- xs, z <- xs, y + z == x]--- this one could be generated but is a bit of a stretch...--- it is unintuitive to provide the given symbols--- gps8g :: Int -> [Int] -> (Int,Int)--- gps8g x xs  =  head $ filter ((x ==) . uncurry (+)) $ liftA2 (,) xs xs--gps8c :: IO ()-gps8c  =  conjure "gps8" gps8p []----- GPSB#9: Fizz Buzz (CW)-gps9p :: Int -> String-gps9p 3  =  "Fizz"-gps9p 4  =  "4"-gps9p 5  =  "Buzz"-gps9p 6  =  "Fizz"-gps9p 10  =  "Buzz"-gps9p 15  =  "FizzBuzz"-gps9p 17  =  "17"--gps9g :: Int -> String-gps9g x-  | x `div` 3 == 0  =  "Fizz" -- 7-  | x `div` 5 == 0  =  "Buzz" -- 14-  | x `div` 3 == 0 && x `div` 5 == 0  =  "FizzBuzz" -- 27-  | otherwise       =  show x -- 29---- probably unreachable performance-wise-gps9c :: IO ()-gps9c  =  conjure "gps9" gps9p []---gps10p :: [Int] -> Int-gps10p [0]  =  -2-gps10p [3]  =  -1-gps10p [6]  =  0-gps10p [9]  =  1-gps10p [0,3]  =  -3-gps10p [3,0]  =  -3-gps10p [3,2,1]  =  -5-gps10p [1,2,3]  =  -5-gps10p [10,20,30]  =  13---- does not do rounding-gps10g :: [Int] -> Int-gps10g []  =  0-gps10g (x:xs)  =  (x `div` 3 - 2) + gps10g xs---- unreachable due to lambda-gps10c :: IO ()-gps10c  =  conjure "gps10" gps10p-  [ unfun (0 :: Int)-  , unfun (1 :: Int)-  , unfun (2 :: Int)-  , unfun (3 :: Int)-  , fun "`div`" (div :: Int -> Int -> Int)-  , fun "+" ((+) :: Int -> Int -> Int)-  , fun "-" ((-) :: Int -> Int -> Int)-  , target 50400-  ]---gps11p :: Int -> Int -> Int-gps11p  =  gcd'-  where-  gcd' :: Int -> Int -> Int-  gcd' 1 1  =  1-  gcd' 1 2  =  1-  gcd' 2 1  =  1-  gcd' 2 2  =  2-  gcd' 2 6  =  2-  gcd' 6 2  =  2-  gcd' 3 6  =  3-  gcd' 6 3  =  3-  gcd' 6 9  =  3-  gcd' 9 6  =  3-  gcd' 12 18  =  6--gps11c :: IO ()-gps11c  =  conjure "gcd a b" gps11p-  [ unfun (0::Int)-  , fun "`mod`" (mod :: Int -> Int -> Int)-  ]-  -- generated function:-  -- gcd x 0  =  x-  -- gcd x y  =  gcd y (x `mod` y)---gps12p :: String -> String -> [Int]-gps12p "a"   "a"   =  [0]-gps12p "aa"  "a"   =  [0,1]-gps12p "aa"  "aa"  =  [0]-gps12p "a a" "a"   =  [0,2]-gps12p "b"   "a"   =  []--gps12g :: String -> String -> [Int]-gps12g s s'  =  findIndices (s' `isPrefixOf`) (tails s)--gps12c :: IO ()-gps12c  =  conjure "gps12" gps12p-  [ fun "findIndices" (findIndices :: (String -> Bool) -> [String] -> [Int])-  , fun "`isPrefixOf`" (isPrefixOf :: String -> String -> Bool)-  , fun "tails" (tails :: String -> [String])-  ]---gps13p :: [Int] -> [Int]-gps13p [0,1]  =  [1]-gps13p [1,0]  =  [1,0]-gps13p [2,0,1]  =  [2,1]-gps13p [1,0,1]  =  [1]--gps13g :: [Int] -> [Int]-gps13g  =  leaders-  where-  leaders []  =  []-  leaders (x:xs)  =  if all (x >) xs-                     then x : leaders xs-                     else leaders xs--gps13c :: IO ()-gps13c  =  conjure "gps13_leaders" gps13p-  [ unfun ([] :: [Int])-  , fun ":" ((:) :: Int -> [Int] -> [Int])-  , fun ">" ((>) :: Int -> Int -> Bool)-  , fun "all" (all :: (Int -> Bool) -> [Int] -> Bool)-  , iif (undefined :: [Int])-  ]---gps14p :: [Int] -> Int-gps14p  =  undefined---- 30 symbols-gps14g :: [Int] -> Int-gps14g  =  luhn-  where-  luhn :: [Int] -> Int-  luhn xs  =  sum (firsts xs ++ map double9 (seconds xs))-    where-    double9 :: Int -> Int-    double9 x  =  if xx > 9-                  then xx - 9-                  else xx-      where-      xx  =  x * 2-    seconds :: [Int] -> [Int]-    seconds []  =  []-    seconds (x:y:xs)  =  y : seconds xs-    firsts :: [Int] -> [Int]-    firsts []  =  []-    firsts (x:y:xs)  =  x : seconds xs---- cannot Conjure directly-gps14c :: IO ()-gps14c  =  conjure "gps14_luhn" gps14p-  [-  ]---gps15p :: () -> ()-gps15p  =  undefined---- skipped-gps15c :: IO ()-gps15c  =  conjure "gps15_mastermind" gps15p []---gps16p :: String -> String-gps16p "a"      =  "a"-gps16p "aaa"    =  "a"-gps16p "aa"     =  "aa"-gps16p "a a"    =  " "-gps16p " a "    =  "a"-gps16p "a a "   =  " a"-gps16p " a a "  =  " "--gps16g1 :: String -> String-gps16g1 s  =  if odd len-              then take 1 (drop (len `div` 2) s)-              else take 2 (drop (len `div` 2 - 1) s)-  where-  len  =  length s--gps16g2 :: String -> String-gps16g2 ""  =  ""-gps16g2 (c:cs)  =  if length cs <= 1-                   then c : cs-                   else gps16g2 (init cs)--gps16c :: IO ()-gps16c  =  conjure "gps16_middle" gps16p-  [ unfun ""-  , unfun (1 :: Int)-  , fun "<=" ((<=) :: Int -> Int -> Bool)-  , fun ":" ((:) :: Char -> String -> String)-  , fun "length" (length :: String -> Int)-  , fun "init" (init :: String -> String)-  , iif (undefined :: String)-  ]---gps17p :: [Int] -> Int-gps17p [0,1,0]  =  0-gps17p [1,1]  =  1-gps17p [1,1,0]  =  1-gps17p [0,1,1]  =  1-gps17p [1,1,1]  =  2--gps17g :: [Int] -> Int-gps17g xs  =  pds xs-  where-  pds []  =  0-  pds (x:xs)  =  if not (null xs) && x == head xs-                 then x + pds xs-                 else pds xs--- surprise:--- gps17_pds []  =  0--- gps17_pds (x:xs)  =  (if not (null xs) && head xs == x then x else 0) + gps17_pds xs----- can generate at size 15 in 18 seconds--- setting limit of 5 for faster automated tests--- BENCHMARK: increase maxSize from 5 to 18-gps17c :: IO ()-gps17c  =  conjure "gps17_pds" gps17p-  [ unfun (0 :: Int)-  , iif (undefined :: Int)-  , fun "not" not-  , fun "null" (null :: [Int] -> Bool)-  , fun "==" ((==) :: Int -> Int -> Bool)-  , fun "head" (head :: [Int] -> Int)-  , fun "+" ((+) :: Int -> Int -> Int)-  , fun "&&" (&&)-  , maxSize 5-  ]---gps18p :: [Double] -> [Double] -> Double-gps18p [1.0] [0.5]  =  0.5-gps18p [2.0] [0.5]  =  1.0-gps18p [1.0,1.0] [0.5,0.0]  =  1.5-gps18p [1.0,1.0] [0.0,0.5]  =  1.5--gps18g :: [Double] -> [Double] -> Double-gps18g prices discounts  =  foldr (+) 0 (zipWith (*) prices (map (1-) discounts))---- this was OOM'd-gps18c :: IO ()-gps18c  =  conjure "gps18_price" gps18p-  [ unfun (0 :: Double)-  , unfun (1 :: Double)-  , fun "+" ((+) :: Double -> Double -> Double)-  , fun "*" ((*) :: Double -> Double -> Double)-  , fun "-" ((-) :: Double -> Double -> Double)---  , fun "foldr" (foldr :: (Double -> Double -> Double) -> Double -> [Double] -> Double)---   , fun "zipWith" (zipWith :: (Double -> Double -> Double) -> [Double] -> [Double] -> [Double])---  , fun "map" (map :: (Double -> Double) -> [Double] -> [Double])-  , maxSize 6-  ]---gps19p :: Int -> Double -> Double -> Double -> Double-gps19p 0 0 1.0 1.0  =  0-gps19p 1 0 1.0 1.0  =  0-gps19p 2 0 1.0 1.0  =  0-gps19p 1 0 1.0 2.0  =  1.0-gps19p 2 0 1.0 2.0  =  2.0-gps19p 1 0 0.5 1.0  =  0.5-gps19p 2 0 0.5 1.0  =  1.0--gps19g :: Int -> Double -> Double -> Double -> Double-gps19g 0 total melt fall  =  total-gps19g n total melt fall  =  gps19p (n-1) (max 0 (total-melt+fall)) melt fall--- size 14, out of reach performance wise.--gps19c :: IO ()-gps19c  =  conjure "gps19_snowday" gps19p-  [ unfun (0 :: Int)-  , unfun (1 :: Int)-  , fun "max" (max :: Double -> Double -> Double)-  , fun "+" ((+) :: Double -> Double -> Double)-  , fun "-" ((-) :: Double -> Double -> Double)-  , maxSize 6-  ]---gps20p :: String -> Bool-gps20p  =  undefined--gps20c :: IO ()-gps20c  =  conjure "gps20" gps20p-  [-  ]---gps21s :: (String -> String) -> [Property]-gps21s s  =-  [ property $ s "word" == "word"-  , property $ s "words" == "sdrow"-  , property $ s "word words" == "word sdrow"-  , property $ s "words word" == "sdrow word"-  ]--spinSpec :: (String -> String) -> [Property]-spinSpec spin  =-  [ property $ spin "abc" == "abc"-  , property $ spin "abcd" == "abcd"-  , property $ spin "word" == "word"-  , property $ spin "abcde" == "edcba"-  , property $ spin "words" == "sdrow"-  , property $ spin "hello" == "olleh"-  , property $ spin "world" == "dlrow"-  ]--spin :: String -> String-spin w  =  if length w >= 5-           then reverse w-           else w--gps21g :: String -> String-gps21g s  =  unwords (map spin (words s))--gps21c :: IO ()-gps21c  =  do-  conjureFromSpec "spin" spinSpec-    [ fun "length"  (length :: String -> Int)-    , fun "reverse" (reverse :: String -> String)-    , iif (undefined :: String)-    , fun ">="      ((>=) :: Int -> Int -> Bool)-    , unfun (5 :: Int)-    ]--  conjureFromSpec "gps21_spinwords" gps21s-    [ fun "words"   words-    , fun "unwords" unwords-    , fun "spin"    (spin :: String -> String)-    , fun "map"     (map :: (String -> String) -> [String] -> [String])-    , fun "length"  (length :: String -> Int)-    , fun "reverse" (reverse :: String -> String)-    , iif (undefined :: String)-    , fun ">="      ((>=) :: Int -> Int -> Bool)-    , unfun (5 :: Int)-    ]---digits :: Int -> [Int]-digits 0  =  []-digits n  =  n `mod` 10 : digits (n `div` 10)--digits' :: Int -> [Int]-digits' 1  =  [1]-digits' 12  =  [2,1]-digits' 21  =  [1,2]-digits' 123  =  [3,2,1]-digits' 321  =  [1,2,3]--gps22p :: Int -> String-gps22p  =  undefined--gps22c :: IO ()-gps22c  =  do-  -- cannot conjure at size 13, maybe beyond?-  conjure "digits" digits'-    [ unfun ([] :: [Int])-    , fun ":" ((:) :: Int -> [Int] -> [Int])-    , fun "`div`" (div :: Int -> Int -> Int)-    , fun "`mod`" (mod :: Int -> Int -> Int)-    , fun "div10" ((`div` 10) :: Int -> Int)-    , unfun (10 :: Int)-    , target 10080-    ]--  conjure "gps22" gps22p-    [-    ]---gps23s :: (String -> String -> String -> String) -> [Property]-gps23s s  =-  [ property $ s "abcd" "abcd" "abcd" == "abcd"-  , property $ s "abcd" "dcba" "abcd" == "dcba"-  , property $ s "abcd" "1234" "abcd" == "1234"-  , property $ s "abcd" "1234" "bacd" == "2134"-  ]--gps23g :: String -> String -> String -> String--- gps23g f t s  =  map (\c -> fromJust $ c `lookup` zipWith (,) f t) s-gps23g f t s  =  map (fromJust . (`lookup` zipWith (,) f t)) s--gps23c :: IO ()-gps23c  =  do-  -- cannot conjure, needs lambda-  conjureFromSpec "gps23" gps23s-    [-    ]---data Twitter  =  Tweet Int-              |  TooMany-              |  Empty-              deriving (Eq, Show)--deriveExpress  ''Twitter-deriveListable ''Twitter-deriveName     ''Twitter--instance Conjurable Twitter where-  conjureExpress   =  reifyExpress-  conjureEquality  =  reifyEquality-  conjureTiers     =  reifyTiers--gps24g_twitter :: String -> Twitter-gps24g_twitter ""  =  Empty-gps24g_twitter s  =  if length s > 140-                     then TooMany-                     else Tweet (length s)--gps24s_twitter :: (String -> Twitter) -> [Property]-gps24s_twitter twitter  =-  [ property $ twitter "" == Empty-  , property $ twitter "abcd" == Tweet 4-  , property $ twitter "0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij" == Tweet 140-  , property $ twitter "0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij0123456789abcdefghijX" == TooMany-  ]--gps24c :: IO ()-gps24c  =  do-  conjureFromSpec "gps24" gps24s_twitter-    [ unfun Empty-    , unfun TooMany-    , fun "Tweet" Tweet-    , iif (undefined :: Twitter)-    , unfun ""-    , fun ":" ((:) :: Char -> String -> String)-    , fun "length" (length :: String -> Int)-    , unfun (140 :: Int)-    , fun ">" ((>) :: Int -> Int -> Bool)-    ]---gps25p :: [Double] -> [Double] -> Double-gps25p [0] [1]  =  1-gps25p [1] [0]  =  1-gps25p [-1] [1]  =  2-gps25p [0,1] [1,0]  =  sqrt 2-gps25p [1,0] [0,1]  =  sqrt 2-gps25p [0,0,1] [1,0,0]  =  sqrt 2-gps25p [0,1,2] [1,2,3]  =  sqrt 3--gps25g :: [Double] -> [Double] -> Double-gps25g v1 v2  =  sqrt (foldr (+) 0 (map (^2) (zipWith (-) v1 v2)))---- out of reach performance-wise-gps25c :: IO ()-gps25c  =  conjure "gps25" gps25p-  [ unfun (0 :: Double)-  , unfun (2 :: Double)-  , fun "+" ((+) :: Double -> Double -> Double)-  , fun "-" ((-) :: Double -> Double -> Double)-  , fun "**" ((**) :: Double -> Double -> Double)-  , fun "zipWith" (zipWith :: (Double -> Double -> Double) -> [Double] -> [Double] -> [Double])-  , fun "map" (map :: (Double -> Double) -> [Double] -> [Double])-  , fun "sqrt" (sqrt :: Double -> Double)-  , maxSize 6-  ]---main :: IO ()-main  =  do-  as <- getArgs-  case as of-    [] -> sequence_ gpss-    (n:_) -> gpss !! (read n - 1)---gpss :: [IO ()]-gpss  =  [ gps1c-         , gps2c-         , gps3c-         , gps4c-         , gps5c-         , gps6c-         , gps7c-         , gps8c-         , gps9c-         , gps10c-         , gps11c-         , gps12c-         , gps13c-         , gps14c-         , gps15c-         , gps16c-         , gps17c-         , gps18c-         , gps19c-         , gps20c-         , gps21c-         , gps22c-         , gps23c-         , gps24c-         , gps25c-         ]
− bench/gps2.txt 
@@ -1,367 +0,0 @@-gps1 :: [Int] -> Maybe Int--- testing 4 combinations of argument values--- pruning with 11/21 rules--- 0 candidates of size 1--- 0 candidates of size 2--- 0 candidates of size 3--- 1 candidates of size 4--- 0 candidates of size 5--- 0 candidates of size 6--- 1 candidates of size 7--- 0 candidates of size 8--- 1 candidates of size 9--- 2 candidates of size 10--- tested 5 candidates-gps1 xs  =  findIndex (0 >) (map (foldr (+) 0) (tail (inits xs)))--gps1 :: [Int] -> Maybe Int--- testing 4 combinations of argument values--- pruning with 11/21 rules--- 0 candidates of size 1--- 0 candidates of size 2--- 0 candidates of size 3--- 1 candidates of size 4--- 1 candidates of size 5--- 0 candidates of size 6--- 1 candidates of size 7--- 4 candidates of size 8--- tested 6 candidates-gps1 xs  =  findIndex (0 >) (map sum (tail (inits xs)))--gps1 :: Int -> [Int] -> Int--- testing 6 combinations of argument values--- pruning with 8/9 rules--- 4 candidates of size 1--- 0 candidates of size 2--- 11 candidates of size 3--- 29 candidates of size 4--- tested 44 candidates-gps1  =  undefined  -- search exhausted--gps2 :: Double -> Double -> Int -> Double--- testing 5 combinations of argument values--- pruning with 2/6 rules--- 2 candidates of size 1--- 2 candidates of size 2--- 16 candidates of size 3--- 64 candidates of size 4--- 256 candidates of size 5--- 1252 candidates of size 6--- tested 1592 candidates-gps2  =  undefined  -- search exhausted--gps3 :: [Char] -> Int-gps3  =  error "could not reify specification, suggestion: conjureFromSpec"--gps4 :: [Char] -> [Char]--- pruning with 13/21 rules--- 2 candidates of size 1--- 3 candidates of size 2--- 8 candidates of size 3--- 20 candidates of size 4--- 51 candidates of size 5--- 119 candidates of size 6--- tested 203 candidates-gps4  =  undefined  -- search exhausted--gps5 :: Int -> [Int]--- testing 6 combinations of argument values--- pruning with 0/0 rules--- 0 candidates of size 1--- tested 0 candidates-gps5  =  undefined  -- search exhausted--tell :: [Int] -> Int -> [Int]--- pruning with 0/0 rules--- 2 candidates of size 1--- 1 candidates of size 2--- 2 candidates of size 3--- 6 candidates of size 4--- 6 candidates of size 5--- 39 candidates of size 6--- 26 candidates of size 7--- 328 candidates of size 8--- 134 candidates of size 9--- 3229 candidates of size 10--- tested 783 candidates-tell [] x  =  []-tell (x:xs) y  =  y `div` x:tell xs (y `mod` x)--gps5 :: Int -> [Int]--- testing 6 combinations of argument values--- pruning with 0/0 rules--- 1 candidates of size 1--- 0 candidates of size 2--- 1 candidates of size 3--- tested 2 candidates-gps5  =  tell [25,10,5,1]--gps5 :: Int -> [Int]--- testing 6 combinations of argument values--- pruning with 12/12 rules--- 1 candidates of size 1--- 0 candidates of size 2--- 5 candidates of size 3--- 9 candidates of size 4--- 45 candidates of size 5--- 82 candidates of size 6--- 428 candidates of size 7--- 882 candidates of size 8--- 4350 candidates of size 9--- 9232 candidates of size 10--- 43847 candidates of size 11--- tested 32290 candidates-gps5  =  tell [25,10,5,1]--gps6 :: [Int] -> Int--- testing 360 combinations of argument values--- pruning with 0/0 rules--- 0 candidates of size 1--- 0 candidates of size 2--- tested 0 candidates-gps6  =  undefined  -- search exhausted--gps7 :: Integer -> Integer -> Ratio Integer--- testing 6 combinations of argument values--- pruning with 0/0 rules--- 0 candidates of size 1--- tested 0 candidates-gps7  =  undefined  -- search exhausted--gps8 :: Int -> [Int] -> (Int,Int)--- testing 3 combinations of argument values--- pruning with 0/0 rules--- 0 candidates of size 1--- 0 candidates of size 2--- tested 0 candidates-gps8  =  undefined  -- search exhausted--gps9 :: Int -> [Char]--- testing 7 combinations of argument values--- pruning with 0/0 rules--- 0 candidates of size 1--- tested 0 candidates-gps9  =  undefined  -- search exhausted--gps10 :: [Int] -> Int--- testing 7 combinations of argument values--- pruning with 67/100 rules--- 4 candidates of size 1--- 0 candidates of size 2--- 0 candidates of size 3--- 0 candidates of size 4--- 80 candidates of size 5--- 8 candidates of size 6--- 1428 candidates of size 7--- 432 candidates of size 8--- 30712 candidates of size 9--- tested 7064 candidates-gps10 []  =  0-gps10 (x:xs)  =  (x `div` 3 - 2) + gps10 xs--gcd :: Int -> Int -> Int--- testing 11 combinations of argument values--- pruning with 0/0 rules--- 3 candidates of size 1--- 6 candidates of size 2--- 11 candidates of size 3--- 50 candidates of size 4--- 98 candidates of size 5--- 330 candidates of size 6--- tested 172 candidates-gcd x 0  =  x-gcd x y  =  gcd y (x `mod` y)--gps12 :: [Char] -> [Char] -> [Int]--- testing 5 combinations of argument values--- pruning with 1/2 rules--- 0 candidates of size 1--- 0 candidates of size 2--- 0 candidates of size 3--- 0 candidates of size 4--- 4 candidates of size 5--- tested 3 candidates-gps12 cs ds  =  findIndices (ds `isPrefixOf`) (tails cs)--gps13_leaders :: [Int] -> [Int]--- testing 4 combinations of argument values--- pruning with 5/5 rules--- 2 candidates of size 1--- 0 candidates of size 2--- 0 candidates of size 3--- 0 candidates of size 4--- 1 candidates of size 5--- 0 candidates of size 6--- 1 candidates of size 7--- 0 candidates of size 8--- 7 candidates of size 9--- 4 candidates of size 10--- 33 candidates of size 11--- 18 candidates of size 12--- tested 53 candidates-gps13_leaders []  =  []-gps13_leaders (x:xs)  =  if all (x >) xs-                         then x:gps13_leaders xs-                         else gps13_leaders xs--gps14_luhn :: [Int] -> Int-gps14_luhn  =  error "could not reify specification, suggestion: conjureFromSpec"--gps15_mastermind :: () -> ()-gps15_mastermind  =  error "could not reify specification, suggestion: conjureFromSpec"--gps16_middle :: [Char] -> [Char]--- testing 7 combinations of argument values--- pruning with 10/11 rules--- 2 candidates of size 1--- 2 candidates of size 2--- 2 candidates of size 3--- 3 candidates of size 4--- 6 candidates of size 5--- 11 candidates of size 6--- 23 candidates of size 7--- 62 candidates of size 8--- 175 candidates of size 9--- 489 candidates of size 10--- 1346 candidates of size 11--- 3709 candidates of size 12--- tested 2390 candidates-gps16_middle ""  =  ""-gps16_middle (c:cs)  =  if length cs <= 1-                        then c:cs-                        else gps16_middle (init cs)--gps17_pds :: [Int] -> Int--- testing 5 combinations of argument values--- pruning with 29/40 rules--- 1 candidates of size 1--- 1 candidates of size 2--- 0 candidates of size 3--- 0 candidates of size 4--- 2 candidates of size 5--- tested 4 candidates-gps17_pds  =  undefined  -- search exhausted--gps18_price :: [Double] -> [Double] -> Double--- testing 4 combinations of argument values--- pruning with 26/35 rules--- 2 candidates of size 1--- 0 candidates of size 2--- 2 candidates of size 3--- 0 candidates of size 4--- 33 candidates of size 5--- 176 candidates of size 6--- tested 213 candidates-gps18_price  =  undefined  -- search exhausted--gps19_snowday :: Int -> Double -> Double -> Double -> Double--- testing 7 combinations of argument values--- pruning with 6/19 rules--- 3 candidates of size 1--- 2 candidates of size 2--- 21 candidates of size 3--- 39 candidates of size 4--- 312 candidates of size 5--- 659 candidates of size 6--- tested 1036 candidates-gps19_snowday  =  undefined  -- search exhausted--gps20 :: [Char] -> Bool-gps20  =  error "could not reify specification, suggestion: conjureFromSpec"--spin :: [Char] -> [Char]--- pruning with 6/6 rules--- reasoning produced 1 incorrect properties, please re-run with more tests for faster results--- 1 candidates of size 1--- 1 candidates of size 2--- 0 candidates of size 3--- 0 candidates of size 4--- 0 candidates of size 5--- 0 candidates of size 6--- 0 candidates of size 7--- 4 candidates of size 8--- tested 3 candidates-spin cs  =  if length cs >= 5-            then reverse cs-            else cs--gps21_spinwords :: [Char] -> [Char]--- pruning with 16/16 rules--- reasoning produced 2 incorrect properties, please re-run with more tests for faster results--- 1 candidates of size 1--- 2 candidates of size 2--- 2 candidates of size 3--- 3 candidates of size 4--- 5 candidates of size 5--- tested 12 candidates-gps21_spinwords cs  =  unwords (map spin (words cs))--digits :: Int -> [Int]--- testing 5 combinations of argument values--- pruning with 7/7 rules--- 1 candidates of size 1--- 0 candidates of size 2--- 2 candidates of size 3--- 3 candidates of size 4--- 11 candidates of size 5--- 13 candidates of size 6--- 91 candidates of size 7--- 104 candidates of size 8--- 850 candidates of size 9--- 923 candidates of size 10--- 8902 candidates of size 11--- tested 10900 candidates-digits  =  undefined  -- search exhausted--gps22 :: Int -> [Char]-gps22  =  error "could not reify specification, suggestion: conjureFromSpec"--gps23 :: [Char] -> [Char] -> [Char] -> [Char]--- pruning with 0/0 rules--- 3 candidates of size 1--- 12 candidates of size 2--- 33 candidates of size 3--- 36 candidates of size 4--- 127 candidates of size 5--- 507 candidates of size 6--- 839 candidates of size 7--- 784 candidates of size 8--- 600 candidates of size 9--- 2722 candidates of size 10--- 5292 candidates of size 11--- tested 10955 candidates-gps23  =  undefined  -- search exhausted--gps24 :: [Char] -> Twitter--- pruning with 4/8 rules--- reasoning produced 4 incorrect properties, please re-run with more tests for faster results--- 2 candidates of size 1--- 3 candidates of size 2--- 6 candidates of size 3--- 6 candidates of size 4--- 3 candidates of size 5--- 5 candidates of size 6--- 10 candidates of size 7--- 48 candidates of size 8--- 134 candidates of size 9--- 216 candidates of size 10--- 308 candidates of size 11--- 466 candidates of size 12--- tested 881 candidates-gps24 ""  =  Empty-gps24 (c:cs)  =  if 140 > length cs-                 then Tweet (length (c:cs))-                 else TooMany--gps25 :: [Double] -> [Double] -> Double--- testing 6 combinations of argument values--- pruning with 31/59 rules--- 2 candidates of size 1--- 1 candidates of size 2--- 5 candidates of size 3--- 10 candidates of size 4--- 76 candidates of size 5--- 438 candidates of size 6--- tested 532 candidates-gps25  =  undefined  -- search exhausted-
+ bench/i12.hs view
@@ -0,0 +1,71 @@+-- 12 background ingredients+--+-- Copyright (C) 2021-2025 Rudy Matela+-- Distributed under the 3-Clause BSD licence (see the file LICENSE).+import Conjure+import System.Environment++factorial :: Int -> Int+factorial 0  =  1+factorial 1  =  1+factorial 2  =  2+factorial 3  =  6+factorial 4  =  24+factorial 5  =  120++count' :: Int -> [Int] -> Int+count' 0 [0]  =  1+count' 0 [1]  =  0+count' 1 [0]  =  0+count' 1 [1]  =  1+count' 0 [0,0]  =  2+count' 0 [0,1]  =  1+count' 0 [1,2]  =  0+count' 1 [0,0]  =  0+count' 1 [0,1]  =  1+count' 1 [1,2]  =  1+count' 0 [0,0,0]  =  3+count' 0 [0,0,1]  =  2+count' 0 [1,0,0]  =  2++main :: IO ()+main  =  do+  putStrLn $ "running with " ++ show (length ingredients) ++ " ingredients"+  as <- getArgs+  case as of+    ["factorial"]     -> conjure "factorial n" factorial   ingredients+    ["factorial","t"] -> conjure "factorial n" factorial $ ingredients ++ [maxSize 1]+    ["sum"]           -> conjure "sum"     (sum     :: [Int] -> Int)   ingredients+    ["sum","t"]       -> conjure "sum"     (sum     :: [Int] -> Int) $ ingredients ++ [maxSize 1]+    ["product"]       -> conjure "product" (product :: [Int] -> Int)   ingredients+    ["product","t"]   -> conjure "product" (product :: [Int] -> Int) $ ingredients ++ [maxSize 1]+    ["length"]        -> conjure "length"  (length  :: [Int] -> Int)   ingredients+    ["length","t"]    -> conjure "length"  (length  :: [Int] -> Int) $ ingredients ++ [maxSize 1]+    ["count"]         -> conjure "count"   count' $ ingredients ++ primsCount+    ["count","t"]     -> conjure "count"   count' $ ingredients ++ primsCount ++ [maxSize 1]+    _                 -> conjure "factorial n" factorial ingredients++ingredients :: [Ingredient]+ingredients  =+  [ con (0::Int)+  , con (1::Int)+  , fun "+" ((+) :: Int -> Int -> Int)+  , fun "*" ((*) :: Int -> Int -> Int)+  , fun "dec" (subtract 1 :: Int -> Int)++  , fun "==" ((==) :: Int -> Int -> Bool)++  , con ([] :: [Int])+  , fun ":" ((:) :: Int -> [Int] -> [Int])+  , fun "head" (head :: [Int] -> Int)+  , fun "tail" (tail :: [Int] -> [Int])+  , fun "null" (null :: [Int] -> Bool)+  , fun "foldr" (foldr :: (Int -> Int -> Int) -> Int -> [Int] -> Int)+  , fun ".." (enumFromTo :: Int -> Int -> [Int])+  ]++primsCount :: [Ingredient]+primsCount  =+  [ fun "length" (length :: [Int] -> Int)+  , fun "filter" (filter :: (Int -> Bool) -> [Int] -> [Int])+  ]
+ bench/i12.txt view
@@ -0,0 +1,13 @@+running with 13 ingredients+factorial :: Int -> Int+-- testing 6 combinations of argument values+-- pruning with 67/101 rules+-- 3 candidates of size 1+-- 1 candidates of size 2+-- 4 candidates of size 3+-- 8 candidates of size 4+-- 28 candidates of size 5+-- 109 candidates of size 6+-- tested 146 candidates+factorial x  =  foldr (*) 1 [1..x]+
+ bench/i30.hs view
@@ -0,0 +1,87 @@+-- 30 background ingredients, does Conjure scale?+--+-- Copyright (C) 2021-2025 Rudy Matela+-- Distributed under the 3-Clause BSD licence (see the file LICENSE).+import Conjure+import System.Environment++factorial :: Int -> Int+factorial 0  =  1+factorial 1  =  1+factorial 2  =  2+factorial 3  =  6+factorial 4  =  24+factorial 5  =  120++count' :: Int -> [Int] -> Int+count' 0 [0]  =  1+count' 0 [1]  =  0+count' 1 [0]  =  0+count' 1 [1]  =  1+count' 0 [0,0]  =  2+count' 0 [0,1]  =  1+count' 0 [1,2]  =  0+count' 1 [0,0]  =  0+count' 1 [0,1]  =  1+count' 1 [1,2]  =  1+count' 0 [0,0,0]  =  3+count' 0 [0,0,1]  =  2+count' 0 [1,0,0]  =  2++main :: IO ()+main  =  do+  putStrLn $ "running with " ++ show (length ingredients) ++ " ingredients"+  as <- getArgs+  case as of+    ["factorial"]     -> conjure "factorial n" factorial   ingredients+    ["factorial","t"] -> conjure "factorial n" factorial $ ingredients ++ [maxSize 1]+    ["sum"]           -> conjure "sum"     (sum     :: [Int] -> Int)   ingredients+    ["sum","t"]       -> conjure "sum"     (sum     :: [Int] -> Int) $ ingredients ++ [maxSize 1]+    ["product"]       -> conjure "product" (product :: [Int] -> Int)   ingredients+    ["product","t"]   -> conjure "product" (product :: [Int] -> Int) $ ingredients ++ [maxSize 1]+    ["length"]        -> conjure "length"  (length  :: [Int] -> Int)   ingredients+    ["length","t"]    -> conjure "length"  (length  :: [Int] -> Int) $ ingredients ++ [maxSize 1]+    ["count"]         -> conjure "count"   count' $ ingredients ++ primsLength+    ["count","t"]     -> conjure "count"   count' $ ingredients ++ primsLength ++ [maxSize 1]+    _                 -> putStrLn "usage: p30 <factorial|sum|product|length|count> [t]"++ingredients :: [Ingredient]+ingredients  =+  [ con False+  , con True+  , fun "&&" (&&)+  , fun "||" (||)+  , fun "not" not++  , con (0::Int)+  , con (1::Int)+  , fun "+" ((+) :: Int -> Int -> Int)+  , fun "*" ((*) :: Int -> Int -> Int)+  , fun "dec" (subtract 1 :: Int -> Int)+  , fun "-" ((-) :: Int -> Int -> Int)++  , fun "==" ((==) :: Int -> Int -> Bool)+  , fun "<=" ((<=) :: Int -> Int -> Bool)+  , fun "<"  ((<) :: Int -> Int -> Bool)++  , fun "const" (const :: Int -> Int -> Int)++  , con ([] :: [Int])+  , fun ":" ((:) :: Int -> [Int] -> [Int])+  , fun "head" (head :: [Int] -> Int)+  , fun "tail" (tail :: [Int] -> [Int])+  , fun "null" (null :: [Int] -> Bool)+  , fun "foldr" (foldr :: (Int -> Int -> Int) -> Int -> [Int] -> Int)++  , fun "map" (map :: (Int -> Int) -> [Int] -> [Int])+  , fun "filter" (filter :: (Int -> Bool) -> [Int] -> [Int])+  , fun ".." (enumFromTo :: Int -> Int -> [Int])++  , fun "++" ((++) :: [Int] -> [Int] -> [Int])+  , fun "elem" (elem :: Int -> [Int] -> Bool)+  ]++primsLength :: [Ingredient]+primsLength =+  [ fun "length" (length :: [Int] -> Int)+  ]
+ bench/i30.txt view
@@ -0,0 +1,2 @@+running with 26 ingredients+usage: p30 <factorial|sum|product|length|count> [t]
bench/ill-hit.hs view
@@ -38,8 +38,8 @@  ingredients :: [Ingredient] ingredients =-  [ unfun (0 :: Int)-  , unfun (1 :: Int)+  [ con (0 :: Int)+  , con (1 :: Int)   , fun "+" ((+) :: Int -> Int -> Int)   , fun "*" ((*) :: Int -> Int -> Int)   , fun "null" (null :: [Int] -> Bool)
bench/ill-hit.txt view
@@ -9,7 +9,7 @@ -- 1 candidates of size 3 -- 2 candidates of size 4 -- 7 candidates of size 5--- tested 7 candidates+-- tested 11 candidates sum []  =  0 sum (x:xs)  =  x + sum xs @@ -20,7 +20,7 @@ -- 3 candidates of size 3 -- 10 candidates of size 4 -- 18 candidates of size 5--- tested 21 candidates+-- tested 33 candidates sum []  =  0 sum (x:xs)  =  x + sum xs
− bench/p12.hs 
@@ -1,71 +0,0 @@--- 12 background ingredients------ Copyright (C) 2021-2025 Rudy Matela--- Distributed under the 3-Clause BSD licence (see the file LICENSE).-import Conjure-import System.Environment--factorial :: Int -> Int-factorial 0  =  1-factorial 1  =  1-factorial 2  =  2-factorial 3  =  6-factorial 4  =  24-factorial 5  =  120--count' :: Int -> [Int] -> Int-count' 0 [0]  =  1-count' 0 [1]  =  0-count' 1 [0]  =  0-count' 1 [1]  =  1-count' 0 [0,0]  =  2-count' 0 [0,1]  =  1-count' 0 [1,2]  =  0-count' 1 [0,0]  =  0-count' 1 [0,1]  =  1-count' 1 [1,2]  =  1-count' 0 [0,0,0]  =  3-count' 0 [0,0,1]  =  2-count' 0 [1,0,0]  =  2--main :: IO ()-main  =  do-  putStrLn $ "running with " ++ show (length ingredients) ++ " ingredients"-  as <- getArgs-  case as of-    ["factorial"]     -> conjure "factorial n" factorial   ingredients-    ["factorial","t"] -> conjure "factorial n" factorial $ ingredients ++ [maxSize 1]-    ["sum"]           -> conjure "sum"     (sum     :: [Int] -> Int)   ingredients-    ["sum","t"]       -> conjure "sum"     (sum     :: [Int] -> Int) $ ingredients ++ [maxSize 1]-    ["product"]       -> conjure "product" (product :: [Int] -> Int)   ingredients-    ["product","t"]   -> conjure "product" (product :: [Int] -> Int) $ ingredients ++ [maxSize 1]-    ["length"]        -> conjure "length"  (length  :: [Int] -> Int)   ingredients-    ["length","t"]    -> conjure "length"  (length  :: [Int] -> Int) $ ingredients ++ [maxSize 1]-    ["count"]         -> conjure "count"   count' $ ingredients ++ primsCount-    ["count","t"]     -> conjure "count"   count' $ ingredients ++ primsCount ++ [maxSize 1]-    _                 -> conjure "factorial n" factorial ingredients--ingredients :: [Ingredient]-ingredients  =-  [ unfun (0::Int)-  , unfun (1::Int)-  , fun "+" ((+) :: Int -> Int -> Int)-  , fun "*" ((*) :: Int -> Int -> Int)-  , fun "dec" (subtract 1 :: Int -> Int)--  , fun "==" ((==) :: Int -> Int -> Bool)--  , unfun ([] :: [Int])-  , fun ":" ((:) :: Int -> [Int] -> [Int])-  , fun "head" (head :: [Int] -> Int)-  , fun "tail" (tail :: [Int] -> [Int])-  , fun "null" (null :: [Int] -> Bool)-  , fun "foldr" (foldr :: (Int -> Int -> Int) -> Int -> [Int] -> Int)-  , fun ".." (enumFromTo :: Int -> Int -> [Int])-  ]--primsCount :: [Ingredient]-primsCount  =-  [ fun "length" (length :: [Int] -> Int)-  , fun "filter" (filter :: (Int -> Bool) -> [Int] -> [Int])-  ]
− bench/p12.txt 
@@ -1,14 +0,0 @@-running with 13 ingredients-factorial :: Int -> Int--- testing 6 combinations of argument values--- pruning with 67/101 rules--- 3 candidates of size 1--- 3 candidates of size 2--- 6 candidates of size 3--- 13 candidates of size 4--- 40 candidates of size 5--- 138 candidates of size 6--- tested 69 candidates-factorial 0  =  1-factorial x  =  x * factorial (dec x)-
− bench/p30.hs 
@@ -1,87 +0,0 @@--- 30 background ingredients, does Conjure scale?------ Copyright (C) 2021-2025 Rudy Matela--- Distributed under the 3-Clause BSD licence (see the file LICENSE).-import Conjure-import System.Environment--factorial :: Int -> Int-factorial 0  =  1-factorial 1  =  1-factorial 2  =  2-factorial 3  =  6-factorial 4  =  24-factorial 5  =  120--count' :: Int -> [Int] -> Int-count' 0 [0]  =  1-count' 0 [1]  =  0-count' 1 [0]  =  0-count' 1 [1]  =  1-count' 0 [0,0]  =  2-count' 0 [0,1]  =  1-count' 0 [1,2]  =  0-count' 1 [0,0]  =  0-count' 1 [0,1]  =  1-count' 1 [1,2]  =  1-count' 0 [0,0,0]  =  3-count' 0 [0,0,1]  =  2-count' 0 [1,0,0]  =  2--main :: IO ()-main  =  do-  putStrLn $ "running with " ++ show (length ingredients) ++ " ingredients"-  as <- getArgs-  case as of-    ["factorial"]     -> conjure "factorial n" factorial   ingredients-    ["factorial","t"] -> conjure "factorial n" factorial $ ingredients ++ [maxSize 1]-    ["sum"]           -> conjure "sum"     (sum     :: [Int] -> Int)   ingredients-    ["sum","t"]       -> conjure "sum"     (sum     :: [Int] -> Int) $ ingredients ++ [maxSize 1]-    ["product"]       -> conjure "product" (product :: [Int] -> Int)   ingredients-    ["product","t"]   -> conjure "product" (product :: [Int] -> Int) $ ingredients ++ [maxSize 1]-    ["length"]        -> conjure "length"  (length  :: [Int] -> Int)   ingredients-    ["length","t"]    -> conjure "length"  (length  :: [Int] -> Int) $ ingredients ++ [maxSize 1]-    ["count"]         -> conjure "count"   count' $ ingredients ++ primsLength-    ["count","t"]     -> conjure "count"   count' $ ingredients ++ primsLength ++ [maxSize 1]-    _                 -> putStrLn "usage: p30 <factorial|sum|product|length|count> [t]"--ingredients :: [Ingredient]-ingredients  =-  [ unfun False-  , unfun True-  , fun "&&" (&&)-  , fun "||" (||)-  , fun "not" not--  , unfun (0::Int)-  , unfun (1::Int)-  , fun "+" ((+) :: Int -> Int -> Int)-  , fun "*" ((*) :: Int -> Int -> Int)-  , fun "dec" (subtract 1 :: Int -> Int)-  , fun "-" ((-) :: Int -> Int -> Int)--  , fun "==" ((==) :: Int -> Int -> Bool)-  , fun "<=" ((<=) :: Int -> Int -> Bool)-  , fun "<"  ((<) :: Int -> Int -> Bool)--  , fun "const" (const :: Int -> Int -> Int)--  , unfun ([] :: [Int])-  , fun ":" ((:) :: Int -> [Int] -> [Int])-  , fun "head" (head :: [Int] -> Int)-  , fun "tail" (tail :: [Int] -> [Int])-  , fun "null" (null :: [Int] -> Bool)-  , fun "foldr" (foldr :: (Int -> Int -> Int) -> Int -> [Int] -> Int)--  , fun "map" (map :: (Int -> Int) -> [Int] -> [Int])-  , fun "filter" (filter :: (Int -> Bool) -> [Int] -> [Int])-  , fun ".." (enumFromTo :: Int -> Int -> [Int])--  , fun "++" ((++) :: [Int] -> [Int] -> [Int])-  , fun "elem" (elem :: Int -> [Int] -> Bool)-  ]--primsLength :: [Ingredient]-primsLength =-  [ fun "length" (length :: [Int] -> Int)-  ]
− bench/p30.txt 
@@ -1,2 +0,0 @@-running with 26 ingredients-usage: p30 <factorial|sum|product|length|count> [t]
+ bench/psb2.hs view
@@ -0,0 +1,851 @@+-- gps2.hs: General Program Synthesis Benchmark Suite II+--+-- Copyright (C) 2021-2025 Rudy Matela+-- Distributed under the 3-Clause BSD licence (see the file LICENSE).+{-# LANGUAGE CPP, TemplateHaskell #-}+import Conjure+import System.Environment (getArgs)++import Data.List (findIndex, inits)               -- for  #1+import Data.Char (toUpper)                        -- for  #4+import Data.Ratio ((%))                           -- for  #7+import Data.List (findIndices, tails, isPrefixOf) -- for #12+import Data.Maybe (fromJust)                      -- for #23+import Test.LeanCheck                             -- for #24+import Data.Express                               -- for #24+++-- PSB2 #1 -- Basement (AoC) ---+-- Given a vector of integers, return the first index such that the sum of all+-- integers from the start of the vector to the index (inclusive) is negative++gps1p :: [Int] -> Maybe Int+gps1p [0,-1,2]   =  Just 1+gps1p [-1,0,1]   =  Just 0+gps1p [0,-1]     =  Just 1+gps1p [1,-1,-1]  =  Just 2++gps1g :: [Int] -> Maybe Int+gps1g xs  =  findIndex (0 >) (map sum (tail (inits xs)))++gps1p2 :: Int -> [Int] -> Int+gps1p2 0 [0,-1,2]   =  1+gps1p2 0 [-1,0,1]   =  0+gps1p2 0 [0,-1]     =  1+gps1p2 0 [1,-1,-1]  =  2+gps1p2 0 [0,0,0,-1]  =  3+gps1p2 0 [1,0,0,-2]  =  3++-- efficient gps1, unreachable performance-wise+gps1g2 :: Int -> [Int] -> Int+gps1g2 t []  =  undefined -- 1+gps1g2 t (x:xs)  =  if t + x < 0 -- 7+                    then 0 -- 8+                    else 1 + gps1g2 (t + x) xs -- 15++gps1c :: IO ()+gps1c  =  do+  conjure "gps1" gps1p+    [ con (0 :: Int)+    , fun "+" ((+) :: Int -> Int -> Int)+    , fun ">" ((>) :: Int -> Int -> Bool)+    , fun "foldr" (foldr :: (Int -> Int -> Int) -> Int -> [Int] -> Int)+    , fun "sum" (sum :: [Int] -> Int)+    , fun "findIndex" (findIndex :: (Int -> Bool) -> [Int] -> Maybe Int)+    , fun "map" (map :: ([Int] -> Int) -> [[Int]] -> [Int])+    , fun "inits" (inits :: [Int] -> [[Int]])+    , fun "tail" (tail :: [[Int]] -> [[Int]])+    ]++  conjure "gps1" gps1p+    [ con (0 :: Int)+    , fun "+" ((+) :: Int -> Int -> Int)+    , fun ">" ((>) :: Int -> Int -> Bool)+    , fun "sum" (sum :: [Int] -> Int)+    , fun "foldr" (foldr :: (Int -> Int -> Int) -> Int -> [Int] -> Int)+    , fun "findIndex" (findIndex :: (Int -> Bool) -> [Int] -> Maybe Int)+    , fun "map" (map :: ([Int] -> Int) -> [[Int]] -> [Int])+    , fun "inits" (inits :: [Int] -> [[Int]])+    , fun "tail" (tail :: [[Int]] -> [[Int]])+    ]++  conjure "gps1" gps1p2+    [ con (0 :: Int)+    , con (1 :: Int)+    , fun "+" ((+) :: Int -> Int -> Int)+    , fun "<" ((<) :: Int -> Int -> Bool)+    , guard+    , fun "undefined" (undefined :: Int)+    , maxSize 4+    , maxEquationSize 4+    ]+++-- PSB2 #2 -- Bouncing Balls (CW) --++gps2p :: Double -> Double -> Int -> Double+gps2p 2 1 1  =  2 + 1+gps2p 2 1 2  =  2 + 1 + 1 + 0.5+gps2p 2 1 3  =  2 + 1 + 1 + 0.5 + 0.5 + 0.25+gps2p 3 1 1  =  3 + 1+gps2p 3 1 2  =  3 + 1 + 1/3++-- apex to apex+gps2g :: Double -> Double -> Int -> Double+gps2g h0 h1 0  =  h0 + h1+gps2g h0 h1 n  =  h0 + h1 + gps2g h1 (h1 * (h1 / h0)) (n - 1)+-- size 17, out of reach performance-wise++gps2c :: IO ()+gps2c  =  do+  conjure "gps2" gps2p+    [ con (0 :: Int)+    , con (1 :: Int)+    , fun "*" ((*) :: Double -> Double -> Double)+    , fun "/" ((/) :: Double -> Double -> Double)+    , fun "+" ((+) :: Double -> Double -> Double)+    , fun "-" ((-) :: Double -> Double -> Double)+    , maxSize 6+    ]+++gps3p :: String -> Int+gps3p "X X X X X X X X X XXX"  =  300+gps3p "11 11 11 11 11 11 11 11 11 11"  =  20++-- unreachable performance wise+-- I presume a correct solution would need around 30 symbols+gps3c :: IO ()+gps3c  =  conjure "gps3" gps3p []++++-- PSB2 #4: https://www.codewars.com/kata/517abf86da9663f1d2000003+-- Here we're using the problem description as in the PSB2 paper+-- considering we're getting input as kebab-case.+-- Nevertheless, this one is out of reach performance-wise (and OOM-wise)++gps4s :: (String -> String) -> [Property]+gps4s g  =+  [ property $ g "the-stealth-warrior" == "theStealthWarrior"+  , property $ g "camel-case" == "camelCase"+  , property $ g "Kebab-Case" == "KebabCase"+  ]++gps4g :: String -> String+gps4g ""  =  ""+-- gps4g ('-':c:cs)  =  toUpper c : gps4g cs+-- gps4g ('_':c:cs)  =  toUpper c : gps4g cs+gps4g (c:cs)  =  if c == '-'                                   --  5+                 then if null cs                               --  8+                      then ""                                  --  9+                      else toUpper (head cs) : gps4g (tail cs) -- 16+                 else c : gps4g cs                             -- 19++gps4c :: IO ()+gps4c  =  do+  conjureFromSpec "gps4" gps4s+    [ con '-'+    , con ("" :: String)+    , fun ":" ((:) :: Char -> String -> String)+    , fun "==" ((==) :: Char -> Char -> Bool)+    , fun "head" (head :: String -> Char)+    , fun "tail" (tail :: String -> String)+    , iif (undefined :: Char)+    , iif (undefined :: String)+    , fun "toUpper" (toUpper :: Char -> Char)+    , maxSize 6+    ]+++-- PSB2 #5: Coin Sums+-- https://projecteuler.net/problem=31+--+-- The problem description is inconsistent with the one given in the paper.+--+-- Paper: change-making problem in USD+-- Euler: How many different ways can £2 be made using any number of coins?+--+-- I'm considering the Paper to be canonical, as the one in Project Euler can be solved by a constant function:+--+-- solution :: Int+-- solution  =  6378216738  -- <-- arbitrary example here, I didn't run the numbers+gps5p :: Int -> [Int]+gps5p 100  =  [4, 0, 0, 0]+gps5p  50  =  [2, 0, 0, 0]+gps5p  25  =  [1, 0, 0, 0]+gps5p  30  =  [1, 0, 1, 0]+gps5p  20  =  [0, 2, 0, 0]+gps5p   3  =  [0, 0, 0, 3]++gps5s :: ([Int] -> Int -> [Int]) -> [Property]+gps5s t  =+  [ property $ t [25, 10, 5, 1] 100 == [4, 0, 0, 0]+  , property $ t [25, 10, 5, 1]  50 == [2, 0, 0, 0]+  , property $ t [25, 10, 5, 1]  25 == [1, 0, 0, 0]+  , property $ t [25, 10, 5, 1]  30 == [1, 0, 1, 0]+  , property $ t [25, 10, 5, 1]  20 == [0, 2, 0, 0]+  , property $ t [25, 10, 5, 1]   3 == [0, 0, 0, 3]+  ]++coins :: [Int]+coins  =  [25, 10, 5, 1]++gps5g :: Int -> [Int]+gps5g  =  tell coins++tell :: [Int] -> Int -> [Int]+tell []     a  =  []+tell (n:ns) a  =  a `div` n : tell ns (a `mod` n)++gps5c :: IO ()+gps5c  =  do+  -- cannot conjure directly due to needing to introduce a local definition+  conjure "gps5" gps5p+    [+    ]++  conjureFromSpec "tell" gps5s+    [ con ([] :: [Int])+    , fun ":" ((:) :: Int -> [Int] -> [Int])+    , fun "`div`" (div :: Int -> Int -> Int)+    , fun "`mod`" (mod :: Int -> Int -> Int)+    ]++  conjure "gps5" gps5p+    [ con coins+    , fun "tell" tell+    ]++  conjure "gps5" gps5p+    [ con (1 :: Int)+    , con (5 :: Int)+    , con (10 :: Int)+    , con (25 :: Int)+    , con ([] :: [Int])+    , fun ":" ((:) :: Int -> [Int] -> [Int])+    , fun "tell" tell+    , target 50400+    ]+++-- PSB2 #6: Cut Vector+gps6g :: [Int] -> Int+gps6g xs  =  snd+          $  minimum+          [  (abs (sum xs0 - sum xs1), i)+          |  i <- [0 .. length xs]+          ,  let (xs0, xs1) = splitAt i xs+          ]++-- not Conjurable due to needing local definition+-- I conjecture it _perhaps-maybe_ this could be done in 3 steps,+-- but I'll leave this as-is for now.+gps6c :: IO ()+gps6c  =+  conjure "gps6" gps6g []+++-- PSB2 #7: Dice Game+-- https://projecteuler.net/problem=31+-- https://github.com/thelmuth/Clojush/blob/psb2-v1.0/src/clojush/problems/psb2/dice_game.clj+-- again, paper and problem are inconsistent, going with paper+gps7p :: Integer -> Integer -> Rational+gps7p 4 6  =  1 % 4+gps7p 6 4  =  7 % 12+gps7p 2 4  =  1 % 8+gps7p 4 2  =  5 % 8+gps7p 2 6  =  1 % 12+gps7p 6 2  =  3 % 4++gps7g :: Integer -> Integer -> Rational+gps7g peter colin  =  sum (map (min colin) [0 .. (peter-1)]) % (colin*peter)++-- out of reach performance-wise+gps7c :: IO ()+gps7c  =  do+  conjure "gps7" gps7p $ take 0+    [ con (0 :: Integer)+    , con (1 :: Integer)+    , fun "%" ((%) :: Integer -> Integer -> Rational)+    , fun "+" ((+) :: Integer -> Integer -> Integer)+    , fun "-" ((-) :: Integer -> Integer -> Integer)+    , fun "*" ((*) :: Integer -> Integer -> Integer)+    , fun "min" (min :: Integer -> Integer -> Integer)+    , fun ".." (enumFromTo :: Integer -> Integer -> [Integer])+    , fun "map" (map :: (Integer -> Integer) -> [Integer] -> [Integer])+    , fun "sum" (sum :: [Integer] -> Integer)+    , maxSize 6+    ]+++gps8p :: Int -> [Int] -> (Int,Int)+gps8p 2 [1,1,2]  =  (1,1)+gps8p 3 [1,1,2]  =  (1,2)+gps8p 2 [0,1,0,2]  =  (0,2)++gps8g :: Int -> [Int] -> (Int,Int)+gps8g x xs  =  head [(y,z) | y <- xs, z <- xs, y + z == x]+-- this one could be generated but is a bit of a stretch...+-- it is unintuitive to provide the given symbols+-- gps8g :: Int -> [Int] -> (Int,Int)+-- gps8g x xs  =  head $ filter ((x ==) . uncurry (+)) $ liftA2 (,) xs xs++gps8c :: IO ()+gps8c  =  conjure "gps8" gps8p []+++-- PSB2 #9: Fizz Buzz (CW)+gps9p :: Int -> String+gps9p 3  =  "Fizz"+gps9p 4  =  "4"+gps9p 5  =  "Buzz"+gps9p 6  =  "Fizz"+gps9p 10  =  "Buzz"+gps9p 15  =  "FizzBuzz"+gps9p 17  =  "17"++gps9g :: Int -> String+gps9g x+  | x `mod` 3 == 0  =  "Fizz" -- 7+  | x `mod` 5 == 0  =  "Buzz" -- 14+  | x `mod` 3 == 0 && x `mod` 5 == 0  =  "FizzBuzz" -- 27+  | otherwise       =  show x -- 29++-- unreachable performance-wise:+-- too many candidates to sift through+-- even in two steps+gps9c :: IO ()+gps9c  =  conjure "gps9" gps9p+  [ con "Fizz"+  , con "Buzz"+  , con "FizzBuzz"+  , con (0 :: Int)+  , con (3 :: Int)+  , con (5 :: Int)+  , con False+  , con True+  , fun "`divBy`" divBy+--, fun "`mod`" (mod :: Int -> Int -> Int)+  , fun "&&" (&&)+--, fun "==" ((==) :: Int -> Int -> Bool)+  , fun "show" (show :: Int -> String)+  , iif (undefined :: String)+  , target 1080 -- so this fails quickly...+  ]+  where+  -- two-step try:+  divBy :: Int -> Int -> Bool+  x `divBy` 0  =  False+  x `divBy` y  =  x `mod` y == 0+++gps10p :: [Int] -> Int+gps10p [0]  =  -2+gps10p [3]  =  -1+gps10p [6]  =  0+gps10p [9]  =  1+gps10p [0,3]  =  -3+gps10p [3,0]  =  -3+gps10p [3,2,1]  =  -5+gps10p [1,2,3]  =  -5+gps10p [10,20,30]  =  13++-- does not do rounding+gps10g :: [Int] -> Int+gps10g []  =  0+gps10g (x:xs)  =  (x `div` 3 - 2) + gps10g xs++-- unreachable due to lambda+gps10c :: IO ()+gps10c  =  conjure "gps10" gps10p+  [ con (0 :: Int)+  , con (1 :: Int)+  , con (2 :: Int)+  , con (3 :: Int)+  , fun "`div`" (div :: Int -> Int -> Int)+  , fun "+" ((+) :: Int -> Int -> Int)+  , fun "-" ((-) :: Int -> Int -> Int)+  , target 50400+  ]+++gps11p :: Int -> Int -> Int+gps11p  =  gcd'+  where+  gcd' :: Int -> Int -> Int+  gcd' 1 1  =  1+  gcd' 1 2  =  1+  gcd' 2 1  =  1+  gcd' 2 2  =  2+  gcd' 2 6  =  2+  gcd' 6 2  =  2+  gcd' 3 6  =  3+  gcd' 6 3  =  3+  gcd' 6 9  =  3+  gcd' 9 6  =  3+  gcd' 12 18  =  6++gps11c :: IO ()+gps11c  =  conjure "gcd a b" gps11p+  [ con (0::Int)+  , fun "`mod`" (mod :: Int -> Int -> Int)+  ]+  -- generated function:+  -- gcd x 0  =  x+  -- gcd x y  =  gcd y (x `mod` y)+++gps12p :: String -> String -> [Int]+gps12p "a"   "a"   =  [0]+gps12p "aa"  "a"   =  [0,1]+gps12p "aa"  "aa"  =  [0]+gps12p "a a" "a"   =  [0,2]+gps12p "b"   "a"   =  []++gps12g :: String -> String -> [Int]+gps12g s s'  =  findIndices (s' `isPrefixOf`) (tails s)++gps12c :: IO ()+gps12c  =  conjure "gps12" gps12p+  [ fun "findIndices" (findIndices :: (String -> Bool) -> [String] -> [Int])+  , fun "`isPrefixOf`" (isPrefixOf :: String -> String -> Bool)+  , fun "tails" (tails :: String -> [String])+  ]+++gps13p :: [Int] -> [Int]+gps13p [0,1]  =  [1]+gps13p [1,0]  =  [1,0]+gps13p [2,0,1]  =  [2,1]+gps13p [1,0,1]  =  [1]++gps13g :: [Int] -> [Int]+gps13g  =  leaders+  where+  leaders []  =  []+  leaders (x:xs)  =  if all (x >) xs+                     then x : leaders xs+                     else leaders xs++gps13c :: IO ()+gps13c  =  conjure "gps13_leaders" gps13p+  [ con ([] :: [Int])+  , fun ":" ((:) :: Int -> [Int] -> [Int])+  , fun ">" ((>) :: Int -> Int -> Bool)+  , fun "<" ((<) :: Int -> Int -> Bool)+  , fun "all" (all :: (Int -> Bool) -> [Int] -> Bool)+  , fun "any" (any :: (Int -> Bool) -> [Int] -> Bool)+  , guard+  ]+++gps14p :: [Int] -> Int+gps14p  =  undefined++-- 30 symbols+gps14g :: [Int] -> Int+gps14g  =  luhn+  where+  luhn :: [Int] -> Int+  luhn xs  =  sum (firsts xs ++ map double9 (seconds xs))+    where+    double9 :: Int -> Int+    double9 x  =  if xx > 9+                  then xx - 9+                  else xx+      where+      xx  =  x * 2+    seconds :: [Int] -> [Int]+    seconds []  =  []+    seconds (x:y:xs)  =  y : seconds xs+    firsts :: [Int] -> [Int]+    firsts []  =  []+    firsts (x:y:xs)  =  x : seconds xs++-- cannot Conjure directly+gps14c :: IO ()+gps14c  =  conjure "gps14_luhn" gps14p+  [+  ]+++gps15p :: () -> ()+gps15p  =  undefined++-- skipped+gps15c :: IO ()+gps15c  =  conjure "gps15_mastermind" gps15p []+++gps16p :: String -> String+gps16p "a"      =  "a"+gps16p "aaa"    =  "a"+gps16p "aa"     =  "aa"+gps16p "a a"    =  " "+gps16p " a "    =  "a"+gps16p "a a "   =  " a"+gps16p " a a "  =  " "+gps16p "aba"    =  "b"+gps16p "bab"    =  "a"+gps16p "abba"   =  "bb"+gps16p "aaaaa"  =  "a"++gps16g1 :: String -> String+gps16g1 s  =  if odd len+              then take 1 (drop (len `div` 2) s)+              else take 2 (drop (len `div` 2 - 1) s)+  where+  len  =  length s++gps16g2 :: String -> String+gps16g2 ""  =  ""+gps16g2 (c:cs)  =  if length cs <= 1+                   then c : cs+                   else gps16g2 (init cs)++gps16c :: IO ()+gps16c  =  conjure "gps16_middle" gps16p+  [ con ""+  , con (1 :: Int)+  , fun "<=" ((<=) :: Int -> Int -> Bool)+  , fun ":" ((:) :: Char -> String -> String)+  , fun "length" (length :: String -> Int)+  , fun "init" (init :: String -> String)+  , iif (undefined :: String) -- TODO: can't replace by guard, why? (July 2025)+  -- update: it is enumerated, but somehow does not passes the tests, why?+  ]+++-- PSB2 #17 -- Paired Digits (AoC) --+-- Given a string of digits,+-- return the sum of the digits+-- whose following digit are the same.+-- Originally called "Inverse Captcha":+-- https://adventofcode.com/2017/day/1++gps17p :: [Int] -> Int+gps17p [0,1,0]  =  0+gps17p [1,1]  =  1+gps17p [0,0,1,1]  =  1+gps17p [1,1,0]  =  1+gps17p [0,1,1]  =  1+gps17p [1,1,1]  =  2+gps17p [0,1,2]  =  0+gps17p [1,1,2,2]  =  3+gps17p [1,1,1,1]  =  3  -- variation from advent+gps17p [1,2,3,4]  =  0++gps17g :: [Int] -> Int+gps17g xs  =  pds xs+  where+  pds []  =  0+  pds (x:xs)  =  if not (null xs) && x == head xs+                 then x + pds xs+                 else pds xs+-- surprise:+-- gps17_pds []  =  0+-- gps17_pds (x:xs)  =  (if not (null xs) && head xs == x then x else 0) + gps17_pds xs+++-- can generate at size 15 in 6+-- setting limit of 5 for faster automated tests+-- BENCHMARK: increase maxSize from 6 to 18+gps17c :: IO ()+gps17c  =  do+  conjure "gps17_pds" gps17p+    [ con (0 :: Int)+    , guard+    , fun "not" not+    , fun "null" (null :: [Int] -> Bool)+    , fun "==" ((==) :: Int -> Int -> Bool)+    , fun "head" (head :: [Int] -> Int)+    , fun "+" ((+) :: Int -> Int -> Int)+    , fun "&&" (&&)+    , maxSize 6 -- 18+    ]++  -- OOM after size 16, unreachable by increasing pattern depth+  conjure "gps17_pds" gps17p+    [ con (0 :: Int)+    , guard+    , fun "==" ((==) :: Int -> Int -> Bool)+    , fun "+" ((+) :: Int -> Int -> Int)+    , maxPatternDepth 2+    , maxSize 6 -- 18+    ]+++gps18p :: [Double] -> [Double] -> Double+gps18p [1.0] [0.5]  =  0.5+gps18p [2.0] [0.5]  =  1.0+gps18p [1.0,1.0] [0.5,0.0]  =  1.5+gps18p [1.0,1.0] [0.0,0.5]  =  1.5++gps18g :: [Double] -> [Double] -> Double+gps18g prices discounts  =  foldr (+) 0 (zipWith (*) prices (map (1-) discounts))++-- this was OOM'd+gps18c :: IO ()+gps18c  =  conjure "gps18_price" gps18p+  [ con (0 :: Double)+  , con (1 :: Double)+  , fun "+" ((+) :: Double -> Double -> Double)+  , fun "*" ((*) :: Double -> Double -> Double)+  , fun "-" ((-) :: Double -> Double -> Double)+--  , fun "foldr" (foldr :: (Double -> Double -> Double) -> Double -> [Double] -> Double)+--   , fun "zipWith" (zipWith :: (Double -> Double -> Double) -> [Double] -> [Double] -> [Double])+--  , fun "map" (map :: (Double -> Double) -> [Double] -> [Double])+  , maxSize 6+  ]+++gps19p :: Int -> Double -> Double -> Double -> Double+gps19p 0 0 1.0 1.0  =  0+gps19p 1 0 1.0 1.0  =  0+gps19p 2 0 1.0 1.0  =  0+gps19p 1 0 1.0 2.0  =  1.0+gps19p 2 0 1.0 2.0  =  2.0+gps19p 1 0 0.5 1.0  =  0.5+gps19p 2 0 0.5 1.0  =  1.0++gps19g :: Int -> Double -> Double -> Double -> Double+gps19g 0 total melt fall  =  total+gps19g n total melt fall  =  gps19p (n-1) (max 0 (total-melt+fall)) melt fall+-- size 14, out of reach performance wise.++gps19c :: IO ()+gps19c  =  conjure "gps19_snowday" gps19p+  [ con (0 :: Int)+  , con (1 :: Int)+  , fun "max" (max :: Double -> Double -> Double)+  , fun "+" ((+) :: Double -> Double -> Double)+  , fun "-" ((-) :: Double -> Double -> Double)+  , maxSize 6+  ]+++gps20p :: String -> Bool+gps20p  =  undefined++gps20c :: IO ()+gps20c  =  conjure "gps20" gps20p+  [+  ]+++gps21s :: (String -> String) -> [Property]+gps21s s  =+  [ property $ s "word" == "word"+  , property $ s "words" == "sdrow"+  , property $ s "word words" == "word sdrow"+  , property $ s "words word" == "sdrow word"+  ]++spinSpec :: (String -> String) -> [Property]+spinSpec spin  =+  [ property $ spin "abc" == "abc"+  , property $ spin "abcd" == "abcd"+  , property $ spin "word" == "word"+  , property $ spin "abcde" == "edcba"+  , property $ spin "words" == "sdrow"+  , property $ spin "hello" == "olleh"+  , property $ spin "world" == "dlrow"+  ]++spin :: String -> String+spin w  =  if length w >= 5+           then reverse w+           else w++gps21g :: String -> String+gps21g s  =  unwords (map spin (words s))++gps21c :: IO ()+gps21c  =  do+  conjureFromSpec "spin" spinSpec+    [ fun "length"  (length :: String -> Int)+    , fun "reverse" (reverse :: String -> String)+    , guard+    , fun ">="      ((>=) :: Int -> Int -> Bool)+    , con (5 :: Int)+    ]++  conjureFromSpec "gps21_spinwords" gps21s+    [ fun "words"   words+    , fun "unwords" unwords+    , fun "spin"    (spin :: String -> String)+    , fun "map"     (map :: (String -> String) -> [String] -> [String])+    , fun "length"  (length :: String -> Int)+    , fun "reverse" (reverse :: String -> String)+    , guard+    , fun ">="      ((>=) :: Int -> Int -> Bool)+    , con (5 :: Int)+    ]+++-- PSB2 #22 -- Square Digits (CW) --+-- Given a positive integer, square each digit and+-- concatenate the squares into a returned string.++gps22p :: Int -> String+gps22p 1  =  "1"+gps22p 12  =  "14"+gps22p 21  =  "41"+gps22p 123  =  "149"+gps22p 321  =  "941"+gps22p 1234  =  "14916"+gps22p 4321  =  "16941"++-- unreachable as-is+-- reachable with auxiliary functions: div10, mod10 and square+gps22g :: Int -> String+gps22g 0  =  ""  -- 1+gps22g x  =  gps22g (x `div` 10) ++ show (x `mod` 10 * x `mod` 10)  -- 14+-- gps22g x  =  gps22g (x `div` 10) ++ show ((x `mod` 10) ^ 2)  -- 12++gps22c :: IO ()+gps22c  =  do+  conjure "gps22" gps22p+    [ con (0 :: Int)++    -- uncomment the following four for the a runtime of 15s @ size 11+    -- , con (10 :: Int)+    -- , fun "`div`" (div :: Int -> Int -> Int)+    -- , fun "`mod`" (mod :: Int -> Int -> Int)+    -- , fun "square" ((^2) :: Int -> Int)+    , fun "div10" ((`div` 10) :: Int -> Int)+    , fun "mod10" ((`mod` 10) :: Int -> Int)+    , fun "*" ((*) :: Int -> Int -> Int)++    , fun "show" (show :: Int -> String)+    , con ""+    , fun "++" ((++) :: String -> String -> String)+    ]+++gps23s :: (String -> String -> String -> String) -> [Property]+gps23s s  =+  [ property $ s "abcd" "abcd" "abcd" == "abcd"+  , property $ s "abcd" "dcba" "abcd" == "dcba"+  , property $ s "abcd" "1234" "abcd" == "1234"+  , property $ s "abcd" "1234" "bacd" == "2134"+  ]++gps23g :: String -> String -> String -> String+-- gps23g f t s  =  map (\c -> fromJust $ c `lookup` zipWith (,) f t) s+gps23g f t s  =  map (fromJust . (`lookup` zipWith (,) f t)) s++gps23c :: IO ()+gps23c  =  do+  -- cannot conjure, needs lambda+  conjureFromSpec "gps23" gps23s+    [+    ]+++data Twitter  =  Tweet Int+              |  TooMany+              |  Empty+              deriving (Eq, Show)++deriveExpress  ''Twitter+deriveListable ''Twitter+deriveName     ''Twitter++instance Conjurable Twitter where+  conjureExpress   =  reifyExpress+  conjureEquality  =  reifyEquality+  conjureTiers     =  reifyTiers++gps24g_twitter :: String -> Twitter+gps24g_twitter ""  =  Empty+gps24g_twitter s  =  if length s > 140+                     then TooMany+                     else Tweet (length s)++gps24s_twitter :: (String -> Twitter) -> [Property]+gps24s_twitter twitter  =+  [ property $ twitter "" == Empty+  , property $ twitter "abcd" == Tweet 4+  , property $ twitter "0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij" == Tweet 140+  , property $ twitter "0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij0123456789abcdefghij0123456789abcdefghijX" == TooMany+  ]++gps24c :: IO ()+gps24c  =  do+  conjureFromSpec "gps24" gps24s_twitter+    [ con Empty+    , con TooMany+    , fun "Tweet" Tweet+    , guard+    , con ""+    , fun ":" ((:) :: Char -> String -> String)+    , fun "length" (length :: String -> Int)+    , con (140 :: Int)+    , fun ">" ((>) :: Int -> Int -> Bool)+    ]+++gps25p :: [Double] -> [Double] -> Double+gps25p [0] [1]  =  1+gps25p [1] [0]  =  1+gps25p [-1] [1]  =  2+gps25p [0,1] [1,0]  =  sqrt 2+gps25p [1,0] [0,1]  =  sqrt 2+gps25p [0,0,1] [1,0,0]  =  sqrt 2+gps25p [0,1,2] [1,2,3]  =  sqrt 3++gps25g :: [Double] -> [Double] -> Double+gps25g v1 v2  =  sqrt (foldr (+) 0 (map (^2) (zipWith (-) v1 v2)))++-- out of reach performance-wise+gps25c :: IO ()+gps25c  =  conjure "gps25" gps25p+  [ con (0 :: Double)+  , con (2 :: Double)+  , fun "+" ((+) :: Double -> Double -> Double)+  , fun "-" ((-) :: Double -> Double -> Double)+  , fun "**" ((**) :: Double -> Double -> Double)+  , fun "zipWith" (zipWith :: (Double -> Double -> Double) -> [Double] -> [Double] -> [Double])+  , fun "map" (map :: (Double -> Double) -> [Double] -> [Double])+  , fun "sqrt" (sqrt :: Double -> Double)+  , maxSize 6+  ]+++main :: IO ()+main  =  do+  as <- getArgs+  case as of+    [] -> sequence_ gpss+    (n:_) -> gpss !! (read n - 1)+++gpss :: [IO ()]+gpss  =  [ gps1c+         , gps2c+         , gps3c+         , gps4c+         , gps5c+         , gps6c+         , gps7c+         , gps8c+         , gps9c+         , gps10c+         , gps11c+         , gps12c+         , gps13c+         , gps14c+         , gps15c+         , gps16c+         , gps17c+         , gps18c+         , gps19c+         , gps20c+         , gps21c+         , gps22c+         , gps23c+         , gps24c+         , gps25c+         ]
+ bench/psb2.txt view
@@ -0,0 +1,388 @@+gps1 :: [Int] -> Maybe Int+-- testing 4 combinations of argument values+-- pruning with 11/21 rules+-- 0 candidates of size 1+-- 0 candidates of size 2+-- 0 candidates of size 3+-- 1 candidates of size 4+-- 0 candidates of size 5+-- 0 candidates of size 6+-- 1 candidates of size 7+-- 0 candidates of size 8+-- 1 candidates of size 9+-- 2 candidates of size 10+-- tested 4 candidates+gps1 xs  =  findIndex (0 >) (map (foldr (+) 0) (tail (inits xs)))++gps1 :: [Int] -> Maybe Int+-- testing 4 combinations of argument values+-- pruning with 11/21 rules+-- 0 candidates of size 1+-- 0 candidates of size 2+-- 0 candidates of size 3+-- 1 candidates of size 4+-- 1 candidates of size 5+-- 0 candidates of size 6+-- 1 candidates of size 7+-- 4 candidates of size 8+-- tested 4 candidates+gps1 xs  =  findIndex (0 >) (map sum (tail (inits xs)))++gps1 :: Int -> [Int] -> Int+-- testing 6 combinations of argument values+-- pruning with 8/9 rules+-- 4 candidates of size 1+-- 0 candidates of size 2+-- 3 candidates of size 3+-- 5 candidates of size 4+-- tested 12 candidates+gps1  =  undefined  -- search exhausted++gps2 :: Double -> Double -> Int -> Double+-- testing 5 combinations of argument values+-- pruning with 2/6 rules+-- 2 candidates of size 1+-- 0 candidates of size 2+-- 16 candidates of size 3+-- 0 candidates of size 4+-- 252 candidates of size 5+-- 0 candidates of size 6+-- tested 270 candidates+gps2  =  undefined  -- search exhausted++gps3 :: [Char] -> Int+gps3  =  error "could not reify specification, suggestion: conjureFromSpec"++gps4 :: [Char] -> [Char]+-- pruning with 13/21 rules+-- 2 candidates of size 1+-- 3 candidates of size 2+-- 8 candidates of size 3+-- 20 candidates of size 4+-- 51 candidates of size 5+-- 119 candidates of size 6+-- tested 203 candidates+gps4  =  undefined  -- search exhausted++gps5 :: Int -> [Int]+-- testing 6 combinations of argument values+-- pruning with 0/0 rules+-- 0 candidates of size 1+-- tested 0 candidates+gps5  =  undefined  -- search exhausted++tell :: [Int] -> Int -> [Int]+-- pruning with 0/0 rules+-- 2 candidates of size 1+-- 1 candidates of size 2+-- 2 candidates of size 3+-- 6 candidates of size 4+-- 6 candidates of size 5+-- 39 candidates of size 6+-- 26 candidates of size 7+-- 328 candidates of size 8+-- 134 candidates of size 9+-- 3229 candidates of size 10+-- tested 3476 candidates+tell [] x  =  []+tell (x:xs) y  =  y `div` x:tell xs (y `mod` x)++gps5 :: Int -> [Int]+-- testing 6 combinations of argument values+-- pruning with 0/0 rules+-- 1 candidates of size 1+-- 0 candidates of size 2+-- 1 candidates of size 3+-- tested 2 candidates+gps5  =  tell [25,10,5,1]++gps5 :: Int -> [Int]+-- testing 6 combinations of argument values+-- pruning with 12/12 rules+-- 1 candidates of size 1+-- 0 candidates of size 2+-- 5 candidates of size 3+-- 0 candidates of size 4+-- 35 candidates of size 5+-- 0 candidates of size 6+-- 350 candidates of size 7+-- 0 candidates of size 8+-- 3500 candidates of size 9+-- 0 candidates of size 10+-- 35000 candidates of size 11+-- tested 21147 candidates+gps5  =  tell [25,10,5,1]++gps6 :: [Int] -> Int+-- testing 360 combinations of argument values+-- pruning with 0/0 rules+-- 0 candidates of size 1+-- 0 candidates of size 2+-- tested 0 candidates+gps6  =  undefined  -- search exhausted++gps7 :: Integer -> Integer -> Ratio Integer+-- testing 6 combinations of argument values+-- pruning with 0/0 rules+-- 0 candidates of size 1+-- tested 0 candidates+gps7  =  undefined  -- search exhausted++gps8 :: Int -> [Int] -> (Int,Int)+-- testing 3 combinations of argument values+-- pruning with 0/0 rules+-- 0 candidates of size 1+-- 0 candidates of size 2+-- tested 0 candidates+gps8  =  undefined  -- search exhausted++gps9 :: Int -> [Char]+-- testing 7 combinations of argument values+-- pruning with 18/25 rules+-- 3 candidates of size 1+-- 4 candidates of size 2+-- 0 candidates of size 3+-- 0 candidates of size 4+-- 0 candidates of size 5+-- 48 candidates of size 6+-- 192 candidates of size 7+-- 96 candidates of size 8+-- 0 candidates of size 9+-- 168 candidates of size 10+-- 2976 candidates of size 11+-- tested 3487 candidates+gps9  =  undefined  -- search exhausted++gps10 :: [Int] -> Int+-- testing 7 combinations of argument values+-- pruning with 67/100 rules+-- 4 candidates of size 1+-- 0 candidates of size 2+-- 0 candidates of size 3+-- 0 candidates of size 4+-- 80 candidates of size 5+-- 8 candidates of size 6+-- 1428 candidates of size 7+-- 432 candidates of size 8+-- 30712 candidates of size 9+-- tested 4552 candidates+gps10 []  =  0+gps10 (x:xs)  =  (x `div` 3 - 2) + gps10 xs++gcd :: Int -> Int -> Int+-- testing 11 combinations of argument values+-- pruning with 0/0 rules+-- 3 candidates of size 1+-- 0 candidates of size 2+-- 8 candidates of size 3+-- 0 candidates of size 4+-- 48 candidates of size 5+-- 28 candidates of size 6+-- tested 63 candidates+gcd x 0  =  x+gcd x y  =  gcd y (x `mod` y)++gps12 :: [Char] -> [Char] -> [Int]+-- testing 5 combinations of argument values+-- pruning with 1/2 rules+-- 0 candidates of size 1+-- 0 candidates of size 2+-- 0 candidates of size 3+-- 0 candidates of size 4+-- 4 candidates of size 5+-- tested 3 candidates+gps12 cs ds  =  findIndices (ds `isPrefixOf`) (tails cs)++gps13_leaders :: [Int] -> [Int]+-- testing 4 combinations of argument values+-- pruning with 9/9 rules+-- 2 candidates of size 1+-- 0 candidates of size 2+-- 0 candidates of size 3+-- 0 candidates of size 4+-- 0 candidates of size 5+-- 0 candidates of size 6+-- 0 candidates of size 7+-- 0 candidates of size 8+-- 11 candidates of size 9+-- 16 candidates of size 10+-- 53 candidates of size 11+-- 48 candidates of size 12+-- tested 101 candidates+gps13_leaders []  =  []+gps13_leaders (x:xs)+  | all (x >) xs  =  x:gps13_leaders xs+  | otherwise  =  gps13_leaders xs++gps14_luhn :: [Int] -> Int+gps14_luhn  =  error "could not reify specification, suggestion: conjureFromSpec"++gps15_mastermind :: () -> ()+gps15_mastermind  =  error "could not reify specification, suggestion: conjureFromSpec"++gps16_middle :: [Char] -> [Char]+-- testing 11 combinations of argument values+-- pruning with 10/11 rules+-- 2 candidates of size 1+-- 2 candidates of size 2+-- 2 candidates of size 3+-- 3 candidates of size 4+-- 5 candidates of size 5+-- 8 candidates of size 6+-- 17 candidates of size 7+-- 50 candidates of size 8+-- 145 candidates of size 9+-- 391 candidates of size 10+-- 993 candidates of size 11+-- 2480 candidates of size 12+-- tested 3719 candidates+gps16_middle ""  =  ""+gps16_middle (c:cs)  =  if length cs <= 1+                        then c:cs+                        else gps16_middle (init cs)++gps17_pds :: [Int] -> Int+-- testing 9 combinations of argument values+-- pruning with 29/40 rules+-- 1 candidates of size 1+-- 1 candidates of size 2+-- 0 candidates of size 3+-- 0 candidates of size 4+-- 2 candidates of size 5+-- 4 candidates of size 6+-- tested 8 candidates+gps17_pds  =  undefined  -- search exhausted++gps17_pds :: [Int] -> Int+-- testing 9 combinations of argument values+-- pruning with 13/19 rules+-- 1 candidates of size 1+-- 0 candidates of size 2+-- 0 candidates of size 3+-- 1 candidates of size 4+-- 4 candidates of size 5+-- 8 candidates of size 6+-- tested 14 candidates+gps17_pds  =  undefined  -- search exhausted++gps18_price :: [Double] -> [Double] -> Double+-- testing 4 combinations of argument values+-- pruning with 26/35 rules+-- 2 candidates of size 1+-- 0 candidates of size 2+-- 2 candidates of size 3+-- 0 candidates of size 4+-- 33 candidates of size 5+-- 176 candidates of size 6+-- tested 213 candidates+gps18_price  =  undefined  -- search exhausted++gps19_snowday :: Int -> Double -> Double -> Double -> Double+-- testing 7 combinations of argument values+-- pruning with 6/19 rules+-- 3 candidates of size 1+-- 0 candidates of size 2+-- 21 candidates of size 3+-- 0 candidates of size 4+-- 309 candidates of size 5+-- 0 candidates of size 6+-- tested 333 candidates+gps19_snowday  =  undefined  -- search exhausted++gps20 :: [Char] -> Bool+gps20  =  error "could not reify specification, suggestion: conjureFromSpec"++spin :: [Char] -> [Char]+-- pruning with 6/6 rules+-- reasoning produced 1 incorrect properties, please re-run with more tests for faster results+-- 1 candidates of size 1+-- 1 candidates of size 2+-- 0 candidates of size 3+-- 0 candidates of size 4+-- 0 candidates of size 5+-- 0 candidates of size 6+-- 0 candidates of size 7+-- 4 candidates of size 8+-- tested 6 candidates+spin cs+  | length cs >= 5  =  reverse cs+  | otherwise  =  cs++gps21_spinwords :: [Char] -> [Char]+-- pruning with 16/16 rules+-- reasoning produced 2 incorrect properties, please re-run with more tests for faster results+-- 1 candidates of size 1+-- 2 candidates of size 2+-- 2 candidates of size 3+-- 3 candidates of size 4+-- 5 candidates of size 5+-- tested 12 candidates+gps21_spinwords cs  =  unwords (map spin (words cs))++gps22 :: Int -> [Char]+-- testing 7 combinations of argument values+-- pruning with 13/17 rules+-- 1 candidates of size 1+-- 2 candidates of size 2+-- 2 candidates of size 3+-- 3 candidates of size 4+-- 10 candidates of size 5+-- 20 candidates of size 6+-- 45 candidates of size 7+-- 117 candidates of size 8+-- 273 candidates of size 9+-- 645 candidates of size 10+-- 1567 candidates of size 11+-- tested 2609 candidates+gps22 0  =  ""+gps22 x  =  gps22 (div10 x) ++ show (mod10 x * mod10 x)++gps23 :: [Char] -> [Char] -> [Char] -> [Char]+-- pruning with 0/0 rules+-- 3 candidates of size 1+-- 12 candidates of size 2+-- 33 candidates of size 3+-- 36 candidates of size 4+-- 127 candidates of size 5+-- 507 candidates of size 6+-- 839 candidates of size 7+-- 784 candidates of size 8+-- 600 candidates of size 9+-- 2722 candidates of size 10+-- 5292 candidates of size 11+-- tested 10955 candidates+gps23  =  undefined  -- search exhausted++gps24 :: [Char] -> Twitter+-- pruning with 4/8 rules+-- reasoning produced 4 incorrect properties, please re-run with more tests for faster results+-- 2 candidates of size 1+-- 3 candidates of size 2+-- 6 candidates of size 3+-- 6 candidates of size 4+-- 3 candidates of size 5+-- 5 candidates of size 6+-- 10 candidates of size 7+-- 48 candidates of size 8+-- 134 candidates of size 9+-- 216 candidates of size 10+-- 308 candidates of size 11+-- 466 candidates of size 12+-- tested 803 candidates+gps24 ""  =  Empty+gps24 (c:cs)+  | 140 > length cs  =  Tweet (length (c:cs))+  | otherwise  =  TooMany++gps25 :: [Double] -> [Double] -> Double+-- testing 6 combinations of argument values+-- pruning with 31/59 rules+-- 2 candidates of size 1+-- 1 candidates of size 2+-- 5 candidates of size 3+-- 10 candidates of size 4+-- 76 candidates of size 5+-- 438 candidates of size 6+-- tested 532 candidates+gps25  =  undefined  -- search exhausted+
bench/redundants.hs view
@@ -66,43 +66,43 @@   -- We can also customize the n per-function below:    printRedundantCandidates (n+1) "foo" (undefined :: Int -> Int)-    [ unfun (0 :: Int)-    , unfun (1 :: Int)+    [ con (0 :: Int)+    , con (1 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "*" ((*) :: Int -> Int -> Int)     , fun "-" ((-) :: Int -> Int -> Int)     ]    printRedundantCandidates n "?" (undefined :: Int -> Int -> Int)-    [ unfun (0 :: Int)+    [ con (0 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "*" ((*) :: Int -> Int -> Int)     , fun "dec" (subtract 1 :: Int -> Int)     ]    printRedundantCandidates (n+1) "goo" (undefined :: [Int] -> [Int])-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "++" ((++) :: [Int] -> [Int] -> [Int])     ]    printRedundantCandidates n "??" (undefined :: [Int] -> [Int] -> [Int])-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "++" ((++) :: [Int] -> [Int] -> [Int])     ]    printRedundantCandidates (n+1) "ton" (undefined :: Bool -> Bool)-    [ unfun False-    , unfun True+    [ con False+    , con True     , fun "&&" (&&)     , fun "||" (||)     , fun "not" not     ]    printRedundantCandidates n "&|" (undefined :: Bool -> Bool -> Bool)-    [ unfun False-    , unfun True+    [ con False+    , con True     , fun "&&" (&&)     , fun "||" (||)     , fun "not" not@@ -115,7 +115,7 @@   -- through other means   {-   printRedundantCandidates n "gcd" (undefined :: Int -> Int -> Int)-    [ unfun (0::Int)+    [ con (0::Int)     , fun "`mod`" (mod :: Int -> Int -> Int)     ]   -}
bench/redundants.txt view
@@ -228,32 +228,32 @@  class of 2 equivalent candidates: -    x ? y  =  x + (x + y)+    x ? y  =  x + dec (dec x) -    x ? y  =  y + (x + x)+    x ? y  =  dec x + dec x  -class of 2 equivalent candidates:+class of 3 equivalent candidates: -    x ? y  =  x + (y + y)+    x ? y  =  x + dec (dec y) -    x ? y  =  y + (x + y)+    x ? y  =  y + dec (dec x) +    x ? y  =  dec x + dec y + class of 2 equivalent candidates: -    x ? y  =  x + dec (dec x)+    x ? y  =  x + (x + y) -    x ? y  =  dec x + dec x+    x ? y  =  y + (x + x)  -class of 3 equivalent candidates:--    x ? y  =  x + dec (dec y)+class of 2 equivalent candidates: -    x ? y  =  y + dec (dec x)+    x ? y  =  x + (y + y) -    x ? y  =  dec x + dec y+    x ? y  =  y + (x + y)   class of 2 equivalent candidates:@@ -600,55 +600,44 @@  class of 2 equivalent candidates: -    [] ?? xs  =  []-    (x:xs) ?? []  =  xs-    (x:xs) ?? (y:ys)  =  xs ?? ys--    [] ?? xs  =  []-    (x:xs) ?? []  =  xs-    (x:xs) ?? (y:ys)  =  xs ?? []---class of 2 equivalent candidates:--    [] ?? xs  =  []+    [] ?? xs  =  xs     (x:xs) ?? []  =  xs-    (x:xs) ?? (y:ys)  =  ys ?? xs+    (x:xs) ?? (y:ys)  =  xs ++ ys -    [] ?? xs  =  []+    [] ?? xs  =  xs     (x:xs) ?? []  =  xs-    (x:xs) ?? (y:ys)  =  ys ?? []+    (x:xs) ?? (y:ys)  =  ys ++ xs   class of 2 equivalent candidates: -    [] ?? []  =  []-    [] ?? (x:xs)  =  xs ?? xs-    (x:xs) ?? ys  =  xs+    [] ?? xs  =  xs+    (x:xs) ?? []  =  []+    (x:xs) ?? (y:ys)  =  xs ++ ys -    [] ?? []  =  []-    [] ?? (x:xs)  =  xs ?? []-    (x:xs) ?? ys  =  xs+    [] ?? xs  =  xs+    (x:xs) ?? []  =  []+    (x:xs) ?? (y:ys)  =  ys ++ xs   class of 2 equivalent candidates: -    [] ?? xs  =  xs+    [] ?? xs  =  []     (x:xs) ?? []  =  xs     (x:xs) ?? (y:ys)  =  xs ++ ys -    [] ?? xs  =  xs+    [] ?? xs  =  []     (x:xs) ?? []  =  xs     (x:xs) ?? (y:ys)  =  ys ++ xs   class of 2 equivalent candidates: -    [] ?? xs  =  xs+    [] ?? xs  =  []     (x:xs) ?? []  =  []     (x:xs) ?? (y:ys)  =  xs ++ ys -    [] ?? xs  =  xs+    [] ?? xs  =  []     (x:xs) ?? []  =  []     (x:xs) ?? (y:ys)  =  ys ++ xs @@ -657,22 +646,33 @@      [] ?? xs  =  []     (x:xs) ?? []  =  xs-    (x:xs) ?? (y:ys)  =  xs ++ ys+    (x:xs) ?? (y:ys)  =  xs ?? ys      [] ?? xs  =  []     (x:xs) ?? []  =  xs-    (x:xs) ?? (y:ys)  =  ys ++ xs+    (x:xs) ?? (y:ys)  =  xs ?? []   class of 2 equivalent candidates:      [] ?? xs  =  []-    (x:xs) ?? []  =  []-    (x:xs) ?? (y:ys)  =  xs ++ ys+    (x:xs) ?? []  =  xs+    (x:xs) ?? (y:ys)  =  ys ?? xs      [] ?? xs  =  []-    (x:xs) ?? []  =  []-    (x:xs) ?? (y:ys)  =  ys ++ xs+    (x:xs) ?? []  =  xs+    (x:xs) ?? (y:ys)  =  ys ?? []+++class of 2 equivalent candidates:++    [] ?? []  =  []+    [] ?? (x:xs)  =  xs ?? xs+    (x:xs) ?? ys  =  xs++    [] ?? []  =  []+    [] ?? (x:xs)  =  xs ?? []+    (x:xs) ?? ys  =  xs
bench/runtime/lapmatrud/bench/candidates.runtime view
@@ -1,1 +1,1 @@-10.0+9.4
bench/runtime/lapmatrud/bench/carry-on.runtime view
@@ -1,1 +1,1 @@-2.6+2.4
bench/runtime/lapmatrud/bench/erroneous.runtime view
@@ -1,1 +1,1 @@-3.1+2.9
bench/runtime/lapmatrud/bench/gps.runtime view
@@ -1,1 +1,1 @@-15.8+14.2
bench/runtime/lapmatrud/bench/gps2.runtime view
@@ -1,1 +1,1 @@-12.7+11.7
bench/runtime/lapmatrud/bench/ill-hit.runtime view
@@ -1,1 +1,1 @@-0.7+0.5
bench/runtime/lapmatrud/bench/lowtests.runtime view
@@ -1,1 +1,1 @@-0.5+0.2
bench/runtime/lapmatrud/bench/p12.runtime view
@@ -1,1 +1,1 @@-1.7+1.6
bench/runtime/lapmatrud/bench/redundants.runtime view
@@ -1,1 +1,1 @@-3.2+3.1
bench/runtime/lapmatrud/bench/strategies.runtime view
@@ -1,1 +1,1 @@-6.0+4.6
bench/runtime/lapmatrud/bench/terpret.runtime view
@@ -1,1 +1,1 @@-7.7+10.2
bench/runtime/lapmatrud/bench/unique.runtime view
@@ -1,1 +1,1 @@-2.5+2.4
bench/runtime/lapmatrud/bench/weird.runtime view
@@ -1,1 +1,1 @@-2.6+3.3
bench/runtime/lapmatrud/eg/bits.runtime view
@@ -1,1 +1,1 @@-3.2+3.1
bench/runtime/lapmatrud/eg/bools.runtime view
@@ -1,1 +1,1 @@-1.9+1.6
bench/runtime/lapmatrud/eg/bst.runtime view
@@ -1,1 +1,1 @@-4.8+4.1
+ bench/runtime/lapmatrud/eg/conditionals.runtime view
@@ -0,0 +1,1 @@+8.7
bench/runtime/lapmatrud/eg/count.runtime view
@@ -1,1 +1,1 @@-0.8+0.5
+ bench/runtime/lapmatrud/eg/digits.runtime view
@@ -0,0 +1,1 @@+5.5
bench/runtime/lapmatrud/eg/dupos.runtime view
@@ -1,1 +1,1 @@-2.2+1.1
bench/runtime/lapmatrud/eg/factorial.runtime view
@@ -1,1 +1,1 @@-1.6+1.4
bench/runtime/lapmatrud/eg/fib01.runtime view
@@ -1,1 +1,1 @@-0.6+0.5
bench/runtime/lapmatrud/eg/fibonacci.runtime view
@@ -1,1 +1,1 @@-3.5+3.2
bench/runtime/lapmatrud/eg/gcd.runtime view
@@ -1,1 +1,1 @@-0.2+0.1
bench/runtime/lapmatrud/eg/higher.runtime view
@@ -1,1 +1,1 @@-1.4+0.9
bench/runtime/lapmatrud/eg/ints.runtime view
@@ -1,1 +1,1 @@-1.2+0.9
bench/runtime/lapmatrud/eg/list.runtime view
@@ -1,1 +1,1 @@-0.6+0.8
bench/runtime/lapmatrud/eg/oddeven.runtime view
@@ -1,1 +1,1 @@-1.6+1.7
bench/runtime/lapmatrud/eg/pow.runtime view
@@ -1,1 +1,1 @@-3.0+1.6
bench/runtime/lapmatrud/eg/setelem.runtime view
@@ -1,1 +1,1 @@-0.8+1.0
bench/runtime/lapmatrud/eg/sort.runtime view
@@ -1,1 +1,1 @@-3.4+1.8
bench/runtime/lapmatrud/eg/subset.runtime view
@@ -1,1 +1,1 @@-0.6+0.5
bench/runtime/lapmatrud/eg/these.runtime view
@@ -1,1 +1,1 @@-1.9+1.1
bench/runtime/lapmatrud/eg/tri.runtime view
@@ -1,1 +1,1 @@-0.3+0.2
bench/runtime/lapmatrud/eg/tuple.runtime view
@@ -1,1 +1,1 @@-0.8+0.7
bench/runtime/zero/bench/candidates.runtime view
@@ -1,1 +1,1 @@-17.4+18.5
bench/runtime/zero/bench/carry-on.runtime view
@@ -1,1 +1,1 @@-4.8+5.4
bench/runtime/zero/bench/erroneous.runtime view
@@ -1,1 +1,1 @@-5.6+6.9
bench/runtime/zero/bench/gps.runtime view
@@ -1,1 +1,1 @@-27.9+34.3
bench/runtime/zero/bench/gps2.runtime view
@@ -1,1 +1,1 @@-22.8+24.9
bench/runtime/zero/bench/ill-hit.runtime view
@@ -1,1 +1,1 @@-1.1+1.2
bench/runtime/zero/bench/lowtests.runtime view
@@ -1,1 +1,1 @@-0.8+0.6
bench/runtime/zero/bench/p12.runtime view
@@ -1,1 +1,1 @@-3.0+3.5
bench/runtime/zero/bench/redundants.runtime view
@@ -1,1 +1,1 @@-6.2+8.1
bench/runtime/zero/bench/strategies.runtime view
@@ -1,1 +1,1 @@-9.1+10.7
bench/runtime/zero/bench/terpret.runtime view
@@ -1,1 +1,1 @@-14.2+22.8
bench/runtime/zero/bench/unique.runtime view
@@ -1,1 +1,1 @@-4.8+5.3
bench/runtime/zero/bench/weird.runtime view
@@ -1,1 +1,1 @@-4.7+7.3
bench/runtime/zero/eg/arith.runtime view
@@ -1,1 +1,1 @@-1.9+2.4
bench/runtime/zero/eg/bits.runtime view
@@ -1,1 +1,1 @@-5.8+6.1
bench/runtime/zero/eg/bools.runtime view
@@ -1,1 +1,1 @@-3.2+3.4
+ bench/runtime/zero/eg/conditionals.runtime view
@@ -0,0 +1,1 @@+16.4
bench/runtime/zero/eg/count.runtime view
@@ -1,1 +1,1 @@-1.1+1.2
+ bench/runtime/zero/eg/digits.runtime view
@@ -0,0 +1,1 @@+10.9
bench/runtime/zero/eg/dupos.runtime view
@@ -1,1 +1,1 @@-3.7+2.5
bench/runtime/zero/eg/either.runtime view
@@ -1,1 +1,1 @@-0.3+0.4
bench/runtime/zero/eg/factorial.runtime view
@@ -1,1 +1,1 @@-2.5+2.8
bench/runtime/zero/eg/fib01.runtime view
@@ -1,1 +1,1 @@-1.1+1.2
bench/runtime/zero/eg/fibonacci.runtime view
@@ -1,1 +1,1 @@-6.2+6.9
bench/runtime/zero/eg/higher.runtime view
@@ -1,1 +1,1 @@-1.8+2.0
bench/runtime/zero/eg/ints.runtime view
@@ -1,1 +1,1 @@-1.9+2.2
bench/runtime/zero/eg/list.runtime view
@@ -1,1 +1,1 @@-1.6+1.8
bench/runtime/zero/eg/oddeven.runtime view
@@ -1,1 +1,1 @@-3.0+3.7
bench/runtime/zero/eg/pow.runtime view
@@ -1,1 +1,1 @@-5.2+3.6
bench/runtime/zero/eg/replicate.runtime view
@@ -1,1 +1,1 @@-0.4+0.5
bench/runtime/zero/eg/setelem.runtime view
@@ -1,1 +1,1 @@-1.9+2.1
bench/runtime/zero/eg/sort.runtime view
@@ -1,1 +1,1 @@-6.0+3.9
bench/runtime/zero/eg/spec.runtime view
@@ -1,1 +1,1 @@-1.5+1.9
bench/runtime/zero/eg/take-drop.runtime view
@@ -1,1 +1,1 @@-0.6+0.7
bench/runtime/zero/eg/tapps.runtime view
@@ -1,1 +1,1 @@-0.8+1.0
bench/runtime/zero/eg/these.runtime view
@@ -1,1 +1,1 @@-3.4+2.3
bench/runtime/zero/eg/tree.runtime view
@@ -1,1 +1,1 @@-2.6+3.2
bench/runtime/zero/proto/u-conjure.runtime view
@@ -1,1 +1,1 @@-0.4+0.5
bench/self.hs view
@@ -13,8 +13,8 @@  ingredients :: [Ingredient] ingredients =-  [ unfun (0::Int)-  , unfun (1::Int)+  [ con (0::Int)+  , con (1::Int)   , fun "+" ((+) :: Int -> Int -> Int)   , fun "*" ((*) :: Int -> Int -> Int)   , maxSize 3
bench/self.txt view
@@ -2,35 +2,35 @@ -- testing 360 combinations of argument values -- pruning with 0/0 rules -- 4 candidates of size 1--- 6 candidates of size 2--- 26 candidates of size 3--- tested 12 candidates+-- 0 candidates of size 2+-- 24 candidates of size 3+-- tested 6 candidates x ? y  =  x + y  (?) :: Int -> Int -> Int -- testing 360 combinations of argument values -- pruning with 0/0 rules -- 4 candidates of size 1--- 4 candidates of size 2--- 31 candidates of size 3--- tested 22 candidates+-- 0 candidates of size 2+-- 24 candidates of size 3+-- tested 18 candidates x ? y  =  x * y  i :: Int -> Int -- testing 360 combinations of argument values -- pruning with 0/0 rules -- 3 candidates of size 1--- 2 candidates of size 2--- 13 candidates of size 3--- tested 8 candidates+-- 0 candidates of size 2+-- 10 candidates of size 3+-- tested 6 candidates i x  =  x + 1  d :: Int -> Int -- testing 360 combinations of argument values -- pruning with 0/0 rules -- 3 candidates of size 1--- 3 candidates of size 2--- 12 candidates of size 3--- tested 18 candidates+-- 0 candidates of size 2+-- 10 candidates of size 3+-- tested 13 candidates d  =  undefined  -- search exhausted
bench/strategies.hs view
@@ -27,10 +27,10 @@     "default"           -> [1,1,1,0]     "without reasoning" -> [0,1,1,0]     "without descent"   -> [1,0,1,0]-    "without ad-hoc"    -> [1,1,0,0]+    "without assorted"  -> [1,1,0,0]     "only reasoning"    -> [1,0,0,0]     "only descent"      -> [0,1,0,0]-    "only ad-hoc"       -> [0,0,1,0]+    "only assorted"     -> [0,0,1,0]     "only typed"        -> [0,0,0,0]     _                   -> error "unknown strategy" @@ -45,10 +45,10 @@   , "default"   , "without reasoning"   , "without descent"-  , "without ad-hoc"+  , "without assorted"   , "only reasoning"   , "only descent"-  , "only ad-hoc"+  , "only assorted"   , "only typed"   ] @@ -61,8 +61,8 @@  ingredients :: [Ingredient] ingredients = -    [ unfun (0::Int)-    , unfun (1::Int)+    [ con (0::Int)+    , con (1::Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "*" ((*) :: Int -> Int -> Int)     , fun "-" ((-) :: Int -> Int -> Int)
bench/strategies.txt view
@@ -3,13 +3,13 @@ -- testing 4 combinations of argument values -- pruning with 27/65 rules -- 3 candidates of size 1--- 3 candidates of size 2--- 7 candidates of size 3--- 8 candidates of size 4--- 23 candidates of size 5--- 30 candidates of size 6--- 82 candidates of size 7--- tested 84 candidates+-- 0 candidates of size 2+-- 6 candidates of size 3+-- 0 candidates of size 4+-- 18 candidates of size 5+-- 0 candidates of size 6+-- 67 candidates of size 7+-- tested 88 candidates factorial 0  =  1 factorial x  =  x * factorial (x - 1) @@ -18,13 +18,13 @@ -- testing 4 combinations of argument values -- pruning with 27/65 rules -- 3 candidates of size 1--- 3 candidates of size 2--- 7 candidates of size 3--- 8 candidates of size 4--- 28 candidates of size 5--- 35 candidates of size 6--- 167 candidates of size 7--- tested 95 candidates+-- 0 candidates of size 2+-- 6 candidates of size 3+-- 0 candidates of size 4+-- 23 candidates of size 5+-- 0 candidates of size 6+-- 147 candidates of size 7+-- tested 173 candidates factorial 0  =  1 factorial x  =  x * factorial (x - 1) @@ -33,13 +33,13 @@ -- testing 4 combinations of argument values -- pruning with 27/65 rules -- 3 candidates of size 1--- 3 candidates of size 2--- 16 candidates of size 3--- 17 candidates of size 4--- 279 candidates of size 5--- 313 candidates of size 6--- 5763 candidates of size 7--- tested 656 candidates+-- 0 candidates of size 2+-- 15 candidates of size 3+-- 0 candidates of size 4+-- 270 candidates of size 5+-- 0 candidates of size 6+-- 5572 candidates of size 7+-- tested 5848 candidates factorial 0  =  1 factorial x  =  x * factorial (x - 1) @@ -48,28 +48,28 @@ -- testing 4 combinations of argument values -- pruning with 27/65 rules -- 3 candidates of size 1--- 3 candidates of size 2--- 7 candidates of size 3--- 8 candidates of size 4--- 28 candidates of size 5--- 35 candidates of size 6--- 252 candidates of size 7--- tested 148 candidates+-- 0 candidates of size 2+-- 6 candidates of size 3+-- 0 candidates of size 4+-- 23 candidates of size 5+-- 0 candidates of size 6+-- 232 candidates of size 7+-- tested 226 candidates factorial 0  =  1 factorial x  =  x * factorial (x - 1) --- strategy: without ad-hoc+-- strategy: without assorted factorial :: Int -> Int -- testing 4 combinations of argument values -- pruning with 27/65 rules -- 3 candidates of size 1--- 6 candidates of size 2--- 9 candidates of size 3--- 18 candidates of size 4--- 31 candidates of size 5--- 59 candidates of size 6--- 171 candidates of size 7--- tested 137 candidates+-- 0 candidates of size 2+-- 6 candidates of size 3+-- 0 candidates of size 4+-- 25 candidates of size 5+-- 1 candidates of size 6+-- 148 candidates of size 7+-- tested 176 candidates factorial 0  =  1 factorial x  =  x * factorial (x - 1) @@ -78,13 +78,13 @@ -- testing 4 combinations of argument values -- pruning with 27/65 rules -- 3 candidates of size 1--- 6 candidates of size 2--- 9 candidates of size 3--- 18 candidates of size 4--- 41 candidates of size 5--- 64 candidates of size 6--- 307 candidates of size 7--- tested 251 candidates+-- 0 candidates of size 2+-- 6 candidates of size 3+-- 0 candidates of size 4+-- 35 candidates of size 5+-- 6 candidates of size 6+-- 284 candidates of size 7+-- tested 244 candidates factorial 0  =  1 factorial x  =  x * factorial (x - 1) @@ -93,28 +93,28 @@ -- testing 4 combinations of argument values -- pruning with 27/65 rules -- 3 candidates of size 1--- 6 candidates of size 2--- 18 candidates of size 3--- 36 candidates of size 4--- 287 candidates of size 5--- 571 candidates of size 6--- 5843 candidates of size 7--- tested 946 candidates+-- 0 candidates of size 2+-- 15 candidates of size 3+-- 0 candidates of size 4+-- 272 candidates of size 5+-- 1 candidates of size 6+-- 5573 candidates of size 7+-- tested 5851 candidates factorial 0  =  1 factorial x  =  x * factorial (x - 1) --- strategy: only ad-hoc+-- strategy: only assorted factorial :: Int -> Int -- testing 4 combinations of argument values -- pruning with 27/65 rules -- 3 candidates of size 1--- 3 candidates of size 2--- 16 candidates of size 3--- 17 candidates of size 4--- 279 candidates of size 5--- 313 candidates of size 6--- 6281 candidates of size 7--- tested 1004 candidates+-- 0 candidates of size 2+-- 15 candidates of size 3+-- 0 candidates of size 4+-- 270 candidates of size 5+-- 0 candidates of size 6+-- 6090 candidates of size 7+-- tested 6196 candidates factorial 0  =  1 factorial x  =  x * factorial (x - 1) @@ -123,13 +123,13 @@ -- testing 4 combinations of argument values -- pruning with 27/65 rules -- 3 candidates of size 1--- 6 candidates of size 2--- 18 candidates of size 3--- 36 candidates of size 4--- 315 candidates of size 5--- 585 candidates of size 6--- 6915 candidates of size 7--- tested 1876 candidates+-- 0 candidates of size 2+-- 15 candidates of size 3+-- 0 candidates of size 4+-- 300 candidates of size 5+-- 15 candidates of size 6+-- 6645 candidates of size 7+-- tested 6241 candidates factorial 0  =  1 factorial x  =  x * factorial (x - 1)
bench/terpret.hs view
@@ -33,15 +33,15 @@ -- the same ingredients are used for TerpreT #1, #2 and #3 ingredients123 :: [Ingredient] ingredients123  =-  [ unfun False-  , unfun True+  [ con False+  , con True   , fun "not" not   , fun "&&" (&&)   , fun "||" (||)-  , unfun ([] :: [Bool])+  , con ([] :: [Bool])   , fun ":" ((:) :: Bool -> [Bool] -> [Bool]) --, fun "map" (map :: (Bool -> Bool) -> [Bool] -> [Bool])-  , iif (undefined :: [Bool])+  , guard   ]  @@ -110,13 +110,13 @@    conjure "cshift" t4p1 $ ingredients123 ++     [ fun ",," ((,,) :: Bool -> Bool -> Bool -> (Bool,Bool,Bool))-    , iif (undefined :: (Bool,Bool,Bool))+    , guard     , target 50400     ]    conjure "cshift" t4p2 $ ingredients123 ++     [ fun ",," ((,,) :: Bool -> Bool -> Bool -> (Bool,Bool,Bool))-    , iif (undefined :: (Bool,Bool,Bool))+    , guard     ]  @@ -136,15 +136,12 @@ t5c  =  do   putStrLn "TerpreT benchmark #5: full adder\n" -  -- using ingredients123 below works, but increases the runtime to 18 seconds-  -- let's leave it commented out so runtime is faster when running automated tests-  -- BENCHMARK: uncomment ingredients123-  conjure "fadder" t5p $ -- ingredients123 +++  conjure "fadder" t5p $ ingredients123 ++     [ fun "not" not     , fun "," ((,) :: Bool -> Bool -> (Bool,Bool))     , fun "==" ((==) :: Bool -> Bool -> Bool) --  , fun "^^" ((/=) :: Bool -> Bool -> Bool) -- poor man's xor-    , iif (undefined :: (Bool,Bool))+    , guard     ] -- the printed function is weird, but correct -- fadder p q r  =  if p == q then (p,r) else (r,not r)@@ -165,7 +162,7 @@     [ fun ",," ((,,) :: Bool -> Bool -> Bool -> (Bool,Bool,Bool))     , fun "==" ((==) :: Bool -> Bool -> Bool)     , fun "^^" ((/=) :: Bool -> Bool -> Bool) -- poor man's xor-    , iif (undefined :: (Bool,Bool,Bool))+    , guard     , maxSize 6     ] @@ -192,9 +189,9 @@     ]    conjure "`access`" t7p-    [ unfun (0 :: Int)-    , unfun (1 :: Int)-    , unfun ([] :: [A])+    [ con (0 :: Int)+    , con (1 :: Int)+    , con ([] :: [A])     , fun ":" ((:) :: A -> [A] -> [A])     , fun "-" ((-) :: Int -> Int -> Int)     , fun "undefined" (undefined :: A)@@ -212,8 +209,8 @@   putStrLn "TerpreT benchmark #8: decrement elements\n"    conjure "decrelements" t8p-    [ unfun (1 :: Int)-    , unfun ([] :: [Int])+    [ con (1 :: Int)+    , con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "-" ((-) :: Int -> Int -> Int)     , fun "map" (map :: (Int -> Int) -> [Int] -> [Int])@@ -222,8 +219,8 @@   -- introduce lambdas    conjure "decrelements" t8p-    [ unfun (1 :: Int)-    , unfun ([] :: [Int])+    [ con (1 :: Int)+    , con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "-" ((-) :: Int -> Int -> Int)     , fun "map" (map :: (Int -> Int) -> [Int] -> [Int])
bench/terpret.txt view
@@ -7,9 +7,9 @@ -- 0 candidates of size 2 -- 4 candidates of size 3 -- 0 candidates of size 4--- 11 candidates of size 5--- 5 candidates of size 6--- tested 18 candidates+-- 8 candidates of size 5+-- 1 candidates of size 6+-- tested 15 candidates invert []  =  [] invert (p:ps)  =  not p:invert ps @@ -33,40 +33,43 @@ -- 0 candidates of size 2 -- 4 candidates of size 3 -- 0 candidates of size 4--- 11 candidates of size 5--- 5 candidates of size 6--- 31 candidates of size 7--- 52 candidates of size 8--- 128 candidates of size 9--- tested 154 candidates+-- 8 candidates of size 5+-- 1 candidates of size 6+-- 16 candidates of size 7+-- 4 candidates of size 8+-- 35 candidates of size 9+-- 15 candidates of size 10+-- tested 71 candidates decrement []  =  []-decrement (p:ps)  =  not p:(if p then ps else decrement ps)+decrement (p:ps)+  | p  =  False:ps+  | otherwise  =  True:decrement ps  TerpreT benchmark #4: controlled shift  cshift :: (Bool,Bool,Bool) -> (Bool,Bool,Bool) -- testing 4 combinations of argument values--- pruning with 41/51 rules+-- pruning with 37/47 rules -- reasoning produced 2 incorrect properties, please re-run with more tests for faster results -- 1 candidates of size 1 -- 0 candidates of size 2 -- 0 candidates of size 3--- 10 candidates of size 4--- 0 candidates of size 5--- 0 candidates of size 6--- 40 candidates of size 7--- 0 candidates of size 8--- 0 candidates of size 9--- 360 candidates of size 10--- 4 candidates of size 11--- tested 412 candidates-cshift (p,q,r)  =  if p-                   then (p,r,q)-                   else (p,q,r)+-- 12 candidates of size 4+-- 125 candidates of size 5+-- 225 candidates of size 6+-- 665 candidates of size 7+-- 1242 candidates of size 8+-- 3087 candidates of size 9+-- 9281 candidates of size 10+-- 180325 candidates of size 11+-- tested 40096 candidates+cshift (p,q,r)+  | p  =  (p,r,q)+  | otherwise  =  (p,q,r)  cshift :: Bool -> Bool -> Bool -> (Bool,Bool,Bool) -- testing 4 combinations of argument values--- pruning with 41/51 rules+-- pruning with 37/47 rules -- reasoning produced 2 incorrect properties, please re-run with more tests for faster results -- 0 candidates of size 1 -- 0 candidates of size 2@@ -84,16 +87,16 @@  fadder :: Bool -> Bool -> Bool -> (Bool,Bool) -- testing 8 combinations of argument values--- pruning with 18/22 rules+-- pruning with 72/90 rules -- 0 candidates of size 1 -- 0 candidates of size 2--- 9 candidates of size 3--- 18 candidates of size 4--- 27 candidates of size 5--- 36 candidates of size 6--- 45 candidates of size 7--- 271 candidates of size 8--- tested 406 candidates+-- 25 candidates of size 3+-- 60 candidates of size 4+-- 126 candidates of size 5+-- 348 candidates of size 6+-- 999 candidates of size 7+-- 7009 candidates of size 8+-- tested 8567 candidates fadder False False False  =  (False,False) fadder False False True  =  (False,True) fadder False True False  =  (False,True)@@ -107,15 +110,15 @@  adder2 :: (Bool,Bool) -> (Bool,Bool) -> (Bool,Bool,Bool) -- testing 5 combinations of argument values--- pruning with 74/92 rules+-- pruning with 70/88 rules -- reasoning produced 2 incorrect properties, please re-run with more tests for faster results -- 0 candidates of size 1 -- 0 candidates of size 2 -- 0 candidates of size 3 -- 8 candidates of size 4--- 0 candidates of size 5--- 0 candidates of size 6--- tested 8 candidates+-- 128 candidates of size 5+-- 408 candidates of size 6+-- tested 544 candidates adder2  =  undefined  -- search exhausted  TerpreT benchmark #7: access@@ -153,10 +156,10 @@ -- 0 candidates of size 2 -- 2 candidates of size 3 -- 1 candidates of size 4--- 6 candidates of size 5+-- 4 candidates of size 5 -- 6 candidates of size 6--- 19 candidates of size 7--- tested 19 candidates+-- 10 candidates of size 7+-- tested 25 candidates decrelements []  =  [] decrelements (x:xs)  =  x - 1:decrelements xs
bench/unique.hs view
@@ -64,43 +64,43 @@   let n = 5    printUniqueCandidates (n+2) "foo" (undefined :: Int -> Int)-    [ unfun (0 :: Int)-    , unfun (1 :: Int)+    [ con (0 :: Int)+    , con (1 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "*" ((*) :: Int -> Int -> Int)     , fun "-" ((-) :: Int -> Int -> Int)     ]    printUniqueCandidates n "?" (undefined :: Int -> Int -> Int)-    [ unfun (0 :: Int)+    [ con (0 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "*" ((*) :: Int -> Int -> Int)     , fun "dec" (subtract 1 :: Int -> Int)     ]    printUniqueCandidates (n+2) "goo" (undefined :: [Int] -> [Int])-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "++" ((++) :: [Int] -> [Int] -> [Int])     ]    printUniqueCandidates n "??" (undefined :: [Int] -> [Int] -> [Int])-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "++" ((++) :: [Int] -> [Int] -> [Int])     ]    printUniqueCandidates (n+2) "ton" (undefined :: Bool -> Bool)-    [ unfun False-    , unfun True+    [ con False+    , con True     , fun "&&" (&&)     , fun "||" (||)     , fun "not" not     ]    printUniqueCandidates n "&|" (undefined :: Bool -> Bool -> Bool)-    [ unfun False-    , unfun True+    [ con False+    , con True     , fun "&&" (&&)     , fun "||" (||)     , fun "not" not
bench/unique.txt view
@@ -142,8 +142,6 @@ foo 1  =  1 foo x  =  0 -foo x  =  x * x - 1- foo x  =  x + (x + x)  foo x  =  x + (x + 1)@@ -178,6 +176,8 @@  foo x  =  1 - x * x +foo x  =  x * x - 1+ foo 1  =  0 foo x  =  x + x @@ -206,9 +206,6 @@ foo x  =  1 - x  foo 0  =  0-foo x  =  x * x - 1--foo 0  =  0 foo x  =  x + (x + 1)  foo 0  =  0@@ -235,7 +232,7 @@ foo 0  =  0 foo x  =  1 - x * x -foo 0  =  1+foo 0  =  0 foo x  =  x * x - 1  foo 0  =  1@@ -277,6 +274,9 @@ foo 0  =  1 foo x  =  0 - (x + 1) +foo 0  =  1+foo x  =  x * x - 1+ foo 0  =  0 foo 1  =  0 foo x  =  x + 1@@ -317,63 +317,6 @@ foo 1  =  1 foo x  =  0 - x -foo 0  =  0-foo x  =  x + foo (x - 1)--foo 0  =  0-foo x  =  foo (x - 1) + 1--foo 0  =  0-foo x  =  x * foo (x - 1)--foo 0  =  0-foo x  =  x - foo (x - 1)--foo 0  =  0-foo x  =  foo (x - 1) - x--foo 0  =  0-foo x  =  foo (x - 1) - 1--foo 0  =  0-foo x  =  1 - foo (x - 1)--foo 0  =  1-foo x  =  x + foo (x - 1)--foo 0  =  1-foo x  =  foo (x - 1) + 1--foo 0  =  1-foo x  =  x * foo (x - 1)--foo 0  =  1-foo x  =  x - foo (x - 1)--foo 0  =  1-foo x  =  foo (x - 1) - x--foo 0  =  1-foo x  =  foo (x - 1) - 1--foo 0  =  1-foo x  =  0 - foo (x - 1)--foo 0  =  1-foo x  =  1 - foo (x - 1)--foo x  =  x * (x + x) - 1--foo x  =  x * (x * x) - 1--foo x  =  x * (x - 1) - 1--foo x  =  x * (0 - x) - 1--foo x  =  x * (1 - x) - 1--foo x  =  x + (x * x - 1)- foo x  =  x + (x + (x + x))  foo x  =  x + (x + (x + 1))@@ -396,6 +339,8 @@  foo x  =  x + (1 - x * x) +foo x  =  x + (x * x - 1)+ foo x  =  1 + (1 + (x + 1))  foo x  =  1 + (1 + x * x)@@ -412,8 +357,6 @@  foo x  =  1 + (1 - x * x) -foo x  =  x * (x * x - 1)- foo x  =  x * (x + (x + x))  foo x  =  x * (x + x * x)@@ -438,8 +381,12 @@  foo x  =  x * (1 - x * x) +foo x  =  x * (x * x - 1)+ foo x  =  x - (1 + (x + 1)) +foo x  =  x - (1 + x * x)+ foo x  =  x - (1 + (1 - x))  foo x  =  0 - (x + (x + x))@@ -448,6 +395,8 @@  foo x  =  0 - (1 + (x + 1)) +foo x  =  0 - (1 + x * x)+ foo x  =  0 - (1 + (1 - x))  foo x  =  1 - (x + (x + x))@@ -464,6 +413,12 @@  foo x  =  x * x - (x + x) +foo x  =  x * x - (x + 1)++foo x  =  x * (x + x) - 1++foo x  =  x * (x * x) - 1+ foo 1  =  0 foo x  =  x + (x + x) @@ -507,9 +462,6 @@ foo x  =  1 - (x + x)  foo 1  =  1-foo x  =  x * x - 1--foo 1  =  1 foo x  =  x + (x + x)  foo 1  =  1@@ -551,7 +503,55 @@ foo 1  =  1 foo x  =  1 - x * x +foo 1  =  1+foo x  =  x * x - 1 +foo 0  =  0+foo x  =  x + foo (x - 1)++foo 0  =  0+foo x  =  foo (x - 1) + 1++foo 0  =  0+foo x  =  x * foo (x - 1)++foo 0  =  0+foo x  =  x - foo (x - 1)++foo 0  =  0+foo x  =  foo (x - 1) - x++foo 0  =  0+foo x  =  foo (x - 1) - 1++foo 0  =  0+foo x  =  1 - foo (x - 1)++foo 0  =  1+foo x  =  x + foo (x - 1)++foo 0  =  1+foo x  =  foo (x - 1) + 1++foo 0  =  1+foo x  =  x * foo (x - 1)++foo 0  =  1+foo x  =  x - foo (x - 1)++foo 0  =  1+foo x  =  foo (x - 1) - x++foo 0  =  1+foo x  =  foo (x - 1) - 1++foo 0  =  1+foo x  =  0 - foo (x - 1)++foo 0  =  1+foo x  =  1 - foo (x - 1)++ Unique candidates for: ? :: Int -> Int -> Int   pruning with 13/34 rules   [3,8,25,71,205] candidates@@ -624,6 +624,10 @@ 0 ? x  =  0 x ? y  =  y +x ? y  =  dec (dec x)++x ? y  =  dec (dec y)+ x ? y  =  x + x  x ? y  =  x + y@@ -636,10 +640,6 @@  x ? y  =  y * y -x ? y  =  dec (dec x)--x ? y  =  dec (dec y)- x ? 0  =  x x ? y  =  dec x @@ -694,16 +694,16 @@ x ? 0  =  x x ? y  =  y +x ? y  =  dec (dec (dec x))++x ? y  =  dec (dec (dec y))+ x ? y  =  dec (x * x)  x ? y  =  dec (x * y)  x ? y  =  dec (y * y) -x ? y  =  dec (dec (dec x))--x ? y  =  dec (dec (dec y))- x ? y  =  x + dec x  x ? y  =  x + dec y@@ -719,6 +719,12 @@ x ? y  =  y * dec y  x ? 0  =  x+x ? y  =  dec (dec x)++x ? 0  =  x+x ? y  =  dec (dec y)++x ? 0  =  x x ? y  =  x + x  x ? 0  =  x@@ -733,10 +739,10 @@ x ? 0  =  x x ? y  =  y * y -x ? 0  =  x+x ? 0  =  0 x ? y  =  dec (dec x) -x ? 0  =  x+x ? 0  =  0 x ? y  =  dec (dec y)  x ? 0  =  0@@ -748,15 +754,18 @@ x ? 0  =  0 x ? y  =  x * x -x ? 0  =  0-x ? y  =  dec (dec x)--x ? 0  =  0-x ? y  =  dec (dec y)- x ? 0  =  dec x x ? y  =  dec y +x ? 0  =  dec (dec x)+x ? y  =  x++x ? 0  =  dec (dec x)+x ? y  =  y++x ? 0  =  dec (dec x)+x ? y  =  0+ x ? 0  =  x + x x ? y  =  x @@ -775,14 +784,11 @@ x ? 0  =  x * x x ? y  =  0 -x ? 0  =  dec (dec x)-x ? y  =  x--x ? 0  =  dec (dec x)-x ? y  =  y+0 ? x  =  x+x ? y  =  dec (dec x) -x ? 0  =  dec (dec x)-x ? y  =  0+0 ? x  =  x+x ? y  =  dec (dec y)  0 ? x  =  x x ? y  =  x + x@@ -799,10 +805,10 @@ 0 ? x  =  x x ? y  =  y * y -0 ? x  =  x+0 ? x  =  0 x ? y  =  dec (dec x) -0 ? x  =  x+0 ? x  =  0 x ? y  =  dec (dec y)  0 ? x  =  0@@ -814,40 +820,34 @@ 0 ? x  =  0 x ? y  =  y * y -0 ? x  =  0-x ? y  =  dec (dec x)--0 ? x  =  0-x ? y  =  dec (dec y)- 0 ? x  =  dec x x ? y  =  dec x -0 ? x  =  x + x+0 ? x  =  dec (dec x) x ? y  =  x -0 ? x  =  x + x+0 ? x  =  dec (dec x) x ? y  =  y -0 ? x  =  x + x+0 ? x  =  dec (dec x) x ? y  =  0 -0 ? x  =  x * x+0 ? x  =  x + x x ? y  =  x -0 ? x  =  x * x+0 ? x  =  x + x x ? y  =  y -0 ? x  =  x * x+0 ? x  =  x + x x ? y  =  0 -0 ? x  =  dec (dec x)+0 ? x  =  x * x x ? y  =  x -0 ? x  =  dec (dec x)+0 ? x  =  x * x x ? y  =  y -0 ? x  =  dec (dec x)+0 ? x  =  x * x x ? y  =  0  0 ? x  =  x@@ -906,35 +906,9 @@ x ? 0  =  0 x ? y  =  x -x ? 0  =  x-x ? y  =  y ? dec x--x ? 0  =  x-x ? y  =  y ? dec y--x ? 0  =  x-x ? y  =  dec x ? x--x ? 0  =  x-x ? y  =  dec x ? y--x ? 0  =  x-x ? y  =  dec y ? x--0 ? x  =  x-x ? y  =  x ? dec y--0 ? x  =  x-x ? y  =  y ? dec x--0 ? x  =  x-x ? y  =  y ? dec y--0 ? x  =  x-x ? y  =  dec x ? x+x ? y  =  dec (dec (dec (dec x))) -0 ? x  =  x-x ? y  =  dec y ? x+x ? y  =  dec (dec (dec (dec y)))  x ? y  =  dec (dec (x * x)) @@ -942,10 +916,6 @@  x ? y  =  dec (dec (y * y)) -x ? y  =  dec (dec (dec (dec x)))--x ? y  =  dec (dec (dec (dec y)))- x ? y  =  dec (x * dec x)  x ? y  =  dec (x * dec y)@@ -954,6 +924,10 @@  x ? y  =  dec (y * dec y) +x ? y  =  x + dec (dec x)++x ? y  =  x + dec (dec y)+ x ? y  =  x + (x + x)  x ? y  =  x + (x + y)@@ -966,9 +940,7 @@  x ? y  =  x + y * y -x ? y  =  x + dec (dec x)--x ? y  =  x + dec (dec y)+x ? y  =  y + dec (dec y)  x ? y  =  y + (y + y) @@ -978,8 +950,10 @@  x ? y  =  y + y * y -x ? y  =  y + dec (dec y)+x ? y  =  x * dec (dec x) +x ? y  =  x * dec (dec y)+ x ? y  =  x * (x + x)  x ? y  =  x * (x + y)@@ -992,9 +966,9 @@  x ? y  =  x * (y * y) -x ? y  =  x * dec (dec x)+x ? y  =  y * dec (dec x) -x ? y  =  x * dec (dec y)+x ? y  =  y * dec (dec y)  x ? y  =  y * (x + y) @@ -1002,10 +976,6 @@  x ? y  =  y * (y * y) -x ? y  =  y * dec (dec x)--x ? y  =  y * dec (dec y)- x ? y  =  dec x * dec x  x ? y  =  dec x * dec y@@ -1013,19 +983,19 @@ x ? y  =  dec y * dec y  x ? 0  =  x-x ? y  =  dec (x * x)+x ? y  =  dec (dec (dec x))  x ? 0  =  x-x ? y  =  dec (x * y)+x ? y  =  dec (dec (dec y))  x ? 0  =  x-x ? y  =  dec (y * y)+x ? y  =  dec (x * x)  x ? 0  =  x-x ? y  =  dec (dec (dec x))+x ? y  =  dec (x * y)  x ? 0  =  x-x ? y  =  dec (dec (dec y))+x ? y  =  dec (y * y)  x ? 0  =  x x ? y  =  x + dec x@@ -1049,19 +1019,19 @@ x ? y  =  y * dec y  x ? 0  =  0-x ? y  =  dec (x * x)+x ? y  =  dec (dec (dec x))  x ? 0  =  0-x ? y  =  dec (x * y)+x ? y  =  dec (dec (dec y))  x ? 0  =  0-x ? y  =  dec (y * y)+x ? y  =  dec (x * x)  x ? 0  =  0-x ? y  =  dec (dec (dec x))+x ? y  =  dec (x * y)  x ? 0  =  0-x ? y  =  dec (dec (dec y))+x ? y  =  dec (y * y)  x ? 0  =  0 x ? y  =  x + dec x@@ -1079,6 +1049,12 @@ x ? y  =  x * dec y  x ? 0  =  dec x+x ? y  =  dec (dec x)++x ? 0  =  dec x+x ? y  =  dec (dec y)++x ? 0  =  dec x x ? y  =  x + x  x ? 0  =  dec x@@ -1096,11 +1072,11 @@ x ? 0  =  dec x x ? y  =  y * y -x ? 0  =  dec x-x ? y  =  dec (dec x)+x ? 0  =  dec (dec x)+x ? y  =  dec x -x ? 0  =  dec x-x ? y  =  dec (dec y)+x ? 0  =  dec (dec x)+x ? y  =  dec y  x ? 0  =  x + x x ? y  =  dec x@@ -1114,28 +1090,22 @@ x ? 0  =  x * x x ? y  =  dec y -x ? 0  =  dec (dec x)-x ? y  =  dec x--x ? 0  =  dec (dec x)-x ? y  =  dec y--x ? 0  =  dec (x * x)+x ? 0  =  dec (dec (dec x)) x ? y  =  x -x ? 0  =  dec (x * x)+x ? 0  =  dec (dec (dec x)) x ? y  =  y -x ? 0  =  dec (x * x)+x ? 0  =  dec (dec (dec x)) x ? y  =  0 -x ? 0  =  dec (dec (dec x))+x ? 0  =  dec (x * x) x ? y  =  x -x ? 0  =  dec (dec (dec x))+x ? 0  =  dec (x * x) x ? y  =  y -x ? 0  =  dec (dec (dec x))+x ? 0  =  dec (x * x) x ? y  =  0  x ? 0  =  x + dec x@@ -1157,19 +1127,19 @@ x ? y  =  0  0 ? x  =  x-x ? y  =  dec (x * x)+x ? y  =  dec (dec (dec x))  0 ? x  =  x-x ? y  =  dec (x * y)+x ? y  =  dec (dec (dec y))  0 ? x  =  x-x ? y  =  dec (y * y)+x ? y  =  dec (x * x)  0 ? x  =  x-x ? y  =  dec (dec (dec x))+x ? y  =  dec (x * y)  0 ? x  =  x-x ? y  =  dec (dec (dec y))+x ? y  =  dec (y * y)  0 ? x  =  x x ? y  =  x + dec x@@ -1193,19 +1163,19 @@ x ? y  =  y * dec y  0 ? x  =  0-x ? y  =  dec (x * x)+x ? y  =  dec (dec (dec x))  0 ? x  =  0-x ? y  =  dec (x * y)+x ? y  =  dec (dec (dec y))  0 ? x  =  0-x ? y  =  dec (y * y)+x ? y  =  dec (x * x)  0 ? x  =  0-x ? y  =  dec (dec (dec x))+x ? y  =  dec (x * y)  0 ? x  =  0-x ? y  =  dec (dec (dec y))+x ? y  =  dec (y * y)  0 ? x  =  0 x ? y  =  x + dec x@@ -1223,6 +1193,12 @@ x ? y  =  y * dec y  0 ? x  =  dec x+x ? y  =  dec (dec x)++0 ? x  =  dec x+x ? y  =  dec (dec y)++0 ? x  =  dec x x ? y  =  x + x  0 ? x  =  dec x@@ -1240,11 +1216,11 @@ 0 ? x  =  dec x x ? y  =  y * y -0 ? x  =  dec x-x ? y  =  dec (dec x)+0 ? x  =  dec (dec x)+x ? y  =  dec x -0 ? x  =  dec x-x ? y  =  dec (dec y)+0 ? x  =  dec (dec x)+x ? y  =  dec y  0 ? x  =  x + x x ? y  =  dec x@@ -1258,28 +1234,22 @@ 0 ? x  =  x * x x ? y  =  dec y -0 ? x  =  dec (dec x)-x ? y  =  dec x--0 ? x  =  dec (dec x)-x ? y  =  dec y--0 ? x  =  dec (x * x)+0 ? x  =  dec (dec (dec x)) x ? y  =  x -0 ? x  =  dec (x * x)+0 ? x  =  dec (dec (dec x)) x ? y  =  y -0 ? x  =  dec (x * x)+0 ? x  =  dec (dec (dec x)) x ? y  =  0 -0 ? x  =  dec (dec (dec x))+0 ? x  =  dec (x * x) x ? y  =  x -0 ? x  =  dec (dec (dec x))+0 ? x  =  dec (x * x) x ? y  =  y -0 ? x  =  dec (dec (dec x))+0 ? x  =  dec (x * x) x ? y  =  0  0 ? x  =  x + dec x@@ -1302,6 +1272,14 @@  0 ? x  =  x x ? 0  =  x+x ? y  =  dec (dec x)++0 ? x  =  x+x ? 0  =  x+x ? y  =  dec (dec y)++0 ? x  =  x+x ? 0  =  x x ? y  =  x + x  0 ? x  =  x@@ -1321,11 +1299,11 @@ x ? y  =  y * y  0 ? x  =  x-x ? 0  =  x+x ? 0  =  0 x ? y  =  dec (dec x)  0 ? x  =  x-x ? 0  =  x+x ? 0  =  0 x ? y  =  dec (dec y)  0 ? x  =  x@@ -1337,83 +1315,75 @@ x ? y  =  x * x  0 ? x  =  x-x ? 0  =  0-x ? y  =  dec (dec x)--0 ? x  =  x-x ? 0  =  0-x ? y  =  dec (dec y)--0 ? x  =  x x ? 0  =  dec x x ? y  =  dec y  0 ? x  =  x-x ? 0  =  x + x+x ? 0  =  dec (dec x) x ? y  =  x  0 ? x  =  x-x ? 0  =  x + x+x ? 0  =  dec (dec x) x ? y  =  0  0 ? x  =  x-x ? 0  =  x * x+x ? 0  =  x + x x ? y  =  x  0 ? x  =  x-x ? 0  =  x * x+x ? 0  =  x + x x ? y  =  0  0 ? x  =  x-x ? 0  =  dec (dec x)+x ? 0  =  x * x x ? y  =  x  0 ? x  =  x-x ? 0  =  dec (dec x)+x ? 0  =  x * x x ? y  =  0  0 ? x  =  0 x ? 0  =  x-x ? y  =  y + y+x ? y  =  dec (dec x)  0 ? x  =  0 x ? 0  =  x-x ? y  =  y * y+x ? y  =  dec (dec y)  0 ? x  =  0 x ? 0  =  x-x ? y  =  dec (dec x)+x ? y  =  y + y  0 ? x  =  0 x ? 0  =  x-x ? y  =  dec (dec y)+x ? y  =  y * y  0 ? x  =  0 x ? 0  =  0-x ? y  =  x + y+x ? y  =  dec (dec x)  0 ? x  =  0 x ? 0  =  0-x ? y  =  dec (dec x)+x ? y  =  dec (dec y)  0 ? x  =  0 x ? 0  =  0-x ? y  =  dec (dec y)+x ? y  =  x + y  0 ? x  =  0 x ? 0  =  dec x x ? y  =  dec y  0 ? x  =  0-x ? 0  =  x + x+x ? 0  =  dec (dec x) x ? y  =  y  0 ? x  =  0-x ? 0  =  x * x+x ? 0  =  x + x x ? y  =  y  0 ? x  =  0-x ? 0  =  dec (dec x)+x ? 0  =  x * x x ? y  =  y  0 ? x  =  dec x@@ -1436,39 +1406,39 @@ x ? 0  =  dec x x ? y  =  0 -0 ? x  =  x + x+0 ? x  =  dec (dec x) x ? 0  =  x x ? y  =  y -0 ? x  =  x + x+0 ? x  =  dec (dec x) x ? 0  =  x x ? y  =  0 -0 ? x  =  x + x+0 ? x  =  dec (dec x) x ? 0  =  0 x ? y  =  x -0 ? x  =  x * x+0 ? x  =  x + x x ? 0  =  x x ? y  =  y -0 ? x  =  x * x+0 ? x  =  x + x x ? 0  =  x x ? y  =  0 -0 ? x  =  x * x+0 ? x  =  x + x x ? 0  =  0 x ? y  =  x -0 ? x  =  dec (dec x)+0 ? x  =  x * x x ? 0  =  x x ? y  =  y -0 ? x  =  dec (dec x)+0 ? x  =  x * x x ? 0  =  x x ? y  =  0 -0 ? x  =  dec (dec x)+0 ? x  =  x * x x ? 0  =  0 x ? y  =  x @@ -1476,7 +1446,37 @@ 0 ? x  =  dec x x ? y  =  dec x +x ? 0  =  x+x ? y  =  y ? dec x +x ? 0  =  x+x ? y  =  y ? dec y++x ? 0  =  x+x ? y  =  dec x ? x++x ? 0  =  x+x ? y  =  dec x ? y++x ? 0  =  x+x ? y  =  dec y ? x++0 ? x  =  x+x ? y  =  x ? dec y++0 ? x  =  x+x ? y  =  y ? dec x++0 ? x  =  x+x ? y  =  y ? dec y++0 ? x  =  x+x ? y  =  dec x ? x++0 ? x  =  x+x ? y  =  dec y ? x++ Unique candidates for: goo :: [Int] -> [Int]   pruning with 4/4 rules   [2,1,1,2,4,7,10] candidates@@ -1505,14 +1505,14 @@ goo []  =  [] goo (x:xs)  =  xs ++ xs +goo xs  =  xs ++ (xs ++ xs)+ goo []  =  [] goo (x:xs)  =  xs ++ goo xs  goo []  =  [] goo (x:xs)  =  goo xs ++ xs -goo xs  =  xs ++ (xs ++ xs)- goo []  =  [] goo (x:xs)  =  x:x:xs @@ -1531,6 +1531,8 @@ goo []  =  [] goo (x:xs)  =  xs ++ (xs ++ xs) +goo xs  =  xs ++ (xs ++ (xs ++ xs))+ goo []  =  [] goo (x:xs)  =  x:x:goo xs @@ -1558,9 +1560,7 @@ goo []  =  [] goo (x:xs)  =  goo xs ++ (xs ++ xs) -goo xs  =  xs ++ (xs ++ (xs ++ xs)) - Unique candidates for: ?? :: [Int] -> [Int] -> [Int]   pruning with 4/4 rules   [3,8,15,43,122] candidates@@ -1657,12 +1657,6 @@ (x:xs) ?? ys  =  []  xs ?? []  =  xs-xs ?? (x:ys)  =  ys ?? xs--[] ?? xs  =  xs-(x:xs) ?? ys  =  ys ?? xs--xs ?? []  =  xs xs ?? (x:ys)  =  x:xs  xs ?? []  =  xs@@ -1763,62 +1757,12 @@ (x:xs) ?? []  =  xs (x:xs) ?? (y:ys)  =  [] -[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  xs ?? []--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ?? xs--[] ?? xs  =  xs-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ?? []--[] ?? xs  =  xs-(x:xs) ?? []  =  xs ?? xs-(x:xs) ?? (y:ys)  =  xs--[] ?? xs  =  xs-(x:xs) ?? []  =  xs ?? xs-(x:xs) ?? (y:ys)  =  ys--[] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  xs ?? ys+xs ?? []  =  xs+xs ?? (x:ys)  =  ys ?? xs  [] ?? xs  =  xs-(x:xs) ?? []  =  []-(x:xs) ?? (y:ys)  =  ys ?? xs--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  xs ?? ys--[] ?? xs  =  []-(x:xs) ?? []  =  xs-(x:xs) ?? (y:ys)  =  ys ?? xs--[] ?? xs  =  []-(x:xs) ?? []  =  xs ?? xs-(x:xs) ?? (y:ys)  =  xs--[] ?? xs  =  []-(x:xs) ?? []  =  xs ?? xs-(x:xs) ?? (y:ys)  =  ys--[] ?? []  =  []-[] ?? (x:xs)  =  xs (x:xs) ?? ys  =  ys ?? xs -[] ?? []  =  []-[] ?? (x:xs)  =  xs-(x:xs) ?? ys  =  [] ?? xs--[] ?? []  =  []-[] ?? (x:xs)  =  xs ?? xs-(x:xs) ?? ys  =  xs- xs ?? ys  =  xs ++ (xs ++ xs)  xs ?? ys  =  xs ++ (xs ++ ys)@@ -2102,6 +2046,62 @@ [] ?? []  =  [] [] ?? (x:xs)  =  xs ++ xs (x:xs) ?? ys  =  []++[] ?? xs  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  xs ?? []++[] ?? xs  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  ys ?? xs++[] ?? xs  =  xs+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  ys ?? []++[] ?? xs  =  xs+(x:xs) ?? []  =  xs ?? xs+(x:xs) ?? (y:ys)  =  xs++[] ?? xs  =  xs+(x:xs) ?? []  =  xs ?? xs+(x:xs) ?? (y:ys)  =  ys++[] ?? xs  =  xs+(x:xs) ?? []  =  []+(x:xs) ?? (y:ys)  =  xs ?? ys++[] ?? xs  =  xs+(x:xs) ?? []  =  []+(x:xs) ?? (y:ys)  =  ys ?? xs++[] ?? xs  =  []+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  xs ?? ys++[] ?? xs  =  []+(x:xs) ?? []  =  xs+(x:xs) ?? (y:ys)  =  ys ?? xs++[] ?? xs  =  []+(x:xs) ?? []  =  xs ?? xs+(x:xs) ?? (y:ys)  =  xs++[] ?? xs  =  []+(x:xs) ?? []  =  xs ?? xs+(x:xs) ?? (y:ys)  =  ys++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? ys  =  ys ?? xs++[] ?? []  =  []+[] ?? (x:xs)  =  xs+(x:xs) ?? ys  =  [] ?? xs++[] ?? []  =  []+[] ?? (x:xs)  =  xs ?? xs+(x:xs) ?? ys  =  xs   Unique candidates for: ton :: Bool -> Bool
bench/weird.hs view
@@ -19,8 +19,19 @@ x ^^^ 0  =  x _ ^^^ _  =  0 +-- | inc or square based on boolean argument+--   except for 0 where the answer is swapped+isq :: Bool -> Int -> Int+isq False 0  =  0+isq True  0  =  1+isq False x  =  x + 1+isq True  x  =  x * x+ main :: IO () main  =  do+  -- TODO: Conjure should find isq, but doesn't due to overpruning+  conjure "isq" isq ingredients+   conjure "^^^" (^^^)   ingredients   conjure "^^^" (^^^) $ ingredients ++ [singlePattern] @@ -31,8 +42,8 @@  ingredients :: [Ingredient] ingredients  =-  [ unfun (0::Int)-  , unfun (1::Int)+  [ con (0::Int)+  , con (1::Int)   , fun "+" ((+) :: Int -> Int -> Int)   , fun "*" ((*) :: Int -> Int -> Int)   , fun "==" ((==) :: Int -> Int -> Bool)
bench/weird.txt view
@@ -1,10 +1,27 @@+isq :: Bool -> Int -> Int+-- testing 360 combinations of argument values+-- pruning with 56/91 rules+-- 3 candidates of size 1+-- 0 candidates of size 2+-- 3 candidates of size 3+-- 6 candidates of size 4+-- 8 candidates of size 5+-- 48 candidates of size 6+-- 63 candidates of size 7+-- 301 candidates of size 8+-- tested 432 candidates+isq False 0  =  0+isq False x  =  x + 1+isq True 0  =  1+isq True x  =  x * x+ (^^^) :: Int -> Int -> Int -- testing 360 combinations of argument values -- pruning with 56/91 rules -- 4 candidates of size 1--- 6 candidates of size 2--- 10 candidates of size 3--- tested 19 candidates+-- 0 candidates of size 2+-- 9 candidates of size 3+-- tested 13 candidates 0 ^^^ x  =  x x ^^^ 0  =  x x ^^^ y  =  0@@ -22,7 +39,7 @@ -- 996 candidates of size 8 -- 1266 candidates of size 9 -- 11700 candidates of size 10--- tested 6683 candidates+-- tested 11507 candidates x ^^^ y  =  if 0 == x * y             then x + y             else 0
changelog.md view
@@ -2,6 +2,19 @@ ============================  +v0.7.6 (August 2025)+--------------------++* Flip-flop: `con` replaces `unfun`.+* Allow chains of guards, or multiple guards.+* Replace `omitEarlyTests` by `maxEarlyTests`, defaulting to 12.+* Improve pruning through early tests.+* Fix `requireDescent` switch+* Fix overpruning in early tests.+* Refactor parts of `Engine.candidateDefnsC`.+* Cleanup built-in examples.++ v0.7.4 (May 2025) -----------------
code-conjure.cabal view
@@ -3,7 +3,7 @@ -- Copyright (C) 2021-2025 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). name:                code-conjure-version:             0.7.4+version:             0.7.6 synopsis:            synthesize Haskell functions out of partial definitions description:   Conjure is a tool that synthesizes Haskell functions out of partial definitions.@@ -58,7 +58,6 @@            , GHC==9.8            , GHC==9.6            , GHC==9.4-           , GHC==9.2            , GHC==9.0            , GHC==8.8 @@ -69,7 +68,7 @@ source-repository this   type:            git   location:        https://github.com/rudymatela/conjure-  tag:             v0.7.4+  tag:             v0.7.6  library   exposed-modules: Conjure
eg/arith.hs view
@@ -48,8 +48,8 @@  ingredients :: [Ingredient] ingredients =-  [ unfun (0::Int)-  , unfun (1::Int)+  [ con (0::Int)+  , con (1::Int)   , fun "+" ((+) :: Int -> Int -> Int)   , fun "*" ((*) :: Int -> Int -> Int)   ]
eg/arith.txt view
@@ -2,61 +2,61 @@ -- testing 4 combinations of argument values -- pruning with 14/25 rules -- 3 candidates of size 1--- 1 candidates of size 2--- 6 candidates of size 3--- tested 5 candidates+-- 0 candidates of size 2+-- 3 candidates of size 3+-- tested 4 candidates double x  =  x + x  triple :: Int -> Int -- testing 4 combinations of argument values -- pruning with 14/25 rules -- 3 candidates of size 1--- 1 candidates of size 2--- 6 candidates of size 3--- 2 candidates of size 4--- 11 candidates of size 5--- tested 13 candidates+-- 0 candidates of size 2+-- 3 candidates of size 3+-- 0 candidates of size 4+-- 8 candidates of size 5+-- tested 7 candidates triple x  =  x + (x + x)  add :: Int -> Int -> Int -- testing 4 combinations of argument values -- pruning with 14/25 rules -- 4 candidates of size 1--- 6 candidates of size 2--- 10 candidates of size 3--- tested 12 candidates+-- 0 candidates of size 2+-- 8 candidates of size 3+-- tested 6 candidates add x y  =  x + y  square :: Int -> Int -- testing 3 combinations of argument values -- pruning with 14/25 rules -- 3 candidates of size 1--- 1 candidates of size 2--- 4 candidates of size 3--- tested 7 candidates+-- 0 candidates of size 2+-- 3 candidates of size 3+-- tested 6 candidates square x  =  x * x  cube :: Int -> Int -- testing 3 combinations of argument values -- pruning with 14/25 rules -- 3 candidates of size 1--- 1 candidates of size 2--- 4 candidates of size 3--- 1 candidates of size 4--- 10 candidates of size 5--- tested 17 candidates+-- 0 candidates of size 2+-- 3 candidates of size 3+-- 0 candidates of size 4+-- 8 candidates of size 5+-- tested 14 candidates cube x  =  x * (x * x)  tnpo :: Int -> Int -- testing 3 combinations of argument values -- pruning with 14/25 rules -- 3 candidates of size 1--- 2 candidates of size 2--- 6 candidates of size 3--- 4 candidates of size 4--- 11 candidates of size 5--- 7 candidates of size 6--- 35 candidates of size 7--- tested 35 candidates+-- 0 candidates of size 2+-- 3 candidates of size 3+-- 0 candidates of size 4+-- 8 candidates of size 5+-- 0 candidates of size 6+-- 27 candidates of size 7+-- tested 16 candidates tnpo x  =  x + (x + (x + 1))
eg/bits.hs view
@@ -19,8 +19,8 @@ main :: IO () main  =  do   conjure "bitsum" bitsum-    [ unfun (0 :: Int)-    , unfun (1 :: Int)+    [ con (0 :: Int)+    , con (1 :: Int)     , fun "halve" ((`div` 2) :: Int -> Int)     , fun "parity" ((`mod` 2) :: Int -> Int)     , fun "+" ((+) :: Int -> Int -> Int)@@ -29,9 +29,9 @@   -- bitsum n  =  parity n + bitsum (halve n)    conjure "bitsum" bitsum-    [ unfun (0 :: Int)-    , unfun (1 :: Int)-    , unfun (2 :: Int)+    [ con (0 :: Int)+    , con (1 :: Int)+    , con (2 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "`div`" (div :: Int -> Int -> Int)     , fun "`mod`" (mod :: Int -> Int -> Int)
eg/bits.txt view
@@ -2,13 +2,13 @@ -- testing 8 combinations of argument values -- pruning with 21/25 rules -- 3 candidates of size 1--- 3 candidates of size 2--- 5 candidates of size 3--- 10 candidates of size 4--- 26 candidates of size 5--- 68 candidates of size 6--- 182 candidates of size 7--- tested 145 candidates+-- 2 candidates of size 2+-- 4 candidates of size 3+-- 8 candidates of size 4+-- 19 candidates of size 5+-- 56 candidates of size 6+-- 152 candidates of size 7+-- tested 216 candidates bitsum 0  =  0 bitsum x  =  parity x + bitsum (halve x) @@ -16,15 +16,15 @@ -- testing 8 combinations of argument values -- pruning with 27/32 rules -- 4 candidates of size 1--- 2 candidates of size 2--- 17 candidates of size 3--- 16 candidates of size 4--- 246 candidates of size 5--- 239 candidates of size 6--- 4504 candidates of size 7--- 4542 candidates of size 8--- 89215 candidates of size 9--- tested 10191 candidates+-- 0 candidates of size 2+-- 15 candidates of size 3+-- 0 candidates of size 4+-- 233 candidates of size 5+-- 0 candidates of size 6+-- 4297 candidates of size 7+-- 72 candidates of size 8+-- 85204 candidates of size 9+-- tested 88434 candidates bitsum 0  =  0 bitsum x  =  x `mod` 2 + bitsum (x `div` 2)
eg/bools.hs view
@@ -25,8 +25,8 @@  ingredients :: [Ingredient] ingredients =-  [ unfun False-  , unfun True+  [ con False+  , con True   , fun "not" not   , fun "||" (||)   , fun "&&" (&&)
eg/bools.txt view
@@ -5,8 +5,8 @@ -- 0 candidates of size 2 -- 0 candidates of size 3 -- 2 candidates of size 4--- 4 candidates of size 5--- tested 8 candidates+-- 2 candidates of size 5+-- tested 6 candidates and []  =  True and (p:ps)  =  p && and ps @@ -17,7 +17,7 @@ -- 0 candidates of size 2 -- 0 candidates of size 3 -- 2 candidates of size 4--- 4 candidates of size 5+-- 2 candidates of size 5 -- tested 5 candidates or []  =  False or (p:ps)  =  p || or ps@@ -29,7 +29,7 @@ -- 0 candidates of size 2 -- 0 candidates of size 3 -- 4 candidates of size 4--- tested 6 candidates+-- tested 4 candidates and  =  foldr (&&) True  or :: [Bool] -> Bool@@ -39,6 +39,6 @@ -- 0 candidates of size 2 -- 0 candidates of size 3 -- 4 candidates of size 4--- tested 5 candidates+-- tested 3 candidates or  =  foldr (||) False
eg/bst.hs view
@@ -123,7 +123,7 @@ main :: IO () main = do   conjure "mem" mem-    [ unfun False+    [ con False     , fun "||" (||)     , fun "==" ((==) :: Int -> Int -> Bool)     , fun "<" ((<) :: Int -> Int -> Bool)@@ -131,15 +131,15 @@     ]    conjure "mem" mem-    [ unfun False-    , unfun True+    [ con False+    , con True     , fun "`compare`" (compare :: Int -> Int -> Ordering)     , ordcase (undefined :: Bool)     ]    -- simply out of reach performance-wise (reaching 16 but need size 22)   conjure "insert" insert-    [ unfun Leaf+    [ con Leaf     , fun "Node" Node     , fun "unit" unit     , fun "`compare`" (compare :: Int -> Int -> Ordering)@@ -150,7 +150,7 @@   -- reachable in 15s, candidate #32878 at size 14.   -- increase target to 50400 to reach...   conjureFromSpec "before" beforeSpec-    [ unfun Leaf+    [ con Leaf     , fun "Node" Node     , fun "==" ((==) :: Int -> Int -> Bool)     , fun "<" ((<) :: Int -> Int -> Bool)@@ -161,7 +161,7 @@   -- reachable in 14s, candidate #32747 at size 14.   -- increase target to 50400 to reach...   conjureFromSpec "beyond" beyondSpec-    [ unfun Leaf+    [ con Leaf     , fun "Node" Node     , fun "==" ((==) :: Int -> Int -> Bool)     , fun "<=" ((<) :: Int -> Int -> Bool)@@ -172,7 +172,7 @@   -- with 15, this reaches the solution, using 12 for shorter runtime   -- using maxEquationSize = 7 reduces runtime from 13s to 11s   conjureFromSpec "before" beforeSpec-    [ unfun Leaf+    [ con Leaf     , fun "Node" Node     , fun "`compare`" (compare :: Int -> Int -> Ordering)     , ordcase (undefined :: Tree)@@ -183,7 +183,7 @@   -- with 15, this reaches the solution, using 12 for shorter runtime   -- using maxEquationSize = 7 reduces runtime from 13s to 11s   conjureFromSpec "beyond" beyondSpec-    [ unfun Leaf+    [ con Leaf     , fun "Node" Node     , fun "`compare`" (compare :: Int -> Int -> Ordering)     , ordcase (undefined :: Tree)@@ -193,7 +193,7 @@    -- reachable in 55s, candidate #173109 at size 13.   conjure "union" union-    [ unfun Leaf+    [ con Leaf     , fun "Node" Node     , fun "before" before     , fun "beyond" beyond
eg/bst.txt view
@@ -9,11 +9,11 @@ -- 0 candidates of size 6 -- 0 candidates of size 7 -- 24 candidates of size 8--- 72 candidates of size 9+-- 48 candidates of size 9 -- 0 candidates of size 10--- 240 candidates of size 11--- 96 candidates of size 12--- tested 362 candidates+-- 180 candidates of size 11+-- 80 candidates of size 12+-- tested 274 candidates mem x Leaf  =  False mem x (Node t1 y t2)  =  mem x t1 || (x == y || mem x t2) @@ -29,10 +29,10 @@ -- 6 candidates of size 7 -- 0 candidates of size 8 -- 0 candidates of size 9--- 192 candidates of size 10+-- 32 candidates of size 10 -- 0 candidates of size 11--- 384 candidates of size 12--- tested 346 candidates+-- 160 candidates of size 12+-- tested 106 candidates mem x Leaf  =  False mem x (Node t1 y t2)  =  case x `compare` y of                          LT -> mem x t1@@ -51,10 +51,10 @@ -- 26 candidates of size 7 -- 0 candidates of size 8 -- 0 candidates of size 9--- 200 candidates of size 10+-- 176 candidates of size 10 -- 0 candidates of size 11 -- 32 candidates of size 12--- tested 264 candidates+-- tested 240 candidates insert  =  undefined  -- search exhausted  before :: Int -> Tree -> Tree@@ -132,10 +132,10 @@ -- 22 candidates of size 4 -- 0 candidates of size 5 -- 68 candidates of size 6--- 240 candidates of size 7+-- 152 candidates of size 7 -- 82 candidates of size 8--- 3018 candidates of size 9--- 8098 candidates of size 10--- tested 11531 candidates+-- 2438 candidates of size 9+-- 3970 candidates of size 10+-- tested 6735 candidates union  =  undefined  -- search exhausted
eg/colin/IntFuns.hs view
@@ -15,7 +15,7 @@ triIngredients :: [Ingredient] triIngredients =   [ fun "==" ((==) :: Int -> Int -> Bool)-  , unfun (1::Int)+  , con (1::Int)   , fun "+" ((+) :: Int -> Int -> Int)   , fun "dec" ((\x -> x-1) :: Int -> Int)   ]@@ -37,8 +37,8 @@ fibIngredients :: [Ingredient] fibIngredients =   [ fun "<=" ((<=) :: Int -> Int -> Bool)-  , unfun (0::Int)-  , unfun (1::Int)+  , con (0::Int)+  , con (1::Int)   , fun "+" ((+) :: Int -> Int -> Int)   , fun "dec" ((\x -> x-1) :: Int -> Int)   ]@@ -79,7 +79,7 @@   [ fun "==" ((==) :: [Int] -> [Int] -> Bool)   , fun "factors" ((\n -> filter (\k -> n `mod` k == 0) [1..n]) :: Int -> [Int])   , fun "list2" ((\i j -> [i,j]) :: Int -> Int -> [Int])-  , unfun (1 :: Int)+  , con (1 :: Int)   ]  -- looking through 38 candidates, 100% match, 7/7 assignments
eg/colin/ListFuns.hs view
@@ -13,7 +13,7 @@  sumBackground :: [Ingredient] sumBackground =-  [ unfun (0::Int)+  [ con (0::Int)   , fun "+" ((+) :: Int -> Int -> Int)   ] @@ -44,7 +44,7 @@  memBackground :: [Ingredient] memBackground =-  [ unfun False+  [ con False   , fun "==" ((==) :: Int -> Int -> Bool)   , fun "&&" ((&&) :: Bool -> Bool -> Bool)   , fun "||" ((||) :: Bool -> Bool -> Bool)@@ -69,8 +69,8 @@  subBackground :: [Ingredient] subBackground  =-  [ unfun True-  , unfun False+  [ con True+  , con False   , fun ":" ((:) :: Int -> [Int] -> [Int])   , fun "==" ((==) :: Int -> Int -> Bool)   , iif (undefined :: Bool)@@ -112,9 +112,9 @@  takeBackground :: [Ingredient] takeBackground  =-  [ unfun (0 :: Int)-  , unfun (1 :: Int)-  , unfun ([] :: [A])+  [ con (0 :: Int)+  , con (1 :: Int)+  , con ([] :: [A])   , fun "-" ((-) :: Int -> Int -> Int)   , fun ":" ((:) :: A -> [A] -> [A])   ]@@ -134,9 +134,9 @@  dropBackground :: [Ingredient] dropBackground  =-  [ unfun (0 :: Int)-  , unfun (1 :: Int)-  , unfun ([] :: [A])+  [ con (0 :: Int)+  , con (1 :: Int)+  , con ([] :: [A])   , fun "-" ((-) :: Int -> Int -> Int)   ] @@ -155,7 +155,7 @@  ordBackground :: [Ingredient] ordBackground  =-  [ unfun True+  [ con True   , fun "null" (null :: [Int] -> Bool)   , fun "head" (head :: [Int] -> Int)   , fun "<=" ((<=) :: Int -> Int -> Bool)@@ -179,7 +179,7 @@ mergeBackground :: [Ingredient] mergeBackground  =   [ fun "<=" ((<=) :: Int -> Int -> Bool)-  , unfun ([] :: [Int])+  , con ([] :: [Int])   , fun ":" ((:) :: Int -> [Int] -> [Int])   , iif (undefined :: [Int])   ]@@ -197,7 +197,7 @@  zipBackground :: [Ingredient] zipBackground  =-  [ unfun ([] :: [(A,B)])+  [ con ([] :: [(A,B)])   , fun "(,)" ((,) :: A -> B -> (A,B))   , fun ":" ((:) :: (A,B) -> [(A,B)] -> [(A,B)])   ]@@ -214,7 +214,7 @@  assocsBackground :: [Ingredient] assocsBackground  =-  [ unfun ([] :: [A])+  [ con ([] :: [A])   , fun "==" ((==) :: Int -> Int -> Bool)   , fun ":" ((:) :: A -> [A] -> [A])   , fun "fst" (fst :: (Int,A) -> Int)
+ eg/conditionals.hs view
@@ -0,0 +1,105 @@+-- conditionals.hs: assorted functions involving conditionals+--+-- Copyright (C) 2021-2025 Rudy Matela+-- Distributed under the 3-Clause BSD licence (see the file LICENSE).+import Conjure++negate' :: Int -> Int+negate' 1  =  -1+negate' 2  =  -2+negate' (-1)  =   1+negate' (-2)  =   2++abs' :: Int -> Int+abs' 1  =  1+abs' 2  =  2+abs' (-1)  =  1+abs' (-2)  =  2++signum' :: Int -> Int+signum' 0  =  0+signum' 1  =  1+signum' 2  =  1+signum' 3  =  1+signum' (-1)  =  -1+signum' (-2)  =  -1+signum' (-3)  =  -1++compare' :: Int -> Int -> Ordering+compare' 0 0  =  EQ+compare' 1 1  =  EQ+compare' 2 2  =  EQ+compare' 0 1  =  LT+compare' 1 2  =  LT+compare' 1 0  =  GT+compare' 2 1  =  GT+compare' (-1) 0  =  LT+compare' 0 (-1)  =  GT++min' :: Int -> Int -> Int -> Int+min' 0 1 2  =  0+min' 0 2 1  =  0+min' 2 3 1  =  1+min' 1 0 2  =  0+min' 4 3 1  =  1+min' 4 1 3  =  1++max' :: Int -> Int -> Int -> Int+max' 0 1 2  =  2+max' 0 2 1  =  2+max' 2 3 1  =  3+max' 1 0 2  =  2+max' 4 3 1  =  4+max' 4 1 3  =  4++median' :: Int -> Int -> Int -> Int+median' 0 1 2  =  1+median' 0 2 1  =  1+median' 2 3 1  =  2+median' 1 0 2  =  1+median' 4 3 1  =  3+median' 4 1 3  =  3++main :: IO ()+main = do+  conjure "negate"  negate' ingredients+  conjure "abs"     abs'    ingredients+  conjure "signum"  signum' ingredients+  conjure "compare" compare' compareIngredients++  conjure "min" min' mmmIngredients+  conjure "max" max' mmmIngredients+  -- median is unreachable performance-wise with ifs+  -- conjure "median" median' mmmIngredients+  -- it is reachale with max and min on the background though...+  -- (cf. bench/gps, #27 Median)++ingredients :: [Ingredient]+ingredients  =+  [ con (0::Int)+  , con (1::Int)+  , con (-1::Int)+  , fun "+" ((+) :: Int -> Int -> Int)+  , fun "-" ((-) :: Int -> Int -> Int)+  , fun "*" ((*) :: Int -> Int -> Int)+  , fun "<"  ((<)  :: Int -> Int -> Bool)+  , guard+  ]++compareIngredients :: [Ingredient]+compareIngredients  =+  [ con EQ+  , con LT+  , con GT+  , fun "==" ((==) :: Int -> Int -> Bool)+  , fun "<"  ((<)  :: Int -> Int -> Bool)+--, fun "<=" ((<=) :: Int -> Int -> Bool)+  , guard+  ]++mmmIngredients :: [Ingredient]+mmmIngredients  =+  [ fun "<=" ((<=) :: Int -> Int -> Bool)+  , iif (undefined :: Int)+  , target 50400+  ]
+ eg/conditionals.txt view
@@ -0,0 +1,109 @@+negate :: Int -> Int+-- testing 4 combinations of argument values+-- pruning with 64/99 rules+-- 4 candidates of size 1+-- 0 candidates of size 2+-- 5 candidates of size 3+-- tested 8 candidates+negate x  =  0 - x++abs :: Int -> Int+-- testing 4 combinations of argument values+-- pruning with 64/99 rules+-- 4 candidates of size 1+-- 0 candidates of size 2+-- 5 candidates of size 3+-- 0 candidates of size 4+-- 19 candidates of size 5+-- 48 candidates of size 6+-- 109 candidates of size 7+-- 253 candidates of size 8+-- tested 249 candidates+abs x+  | 0 < x  =  x+  | otherwise  =  0 - x++signum :: Int -> Int+-- testing 7 combinations of argument values+-- pruning with 64/99 rules+-- 4 candidates of size 1+-- 0 candidates of size 2+-- 5 candidates of size 3+-- 0 candidates of size 4+-- 19 candidates of size 5+-- 48 candidates of size 6+-- 97 candidates of size 7+-- tested 163 candidates+signum 0  =  0+signum x+  | x < 0  =  -1+  | otherwise  =  1++compare :: Int -> Int -> Ordering+-- testing 9 combinations of argument values+-- pruning with 5/6 rules+-- 3 candidates of size 1+-- 0 candidates of size 2+-- 0 candidates of size 3+-- 0 candidates of size 4+-- 0 candidates of size 5+-- 18 candidates of size 6+-- 0 candidates of size 7+-- 0 candidates of size 8+-- 0 candidates of size 9+-- 0 candidates of size 10+-- 162 candidates of size 11+-- tested 31 candidates+compare x y+  | x == y  =  EQ+  | x < y  =  LT+  | otherwise  =  GT++min :: Int -> Int -> Int -> Int+-- testing 6 combinations of argument values+-- pruning with 4/4 rules+-- 3 candidates of size 1+-- 0 candidates of size 2+-- 0 candidates of size 3+-- 0 candidates of size 4+-- 0 candidates of size 5+-- 36 candidates of size 6+-- 0 candidates of size 7+-- 0 candidates of size 8+-- 0 candidates of size 9+-- 0 candidates of size 10+-- 2592 candidates of size 11+-- 0 candidates of size 12+-- 0 candidates of size 13+-- 0 candidates of size 14+-- 0 candidates of size 15+-- 248400 candidates of size 16+-- tested 49553 candidates+min x y z  =  if x <= y+              then if x <= z then x else z+              else if y <= z then y else z++max :: Int -> Int -> Int -> Int+-- testing 6 combinations of argument values+-- pruning with 4/4 rules+-- 3 candidates of size 1+-- 0 candidates of size 2+-- 0 candidates of size 3+-- 0 candidates of size 4+-- 0 candidates of size 5+-- 36 candidates of size 6+-- 0 candidates of size 7+-- 0 candidates of size 8+-- 0 candidates of size 9+-- 0 candidates of size 10+-- 2592 candidates of size 11+-- 0 candidates of size 12+-- 0 candidates of size 13+-- 0 candidates of size 14+-- 0 candidates of size 15+-- 248400 candidates of size 16+-- tested 50103 candidates+max x y z  =  if x <= y+              then if y <= z then z else y+              else if x <= z then z else x+
eg/count.hs view
@@ -38,8 +38,8 @@   -- count x []  =  0   -- count x (y:xs)  =  count x xs + (if x == y then 1 else 0)   conjure "count" count'-    [ unfun (0 :: Int)-    , unfun (1 :: Int)+    [ con (0 :: Int)+    , con (1 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "==" ((==) :: A -> A -> Bool)     , iif (undefined :: Int)@@ -48,8 +48,8 @@   -- a little bit larger, guards are only allowed at the root   -- so there is a need to repeat the recursive call twice   conjure "count" count'-    [ unfun (0 :: Int)-    , unfun (1 :: Int)+    [ con (0 :: Int)+    , con (1 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "==" ((==) :: A -> A -> Bool)     , guard
eg/count.txt view
@@ -23,7 +23,7 @@ -- 16 candidates of size 9 -- 20 candidates of size 10 -- 44 candidates of size 11--- tested 65 candidates+-- tested 57 candidates count x []  =  0 count x (y:xs)  =  (if x == y then 1 else 0) + count x xs @@ -43,7 +43,7 @@ -- 20 candidates of size 11 -- 44 candidates of size 12 -- 64 candidates of size 13--- tested 127 candidates+-- tested 155 candidates count x []  =  0 count x (y:xs)   | x == y  =  1 + count x xs
+ eg/digits.hs view
@@ -0,0 +1,68 @@+-- digits.hs: functions over digits+--+-- Copyright (C) 2025 Rudy Matela+-- Distributed under the 3-Clause BSD licence (see the file LICENSE).+import Conjure++-- decimal digit sum+digitSum :: Int -> Int+digitSum 0  =  0+digitSum 12  =  3+digitSum 42  =  6+digitSum 1337  =  14+digitSum 31337  =  17++digitCount :: Int -> Int -> Int+digitCount 2 42  =  2+digitCount 1 111  =  3+digitCount 4 144  =  144+digitCount 0 1080  =  2+digitCount 3 1337  =  2+digitCount 3 31337  =  3++digits :: Int -> [Int]+digits 12  =  [1,2]+digits 42  =  [4,2]+digits 1337  =  [1,3,3,7]+digits 31337  =  [3,1,3,3,7]++main :: IO ()+main  =  do+  conjure "revdigits" (reverse . digits)+    [ con ([] :: [Int])+    , fun ":" ((:) :: Int -> [Int] -> [Int])+    , fun "`div`" (div :: Int -> Int -> Int)+    , fun "`mod`" (mod :: Int -> Int -> Int)+    , con (0 :: Int)+    , con (10 :: Int)+    ]++  conjure "digits" digits+    [ con ([] :: [Int])+    , fun ":" ((:) :: Int -> [Int] -> [Int])+    , fun "++" ((++) :: [Int] -> [Int] -> [Int])+    , fun "`div`" (div :: Int -> Int -> Int)+    , fun "`mod`" (mod :: Int -> Int -> Int)+    , con (0 :: Int)+    , con (10 :: Int)+    ]++  conjure "digitSum" digitSum+    [ con (0 :: Int)+    , con (10 :: Int)+    , fun "+" ((+) :: Int -> Int -> Int)+    , fun "`div`" (div :: Int -> Int -> Int)+    , fun "`mod`" (mod :: Int -> Int -> Int)+    ]++  -- out-of-reach performance-wise+  conjure "digitCount" digitCount+    [ con (0 :: Int)+    , con (10 :: Int)+    , fun "+" ((+) :: Int -> Int -> Int)+    , fun "`div`" (div :: Int -> Int -> Int)+    , fun "`mod`" (mod :: Int -> Int -> Int)+    , fun "==" ((==) :: Int -> Int -> Bool)+    , guard+    , maxTests 1080+    ]
+ eg/digits.txt view
@@ -0,0 +1,64 @@+revdigits :: Int -> [Int]+-- testing 4 combinations of argument values+-- pruning with 9/9 rules+-- 1 candidates of size 1+-- 0 candidates of size 2+-- 3 candidates of size 3+-- 0 candidates of size 4+-- 24 candidates of size 5+-- 0 candidates of size 6+-- 287 candidates of size 7+-- 0 candidates of size 8+-- 4180 candidates of size 9+-- tested 4481 candidates+revdigits 0  =  []+revdigits x  =  x `mod` 10:revdigits (x `div` 10)++digits :: Int -> [Int]+-- testing 4 combinations of argument values+-- pruning with 13/13 rules+-- 1 candidates of size 1+-- 0 candidates of size 2+-- 3 candidates of size 3+-- 0 candidates of size 4+-- 24 candidates of size 5+-- 0 candidates of size 6+-- 287 candidates of size 7+-- 0 candidates of size 8+-- 4186 candidates of size 9+-- 18 candidates of size 10+-- 67104 candidates of size 11+-- tested 71513 candidates+digits 0  =  []+digits x  =  digits (x `div` 10) ++ [x `mod` 10]++digitSum :: Int -> Int+-- testing 5 combinations of argument values+-- pruning with 18/22 rules+-- 3 candidates of size 1+-- 0 candidates of size 2+-- 12 candidates of size 3+-- 0 candidates of size 4+-- 165 candidates of size 5+-- 0 candidates of size 6+-- 2680 candidates of size 7+-- 84 candidates of size 8+-- 46993 candidates of size 9+-- tested 49164 candidates+digitSum 0  =  0+digitSum x  =  x `mod` 10 + digitSum (x `div` 10)++digitCount :: Int -> Int -> Int+-- testing 3 combinations of argument values+-- pruning with 20/26 rules+-- reasoning produced 15 incorrect properties, please re-run with more tests for faster results+-- 4 candidates of size 1+-- 0 candidates of size 2+-- 29 candidates of size 3+-- 0 candidates of size 4+-- 545 candidates of size 5+-- 156 candidates of size 6+-- 12715 candidates of size 7+-- tested 13449 candidates+digitCount  =  undefined  -- search exhausted+
eg/dupos.hs view
@@ -52,7 +52,7 @@   --                       else duplicates xs                              -- 17   -- within reach performance wise.   conjure "duplicates" duplicates'-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun "not" not     , fun "&&" (&&)     , fun ":" ((:) :: Int -> [Int] -> [Int])@@ -61,7 +61,7 @@     ]    conjureFromSpec "duplicates" duplicatesSpec-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun "not" not     , fun "&&" (&&)     , fun ":" ((:) :: Int -> [Int] -> [Int])@@ -70,8 +70,8 @@     ]    conjure "positionsFrom" positionsFrom'-    [ unfun ([] :: [Int])-    , unfun (1 :: Int)+    [ con ([] :: [Int])+    , con (1 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "==" ((==) :: A -> A -> Bool)
eg/dupos.txt view
@@ -5,20 +5,20 @@ -- 0 candidates of size 2 -- 0 candidates of size 3 -- 0 candidates of size 4--- 1 candidates of size 5+-- 0 candidates of size 5 -- 0 candidates of size 6--- 1 candidates of size 7--- 6 candidates of size 8--- 5 candidates of size 9--- 16 candidates of size 10--- 11 candidates of size 11--- 26 candidates of size 12--- 23 candidates of size 13+-- 0 candidates of size 7+-- 2 candidates of size 8+-- 4 candidates of size 9+-- 8 candidates of size 10+-- 8 candidates of size 11+-- 14 candidates of size 12+-- 22 candidates of size 13 -- 52 candidates of size 14--- 49 candidates of size 15--- 78 candidates of size 16--- 75 candidates of size 17--- tested 271 candidates+-- 74 candidates of size 15+-- 120 candidates of size 16+-- 156 candidates of size 17+-- tested 461 candidates duplicates []  =  [] duplicates (x:xs)   | elem x xs && not (elem x (duplicates xs))  =  x:duplicates xs@@ -37,13 +37,13 @@ -- 13 candidates of size 9 -- 18 candidates of size 10 -- 21 candidates of size 11--- 28 candidates of size 12--- 39 candidates of size 13--- 54 candidates of size 14--- 67 candidates of size 15--- 80 candidates of size 16--- 99 candidates of size 17--- tested 340 candidates+-- 32 candidates of size 12+-- 57 candidates of size 13+-- 102 candidates of size 14+-- 159 candidates of size 15+-- 228 candidates of size 16+-- 331 candidates of size 17+-- tested 979 candidates duplicates []  =  [] duplicates (x:xs)   | elem x xs && not (elem x (duplicates xs))  =  x:duplicates xs@@ -58,13 +58,13 @@ -- 0 candidates of size 4 -- 7 candidates of size 5 -- 0 candidates of size 6--- 34 candidates of size 7+-- 26 candidates of size 7 -- 0 candidates of size 8--- 133 candidates of size 9--- 8 candidates of size 10--- 510 candidates of size 11--- 40 candidates of size 12--- 1943 candidates of size 13--- tested 2678 candidates+-- 97 candidates of size 9+-- 0 candidates of size 10+-- 362 candidates of size 11+-- 0 candidates of size 12+-- 1363 candidates of size 13+-- tested 1858 candidates positionsFrom  =  undefined  -- search exhausted
eg/either.hs view
@@ -59,9 +59,9 @@   [ fun "Left"  (Left :: A -> Either A A)   , fun "Right" (Right :: A -> Either A A) -  , unfun False-  , unfun True+  , con False+  , con True -  , unfun ([] :: [A])+  , con ([] :: [A])   , fun ":" ((:) :: A -> [A] -> [A])   ]
eg/factorial.hs view
@@ -15,8 +15,8 @@ main  =  do   -- explicit recursion   conjure "factorial n" factorial-    [ unfun (0::Int)-    , unfun (1::Int)+    [ con (0::Int)+    , con (1::Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "*" ((*) :: Int -> Int -> Int)     , fun "-" ((-) :: Int -> Int -> Int)@@ -27,8 +27,8 @@    -- using foldr and enumFromTo   conjure "factorial n" factorial-    [ unfun (0::Int)-    , unfun (1::Int)+    [ con (0::Int)+    , con (1::Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "*" ((*) :: Int -> Int -> Int)     , fun "-" ((-) :: Int -> Int -> Int)
eg/factorial.txt view
@@ -2,13 +2,13 @@ -- testing 4 combinations of argument values -- pruning with 27/65 rules -- 3 candidates of size 1--- 3 candidates of size 2--- 7 candidates of size 3--- 8 candidates of size 4--- 28 candidates of size 5--- 35 candidates of size 6--- 167 candidates of size 7--- tested 95 candidates+-- 0 candidates of size 2+-- 6 candidates of size 3+-- 0 candidates of size 4+-- 23 candidates of size 5+-- 0 candidates of size 6+-- 147 candidates of size 7+-- tested 173 candidates factorial 0  =  1 factorial x  =  x * factorial (x - 1) @@ -16,11 +16,11 @@ -- testing 4 combinations of argument values -- pruning with 32/72 rules -- 3 candidates of size 1--- 3 candidates of size 2--- 7 candidates of size 3--- 8 candidates of size 4--- 28 candidates of size 5--- 75 candidates of size 6--- tested 74 candidates+-- 0 candidates of size 2+-- 6 candidates of size 3+-- 0 candidates of size 4+-- 23 candidates of size 5+-- 40 candidates of size 6+-- tested 57 candidates factorial x  =  foldr (*) 1 [1..x]
eg/fib01.hs view
@@ -31,7 +31,7 @@   -- Found!  It takes about 12 seconds to run with maxSize=8   -- running with maxSize = 5 for faster runtime   conjure "fib01" fib01-    [ unfun (0::Int)+    [ con (0::Int)     , fun "dec" (subtract 1 :: Int -> Int)     , fun "+" ((+) :: Int -> Int -> Int)     , maxSize 5@@ -41,7 +41,7 @@   -- It takes about 27 seconds to run with maxSize=12   -- running with maxSize = 9 for faster runtime   conjure "fib01" fib01-    [ unfun (0::Int)+    [ con (0::Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "dec" (subtract 1 :: Int -> Int)     , fun "<=" ((<=) :: Int -> Int -> Bool)
eg/fib01.txt view
@@ -2,11 +2,11 @@ -- testing 8 combinations of argument values -- pruning with 6/10 rules -- 4 candidates of size 1--- 14 candidates of size 2--- 38 candidates of size 3--- 111 candidates of size 4--- 255 candidates of size 5--- tested 422 candidates+-- 3 candidates of size 2+-- 9 candidates of size 3+-- 9 candidates of size 4+-- 27 candidates of size 5+-- tested 52 candidates fib01  =  undefined  -- search exhausted  fib01 :: Int -> Int -> Int -> Int
eg/fibonacci.hs view
@@ -16,9 +16,9 @@ main :: IO () main  =  do   conjure "fibonacci n" fibonacci-    [ unfun (0::Int)-    , unfun (1::Int)-    , unfun (2::Int)+    [ con (0::Int)+    , con (1::Int)+    , con (2::Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "-" ((-) :: Int -> Int -> Int)     ]
eg/fibonacci.txt view
@@ -2,18 +2,18 @@ -- testing 7 combinations of argument values -- pruning with 21/44 rules -- 4 candidates of size 1--- 3 candidates of size 2--- 9 candidates of size 3--- 9 candidates of size 4--- 26 candidates of size 5--- 27 candidates of size 6--- 116 candidates of size 7--- 120 candidates of size 8--- 552 candidates of size 9--- 538 candidates of size 10--- 2661 candidates of size 11--- 2661 candidates of size 12--- tested 4133 candidates+-- 0 candidates of size 2+-- 7 candidates of size 3+-- 0 candidates of size 4+-- 18 candidates of size 5+-- 0 candidates of size 6+-- 94 candidates of size 7+-- 20 candidates of size 8+-- 466 candidates of size 9+-- 92 candidates of size 10+-- 2298 candidates of size 11+-- 542 candidates of size 12+-- tested 3531 candidates fibonacci 0  =  1 fibonacci 1  =  1 fibonacci x  =  fibonacci (x - 1) + fibonacci (x - 2)
eg/gcd.hs view
@@ -19,7 +19,7 @@  main :: IO () main = conjure "gcd a b" gcd'-  [ unfun (0::Int)+  [ con (0::Int)   , fun "`mod`" (mod :: Int -> Int -> Int)   ]   -- desired function:
eg/gcd.txt view
@@ -2,12 +2,12 @@ -- testing 11 combinations of argument values -- pruning with 0/0 rules -- 3 candidates of size 1--- 6 candidates of size 2--- 11 candidates of size 3--- 50 candidates of size 4--- 98 candidates of size 5--- 330 candidates of size 6--- tested 172 candidates+-- 0 candidates of size 2+-- 8 candidates of size 3+-- 0 candidates of size 4+-- 48 candidates of size 5+-- 28 candidates of size 6+-- tested 63 candidates gcd x 0  =  x gcd x y  =  gcd y (x `mod` y)
eg/higher.hs view
@@ -59,7 +59,7 @@  ingredients :: [Ingredient] ingredients  =-  [ unfun ([] :: [Int])+  [ con ([] :: [Int])   , fun ":" ((:) :: Int -> [Int] -> [Int])   , guard   ]
eg/higher.txt view
@@ -30,7 +30,7 @@ -- 2 candidates of size 5 -- 5 candidates of size 6 -- 7 candidates of size 7--- tested 13 candidates+-- tested 19 candidates map f []  =  [] map f (x:xs)  =  f x:map f xs @@ -43,9 +43,9 @@ -- 4 candidates of size 5 -- 23 candidates of size 6 -- 19 candidates of size 7--- tested 38 candidates+-- tested 43 candidates fold f x []  =  x-fold f x (y:xs)  =  fold f (f x y) xs+fold f x (y:xs)  =  f x (fold f y xs)  filter :: (Int -> Bool) -> [Int] -> [Int] -- pruning with 3/3 rules@@ -58,10 +58,10 @@ -- 0 candidates of size 7 -- 15 candidates of size 8 -- 0 candidates of size 9--- 21 candidates of size 10+-- 25 candidates of size 10 -- 0 candidates of size 11--- 33 candidates of size 12--- tested 47 candidates+-- 63 candidates of size 12+-- tested 113 candidates filter f []  =  [] filter f (x:xs)   | f x  =  x:filter f xs
eg/ints.hs view
@@ -39,15 +39,15 @@     ]    conjure "sum" sum-    [ unfun (0 :: Int)-    , unfun (1 :: Int)+    [ con (0 :: Int)+    , con (1 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "*" ((*) :: Int -> Int -> Int)     ]    conjure "product" product-    [ unfun (0 :: Int)-    , unfun (1 :: Int)+    [ con (0 :: Int)+    , con (1 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "*" ((*) :: Int -> Int -> Int)     ]@@ -57,8 +57,8 @@  ingredients :: [Ingredient] ingredients =-  [ unfun (0 :: Int)-  , unfun (1 :: Int)+  [ con (0 :: Int)+  , con (1 :: Int)   , fun "+" ((+) :: Int -> Int -> Int)   , fun "*" ((*) :: Int -> Int -> Int)   ]
eg/list.hs view
@@ -56,30 +56,30 @@ main :: IO () main = do   conjure "length" length'-    [ unfun (0 :: Int)-    , unfun (1 :: Int)+    [ con (0 :: Int)+    , con (1 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     ]    conjure "reverse" reverse'-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "++" ((++) :: [Int] -> [Int] -> [Int])     ]    conjure "++" (+++)-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     ]    conjure "++" (+++)-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "foldr" (foldr :: (Int -> [Int] -> [Int]) -> [Int] -> [Int] -> [Int])     ]    conjure "last" last'-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "null" (null :: [Int] -> Bool)     , guard@@ -87,26 +87,26 @@     ]    conjure "last" last'-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "undefined" (undefined :: Int)     , maxPatternDepth 2     ]    conjure "zip" (zip')-    [ unfun ([] :: [(Int,Int)])+    [ con ([] :: [(Int,Int)])     , fun ":" ((:) :: (Int,Int) -> [(Int,Int)] -> [(Int,Int)])     , fun "," ((,) :: Int -> Int -> (Int,Int))     ]    conjure "\\/" (\/)-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     ]    conjure "ordered" ordered'-    [ unfun False-    , unfun True+    [ con False+    , con True     , fun "&&" (&&)     , fun "||" (||)     , fun "<=" ((<=) :: Int -> Int -> Bool)
eg/list.txt view
@@ -17,10 +17,10 @@ -- 0 candidates of size 2 -- 1 candidates of size 3 -- 0 candidates of size 4--- 4 candidates of size 5+-- 2 candidates of size 5 -- 1 candidates of size 6--- 10 candidates of size 7--- tested 16 candidates+-- 4 candidates of size 7+-- tested 9 candidates reverse []  =  [] reverse (x:xs)  =  reverse xs ++ [x] @@ -32,8 +32,8 @@ -- 0 candidates of size 3 -- 10 candidates of size 4 -- 25 candidates of size 5--- 34 candidates of size 6--- tested 56 candidates+-- 24 candidates of size 6+-- tested 40 candidates [] ++ xs  =  xs (x:xs) ++ ys  =  x:(xs ++ ys) @@ -44,7 +44,7 @@ -- 0 candidates of size 2 -- 0 candidates of size 3 -- 14 candidates of size 4--- tested 16 candidates+-- tested 6 candidates xs ++ ys  =  foldr (:) ys xs  last :: [Int] -> Int@@ -72,7 +72,7 @@ -- 1 candidates of size 4 -- 2 candidates of size 5 -- 2 candidates of size 6--- tested 5 candidates+-- tested 6 candidates last []  =  undefined last [x]  =  x last (x:y:xs)  =  last (y:xs)@@ -87,9 +87,9 @@ -- 0 candidates of size 5 -- 0 candidates of size 6 -- 0 candidates of size 7--- 6 candidates of size 8--- 23 candidates of size 9--- tested 13 candidates+-- 0 candidates of size 8+-- 11 candidates of size 9+-- tested 3 candidates zip [] xs  =  [] zip (x:xs) []  =  [] zip (x:xs) (y:ys)  =  (x,y):zip xs ys@@ -102,8 +102,8 @@ -- 0 candidates of size 3 -- 10 candidates of size 4 -- 25 candidates of size 5--- 34 candidates of size 6--- tested 58 candidates+-- 24 candidates of size 6+-- tested 42 candidates [] \/ xs  =  xs (x:xs) \/ ys  =  x:ys \/ xs @@ -119,9 +119,9 @@ -- 13 candidates of size 7 -- 17 candidates of size 8 -- 25 candidates of size 9--- 65 candidates of size 10--- 115 candidates of size 11--- tested 172 candidates+-- 55 candidates of size 10+-- 103 candidates of size 11+-- tested 168 candidates ordered []  =  True ordered (x:xs)  =  (null xs || x <= head xs) && ordered xs
eg/maybe.hs view
@@ -61,13 +61,13 @@  ingredients :: [Ingredient] ingredients  =-  [ unfun (Nothing :: Maybe A)+  [ con (Nothing :: Maybe A)   , fun "Just" (Just :: A -> Maybe A) -  , unfun False-  , unfun True+  , con False+  , con True -  , unfun ([] :: [A])+  , con ([] :: [A])   , fun ":" ((:) :: A -> [A] -> [A])   ]
eg/maybe.txt view
@@ -65,7 +65,7 @@ -- 0 candidates of size 5 -- 1 candidates of size 6 -- 2 candidates of size 7--- tested 3 candidates+-- tested 4 candidates catMaybes []  =  [] catMaybes (Nothing:mxs)  =  catMaybes mxs catMaybes (Just x:mxs)  =  x:catMaybes mxs
eg/oddeven.hs view
@@ -30,21 +30,21 @@  ingredients1 :: [Ingredient] ingredients1 =-  [ unfun (0::Int)-  , unfun (1::Int)-  , unfun (2::Int)+  [ con (0::Int)+  , con (1::Int)+  , con (2::Int)   , fun "+" ((+) :: Int -> Int -> Int)    , fun "-" ((-) :: Int -> Int -> Int)-  , unfun False-  , unfun True+  , con False+  , con True   ]  ingredients2 :: [Ingredient] ingredients2 =-  [ unfun (0::Int)-  , unfun (1::Int)-  , unfun (2::Int)+  [ con (0::Int)+  , con (1::Int)+  , con (2::Int)   , fun "+" ((+) :: Int -> Int -> Int)    , fun "`mod`" (mod :: Int -> Int -> Int)
eg/oddeven.txt view
@@ -2,13 +2,13 @@ -- testing 6 combinations of argument values -- pruning with 21/44 rules -- 2 candidates of size 1--- 1 candidates of size 2--- 1 candidates of size 3--- 1 candidates of size 4--- 1 candidates of size 5+-- 0 candidates of size 2+-- 0 candidates of size 3+-- 0 candidates of size 4+-- 0 candidates of size 5 -- 0 candidates of size 6 -- 2 candidates of size 7--- tested 8 candidates+-- tested 4 candidates odd 0  =  False odd 1  =  True odd x  =  odd (x - 2)@@ -17,13 +17,13 @@ -- testing 6 combinations of argument values -- pruning with 21/44 rules -- 2 candidates of size 1--- 1 candidates of size 2--- 1 candidates of size 3--- 1 candidates of size 4--- 1 candidates of size 5+-- 0 candidates of size 2+-- 0 candidates of size 3+-- 0 candidates of size 4+-- 0 candidates of size 5 -- 0 candidates of size 6 -- 2 candidates of size 7--- tested 8 candidates+-- tested 4 candidates even 0  =  True even 1  =  False even x  =  even (x - 2)@@ -34,9 +34,9 @@ -- 0 candidates of size 1 -- 0 candidates of size 2 -- 3 candidates of size 3--- 1 candidates of size 4--- 46 candidates of size 5--- tested 31 candidates+-- 0 candidates of size 4+-- 44 candidates of size 5+-- tested 30 candidates odd x  =  1 == x `mod` 2  even :: Int -> Bool@@ -45,8 +45,8 @@ -- 0 candidates of size 1 -- 0 candidates of size 2 -- 3 candidates of size 3--- 2 candidates of size 4--- 45 candidates of size 5--- tested 22 candidates+-- 0 candidates of size 4+-- 44 candidates of size 5+-- tested 20 candidates even x  =  0 == x `mod` 2
eg/peano.hs view
@@ -27,13 +27,13 @@ main :: IO () main  =  do   conjure "+" plus-    [ unfun Z+    [ con Z     , fun "S" S     ]    -- use + to conjure *   conjure "*" times-    [ unfun Z+    [ con Z     , fun "S" S     , fun "+" (let p + Z    =  p                    p + S q  =  S p + q
eg/peano.txt view
@@ -6,9 +6,9 @@ -- 3 candidates of size 3 -- 13 candidates of size 4 -- 19 candidates of size 5--- tested 23 candidates+-- tested 26 candidates p + Z  =  p-p + S q  =  S p + q+p + S q  =  S (p + q)  (*) :: Peano -> Peano -> Peano -- testing 7 combinations of argument values@@ -17,9 +17,9 @@ -- 3 candidates of size 2 -- 6 candidates of size 3 -- 6 candidates of size 4--- 35 candidates of size 5--- 86 candidates of size 6--- tested 71 candidates+-- 25 candidates of size 5+-- 63 candidates of size 6+-- tested 56 candidates p * Z  =  Z p * S q  =  p + p * q
eg/pow.hs view
@@ -16,8 +16,8 @@   -- pow x 0  =  1   -- pow x y  =  x * pow x (y - 1)   conjure "pow" pow-    [ unfun (0::Int)-    , unfun (1::Int)+    [ con (0::Int)+    , con (1::Int)     , fun "*" ((*) :: Int -> Int -> Int)     , fun "-" ((-) :: Int -> Int -> Int)     ]@@ -27,8 +27,8 @@   --             2   3  4     5  6 7   8  9    10 11 12 13 14     15     16   -- out of reach performance wise, OOM at size 9   conjure "pow" pow-    [ unfun (0::Int)-    , unfun (1::Int)+    [ con (0::Int)+    , con (1::Int) --  , fun "sq" ((\x -> x*x) :: Int -> Int) -- cheat! OOM still     , fun "*" ((*) :: Int -> Int -> Int)     , fun "halve" ((`div` 2) :: Int -> Int)
eg/pow.txt view
@@ -2,14 +2,14 @@ -- testing 5 combinations of argument values -- pruning with 14/30 rules -- 4 candidates of size 1--- 11 candidates of size 2--- 31 candidates of size 3--- 92 candidates of size 4--- 244 candidates of size 5--- 730 candidates of size 6--- 2221 candidates of size 7--- 6950 candidates of size 8--- tested 3356 candidates+-- 0 candidates of size 2+-- 11 candidates of size 3+-- 0 candidates of size 4+-- 78 candidates of size 5+-- 9 candidates of size 6+-- 809 candidates of size 7+-- 557 candidates of size 8+-- tested 912 candidates pow x 0  =  1 pow x y  =  x * pow x (y - 1) @@ -17,11 +17,11 @@ -- testing 5 combinations of argument values -- pruning with 15/19 rules -- 4 candidates of size 1--- 13 candidates of size 2--- 40 candidates of size 3--- 103 candidates of size 4--- 259 candidates of size 5--- 750 candidates of size 6--- tested 1169 candidates+-- 2 candidates of size 2+-- 5 candidates of size 3+-- 9 candidates of size 4+-- 31 candidates of size 5+-- 178 candidates of size 6+-- tested 229 candidates pow  =  undefined  -- search exhausted
eg/replicate.hs view
@@ -26,10 +26,10 @@ main :: IO () main = do   conjure "replicate" replicate'-    [ unfun (0 :: Int)-    , unfun (1 :: Int)+    [ con (0 :: Int)+    , con (1 :: Int)     , fun "-" ((-) :: Int -> Int -> Int)-    , unfun ""+    , con ""     , fun ":" ((:) :: Char -> String -> String)     ] @@ -49,7 +49,7 @@    -- alternative generation using recursion   conjure "replicates" replicates'-    [ unfun ""+    [ con ""     , fun ":" ((:) :: Char -> String -> String)     , fun "++" ((++) :: String -> String -> String)     , fun "replicate" (replicate :: Int -> Char -> String)
eg/replicate.txt view
@@ -4,12 +4,12 @@ -- 1 candidates of size 1 -- 0 candidates of size 2 -- 1 candidates of size 3--- 1 candidates of size 4--- 2 candidates of size 5--- 1 candidates of size 6+-- 0 candidates of size 4+-- 1 candidates of size 5+-- 0 candidates of size 6 -- 1 candidates of size 7--- 2 candidates of size 8--- tested 8 candidates+-- 1 candidates of size 8+-- tested 5 candidates replicate 0 c  =  "" replicate x c  =  c:replicate (x - 1) c @@ -43,10 +43,10 @@ -- 1 candidates of size 3 -- 0 candidates of size 4 -- 1 candidates of size 5--- 3 candidates of size 6+-- 2 candidates of size 6 -- 1 candidates of size 7--- 12 candidates of size 8--- tested 10 candidates+-- 8 candidates of size 8+-- tested 14 candidates replicates "" x  =  "" replicates (c:cs) x  =  replicate x c ++ replicates cs x
eg/setelem.hs view
@@ -19,8 +19,8 @@ main :: IO () main = do   conjure "elem" (elem')-    [ unfun True-    , unfun False+    [ con True+    , con False     , fun "||" (||)     , fun "&&" (&&)     , fun "not" not@@ -28,8 +28,8 @@     ]    conjure "set" (set')-    [ unfun True-    , unfun False+    [ con True+    , con False     , fun "||" (||)     , fun "&&" (&&)     , fun "not" not
eg/setelem.txt view
@@ -9,7 +9,7 @@ -- 0 candidates of size 6 -- 0 candidates of size 7 -- 16 candidates of size 8--- tested 19 candidates+-- tested 11 candidates elem x []  =  False elem x (y:xs)  =  x == y || elem x xs
eg/sort.hs view
@@ -3,21 +3,18 @@ -- Copyright (C) 2021-2025 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). import Conjure-import Data.List (insert, sort)+import Data.List (insert)  sort' :: [Int] -> [Int] sort' []       =  []-sort' [x]      =  [x]-sort' [x,y]-  | x <= y     =  [x,y]-  | otherwise  =  [y,x]-sort' [x,y,z]-  | x <= y && y <= z  =  [x,y,z]-  | x <= z && z <= y  =  [x,z,y]-  | y <= x && x <= z  =  [y,x,z]-  | y <= z && z <= x  =  [y,z,x]-  | z <= x && x <= y  =  [z,x,y]-  | z <= y && y <= x  =  [z,y,x]+sort' [0]      =  [0]+sort' [1]      =  [1]+sort' [0,2]    =  [0,2]+sort' [1,0]    =  [0,1]+sort' [0,1,2]  =  [0,1,2]+sort' [2,1,0]  =  [0,1,2]+sort' [1,0,1]  =  [0,1,1]+sort' [0,1,0,1]  =  [0,0,1,1]  insert' :: Int -> [Int] -> [Int] insert' 0 []  =  [0]@@ -25,99 +22,71 @@ insert' 1 [0,2]  =  [0,1,2] insert' 2 [0,1]  =  [0,1,2] --- merge' :: [Int] -> [Int] -> [Int]--- merge' xs ys  =  sort (xs ++ ys)- merge' :: [Int] -> [Int] -> [Int] merge' [] []  =  []-merge' xs []  =  xs-merge' [] ys  =  ys-merge' [x] [y] | x <= y     =  [x,y]-               | otherwise  =  [y,x]+merge' [0] []  =  [0]+merge' [] [0]  =  [0]+merge' [0] [1]  =  [0,1]+merge' [1] [0]  =  [0,1]+merge' [1] [0,2]  =  [0,1,2]+merge' [0,2] [1]  =  [0,1,2]+merge' [2] [0,1]  =  [0,1,2] merge' [0,1] [0,1]  =  [0,0,1,1] merge' [0,1] [2,3]  =  [0,1,2,3] merge' [0,2] [1,3]  =  [0,1,2,3] merge' [0,1] [1,2]  =  [0,1,1,2] merge' [1,2] [0,1]  =  [0,1,1,2]-merge' [0,2] [1,1]  =  [0,1,1,2]  main :: IO () main = do-  -- recursive insertion sort-  -- sort []  =  []-  -- sort (x:xs)  =  insert x (sort xs)-  conjure "sort" sort'-    [ unfun ([] :: [Int])-    , fun "insert" (insert :: Int -> [Int] -> [Int])-    , fun "head" (head :: [Int] -> Int)-    , fun "tail" (tail :: [Int] -> [Int])-    , fun "null" (null :: [Int] -> Bool)-    ]--  -- now through fold-  -- sort xs  =  foldr insert [] xs-  conjure "sort" sort'-    [ unfun ([] :: [Int])-    , fun "insert" (insert :: Int -> [Int] -> [Int])-    , fun "foldr" (foldr :: (Int -> [Int] -> [Int]) -> [Int] -> [Int] -> [Int])-    ]-   -- an insert function   conjure "insert" insert'     [ fun "[]" ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "<=" ((<=) :: Int -> Int -> Bool)     , guard-    , target 50400     ] -  -- qsort []  =  []                           -- 1-  -- qsort (x:xs)  =  qsort (filter (x >) xs)  -- 6-  --            ++ (x:qsort (filter (x <=) xs) -- 14-  -- this one is not out of reach performance wise,-  -- but is not generated because of the deconstruction restriction.-  -- The following does generate a correct but inneficient version of qsort.-  conjure "qsort" sort'-    [ unfun ([] :: [Int])-    , fun ":" ((:) :: Int -> [Int] -> [Int])-    , fun "++" ((++) :: [Int] -> [Int] -> [Int])-    , fun "<=" ((<=) :: Int -> Int -> Bool)-    , fun ">"  ((>)  :: Int -> Int -> Bool)-    , fun "filter" (filter :: (Int -> Bool) -> [Int] -> [Int])+  -- recursive insertion sort+  conjure "sort" sort'+    [ con ([] :: [Int])+    , fun "insert" (insert :: Int -> [Int] -> [Int])     ] -  -- if we disable the descent requirement, we get the efficient qsort-  -- though with a larger search space-  conjure "qsort" sort'-    [ unfun ([] :: [Int])-    , fun ":" ((:) :: Int -> [Int] -> [Int])-    , fun "++" ((++) :: [Int] -> [Int] -> [Int])-    , fun "<=" ((<=) :: Int -> Int -> Bool)-    , fun ">"  ((>)  :: Int -> Int -> Bool)-    , fun "filter" (filter :: (Int -> Bool) -> [Int] -> [Int])-    , dontRequireDescent+  -- folding insertion sort+  conjure "sort" sort'+    [ con ([] :: [Int])+    , fun "insert" (insert :: Int -> [Int] -> [Int])+    , fun "foldr" (foldr :: (Int -> [Int] -> [Int]) -> [Int] -> [Int] -> [Int])     ] -  -- found!  candidate #1703311 @ size 22+  -- found!  candidate #309279 @ size 22 after ~11s   -- merge [] xs  =  xs   -- merge (x:xs) []  =  x:xs   -- merge (x:xs) (y:ys)   --   | x <= y  =  x:merge xs (y:ys)-  --   | otherwise  =  merge (y:x:xs) ys-  -- set target to 2 000 000 to reach it+  --   | otherwise  =  y:merge ys (x:xs)+  -- set target to 360 000 to reach it   conjure "merge" merge'-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "<=" ((<=) :: Int -> Int -> Bool)     , guard     , maxTests 1080-    , target 10080 -- set to 2 000 000 to reach solution+    , target 3600  -- set to 360 000 to reach solution     ] -  -- unreachable: needs about 26, but can only reach 16-  conjure "merge" merge'-    [ fun ":" ((:) :: Int -> [Int] -> [Int])-    , fun "compare" (compare :: Int -> Int -> Ordering)-    , ordcase (undefined :: [Int])-    , target 1080+  -- Produces a inefficient degenerate version of qsort+  -- where filter is applied _after_ sorting.+  conjure "qsort" sort'+    [ con ([] :: [Int])+    , fun ":" ((:) :: Int -> [Int] -> [Int])+    , fun "++" ((++) :: [Int] -> [Int] -> [Int])+    , fun "<=" ((<=) :: Int -> Int -> Bool)+    , fun ">"  ((>)  :: Int -> Int -> Bool)+    , fun "filter" (filter :: (Int -> Bool) -> [Int] -> [Int])+    -- if we disable the descent requirement and carry on,+    -- we eventually get the efficient qsort+    -- , dontRequireDescent+    -- , carryOn     ]
eg/sort.txt view
@@ -1,25 +1,3 @@-sort :: [Int] -> [Int]--- testing 360 combinations of argument values--- pruning with 6/7 rules--- 2 candidates of size 1--- 2 candidates of size 2--- 2 candidates of size 3--- 7 candidates of size 4--- 14 candidates of size 5--- tested 15 candidates-sort []  =  []-sort (x:xs)  =  insert x (sort xs)--sort :: [Int] -> [Int]--- testing 360 combinations of argument values--- pruning with 1/2 rules--- 2 candidates of size 1--- 0 candidates of size 2--- 0 candidates of size 3--- 2 candidates of size 4--- tested 4 candidates-sort  =  foldr insert []- insert :: Int -> [Int] -> [Int] -- testing 4 combinations of argument values -- pruning with 4/4 rules@@ -30,101 +8,84 @@ -- 2 candidates of size 5 -- 2 candidates of size 6 -- 2 candidates of size 7--- 4 candidates of size 8+-- 0 candidates of size 8 -- 2 candidates of size 9--- 8 candidates of size 10--- 18 candidates of size 11--- 16 candidates of size 12--- 70 candidates of size 13--- 32 candidates of size 14--- 226 candidates of size 15--- 64 candidates of size 16--- 602 candidates of size 17--- tested 519 candidates+-- 0 candidates of size 10+-- 2 candidates of size 11+-- 0 candidates of size 12+-- 6 candidates of size 13+-- 0 candidates of size 14+-- 22 candidates of size 15+-- 0 candidates of size 16+-- 22 candidates of size 17+-- tested 45 candidates insert x []  =  [x] insert x (y:xs)-  | x <= y  =  x:insert y xs-  | otherwise  =  y:insert x xs+  | y <= x  =  y:insert x xs+  | otherwise  =  x:y:xs -qsort :: [Int] -> [Int]--- testing 360 combinations of argument values--- pruning with 8/8 rules+sort :: [Int] -> [Int]+-- testing 9 combinations of argument values+-- pruning with 0/0 rules -- 2 candidates of size 1 -- 0 candidates of size 2--- 1 candidates of size 3+-- 0 candidates of size 3 -- 0 candidates of size 4--- 4 candidates of size 5--- 3 candidates of size 6--- 10 candidates of size 7--- 21 candidates of size 8--- 36 candidates of size 9--- 105 candidates of size 10--- 182 candidates of size 11--- 471 candidates of size 12--- 988 candidates of size 13--- 2183 candidates of size 14--- tested 2437 candidates-qsort []  =  []-qsort (x:xs)  =  filter (x >) (qsort xs) ++ (x:filter (x <=) (qsort xs))+-- 1 candidates of size 5+-- tested 3 candidates+sort []  =  []+sort (x:xs)  =  insert x (sort xs) -qsort :: [Int] -> [Int]--- testing 360 combinations of argument values--- pruning with 8/8 rules+sort :: [Int] -> [Int]+-- testing 9 combinations of argument values+-- pruning with 1/2 rules -- 2 candidates of size 1 -- 0 candidates of size 2--- 1 candidates of size 3--- 0 candidates of size 4--- 4 candidates of size 5--- 3 candidates of size 6--- 16 candidates of size 7--- 35 candidates of size 8--- 80 candidates of size 9--- 239 candidates of size 10--- 478 candidates of size 11--- 1325 candidates of size 12--- 2980 candidates of size 13--- 7159 candidates of size 14--- tested 6564 candidates-qsort []  =  []-qsort (x:xs)  =  qsort (filter (x >) xs) ++ (x:qsort (filter (x <=) xs))+-- 0 candidates of size 3+-- 2 candidates of size 4+-- tested 4 candidates+sort  =  foldr insert []  merge :: [Int] -> [Int] -> [Int]--- testing 1080 combinations of argument values+-- testing 13 combinations of argument values -- pruning with 4/4 rules -- 3 candidates of size 1 -- 0 candidates of size 2 -- 0 candidates of size 3 -- 10 candidates of size 4 -- 0 candidates of size 5--- 16 candidates of size 6--- 13 candidates of size 7--- 22 candidates of size 8--- 114 candidates of size 9--- 36 candidates of size 10--- 472 candidates of size 11--- 568 candidates of size 12--- 1442 candidates of size 13--- 4204 candidates of size 14--- 5426 candidates of size 15--- tested 12326 candidates+-- 6 candidates of size 6+-- 26 candidates of size 7+-- 6 candidates of size 8+-- 67 candidates of size 9+-- 38 candidates of size 10+-- 152 candidates of size 11+-- 158 candidates of size 12+-- 296 candidates of size 13+-- 718 candidates of size 14+-- 560 candidates of size 15+-- 3728 candidates of size 16+-- tested 5768 candidates merge  =  undefined  -- search exhausted -merge :: [Int] -> [Int] -> [Int]--- testing 360 combinations of argument values--- pruning with 1/2 rules+qsort :: [Int] -> [Int]+-- testing 9 combinations of argument values+-- pruning with 8/8 rules -- 2 candidates of size 1 -- 0 candidates of size 2--- 0 candidates of size 3--- 6 candidates of size 4--- 0 candidates of size 5--- 10 candidates of size 6--- 7 candidates of size 7--- 14 candidates of size 8--- 41 candidates of size 9--- 106 candidates of size 10--- 144 candidates of size 11--- 588 candidates of size 12--- 958 candidates of size 13--- tested 1876 candidates-merge  =  undefined  -- search exhausted+-- 1 candidates of size 3+-- 0 candidates of size 4+-- 2 candidates of size 5+-- 3 candidates of size 6+-- 4 candidates of size 7+-- 10 candidates of size 8+-- 18 candidates of size 9+-- 39 candidates of size 10+-- 87 candidates of size 11+-- 165 candidates of size 12+-- 409 candidates of size 13+-- 809 candidates of size 14+-- tested 1377 candidates+qsort []  =  []+qsort (x:xs)  =  filter (x >) (qsort xs) ++ (x:filter (x <=) (qsort xs))
eg/spec.hs view
@@ -15,8 +15,8 @@  squareIngredients :: [Ingredient] squareIngredients  =-  [ unfun (0::Int)-  , unfun (1::Int)+  [ con (0::Int)+  , con (1::Int)   , fun "+" ((+) :: Int -> Int -> Int)   , fun "*" ((*) :: Int -> Int -> Int)   ]@@ -39,7 +39,7 @@ sumIngredients :: [Ingredient] sumIngredients  =   [ fun "null" (null :: [Int] -> Bool)-  , unfun (0::Int)+  , con (0::Int)   , fun "+"    ((+) :: Int -> Int -> Int)   , fun "head" (head :: [Int] -> Int)   , fun "tail" (tail :: [Int] -> [Int])
eg/spec.txt view
@@ -21,7 +21,7 @@ -- 2 candidates of size 3 -- 3 candidates of size 4 -- 5 candidates of size 5--- tested 9 candidates+-- tested 13 candidates sum []  =  0 sum (x:xs)  =  x + sum xs @@ -33,7 +33,7 @@ -- 31 candidates of size 4 -- 94 candidates of size 5 -- 225 candidates of size 6--- tested 212 candidates+-- tested 286 candidates [] ++ xs  =  xs (x:xs) ++ ys  =  x:(xs ++ ys)
eg/subset.hs view
@@ -44,9 +44,9 @@   -- subset [] ys  =  True   -- subset (x:xs) ys  =  elem x ys && subset xs ys   conjure "subset" (subset')-    [ unfun ([] :: [Int])-    , unfun True-    , unfun False+    [ con ([] :: [Int])+    , con True+    , con False     , fun "&&" (&&)     , fun "||" (||)     , fun "elem" (elem :: Int -> [Int] -> Bool)
eg/subset.txt view
@@ -9,7 +9,7 @@ -- 0 candidates of size 6 -- 6 candidates of size 7 -- 176 candidates of size 8--- tested 176 candidates+-- tested 48 candidates subset [] xs  =  True subset (x:xs) ys  =  elem x ys && subset xs ys
eg/take-drop.hs view
@@ -27,9 +27,9 @@   -- drop x []  =  []                   -- 2   -- drop x (y:xs)  =  drop (x - 1) xs  -- 7   conjure "drop" (drop' :: Int -> [A] -> [A])-    [ unfun (0 :: Int)-    , unfun (1 :: Int)-    , unfun ([] :: [A])+    [ con (0 :: Int)+    , con (1 :: Int)+    , con ([] :: [A])     , fun ":" ((:) :: A -> [A] -> [A])     , fun "-" ((-) :: Int -> Int -> Int)     ]@@ -38,9 +38,9 @@   -- take x []  =  []                     -- 2   -- take x (y:xs)  =  y:take (x - 1) xs  -- 9   conjure "take" (take' :: Int -> [A] -> [A])-    [ unfun (0 :: Int)-    , unfun (1 :: Int)-    , unfun ([] :: [A])+    [ con (0 :: Int)+    , con (1 :: Int)+    , con ([] :: [A])     , fun "-" ((-) :: Int -> Int -> Int)     , fun ":" ((:) :: A -> [A] -> [A])     ]
eg/take-drop.txt view
@@ -2,13 +2,13 @@ -- testing 360 combinations of argument values -- pruning with 4/7 rules -- 2 candidates of size 1--- 1 candidates of size 2+-- 0 candidates of size 2 -- 0 candidates of size 3 -- 0 candidates of size 4 -- 2 candidates of size 5 -- 5 candidates of size 6--- 5 candidates of size 7--- tested 11 candidates+-- 3 candidates of size 7+-- tested 10 candidates drop 0 xs  =  xs drop x []  =  [] drop x (y:xs)  =  drop (x - 1) xs@@ -17,15 +17,15 @@ -- testing 153 combinations of argument values -- pruning with 4/7 rules -- 2 candidates of size 1--- 1 candidates of size 2+-- 0 candidates of size 2 -- 0 candidates of size 3 -- 0 candidates of size 4 -- 0 candidates of size 5--- 3 candidates of size 6+-- 0 candidates of size 6 -- 2 candidates of size 7--- 6 candidates of size 8--- 5 candidates of size 9--- tested 15 candidates+-- 0 candidates of size 8+-- 3 candidates of size 9+-- tested 5 candidates take 0 xs  =  [] take x []  =  [] take x (y:xs)  =  y:take (x - 1) xs
eg/tapps.hs view
@@ -27,8 +27,8 @@  ingredients :: [Ingredient] ingredients =-  [ unfun (0 :: Int)-  , unfun (1 :: Int)+  [ con (0 :: Int)+  , con (1 :: Int) #if __GLASGOW_HASKELL__ < 800   , fun "+" ((+) :: Int -> Int -> Int)   , fun "*" ((*) :: Int -> Int -> Int)
eg/tapps.txt view
@@ -16,7 +16,7 @@ -- 1 candidates of size 3 -- 2 candidates of size 4 -- 10 candidates of size 5--- tested 12 candidates+-- tested 16 candidates product []  =  1 product (x:xs)  =  x * product xs @@ -27,6 +27,6 @@ -- 1 candidates of size 2 -- 1 candidates of size 3 -- 5 candidates of size 4--- tested 8 candidates+-- tested 9 candidates product  =  foldr (*) 1
eg/these.hs view
@@ -78,12 +78,12 @@     ]    conjure "listhese" listhese'-    [ unfun ([] :: [A])+    [ con ([] :: [A])     , fun ":" ((:) :: A -> [A] -> [A])     ]    conjure "cathis" cathis'-    [ unfun ([] :: [A])+    [ con ([] :: [A])     , fun ":" ((:) :: A -> [A] -> [A])     , fun "isThis" (isThis :: These A B -> Bool)     , fun "fromThis" (fromThis :: These A B -> A)@@ -91,7 +91,7 @@     ]    conjure "cathat" cathat'-    [ unfun ([] :: [B])+    [ con ([] :: [B])     , fun ":" ((:) :: B -> [B] -> [B])     , fun "isThat" (isThat :: These A B -> Bool)     , fun "fromThat" (fromThat :: These A B -> B)@@ -99,19 +99,19 @@     ]    conjure "cathis" cathis'-    [ unfun ([] :: [A])+    [ con ([] :: [A])     , fun ":" ((:) :: A -> [A] -> [A])     , maxPatternDepth 2     ]    conjure "cathat" cathat'-    [ unfun ([] :: [B])+    [ con ([] :: [B])     , fun ":" ((:) :: B -> [B] -> [B])     , maxPatternDepth 2     ]    conjure "cathese" cathese'-    [ unfun ([] :: [A])+    [ con ([] :: [A])     , fun ":" ((:) :: A -> [A] -> [A])     , maxPatternDepth 2     ]
eg/these.txt view
@@ -44,13 +44,13 @@ -- 0 candidates of size 3 -- 0 candidates of size 4 -- 0 candidates of size 5--- 1 candidates of size 6--- 2 candidates of size 7+-- 0 candidates of size 6+-- 0 candidates of size 7 -- 0 candidates of size 8--- 1 candidates of size 9--- 4 candidates of size 10--- 2 candidates of size 11--- tested 10 candidates+-- 0 candidates of size 9+-- 0 candidates of size 10+-- 1 candidates of size 11+-- tested 2 candidates cathis []  =  [] cathis (t:ts)   | isThis t  =  fromThis t:cathis ts@@ -64,13 +64,13 @@ -- 0 candidates of size 3 -- 0 candidates of size 4 -- 0 candidates of size 5--- 1 candidates of size 6--- 2 candidates of size 7+-- 0 candidates of size 6+-- 0 candidates of size 7 -- 0 candidates of size 8--- 1 candidates of size 9--- 4 candidates of size 10--- 2 candidates of size 11--- tested 10 candidates+-- 0 candidates of size 9+-- 0 candidates of size 10+-- 1 candidates of size 11+-- tested 2 candidates cathat []  =  [] cathat (t:ts)   | isThat t  =  fromThat t:cathat ts@@ -88,9 +88,9 @@ -- 0 candidates of size 7 -- 2 candidates of size 8 -- 6 candidates of size 9--- 7 candidates of size 10--- 13 candidates of size 11--- tested 18 candidates+-- 5 candidates of size 10+-- 9 candidates of size 11+-- tested 23 candidates cathis []  =  [] cathis (Neither:ts)  =  cathis ts cathis (This x:ts)  =  x:cathis ts@@ -110,8 +110,8 @@ -- 0 candidates of size 8 -- 2 candidates of size 9 -- 4 candidates of size 10--- 3 candidates of size 11--- tested 9 candidates+-- 1 candidates of size 11+-- tested 8 candidates cathat []  =  [] cathat (Neither:ts)  =  cathat ts cathat (This x:ts)  =  cathat ts@@ -129,14 +129,14 @@ -- 0 candidates of size 6 -- 0 candidates of size 7 -- 0 candidates of size 8--- 4 candidates of size 9--- 8 candidates of size 10--- 11 candidates of size 11--- 38 candidates of size 12--- 26 candidates of size 13--- 140 candidates of size 14--- 57 candidates of size 15--- tested 269 candidates+-- 3 candidates of size 9+-- 7 candidates of size 10+-- 4 candidates of size 11+-- 27 candidates of size 12+-- 3 candidates of size 13+-- 78 candidates of size 14+-- 1 candidates of size 15+-- tested 124 candidates cathese []  =  [] cathese (Neither:ts)  =  cathese ts cathese (That x:ts)  =  x:cathese ts
eg/tree.hs view
@@ -109,31 +109,31 @@     ]    conjure "size" size-    [ unfun (0 :: Int)-    , unfun (1 :: Int)+    [ con (0 :: Int)+    , con (1 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "nil" nil     ]    conjure "height" height-    [ unfun (0 :: Int)-    , unfun (1 :: Int)-    , unfun (-1 :: Int)+    [ con (0 :: Int)+    , con (1 :: Int)+    , con (-1 :: Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "max" (max :: Int -> Int -> Int)     , fun "nil" nil     ]    conjure "mem" mem-    [ unfun False+    [ con False     , fun "||" (||)     , fun "==" ((==) :: Int -> Int -> Bool)     ]    -- unreachable: needs size 22 but OOMs at 19/20 (v0.5.16)   conjure "ordered" ordered-    [ unfun True-    , unfun False+    [ con True+    , con False     , fun "&&" (&&)     , fun "||" (||)     , fun "<" ((<) :: Int -> Int -> Bool)@@ -149,19 +149,19 @@     ]    conjure "preorder" preorder-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "++" ((++) :: [Int] -> [Int] -> [Int])     ]    conjure "inorder" inorder-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "++" ((++) :: [Int] -> [Int] -> [Int])     ]    conjure "posorder" posorder-    [ unfun ([] :: [Int])+    [ con ([] :: [Int])     , fun ":" ((:) :: Int -> [Int] -> [Int])     , fun "++" ((++) :: [Int] -> [Int] -> [Int])     ]
eg/tree.txt view
@@ -75,7 +75,7 @@ -- 0 candidates of size 10 -- 0 candidates of size 11 -- 36 candidates of size 12--- tested 42 candidates+-- tested 18 candidates mem x Leaf  =  False mem x (Node t1 y t2)  =  mem x t1 || (x == y || mem x t2) @@ -90,11 +90,11 @@ -- 12 candidates of size 6 -- 0 candidates of size 7 -- 36 candidates of size 8--- 104 candidates of size 9+-- 72 candidates of size 9 -- 0 candidates of size 10--- 418 candidates of size 11--- 1064 candidates of size 12--- tested 1639 candidates+-- 290 candidates of size 11+-- 712 candidates of size 12+-- tested 1127 candidates ordered  =  undefined  -- search exhausted  ordered :: Tree -> Bool@@ -115,9 +115,9 @@ -- 0 candidates of size 4 -- 2 candidates of size 5 -- 4 candidates of size 6--- 4 candidates of size 7+-- 2 candidates of size 7 -- 8 candidates of size 8--- tested 13 candidates+-- tested 11 candidates preorder Leaf  =  [] preorder (Node t1 x t2)  =  x:(preorder t1 ++ preorder t2) @@ -128,11 +128,11 @@ -- 0 candidates of size 2 -- 0 candidates of size 3 -- 0 candidates of size 4--- 2 candidates of size 5+-- 0 candidates of size 5 -- 4 candidates of size 6--- 4 candidates of size 7--- 8 candidates of size 8--- tested 17 candidates+-- 2 candidates of size 7+-- 4 candidates of size 8+-- tested 9 candidates inorder Leaf  =  [] inorder (Node t1 x t2)  =  inorder t1 ++ (x:inorder t2) @@ -143,13 +143,13 @@ -- 0 candidates of size 2 -- 0 candidates of size 3 -- 0 candidates of size 4--- 2 candidates of size 5+-- 0 candidates of size 5 -- 4 candidates of size 6--- 4 candidates of size 7--- 8 candidates of size 8--- 14 candidates of size 9--- 16 candidates of size 10--- tested 47 candidates+-- 2 candidates of size 7+-- 4 candidates of size 8+-- 10 candidates of size 9+-- 8 candidates of size 10+-- tested 27 candidates posorder Leaf  =  [] posorder (Node t1 x t2)  =  posorder t1 ++ (posorder t2 ++ [x])
eg/tri.hs view
@@ -12,7 +12,7 @@ main :: IO () main  =  do   conjure "tri" tri-    [ unfun (1::Int)+    [ con (1::Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "-" ((-) :: Int -> Int -> Int)     ]
eg/tri.txt view
@@ -4,11 +4,11 @@ -- 2 candidates of size 1 -- 0 candidates of size 2 -- 5 candidates of size 3--- 5 candidates of size 4+-- 0 candidates of size 4 -- 10 candidates of size 5--- 8 candidates of size 6+-- 0 candidates of size 6 -- 41 candidates of size 7--- tested 31 candidates+-- tested 53 candidates tri 1  =  1 tri x  =  x + tri (x - 1)
eg/tuple.txt view
@@ -2,7 +2,7 @@ -- testing 4 combinations of argument values -- pruning with 0/0 rules -- 0 candidates of size 1--- 1 candidates of size 2+-- 2 candidates of size 2 -- tested 1 candidates fst (x,y)  =  x @@ -10,8 +10,8 @@ -- testing 4 combinations of argument values -- pruning with 0/0 rules -- 0 candidates of size 1--- 1 candidates of size 2--- tested 1 candidates+-- 2 candidates of size 2+-- tested 2 candidates snd (x,y)  =  y  swap :: (A,A) -> (A,A)@@ -20,8 +20,8 @@ -- 1 candidates of size 1 -- 0 candidates of size 2 -- 0 candidates of size 3--- 1 candidates of size 4--- tested 2 candidates+-- 4 candidates of size 4+-- tested 4 candidates swap (x,y)  =  (y,x)  curry :: ((A,A) -> A) -> A -> A -> A@@ -51,10 +51,10 @@ -- 0 candidates of size 4 -- 0 candidates of size 5 -- 0 candidates of size 6--- 7 candidates of size 7--- 19 candidates of size 8--- 34 candidates of size 9--- tested 36 candidates+-- 5 candidates of size 7+-- 11 candidates of size 8+-- 17 candidates of size 9+-- tested 32 candidates pairwise []  =  [] pairwise (x:xs)  =  (x,head xs):pairwise (tail xs) @@ -66,11 +66,11 @@ -- 1 candidates of size 3 -- 3 candidates of size 4 -- 5 candidates of size 5--- 11 candidates of size 6--- 22 candidates of size 7--- 46 candidates of size 8--- 106 candidates of size 9--- tested 124 candidates+-- 9 candidates of size 6+-- 17 candidates of size 7+-- 35 candidates of size 8+-- 72 candidates of size 9+-- tested 101 candidates catpairs []  =  [] catpairs (xy:xys)  =  fst xy:snd xy:catpairs xys @@ -83,9 +83,9 @@ -- 0 candidates of size 4 -- 0 candidates of size 5 -- 0 candidates of size 6--- 7 candidates of size 7--- 26 candidates of size 8--- tested 23 candidates+-- 5 candidates of size 7+-- 14 candidates of size 8+-- tested 18 candidates pairwise []  =  [] pairwise [x]  =  [] pairwise (x:y:xs)  =  (x,y):pairwise xs@@ -98,10 +98,10 @@ -- 1 candidates of size 3 -- 3 candidates of size 4 -- 6 candidates of size 5--- 15 candidates of size 6--- 31 candidates of size 7--- 68 candidates of size 8--- tested 97 candidates+-- 12 candidates of size 6+-- 23 candidates of size 7+-- 48 candidates of size 8+-- tested 82 candidates catpairs []  =  [] catpairs ((x,y):xys)  =  x:y:catpairs xys
mk/depend.mk view
@@ -57,10 +57,10 @@   src/Conjure/Conjurable.hs \   src/Conjure/Conjurable/Derive.hs \   bench/erroneous.hs-bench/gps2: \-  bench/gps2.hs \+bench/gps: \+  bench/gps.hs \   mk/toplibs-bench/gps2.o: \+bench/gps.o: \   src/Conjure/Utils.hs \   src/Conjure/Settings.hs \   src/Conjure/Red.hs \@@ -74,11 +74,11 @@   src/Conjure/Defn.hs \   src/Conjure/Conjurable.hs \   src/Conjure/Conjurable/Derive.hs \-  bench/gps2.hs-bench/gps: \-  bench/gps.hs \+  bench/gps.hs+bench/i12: \+  bench/i12.hs \   mk/toplibs-bench/gps.o: \+bench/i12.o: \   src/Conjure/Utils.hs \   src/Conjure/Settings.hs \   src/Conjure/Red.hs \@@ -92,11 +92,11 @@   src/Conjure/Defn.hs \   src/Conjure/Conjurable.hs \   src/Conjure/Conjurable/Derive.hs \-  bench/gps.hs-bench/ill-hit: \-  bench/ill-hit.hs \+  bench/i12.hs+bench/i30: \+  bench/i30.hs \   mk/toplibs-bench/ill-hit.o: \+bench/i30.o: \   src/Conjure/Utils.hs \   src/Conjure/Settings.hs \   src/Conjure/Red.hs \@@ -110,11 +110,11 @@   src/Conjure/Defn.hs \   src/Conjure/Conjurable.hs \   src/Conjure/Conjurable/Derive.hs \-  bench/ill-hit.hs-bench/longshot: \-  bench/longshot.hs \+  bench/i30.hs+bench/ill-hit: \+  bench/ill-hit.hs \   mk/toplibs-bench/longshot.o: \+bench/ill-hit.o: \   src/Conjure/Utils.hs \   src/Conjure/Settings.hs \   src/Conjure/Red.hs \@@ -128,11 +128,11 @@   src/Conjure/Defn.hs \   src/Conjure/Conjurable.hs \   src/Conjure/Conjurable/Derive.hs \-  bench/longshot.hs-bench/lowtests: \-  bench/lowtests.hs \+  bench/ill-hit.hs+bench/longshot: \+  bench/longshot.hs \   mk/toplibs-bench/lowtests.o: \+bench/longshot.o: \   src/Conjure/Utils.hs \   src/Conjure/Settings.hs \   src/Conjure/Red.hs \@@ -146,11 +146,11 @@   src/Conjure/Defn.hs \   src/Conjure/Conjurable.hs \   src/Conjure/Conjurable/Derive.hs \-  bench/lowtests.hs-bench/p12: \-  bench/p12.hs \+  bench/longshot.hs+bench/lowtests: \+  bench/lowtests.hs \   mk/toplibs-bench/p12.o: \+bench/lowtests.o: \   src/Conjure/Utils.hs \   src/Conjure/Settings.hs \   src/Conjure/Red.hs \@@ -164,11 +164,11 @@   src/Conjure/Defn.hs \   src/Conjure/Conjurable.hs \   src/Conjure/Conjurable/Derive.hs \-  bench/p12.hs-bench/p30: \-  bench/p30.hs \+  bench/lowtests.hs+bench/psb2: \+  bench/psb2.hs \   mk/toplibs-bench/p30.o: \+bench/psb2.o: \   src/Conjure/Utils.hs \   src/Conjure/Settings.hs \   src/Conjure/Red.hs \@@ -182,7 +182,7 @@   src/Conjure/Defn.hs \   src/Conjure/Conjurable.hs \   src/Conjure/Conjurable/Derive.hs \-  bench/p30.hs+  bench/psb2.hs bench/redundants: \   bench/redundants.hs \   mk/toplibs@@ -399,6 +399,24 @@   src/Conjure/Conjurable.hs \   src/Conjure/Conjurable/Derive.hs \   eg/colin/ListFuns.hs+eg/conditionals: \+  eg/conditionals.hs \+  mk/toplibs+eg/conditionals.o: \+  src/Conjure/Utils.hs \+  src/Conjure/Settings.hs \+  src/Conjure/Red.hs \+  src/Conjure/Reason.hs \+  src/Conjure.hs \+  src/Conjure/Ingredient.hs \+  src/Conjure/Expr.hs \+  src/Conjure/Engine.hs \+  src/Conjure/Defn/Test.hs \+  src/Conjure/Defn/Redundancy.hs \+  src/Conjure/Defn.hs \+  src/Conjure/Conjurable.hs \+  src/Conjure/Conjurable/Derive.hs \+  eg/conditionals.hs eg/count: \   eg/count.hs \   mk/toplibs@@ -417,6 +435,24 @@   src/Conjure/Conjurable.hs \   src/Conjure/Conjurable/Derive.hs \   eg/count.hs+eg/digits: \+  eg/digits.hs \+  mk/toplibs+eg/digits.o: \+  src/Conjure/Utils.hs \+  src/Conjure/Settings.hs \+  src/Conjure/Red.hs \+  src/Conjure/Reason.hs \+  src/Conjure.hs \+  src/Conjure/Ingredient.hs \+  src/Conjure/Expr.hs \+  src/Conjure/Engine.hs \+  src/Conjure/Defn/Test.hs \+  src/Conjure/Defn/Redundancy.hs \+  src/Conjure/Defn.hs \+  src/Conjure/Conjurable.hs \+  src/Conjure/Conjurable/Derive.hs \+  eg/digits.hs eg/dupos: \   eg/dupos.hs \   mk/toplibs
src/Conjure.hs view
@@ -19,8 +19,8 @@ -- -- > ingredients :: [Ingredient] -- > ingredients =--- >   [ unfun (0::Int)--- >   , unfun (1::Int)+-- >   [ con (0::Int)+-- >   , con (1::Int) -- >   , fun "+" ((+) :: Int -> Int -> Int) -- >   , fun "*" ((*) :: Int -> Int -> Int) -- >   , fun "-" ((-) :: Int -> Int -> Int)@@ -62,9 +62,9 @@ -- > take' 3 [x,y]  =  [x,y] -- -- > > conjure "take" (take' :: Int -> [A] -> [A])--- > >   [ unfun (0 :: Int)--- > >   , unfun (1 :: Int)--- > >   , unfun ([] :: [A])+-- > >   [ con (0 :: Int)+-- > >   , con (1 :: Int)+-- > >   , con ([] :: [A]) -- > >   , fun ":" ((:) :: A -> [A] -> [A]) -- > >   , fun "-" ((-) :: Int -> Int -> Int) -- > >   ]@@ -96,7 +96,7 @@     conjure   , Ingredient   , fun-  , unfun+  , con   , guard   , iif   , ordcase@@ -155,7 +155,7 @@   , dontRewrite   , dontRequireDescent   , omitAssortedPruning-  , omitEarlyTests+  , maxEarlyTests   , dontCopyBindings   , nonAtomicNumbers   , uniqueCandidates@@ -164,7 +164,7 @@   , Prim   , pr   , prim-  , con+  , unfun   ) where
src/Conjure/Conjurable.hs view
@@ -122,9 +122,16 @@ -- -- (cf. 'reifyTiers', 'reifyEquality', 'conjureType') class (Typeable a, Name a) => Conjurable a where+  -- | Returns a list of holes matching arguments of the given function.   conjureArgumentHoles :: a -> [Expr]   conjureArgumentHoles _  =  [] +  -- | Returns a hole with the same type as the given functions final result.+  conjureResultHole :: a -> Expr+  conjureResultHole x  =  value "_" (err `asTypeOf` x)+    where+    err  =  error "conjureResultHole: placeholder for recursive call?"+   -- | Returns 'Just' the '==' function encoded as an 'Expr' when available   --   or 'Nothing' otherwise.   --@@ -610,6 +617,7 @@  instance (Conjurable a, Conjurable b) => Conjurable (a -> b) where   conjureArgumentHoles f  =  hole (argTy f) : conjureArgumentHoles (f undefined)+  conjureResultHole f  =  conjureResultHole (f undefined)   conjureSubTypes f  =  conjureType (argTy f) . conjureType (resTy f)   conjureIf f  =  conjureIf (f undefined)   conjureArgumentCases f  =  conjureCases (argTy f) : conjureArgumentCases (f undefined)
src/Conjure/Defn.hs view
@@ -74,17 +74,15 @@   where   show1 (lhs,rhs)  =     case rhs of-    (Value "|" _ :$ c :$ t :$ e) -> showExpr lhs-                         ++ "\n  | " ++ showExpr c ++ "  =  " ++ showExpr t-                         ++ "\n  | otherwise  =  " ++ showExpr e-    (Value "if" _ :$ c :$ t :$ e) -> lhseqs ++ "if " ++ showExpr c-                          ++ "\n" ++ spaces ++ "then " ++ showExpr t-                          ++ "\n" ++ spaces ++ "else " ++ showExpr e-    (Value "case" _ :$ ep :$ ex :$ ey)+    Value "|" _ :$ _ :$ _ :$ _ -> showExpr lhs ++ showCases rhs+    Value "if" _ :$ c :$ t :$ e -> lhseqs ++ "if " ++ showExpr c+                        ++ "\n" ++ spaces ++ "then " ++ showExpr t+                        ++ "\n" ++ spaces ++ "else " ++ showExpr e+    Value "case" _ :$ ep :$ ex :$ ey       | typ ep == boolTy -> lhseqs ++ "case " ++ showExpr ep ++ " of"                  ++ "\n" ++ spaces ++ "False -> " ++ showExpr ex                  ++ "\n" ++ spaces ++ "True  -> " ++ showExpr ey-    (Value "case" _ :$ eo :$ ex :$ ey :$ ez)+    Value "case" _ :$ eo :$ ex :$ ey :$ ez       | typ eo == orderingTy -> lhseqs ++ "case " ++ showExpr eo ++ " of"                      ++ "\n" ++ spaces ++ "LT -> " ++ showExpr ex                      ++ "\n" ++ spaces ++ "EQ -> " ++ showExpr ey@@ -93,6 +91,11 @@     where     lhseqs  =  showExpr lhs ++ "  =  "     spaces  =  map (const ' ') lhseqs+  showCases (Value "|" _ :$ c :$ e :$ etc)  =+    "\n  | " ++ showExpr c ++ "  =  " ++ showExpr e ++ showCases etc+  showCases e  =+    "\n  | otherwise  =  " ++ showExpr e+  -- | Pretty-prints a 'Defn' to the screen. --
src/Conjure/Defn/Redundancy.hs view
@@ -145,11 +145,21 @@ -- are at the root: we have a redundant function. -- (Modulo error functions, which are undesired anyway.) --+-- Here is an example:+-- -- > xs ? []  =  [] -- > xs ? (x:ys)  =  xs ? ys -- -- Above it does not really pays off to follow the recursive calls, -- at the end we always reach an empty list.+--+-- Here is a more complex example:+--+-- > [] ? xs  =  []+-- > (x:xs) ? []  =  []+-- > (x:xs) ? (y:ys)  =  xs ? ys+--+-- We are bound to reach [] when following the recursion. isRedundantByRootRecursions :: Defn -> Bool isRedundantByRootRecursions d  =  case partition isGround $ map snd d of   ([b], rs@(_:_))  ->  all isHole rs
src/Conjure/Engine.hs view
@@ -47,7 +47,7 @@   , dontRewrite   , dontRequireDescent   , omitAssortedPruning-  , omitEarlyTests+  , maxEarlyTests   , dontCopyBindings   , nonAtomicNumbers   , uniqueCandidates@@ -71,7 +71,7 @@  import Test.LeanCheck import Test.LeanCheck.Tiers-import Test.LeanCheck.Error (errorToFalse)+import Test.LeanCheck.Error (errorToFalse, errorToLeft)  import Conjure.Expr import Conjure.Conjurable@@ -101,8 +101,8 @@ -- > -- > ingredients :: [Ingredient] -- > ingredients  =--- >   [ unfun (0::Int)--- >   , unfun (1::Int)+-- >   [ con (0::Int)+-- >   , con (1::Int) -- >   , fun "+" ((+) :: Int -> Int -> Int) -- >   , fun "*" ((*) :: Int -> Int -> Int) -- >   , fun "-" ((-) :: Int -> Int -> Int)@@ -121,7 +121,7 @@ -- > factorial 0  =  1 -- > factorial x  =  x * factorial (x - 1) ----- The ingredients list is defined with 'unfun' and 'fun'.+-- The ingredients list is defined with 'con' and 'fun'. conjure :: Conjurable f => String -> f -> [Ingredient] -> IO () conjure nm f  =  conjure0 nm f (const []) @@ -385,7 +385,8 @@ --   using pattern matching. candidateDefnsC :: Conjurable f => String -> f -> [Ingredient] -> ([[Defn]], Thy, [[Defn]], [Expr]) candidateDefnsC nm f is =-  ( discardT hasRedundant $ concatMapT fillingsFor fss+  ( discardT hasRedundant $ catconMapT fillingsFor partialDefns+  -- above we catconMapT to prefer smaller recursive calls   , thy   , mapT (map (,eh)) pats   , deconstructions@@ -393,12 +394,12 @@   where   pats | maxPatternSize > 0  =  take maxPatternSize $ conjurePats maxPatternDepth es nm f        | otherwise           =                        conjurePats maxPatternDepth es nm f-  fss  =  concatMapT ps2fss pats+  partialDefns  =  concatMapT partialDefnsFromPats pats   -- replaces the any guard symbol with a guard of the correct type   ps  =  actual is  -- extract actual ingredients/primitives from the list   es  =  [if isGuardSymbol e then conjureGuard f else e | (e,_) <- ps] -  eh  =  holeAsTypeOf efxs+  eh  =  conjureResultHole f   efxs  =  conjureVarApplication nm f   (ef:_)  =  unfoldApp efxs @@ -431,43 +432,57 @@   isNumeric  =  conjureIsNumeric f    (-==-)  =  conjureMkEquation f+  etests  =  map (first (mappArgs exprExpr)) tests   tests  =  conjureTestDefn maxTests maxSearchTests nm f   exprExpr  =  conjureExpress f -  ps2fss :: [Expr] -> [[Defn]]-  ps2fss pats  =  discardT isRedundant-               .  products  -- alt: use delayedProducts-               $  map p2eess pats+  distritests :: [(Expr,Expr)] -> [Expr] -> [([(Expr,Expr)],Expr)]+  distritests _ []  =  []+  distritests ts (pat:pats)  =  (ys, pat) : distritests ns pats+    where+    (ys, ns)  =  partition (\(lhs,_) -> lhs `isInstanceOf` pat) ts++  partialDefnsFromPats :: [Expr] -> [[Defn]]+  partialDefnsFromPats pats  =  discardT isRedundant+                             .  products  -- alt: use delayedProducts+                             .  map (uncurry bindingsForPattern)+                             .  distritests etests+                             $  pats     -- delayedProducts makes the number of patterns counts as the size+1.     where-    p2eess :: Expr -> [[Bndn]]+    bindingsForPattern :: [(Expr,Expr)] -> Expr -> [[Bndn]]     -- the following guarded line is an optional optimization     -- if the function is defined for the given pattern,     -- simply use its return value as the only possible result-    p2eess pat | copyBindings && isGroundPat f pat  =  [[(pat, toValPat f pat)]]-    p2eess pat  =  mapT (pat,)-                .  filterT keepBase-                .  appsWith pat-                .  drop 1 -- this excludes the function name itself-                $  vars pat ++ [eh | any (uncurry should) (zip aess aes)]+    bindingsForPattern ts pat+      | copyBindings && isGroundPat f pat  =  [[(pat, toValPat f pat)]]+      | otherwise  =  mapT (pat,)+                   .  filterT keepB+                   .  appsWith pat+                   .  drop 1 -- this excludes the function name itself+                   $  vars pat ++ [eh | any (uncurry should) (zip aess aes)]       where-      keepBase-        | not earlyTests  =  const True-        | all isVar (unfoldApp pat)  =  const True-        | otherwise  =  \e -> hasHole e || reallyKeepBase e-      reallyKeepBase e  =  and-        [ errorToFalse $ eval False $ (e //- bs) -==- rhs-        | (lhs,rhs) <- tests-        -- filter test bindings that match the current pattern:-        , Just bs <- [lhs `matchArgs` pat]+      keepB+        | maxEarlyTests <= 0  =  const True+        | length pats < 2  =  const True  -- just one pat, test later+        | otherwise  =  \e -> isNumeric eh && hasHole e || reallyKeepB e+      reallyKeepB e  =  and+        [ errholeToTrue $ eval False $ (e //- bs) -==- rhs+        | (lhs,rhs) <- take maxEarlyTests ts+        , Just bs <- [lhs `match` pat]  -- always should match         ]-      matchArgs efxs efys  =  fold (map exprExpr (drop 1 (unfoldApp efxs)))-                      `match` fold               (drop 1 (unfoldApp efys)) -      -- computes whether we should include a recurse for this given argument-      -- numeric arguments additionally require 0 to be present as a case-      -- for recursion-      should aes ae  =  length (nub aes) > 1 && hasVar ae && (isApp ae || isUnbreakable ae)+      -- computes whether we should include a recurse for this given argument:+      -- 1. more than one LHS pattern overall+      -- 2. there should be at least a variable+      -- 3. it should either:+      --    * we do not require descent+      --    * be a breakdown such as _:_ or Tree _ _ _+      --    * or be of an unbreakable/atomic type such as (_ :: Int)+      --      in the presence of deconstructions+      should aes ae  =  length (nub aes) > 1+                     && hasVar ae+                     && (not requireDescent || isApp ae || isUnbreakable ae && notNull deconstructions)       aes   =                  (tail . unfoldApp . rehole) pat       aess  =  transpose $ map (tail . unfoldApp . rehole) pats @@ -546,7 +561,7 @@   maxPatternDepth        =  maxPatternDepthI is   maxPatternSize         =  maxPatternSizeI is   requireDescent         =  requireDescentI is-  earlyTests             =  earlyTestsI is+  maxEarlyTests          =  maxEarlyTestsI is   copyBindings           =  copyBindingsI is   adHocRedundancy        =  assortedPruningI is -- TODO: rename   atomicNumbers          =  atomicNumbersI is@@ -692,3 +707,16 @@  testSpec :: Int -> [Property] -> Bool testSpec maxTests  =  and . map (and . take maxTests)++-- like errorToFalse, but returns True upon finding a placeholder hole+errholeToTrue :: Bool -> Bool+errholeToTrue p  =  case errorToLeft p of+                    Right q -> q+                    Left "conjureResultHole: placeholder for recursive call?" -> True+                    Left _ -> False+++catconMapT :: (a -> [[b]]) -> [[a]] -> [[b]]+catconMapT f  =  foldr (\+:/) [] . map (foldr (\/) []) . mapT f+  where+  xss \+:/ yss  =  ([]:yss) \/ xss
src/Conjure/Expr.hs view
@@ -40,6 +40,8 @@   , isGuard   , hasGuard   , mapInnerFirstOuterLast+  , mappArgs+  , mappFun    , enumerateAppsFor   , enumerateFillings@@ -70,7 +72,7 @@ import Data.Dynamic -- import Control.Applicative ((<$>)) -- for GHC <= 7.8 -import Test.LeanCheck (mapT, filterT, (\/), delay, productWith)+import Test.LeanCheck (mapT, filterT, (\/), delay, productWith, concatMapT) import Test.LeanCheck.Tiers (products) import Test.LeanCheck.Utils.Types (A, B, C, D, E, F) @@ -375,11 +377,15 @@   for h  =  filter (\e -> typ h == typ e) es : apps     where     apps  =  foldr (\/) []-          [  filterT keep $ fliproductWith (:$) (ufor hf) (ufor hx)+          [  filterT keep $ concatMapT afor (ufor hf)           |  hf <- hs           ,  hx <- hs           ,  Just hfx <- [hf $$ hx]           ,  typ h == typ hfx+          -- the following allows chains of guards:+          , let afor ef  =  mapT (ef :$) $ if isGuard (ef :$ hx)+                                           then for hx+                                           else ufor hx           ]   -- unguarded for   ufor | any isGuardSymbol es  =  filterT (not . isGuard) . for@@ -640,6 +646,20 @@   where   m (ef :$ ex)  =  f (m ef :$ m ex)   m e  =  f e++-- TODO: move mappArgs to Express?+mappArgs :: (Expr -> Expr) -> Expr -> Expr+mappArgs f  =  m+  where+  m (ef :$ ex)  =  m ef :$ f ex+  m e  =  e++-- TODO: move mappFun to Express?+mappFun :: (Expr -> Expr) -> Expr -> Expr+mappFun f  =  m+  where+  m (ef :$ ex)  =  m ef :$ ex+  m ef  =  f ef  instance Express A where  expr  =  val instance Express B where  expr  =  val
src/Conjure/Ingredient.hs view
@@ -12,7 +12,7 @@ module Conjure.Ingredient   ( Ingredient   , fun-  , unfun+  , con   , iif   , ordcase   , guard@@ -25,7 +25,7 @@   , prim   , prif   , primOrdCaseFor-  , con+  , unfun   ) where @@ -36,12 +36,12 @@   -- | A single functional ingredient in conjuring.--- Specify conjure ingredients with 'unfun' and 'fun':+-- Specify conjure ingredients with 'con' and 'fun': ----- > conjure "foo" foo [ unfun False--- >                   , unfun True--- >                   , unfun (0 :: Int)--- >                   , unfun (1 :: Int)+-- > conjure "foo" foo [ con False+-- >                   , con True+-- >                   , con (0 :: Int)+-- >                   , con (1 :: Int) -- >                   , ... -- >                   , fun "&&" (&&) -- >                   , fun "||" (||)@@ -53,9 +53,9 @@ -- -- Ingredients may include arbitrary -- functional values ('fun')--- and non-functional values ('unfun').+-- and non-functional (constant) values ('con'). -- These may be built-in or user defined.--- Use 'unfun' on 'Show' instances+-- Use 'con' on 'Show' instances -- and 'fun' otherwise. -- -- This is internally@@ -65,26 +65,26 @@ type Ingredient  =  (Expr, Reification)  --- | Provided a 'Show'-able non-functional value to Conjure.+-- | Provides a 'Show'-able non-functional constant value to Conjure. --   (cf. 'fun') ----- > conjure "foo" foo [ unfun False--- >                   , unfun True--- >                   , unfun (0 :: Int)--- >                   , unfun (1 :: Int)+-- > conjure "foo" foo [ con False+-- >                   , con True+-- >                   , con (0 :: Int)+-- >                   , con (1 :: Int) -- >                   , ... -- >                   ] -- -- Argument types have to be monomorphized, -- so use type bindings when applicable.-unfun :: (Conjurable a, Show a) => a -> Ingredient-unfun x  =  (val x, conjureType x)+con :: (Conjurable a, Show a) => a -> Ingredient+con x  =  (val x, conjureType x)   -- | Provides a functional value as an ingredient to Conjure. --   To be used on values that are not 'Show' instances --   such as functions.---   (cf. 'unfun')+--   (cf. 'con') -- -- > conjure "foo" foo [ ... -- >                   , fun "&&" (&&)@@ -112,7 +112,7 @@ -- > last' [x,y]  =  y -- > last' [x,y,z]  =  z ----- > > conjure "last" last' [ unfun ([] :: [Int])+-- > > conjure "last" last' [ con ([] :: [Int]) -- > >                      , fun ":" ((:) :: Int -> [Int] -> [Int]) -- > >                      , fun "null" (null :: [Int] -> Bool) -- > >                      , iif (undefined :: Int)@@ -142,7 +142,7 @@ -- > last' [x,y,z]  =  z -- -- > > conjure "last" last'--- > >   [ unfun ([] :: [Int])+-- > >   [ con ([] :: [Int]) -- > >   , fun ":" ((:) :: Int -> [Int] -> [Int]) -- > >   , fun "null" (null :: [Int] -> Bool) -- > >   , guard@@ -174,8 +174,8 @@ -- This should be used when one wants Conjure to consider ord-case expressions: -- -- > > conjure "mem" mem--- > >   [ unfun False--- > >   , unfun True+-- > >   [ con False+-- > >   , con True -- > >   , fun "`compare`" (compare :: Int -> Int -> Ordering) -- > >   , ordcase (undefined :: Bool) -- > >   ]@@ -273,7 +273,7 @@ primOrdCaseFor  =  ordcase {-# DEPRECATED primOrdCaseFor "'primOrdCaseFor' is deprecated, please use 'ordcase' instead" #-} --- | __DEPRECATED__. Please use 'unfun' instead.-con :: (Conjurable a, Show a) => a -> Ingredient-con  =  unfun-{-# DEPRECATED con "'con' is deprecated, please use 'unfun' instead" #-}+-- | __DEPRECATED__. Please use 'con' instead.+unfun :: (Conjurable a, Show a) => a -> Ingredient+unfun  =  con+{-# DEPRECATED unfun "'unfun' is deprecated, please use 'con' instead" #-}
src/Conjure/Settings.hs view
@@ -40,7 +40,7 @@   , dontRewrite   , dontRequireDescent   , omitAssortedPruning-  , omitEarlyTests+  , maxEarlyTests   , dontCopyBindings   , nonAtomicNumbers   , uniqueCandidates@@ -74,7 +74,7 @@   , rewriteI   , requireDescentI   , assortedPruningI-  , earlyTestsI+  , maxEarlyTestsI   , copyBindingsI   , atomicNumbersI   , uniqueCandidatesI@@ -117,7 +117,7 @@   | DontRewrite          -- ^ turns off unique-modulo-rewriting candidates   | DontRequireDescent   -- ^ require recursive calls to deconstruct arguments   | OmitAssortedPruning  -- ^ omit other assorted pruning rules-  | OmitEarlyTests       -- ^ don't perform tests early-and-independently on each binding+  | MaxEarlyTests Int    -- ^ don't perform tests early-and-independently on each binding   | DontCopyBindings     -- ^ don't copy partial definition bindings in candidates   | AtomicNumbers        -- ^ restrict constant/ground numeric expressions to atoms   | NonAtomicNumbers     -- ^ lift constant/ground numetic expression restrictions@@ -379,14 +379,17 @@ assortedPruningI :: [Ingredient] -> Bool assortedPruningI is  =  null [False | OmitAssortedPruning <- map extract is] --- | Omits early tests+-- | Sets the maximum number of early tests+--   performed independently bindings/equations --   when provided in the ingredient list --   of 'Conjure.conjure' or 'Conjure.conjureFromSpec'.-omitEarlyTests :: Ingredient-omitEarlyTests  =  setting OmitEarlyTests+--+--   When not set, this defaults to a modest 12.+maxEarlyTests :: Int -> Ingredient+maxEarlyTests  =  setting . MaxEarlyTests -earlyTestsI :: [Ingredient] -> Bool-earlyTestsI is  =  null [False | OmitEarlyTests <- map extract is]+maxEarlyTestsI :: [Ingredient] -> Int+maxEarlyTestsI is  =  headOr 12 [m | MaxEarlyTests m <- map extract is]  -- | Disables the copy-bindings rule --   when provided in the ingredient list
src/Conjure/Utils.hs view
@@ -26,7 +26,6 @@ #endif   , idIO   , mapHead-  , sets   , headOr   , notNull   , allEqual@@ -137,15 +136,6 @@ mapHead :: (a -> a) -> [a] -> [a] mapHead f (x:xs)  =  f x : xs mapHead f []  =  error "Conjure.Utils.mapHead: empty list"---- | Return sets of values based on the list.------ The values in the list must me unique.-sets :: [a] -> [[a]]-sets []  =  [[]]-sets (x:xs)  =  map (x:) ss ++ ss-  where-  ss  =  sets xs  -- | Like 'head' but allows providing a default value. headOr :: a -> [a] -> a
test/factorial.hs view
@@ -13,8 +13,8 @@ main :: IO () main  =  do   conjure "factorial n" factorial-    [ unfun (0::Int)-    , unfun (1::Int)+    [ con (0::Int)+    , con (1::Int)     , fun "+" ((+) :: Int -> Int -> Int)     , fun "*" ((*) :: Int -> Int -> Int)     , fun "-" ((-) :: Int -> Int -> Int)
test/utils.hs view
@@ -16,11 +16,6 @@   , holds n $ \xs ys -> length xs >= length ys                     ==> zipWith (<>) xs (ys <> repeat mempty) == mzip xs (ys :: [[Int]]) -  , sets []  ==  [[] :: [Int]]-  , sets [1]  ==  [[1], [] :: [Int]]-  , sets [1,2]  ==  [[1,2], [1], [2], [] :: [Int]]-  , sets [1,2,3]  ==  [[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3],[] :: [Int]]-   , prods [ [1], [2], [3] ] == [[1,2,3]]   , prods [ [1,2], [3,4], [5] ] == [[1,3,5],[1,4,5],[2,3,5],[2,4,5]]   , prods [ [1,2], [3], [4,5] ] == [[1,3,4],[1,3,5],[2,3,4],[2,3,5]]