code-conjure 0.2.8 → 0.3.0

raw patch · 32 files changed

+465/−274 lines, 32 filesPVP ok

version bump matches the API change (PVP)

API changes (from Hackage documentation)

Files

• .gitignore +1/−0
• Makefile +1/−0
• bench/runtime/zero/bench/ill-hit.runtime +1/−1
• bench/runtime/zero/bench/take-drop.runtime +1/−0
• bench/runtime/zero/eg/arith.runtime +1/−1
• bench/runtime/zero/eg/bools.runtime +1/−1
• bench/runtime/zero/eg/factorial.runtime +1/−1
• bench/runtime/zero/eg/ints.runtime +1/−1
• bench/runtime/zero/eg/list.runtime +1/−1
• bench/runtime/zero/eg/spec.runtime +1/−1
• bench/runtime/zero/eg/tapps.runtime +1/−1
• bench/runtime/zero/proto/u-conjure.runtime +1/−1
• bench/runtime/zero/versions +1/−1
• bench/take-drop.hs +45/−0
• changelog.md +8/−0
• code-conjure.cabal +2/−2
• mk/depend.mk +11/−0
• src/Conjure/Conjurable.hs +4/−0
• src/Conjure/Engine.hs +9/−26
• src/Conjure/Expr.hs +65/−0
• src/Conjure/Utils.hs +10/−0
• test/expr.hs +29/−0
• test/model/bench/ill-hit.out +30/−30
• test/model/bench/self.out +12/−12
• test/model/bench/take-drop.out +33/−0
• test/model/eg/arith.out +16/−16
• test/model/eg/bools.out +28/−28
• test/model/eg/factorial.out +14/−14
• test/model/eg/ints.out +35/−35
• test/model/eg/list.out +62/−62
• test/model/eg/spec.out +21/−21
• test/model/eg/tapps.out +18/−18

@@ -36,6 +36,7 @@ eg/spec bench/self bench/ill-hit+bench/take-drop proto/u-conjure test/expr test/conjurable

@@ -15,6 +15,7 @@   eg/tapps \   bench/ill-hit \   bench/self \+  bench/take-drop \   proto/u-conjure  TESTS = \

@@ -1,1 +1,1 @@-1.89+1.64

@@ -0,0 +1,1 @@+6.42

@@ -1,1 +1,1 @@-0.95+0.94

@@ -1,1 +1,1 @@-7.20+6.83

@@ -1,1 +1,1 @@-7.18+5.26

@@ -1,1 +1,1 @@-1.84+1.44

@@ -1,1 +1,1 @@-10.23+3.20

@@ -1,1 +1,1 @@-1.47+0.68

@@ -1,1 +1,1 @@-0.87+0.73

@@ -1,1 +1,1 @@-0.32+0.33

@@ -1,4 +1,4 @@ GHC 8.10.4-leancheck-0.9.4+leancheck-0.9.6 express-0.1.10 speculate-0.4.6

@@ -0,0 +1,45 @@+-- based code sent by Colin Runciman+import Conjure++drop' :: Int -> [a] -> [a]+drop' 0 []     =  []+drop' 1 []     =  []+drop' 0 [x,y]  =  [x,y]+drop' 1 [x,y]  =  [y]+drop' 2 [x,y]  =  []+drop' 3 [x,y]  =  []++take' :: Int -> [a] -> [a]+take' 0 []     =  []+take' 1 []     =  []+take' 0 [x,y]  =  []+take' 1 [x,y]  =  [x]+take' 2 [x,y]  =  [x,y]+take' 3 [x,y]  =  [x,y]++main :: IO ()+main = do+  -- drop n xs = if n==0 || null xs then xs else drop (dec n) (tail xs)+  -- needs size 13+  conjureWithMaxSize 13 "drop" (drop' :: Int -> [A] -> [A])+    [ val (0 :: Int)+    , value "null" (null :: [A] -> Bool)+    , value "==" ((==) :: Int -> Int -> Bool)+    , value "||" (||)+    , value "dec" (subtract 1 :: Int -> Int)+    , value "tail" (tail :: [A] -> [A])+    ]++  -- take n xs = if n==0 || null xs then [] else head xs : take (dec n) (tail xs)+  -- needs size 16+  conjureWithMaxSize 13 "take" (take' :: Int -> [A] -> [A])+    [ val (0 :: Int)+    , val ([] :: [A])+    , value "null" (null :: [A] -> Bool)+    , value "==" ((==) :: Int -> Int -> Bool)+    , value "||" ((||) :: Bool -> Bool -> Bool)+    , value "dec" ((\n -> n-1) :: Int -> Int)+    , value ":" ((:) :: A -> [A] -> [A])+    , value "head" (head :: [A] -> A)+    , value "tail" (tail :: [A] -> [A])+    ]

@@ -2,6 +2,14 @@ ============================  +v0.3.0+------++* only automatically include an `if` for the return type of the given function+* add the `take-drop` benchmark+* make bottom-up enumeration more type directed++ v0.2.8 ------ 

@@ -3,7 +3,7 @@ -- Copyright (C) 2021 Rudy Matela -- Distributed under the 3-Clause BSD licence (see the file LICENSE). name:                code-conjure-version:             0.2.8+version:             0.3.0 synopsis:            conjure Haskell functions out of partial definitions description:   Conjure is a tool that produces Haskell functions out of partial definitions.@@ -65,7 +65,7 @@ source-repository this   type:            git   location:        https://github.com/rudymatela/conjure-  tag:             v0.2.8+  tag:             v0.3.0  library   exposed-modules: Conjure

@@ -20,6 +20,17 @@   src/Conjure/Engine.hs \   src/Conjure/Conjurable.hs \   bench/self.hs+bench/take-drop: \+  bench/take-drop.hs \+  mk/toplibs+bench/take-drop.o: \+  src/Conjure/Utils.hs \+  src/Conjure/Spec.hs \+  src/Conjure.hs \+  src/Conjure/Expr.hs \+  src/Conjure/Engine.hs \+  src/Conjure/Conjurable.hs \+  bench/take-drop.hs eg/arith: \   eg/arith.hs \   mk/toplibs

@@ -106,7 +106,10 @@   conjureSubTypes :: a -> Reification   conjureSubTypes _  =  id +  conjureIf :: a -> Expr+  conjureIf   =  ifFor + conjureType :: Conjurable a => a -> Reification conjureType x ms  =   if hole x `elem` [h | (h,_,_,_) <- ms]@@ -304,6 +307,7 @@ instance (Conjurable a, Conjurable b) => Conjurable (a -> b) where   conjureArgumentHoles f  =  hole (argTy f) : conjureArgumentHoles (f undefined)   conjureSubTypes f  =  conjureType (argTy f) . conjureType (resTy f)+  conjureIf f  =  conjureIf (f undefined)  argTy :: (a -> b) -> a argTy _  =  undefined

@@ -25,6 +25,8 @@   ) where +import Control.Monad (when)+ import Data.Express import Data.Express.Fixtures hiding ((-==-)) @@ -130,8 +132,9 @@   where   pr n []  =  putStrLn $ "cannot conjure"   pr n ((is,cs,es):rs)  =  do+    -- when (n==1) $ putStrLn $ unlines $ map show es     putStrLn $ "-- looking through "-            ++ show (length cs) ++ "/" ++ show (length es)+            ++ show (length cs)             ++ " candidates of size " ++ show n     case is of       []     ->  pr (n+1) rs@@ -192,33 +195,13 @@                -> [Expr]                -> [[Expr]] candidateExprs nm f sz mc (===) es  =-  candidateExprsT nm f sz mc (===) [nub $ es ++ conjureIfs f]---candidateExprsT :: Conjurable f-                => String -> f-                -> Int-                -> Int-                -> (Expr -> Expr -> Bool)-                -> [[Expr]]-                -> [[Expr]]-candidateExprsT nm f sz mc (===) ess  =-  candidateExprsTT keep $ [ef:exs] \/ ess+  enumerateAppsFor efxs keep $ nub $ (ef:exs) ++ es ++ [conjureIf f]   where-  (ef:exs)  =  unfoldApp $ conjureVarApplication nm f+  efxs  =  conjureVarApplication nm f+  (ef:exs)  =  unfoldApp efxs   keep e  =  isRootNormalE thy e && count (== ef) (vars e) <= mc-  thy  =  theoryFromAtoms (===) sz $ [conjureHoles f ++ falseAndTrue]-                                  \/ filterT (`notElem` falseAndTrue) ess-  falseAndTrue  =  [val False, val True]---candidateExprsTT :: (Expr -> Bool) -> [[Expr]] -> [[Expr]]-candidateExprsTT keep  =  exprT-  where-  exprT ess  =  filterT keep-             $  ess \/ (delay $ productMaybeWith ($$) rss rss)-    where-    rss = exprT ess+  thy  =  theoryFromAtoms (===) sz . (:[]) . nub+       $  conjureHoles f ++ [val False, val True] ++ es ++ [conjureIf f]   candidatesTD :: (Expr -> Bool) -> Expr -> [Expr] -> [[Expr]]

@@ -29,7 +29,11 @@   , rhs   , ($$**)   , ($$|<)+  , possibleHoles +  , enumerateApps+  , enumerateAppsFor+   , module Conjure.Utils   ) where@@ -40,6 +44,8 @@ import Data.Express.Utils.Typeable import Data.Express.Fixtures hiding ((-==-)) +import Test.LeanCheck (filterT, (\/), delay, productWith, productMaybeWith)+ -- | /O(n)/. -- Compares the simplicity of two 'Expr's. -- An expression /e1/ is /strictly simpler/ than another expression /e2/@@ -259,3 +265,62 @@   ktyp :: Expr -> TypeRep   ktyp (e1 :$ e2)  =  resultTy (ktyp e1)   ktyp e  =  typ e++possibleHoles :: [Expr] -> [Expr]+possibleHoles  =  nubSort . ph . nubSort . map holeAsTypeOf+  where+  ph hs  =  case nubSort $ hs ++ [holeAsTypeOf hfx | hf <- hs, hx <- hs, Just hfx <- [hf $$ hx]] of+            hs' | hs' == hs -> hs+                | otherwise -> ph hs'+  nubSort  =  nub . sort -- TODO: this is O(n^2), make this O(n log n)+++-- -- Expression enumeration -- --++enumerateAppsFor :: Expr -> (Expr -> Bool) -> [Expr] -> [[Expr]]+enumerateAppsFor  =  enumerateApps3For++enumerateApps :: (Expr -> Bool) -> [Expr] -> [[Expr]]+enumerateApps  =  enumerateApps1++enumerateApps1For :: Expr -> (Expr -> Bool) -> [Expr] -> [[Expr]]+enumerateApps1For h keep  =  filterT (\e -> typ e == typ h) . enumerateApps1 keep++enumerateApps1 :: (Expr -> Bool) -> [Expr] -> [[Expr]]+enumerateApps1 keep  =  exprT . (:[])+  where+  exprT ess  =  filterT keep+             $  ess \/ (delay $ productMaybeWith ($$) rss rss)+    where+    rss = exprT ess++enumerateApps2For :: Expr -> (Expr -> Bool) -> [Expr] -> [[Expr]]+enumerateApps2For h keep  =  map concat+                          .  filterT (\(e:_) -> typ e == typ h)+                          .  exprT+                          .  map (groupOn typ . sortOn typ)+                          .  (:[])+  where+  exprT :: [[[Expr]]] -> [[[Expr]]]+  exprT ess  =  ess \/ (delay $ productMaybeWith ($$**) rss rss)+    where+    rss = exprT ess+    efs $$** exs+      | isNothing (head efs $$ head exs)  =  Nothing+      | otherwise  =  case [ef :$ ex | ef <- efs, ex <- exs, keep (ef :$ ex)] of+                      [] -> Nothing+                      es -> Just es++enumerateApps3For :: Expr -> (Expr -> Bool) -> [Expr] -> [[Expr]]+enumerateApps3For h keep es  =  for h+  where+  hs :: [Expr]+  hs  =  possibleHoles es+  for :: Expr -> [[Expr]]+  for h  =  [e | e <- es, typ h == typ e]+         :  foldr (\/) [] [ filterT keep $ productWith (:$) (for hf) (for hx)+                          | hf <- hs+                          , hx <- hs+                          , Just hfx <- [hf $$ hx]+                          , typ h == typ hfx+                          ]

@@ -20,6 +20,8 @@   , nubOn   , iterateUntil   , mzip+  , groupOn+  , sortOn   ) where @@ -49,3 +51,11 @@ mzip [] ys  =  ys mzip xs []  =  xs mzip (x:xs) (y:ys)  =  x <> y : mzip xs ys++groupOn :: Eq b => (a -> b) -> [a] -> [[a]]+groupOn f = groupBy ((==) `on` f)++#if __GLASGOW_HASKELL__ < 710+sortOn :: Ord b => (a -> b) -> [a] -> [a]+sortOn f = sortBy (compare `on` f)+#endif

@@ -159,4 +159,33 @@    , holds n $ \e es -> not (any hasHole es)                    ==> boupCandidates e es =$ map sort . take 12 $= townCandidates e es++  , possibleHoles [plus, times, zero, one]+    == [ hole (undefined :: Int)+       , hole (undefined :: Int -> Int)+       , hole (undefined :: Int -> Int -> Int)+       ]++  , possibleHoles [andE, orE, false, true]+    == [ hole (undefined :: Bool)+       , hole (undefined :: Bool -> Bool)+       , hole (undefined :: Bool -> Bool -> Bool)+       ]++  , possibleHoles [plus, times, zero, one, andE, orE, false, true]+    == [ hole (undefined :: Bool)+       , hole (undefined :: Int)+       , hole (undefined :: Bool -> Bool)+       , hole (undefined :: Int -> Int)+       , hole (undefined :: Bool -> Bool -> Bool)+       , hole (undefined :: Int -> Int -> Int)+       ]++  , possibleHoles [plus, times, zero, one, value "odd" (odd :: Int -> Bool)]+    == [ hole (undefined :: Bool)+       , hole (undefined :: Int)+       , hole (undefined :: Int -> Bool)+       , hole (undefined :: Int -> Int)+       , hole (undefined :: Int -> Int -> Int)+       ]   ]

@@ -1,42 +1,42 @@ sum :: [Int] -> Int -- testing 4 combinations of argument values--- looking through 2/11 candidates of size 1--- looking through 2/8 candidates of size 2--- looking through 3/11 candidates of size 3--- looking through 5/18 candidates of size 4--- looking through 13/33 candidates of size 5--- looking through 26/68 candidates of size 6--- looking through 63/143 candidates of size 7--- looking through 152/336 candidates of size 8--- looking through 358/783 candidates of size 9--- looking through 860/1835 candidates of size 10+-- looking through 2 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 3 candidates of size 3+-- looking through 5 candidates of size 4+-- looking through 13 candidates of size 5+-- looking through 26 candidates of size 6+-- looking through 59 candidates of size 7+-- looking through 140 candidates of size 8+-- looking through 326 candidates of size 9+-- looking through 776 candidates of size 10 sum xs  =  if null xs then 0 else head xs + sum (tail xs)  sum :: [Int] -> Int -- testing 6 combinations of argument values--- looking through 2/11 candidates of size 1--- looking through 2/8 candidates of size 2--- looking through 3/11 candidates of size 3--- looking through 5/18 candidates of size 4--- looking through 13/33 candidates of size 5--- looking through 26/68 candidates of size 6--- looking through 63/143 candidates of size 7--- looking through 152/336 candidates of size 8--- looking through 358/783 candidates of size 9--- looking through 860/1835 candidates of size 10+-- looking through 2 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 3 candidates of size 3+-- looking through 5 candidates of size 4+-- looking through 13 candidates of size 5+-- looking through 26 candidates of size 6+-- looking through 59 candidates of size 7+-- looking through 140 candidates of size 8+-- looking through 326 candidates of size 9+-- looking through 776 candidates of size 10 sum xs  =  if null xs then 0 else head xs + sum (tail xs)  sum :: [Int] -> Int -- testing 6 combinations of argument values--- looking through 2/11 candidates of size 1--- looking through 2/8 candidates of size 2--- looking through 3/11 candidates of size 3--- looking through 5/18 candidates of size 4--- looking through 13/33 candidates of size 5--- looking through 26/68 candidates of size 6--- looking through 63/143 candidates of size 7--- looking through 152/336 candidates of size 8--- looking through 358/783 candidates of size 9--- looking through 860/1835 candidates of size 10+-- looking through 2 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 3 candidates of size 3+-- looking through 5 candidates of size 4+-- looking through 13 candidates of size 5+-- looking through 26 candidates of size 6+-- looking through 59 candidates of size 7+-- looking through 140 candidates of size 8+-- looking through 326 candidates of size 9+-- looking through 776 candidates of size 10 sum xs  =  if null xs then 0 else head xs + sum (tail xs) 

@@ -1,27 +1,27 @@ (?) :: Int -> Int -> Int -- testing 60 combinations of argument values--- looking through 4/8 candidates of size 1--- looking through 0/12 candidates of size 2--- looking through 48/48 candidates of size 3+-- looking through 4 candidates of size 1+-- looking through 0 candidates of size 2+-- looking through 48 candidates of size 3 x ? y  =  x + y  (?) :: Int -> Int -> Int -- testing 60 combinations of argument values--- looking through 4/8 candidates of size 1--- looking through 0/12 candidates of size 2--- looking through 48/48 candidates of size 3+-- looking through 4 candidates of size 1+-- looking through 0 candidates of size 2+-- looking through 48 candidates of size 3 x ? y  =  x * y  i :: Int -> Int -- testing 60 combinations of argument values--- looking through 3/7 candidates of size 1--- looking through 3/9 candidates of size 2--- looking through 18/24 candidates of size 3+-- looking through 3 candidates of size 1+-- looking through 3 candidates of size 2+-- looking through 18 candidates of size 3 i x  =  x + 1  d :: Int -> Int -- testing 60 combinations of argument values--- looking through 3/7 candidates of size 1--- looking through 3/9 candidates of size 2--- looking through 18/24 candidates of size 3+-- looking through 3 candidates of size 1+-- looking through 3 candidates of size 2+-- looking through 18 candidates of size 3 cannot conjure

@@ -0,0 +1,33 @@+drop :: Int -> [A] -> [A]+-- testing 60 combinations of argument values+-- looking through 1 candidates of size 1+-- looking through 1 candidates of size 2+-- looking through 3 candidates of size 3+-- looking through 7 candidates of size 4+-- looking through 13 candidates of size 5+-- looking through 23 candidates of size 6+-- looking through 45 candidates of size 7+-- looking through 111 candidates of size 8+-- looking through 301 candidates of size 9+-- looking through 789 candidates of size 10+-- looking through 1919 candidates of size 11+-- looking through 4539 candidates of size 12+-- looking through 10873 candidates of size 13+drop x y  =  if null y || x == 0 then y else drop (dec x) (tail y)++take :: Int -> [A] -> [A]+-- testing 60 combinations of argument values+-- looking through 2 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 6 candidates of size 3+-- looking through 18 candidates of size 4+-- looking through 34 candidates of size 5+-- looking through 94 candidates of size 6+-- looking through 268 candidates of size 7+-- looking through 792 candidates of size 8+-- looking through 2378 candidates of size 9+-- looking through 6912 candidates of size 10+-- looking through 20324 candidates of size 11+-- looking through 61034 candidates of size 12+-- looking through 184544 candidates of size 13+cannot conjure

@@ -1,32 +1,32 @@ double :: Int -> Int -- testing 4 combinations of argument values--- looking through 3/7 candidates of size 1--- looking through 3/9 candidates of size 2--- looking through 5/11 candidates of size 3+-- looking through 3 candidates of size 1+-- looking through 3 candidates of size 2+-- looking through 5 candidates of size 3 double x  =  x + x  add :: Int -> Int -> Int -- testing 4 combinations of argument values--- looking through 4/8 candidates of size 1--- looking through 0/12 candidates of size 2--- looking through 29/29 candidates of size 3+-- looking through 4 candidates of size 1+-- looking through 0 candidates of size 2+-- looking through 29 candidates of size 3 add x y  =  x + y  square :: Int -> Int -- testing 3 combinations of argument values--- looking through 3/7 candidates of size 1--- looking through 3/9 candidates of size 2--- looking through 5/11 candidates of size 3+-- looking through 3 candidates of size 1+-- looking through 3 candidates of size 2+-- looking through 5 candidates of size 3 square x  =  x * x  tnpo :: Int -> Int -- testing 3 combinations of argument values--- looking through 3/7 candidates of size 1--- looking through 3/9 candidates of size 2--- looking through 5/11 candidates of size 3--- looking through 20/30 candidates of size 4--- looking through 13/53 candidates of size 5--- looking through 97/123 candidates of size 6--- looking through 42/236 candidates of size 7+-- looking through 3 candidates of size 1+-- looking through 3 candidates of size 2+-- looking through 5 candidates of size 3+-- looking through 20 candidates of size 4+-- looking through 13 candidates of size 5+-- looking through 97 candidates of size 6+-- looking through 42 candidates of size 7 tnpo x  =  x + (x + (x + 1)) 

@@ -1,44 +1,44 @@ and :: [Bool] -> Bool -- testing 14 combinations of argument values--- looking through 2/12 candidates of size 1--- looking through 3/12 candidates of size 2--- looking through 6/25 candidates of size 3--- looking through 6/48 candidates of size 4--- looking through 16/84 candidates of size 5--- looking through 41/185 candidates of size 6--- looking through 103/447 candidates of size 7--- looking through 278/1123 candidates of size 8--- looking through 752/2982 candidates of size 9+-- looking through 2 candidates of size 1+-- looking through 3 candidates of size 2+-- looking through 6 candidates of size 3+-- looking through 6 candidates of size 4+-- looking through 16 candidates of size 5+-- looking through 41 candidates of size 6+-- looking through 87 candidates of size 7+-- looking through 214 candidates of size 8+-- looking through 592 candidates of size 9 and ps  =  null ps || head ps && and (tail ps)  or :: [Bool] -> Bool -- testing 14 combinations of argument values--- looking through 2/12 candidates of size 1--- looking through 3/12 candidates of size 2--- looking through 6/25 candidates of size 3--- looking through 6/48 candidates of size 4--- looking through 16/84 candidates of size 5--- looking through 41/185 candidates of size 6--- looking through 103/447 candidates of size 7--- looking through 278/1123 candidates of size 8--- looking through 752/2982 candidates of size 9--- looking through 1963/7993 candidates of size 10--- looking through 5427/21497 candidates of size 11+-- looking through 2 candidates of size 1+-- looking through 3 candidates of size 2+-- looking through 6 candidates of size 3+-- looking through 6 candidates of size 4+-- looking through 16 candidates of size 5+-- looking through 41 candidates of size 6+-- looking through 87 candidates of size 7+-- looking through 214 candidates of size 8+-- looking through 592 candidates of size 9+-- looking through 1503 candidates of size 10+-- looking through 3987 candidates of size 11 or ps  =  not (null ps || not (head ps || or (tail ps)))  and :: [Bool] -> Bool -- testing 14 combinations of argument values--- looking through 2/13 candidates of size 1--- looking through 3/14 candidates of size 2--- looking through 6/31 candidates of size 3--- looking through 8/63 candidates of size 4+-- looking through 2 candidates of size 1+-- looking through 3 candidates of size 2+-- looking through 6 candidates of size 3+-- looking through 8 candidates of size 4 and ps  =  foldr (&&) True ps  or :: [Bool] -> Bool -- testing 14 combinations of argument values--- looking through 2/13 candidates of size 1--- looking through 3/14 candidates of size 2--- looking through 6/31 candidates of size 3--- looking through 8/63 candidates of size 4+-- looking through 2 candidates of size 1+-- looking through 3 candidates of size 2+-- looking through 6 candidates of size 3+-- looking through 8 candidates of size 4 or ps  =  foldr (||) False ps 

@@ -1,22 +1,22 @@ factorial :: Int -> Int -- testing 6 combinations of argument values--- looking through 2/6 candidates of size 1--- looking through 2/4 candidates of size 2--- looking through 0/6 candidates of size 3--- looking through 2/10 candidates of size 4+-- looking through 2 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 0 candidates of size 3+-- looking through 2 candidates of size 4 factorial n  =  product (enumFromTo 1 n)  factorial :: Int -> Int -- testing 6 combinations of argument values--- looking through 3/9 candidates of size 1--- looking through 5/14 candidates of size 2--- looking through 8/26 candidates of size 3--- looking through 26/66 candidates of size 4--- looking through 59/180 candidates of size 5--- looking through 167/505 candidates of size 6--- looking through 581/1521 candidates of size 7--- looking through 1654/4809 candidates of size 8--- looking through 5736/15120 candidates of size 9--- looking through 17617/48943 candidates of size 10+-- looking through 3 candidates of size 1+-- looking through 5 candidates of size 2+-- looking through 8 candidates of size 3+-- looking through 26 candidates of size 4+-- looking through 59 candidates of size 5+-- looking through 167 candidates of size 6+-- looking through 581 candidates of size 7+-- looking through 1654 candidates of size 8+-- looking through 5736 candidates of size 9+-- looking through 17617 candidates of size 10 factorial n  =  if n == 0 then 1 else n * factorial (dec n) 

@@ -1,59 +1,59 @@ second :: [Int] -> Int -- testing 60 combinations of argument values--- looking through 2/11 candidates of size 1--- looking through 2/8 candidates of size 2--- looking through 3/11 candidates of size 3+-- looking through 2 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 3 candidates of size 3 second xs  =  head (tail xs)  third :: [Int] -> Int -- testing 60 combinations of argument values--- looking through 2/11 candidates of size 1--- looking through 2/8 candidates of size 2--- looking through 3/11 candidates of size 3--- looking through 5/18 candidates of size 4+-- looking through 2 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 3 candidates of size 3+-- looking through 5 candidates of size 4 third xs  =  head (tail (tail xs))  sum :: [Int] -> Int -- testing 60 combinations of argument values--- looking through 2/11 candidates of size 1--- looking through 2/8 candidates of size 2--- looking through 3/11 candidates of size 3--- looking through 5/18 candidates of size 4--- looking through 13/33 candidates of size 5--- looking through 26/68 candidates of size 6--- looking through 63/143 candidates of size 7--- looking through 152/336 candidates of size 8--- looking through 358/783 candidates of size 9--- looking through 860/1835 candidates of size 10+-- looking through 2 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 3 candidates of size 3+-- looking through 5 candidates of size 4+-- looking through 13 candidates of size 5+-- looking through 26 candidates of size 6+-- looking through 59 candidates of size 7+-- looking through 140 candidates of size 8+-- looking through 326 candidates of size 9+-- looking through 776 candidates of size 10 sum xs  =  if null xs then 0 else head xs + sum (tail xs)  product :: [Int] -> Int -- testing 60 combinations of argument values--- looking through 2/11 candidates of size 1--- looking through 2/8 candidates of size 2--- looking through 3/11 candidates of size 3--- looking through 5/18 candidates of size 4--- looking through 13/33 candidates of size 5--- looking through 26/68 candidates of size 6--- looking through 63/143 candidates of size 7--- looking through 152/336 candidates of size 8--- looking through 358/783 candidates of size 9--- looking through 860/1835 candidates of size 10+-- looking through 2 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 3 candidates of size 3+-- looking through 5 candidates of size 4+-- looking through 13 candidates of size 5+-- looking through 26 candidates of size 6+-- looking through 59 candidates of size 7+-- looking through 140 candidates of size 8+-- looking through 326 candidates of size 9+-- looking through 776 candidates of size 10 product xs  =  if null xs then 1 else head xs * product (tail xs)  sum :: [Int] -> Int -- testing 60 combinations of argument values--- looking through 2/12 candidates of size 1--- looking through 2/10 candidates of size 2--- looking through 3/15 candidates of size 3--- looking through 8/26 candidates of size 4+-- looking through 2 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 3 candidates of size 3+-- looking through 8 candidates of size 4 sum xs  =  foldr (+) 0 xs  product :: [Int] -> Int -- testing 60 combinations of argument values--- looking through 2/12 candidates of size 1--- looking through 2/10 candidates of size 2--- looking through 3/15 candidates of size 3--- looking through 8/26 candidates of size 4+-- looking through 2 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 3 candidates of size 3+-- looking through 8 candidates of size 4 product xs  =  foldr (*) 1 xs 

@@ -1,94 +1,94 @@ length :: [Int] -> Int -- testing 60 combinations of argument values--- looking through 2/9 candidates of size 1--- looking through 1/5 candidates of size 2--- looking through 2/7 candidates of size 3--- looking through 3/12 candidates of size 4--- looking through 5/17 candidates of size 5--- looking through 11/30 candidates of size 6--- looking through 22/57 candidates of size 7--- looking through 51/119 candidates of size 8--- looking through 95/240 candidates of size 9+-- looking through 2 candidates of size 1+-- looking through 1 candidates of size 2+-- looking through 2 candidates of size 3+-- looking through 3 candidates of size 4+-- looking through 5 candidates of size 5+-- looking through 11 candidates of size 6+-- looking through 20 candidates of size 7+-- looking through 45 candidates of size 8+-- looking through 79 candidates of size 9 length xs  =  if null xs then 0 else 1 + length (tail xs)  reverse :: [Int] -> [Int] -- testing 60 combinations of argument values--- looking through 2/10 candidates of size 1--- looking through 4/9 candidates of size 2--- looking through 9/23 candidates of size 3--- looking through 24/56 candidates of size 4--- looking through 65/153 candidates of size 5--- looking through 215/466 candidates of size 6--- looking through 673/1462 candidates of size 7--- looking through 2176/4680 candidates of size 8--- looking through 7126/15229 candidates of size 9--- looking through 23619/50202 candidates of size 10--- looking through 79162/167174 candidates of size 11+-- looking through 2 candidates of size 1+-- looking through 4 candidates of size 2+-- looking through 9 candidates of size 3+-- looking through 24 candidates of size 4+-- looking through 65 candidates of size 5+-- looking through 215 candidates of size 6+-- looking through 673 candidates of size 7+-- looking through 2174 candidates of size 8+-- looking through 7100 candidates of size 9+-- looking through 23503 candidates of size 10+-- looking through 78714 candidates of size 11 reverse xs  =  if null xs then xs else reverse (tail xs) ++ unit (head xs)  sort :: [Int] -> [Int] -- testing 60 combinations of argument values--- looking through 2/9 candidates of size 1--- looking through 4/7 candidates of size 2--- looking through 6/18 candidates of size 3--- looking through 12/38 candidates of size 4--- looking through 31/81 candidates of size 5--- looking through 98/207 candidates of size 6--- looking through 287/576 candidates of size 7--- looking through 790/1661 candidates of size 8--- looking through 2192/4759 candidates of size 9--- looking through 6352/13661 candidates of size 10+-- looking through 2 candidates of size 1+-- looking through 4 candidates of size 2+-- looking through 6 candidates of size 3+-- looking through 12 candidates of size 4+-- looking through 31 candidates of size 5+-- looking through 98 candidates of size 6+-- looking through 287 candidates of size 7+-- looking through 790 candidates of size 8+-- looking through 2188 candidates of size 9+-- looking through 6290 candidates of size 10 sort xs  =  if null xs then xs else insert (head xs) (sort (tail xs))  (++) :: [Int] -> [Int] -> [Int] -- testing 60 combinations of argument values--- looking through 3/10 candidates of size 1--- looking through 3/11 candidates of size 2--- looking through 12/28 candidates of size 3--- looking through 39/81 candidates of size 4--- looking through 83/212 candidates of size 5--- looking through 290/623 candidates of size 6--- looking through 1013/2039 candidates of size 7--- looking through 3482/6732 candidates of size 8--- looking through 11207/22507 candidates of size 9--- looking through 36383/74650 candidates of size 10--- looking through 124785/250463 candidates of size 11+-- looking through 3 candidates of size 1+-- looking through 3 candidates of size 2+-- looking through 12 candidates of size 3+-- looking through 39 candidates of size 4+-- looking through 83 candidates of size 5+-- looking through 290 candidates of size 6+-- looking through 1013 candidates of size 7+-- looking through 3482 candidates of size 8+-- looking through 11171 candidates of size 9+-- looking through 36185 candidates of size 10+-- looking through 123417 candidates of size 11 xs ++ ys  =  if null xs then ys else head xs:(tail xs ++ ys)  length :: [Int] -> Int -- testing 60 combinations of argument values--- looking through 2/9 candidates of size 1--- looking through 1/4 candidates of size 2--- looking through 1/6 candidates of size 3--- looking through 4/13 candidates of size 4--- looking through 2/21 candidates of size 5--- looking through 10/45 candidates of size 6+-- looking through 2 candidates of size 1+-- looking through 1 candidates of size 2+-- looking through 1 candidates of size 3+-- looking through 4 candidates of size 4+-- looking through 2 candidates of size 5+-- looking through 10 candidates of size 6 length xs  =  foldr (const (1 +)) 0 xs  reverse :: [Int] -> [Int] -- testing 60 combinations of argument values--- looking through 2/10 candidates of size 1--- looking through 2/6 candidates of size 2--- looking through 1/8 candidates of size 3--- looking through 5/14 candidates of size 4--- looking through 1/19 candidates of size 5--- looking through 17/43 candidates of size 6--- looking through 37/89 candidates of size 7+-- looking through 2 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 1 candidates of size 3+-- looking through 5 candidates of size 4+-- looking through 1 candidates of size 5+-- looking through 17 candidates of size 6+-- looking through 37 candidates of size 7 reverse xs  =  foldr (flip (++) . unit) [] xs  sort :: [Int] -> [Int] -- testing 60 combinations of argument values--- looking through 2/7 candidates of size 1--- looking through 2/3 candidates of size 2--- looking through 0/2 candidates of size 3--- looking through 2/4 candidates of size 4+-- looking through 2 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 0 candidates of size 3+-- looking through 2 candidates of size 4 sort xs  =  foldr insert [] xs  (++) :: [Int] -> [Int] -> [Int] -- testing 60 combinations of argument values--- looking through 3/8 candidates of size 1--- looking through 0/4 candidates of size 2--- looking through 9/12 candidates of size 3--- looking through 4/4 candidates of size 4+-- looking through 3 candidates of size 1+-- looking through 0 candidates of size 2+-- looking through 9 candidates of size 3+-- looking through 4 candidates of size 4 xs ++ ys  =  foldr (:) ys xs 

@@ -1,29 +1,29 @@ sum :: [Int] -> Int -- testing 3 combinations of argument values--- looking through 1/9 candidates of size 1--- looking through 2/5 candidates of size 2--- looking through 2/8 candidates of size 3--- looking through 2/10 candidates of size 4--- looking through 5/16 candidates of size 5--- looking through 10/29 candidates of size 6--- looking through 23/56 candidates of size 7--- looking through 46/114 candidates of size 8--- looking through 92/228 candidates of size 9--- looking through 189/465 candidates of size 10+-- looking through 1 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 2 candidates of size 3+-- looking through 2 candidates of size 4+-- looking through 5 candidates of size 5+-- looking through 10 candidates of size 6+-- looking through 19 candidates of size 7+-- looking through 34 candidates of size 8+-- looking through 64 candidates of size 9+-- looking through 129 candidates of size 10 sum xs  =  if null xs then 0 else head xs + sum (tail xs)  (++) :: [Int] -> [Int] -> [Int] -- testing 3 combinations of argument values--- looking through 2/9 candidates of size 1--- looking through 2/8 candidates of size 2--- looking through 6/18 candidates of size 3--- looking through 18/42 candidates of size 4--- looking through 38/102 candidates of size 5--- looking through 110/262 candidates of size 6--- looking through 334/746 candidates of size 7--- looking through 1018/2170 candidates of size 8--- looking through 2966/6442 candidates of size 9--- looking through 8662/19142 candidates of size 10--- looking through 26166/57090 candidates of size 11+-- looking through 2 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 6 candidates of size 3+-- looking through 18 candidates of size 4+-- looking through 38 candidates of size 5+-- looking through 110 candidates of size 6+-- looking through 334 candidates of size 7+-- looking through 1018 candidates of size 8+-- looking through 2958 candidates of size 9+-- looking through 8614 candidates of size 10+-- looking through 25910 candidates of size 11 xs ++ ys  =  if null xs then ys else head xs:(tail xs ++ ys) 

@@ -1,30 +1,30 @@ third :: [Int] -> Int -- testing 60 combinations of argument values--- looking through 2/11 candidates of size 1--- looking through 2/8 candidates of size 2--- looking through 3/11 candidates of size 3--- looking through 5/18 candidates of size 4+-- looking through 2 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 3 candidates of size 3+-- looking through 5 candidates of size 4 third xs  =  head (tail (tail xs))  product :: [Int] -> Int -- testing 60 combinations of argument values--- looking through 2/11 candidates of size 1--- looking through 2/8 candidates of size 2--- looking through 3/11 candidates of size 3--- looking through 5/18 candidates of size 4--- looking through 13/33 candidates of size 5--- looking through 26/68 candidates of size 6--- looking through 63/143 candidates of size 7--- looking through 152/336 candidates of size 8--- looking through 358/783 candidates of size 9--- looking through 860/1835 candidates of size 10+-- looking through 2 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 3 candidates of size 3+-- looking through 5 candidates of size 4+-- looking through 13 candidates of size 5+-- looking through 26 candidates of size 6+-- looking through 59 candidates of size 7+-- looking through 140 candidates of size 8+-- looking through 326 candidates of size 9+-- looking through 776 candidates of size 10 product xs  =  if null xs then 1 else head xs * product (tail xs)  product :: [Int] -> Int -- testing 60 combinations of argument values--- looking through 2/12 candidates of size 1--- looking through 2/10 candidates of size 2--- looking through 3/15 candidates of size 3--- looking through 8/26 candidates of size 4+-- looking through 2 candidates of size 1+-- looking through 2 candidates of size 2+-- looking through 3 candidates of size 3+-- looking through 8 candidates of size 4 product xs  =  foldr (*) 1 xs