init, part of lecture 02 practice impl

02.hs

@@ -0,0 +1,60 @@
+import Data.List (elemIndex, sort)
+
+infixl 4 :+:
+
+data IntExpr = Zero
+             | Succ IntExpr
+             | Len ListExpr
+             | FirstZero ListExpr
+
+data ListExpr = Sort ListExpr
+              | SubList ListExpr IntExpr IntExpr
+              | ListExpr :+: ListExpr
+              | Recursive ListExpr
+              | ZeroList
+              | InList
+
+execInt :: [Int] -> ListExpr -> IntExpr -> Maybe Int
+execInt _ _ Zero = Just 0
+execInt input prog (Succ expr) = (+) 1 <$> execInt input prog expr
+execInt input prog (Len listExpr) = Just $ length $ execList input prog listExpr
+execInt input prog (FirstZero listExpr) = do value <- execList input prog listExpr
+                                             0 `elemIndex` value
+
+-- TODO: limit execution steps
+execList :: [Int] -> ListExpr -> ListExpr -> Maybe [Int]
+execList input prog (Sort listExpr) = sort <$> execList input prog listExpr
+execList input prog (SubList listExpr exprFrom exprTo) = do valFrom  <-execInt input prog exprFrom
+                                                            valTo <- execInt input prog exprTo
+                                                            listValue <- execList input prog listExpr
+                                                            return $ drop valFrom $ take valTo listValue
+execList input prog (exprLeft :+: exprRight) = do valLeft <- execList input prog exprLeft
+                                                  valRight <- execList input prog exprRight
+                                                  return $ valLeft ++ valRight
+execList input prog (Recursive listExpr) = do listValue <- execList input prog listExpr
+                                              if null listValue then Just [] else execList listValue prog prog
+execList input prog ZeroList = Just [0]
+execList input prog InList = Just input
+
+data AllExprs = AllExprs {ints :: [IntExpr], lists :: [ListExpr]}
+
+terminals :: AllExprs
+terminals = AllExprs {ints = [Zero], lists = [ZeroList, InList]}
+
+step :: AllExprs -> AllExprs
+step (AllExprs {ints = ints, lists = lists}) = AllExprs {ints = map Succ ints ++ map Len lists ++ map FirstZero lists ++ ints,
+                                                         lists = map Sort lists ++ zipWith3 SubList lists ints ints ++ zipWith (:+:) lists lists ++ map Recursive lists ++ lists}
+
+data Example = Example {input :: [Int], output :: [Int]}
+
+-- check expr on all examples
+isCorrect :: [Example] -> ListExpr -> Bool
+isCorrect examples expr = all (\Example {input = input, output = output} -> execList input expr expr == Just output) examples
+
+-- TODO: remove ones that cannot be executed correctly
+
+-- check are exprs produce same results on all the examples
+-- areSame :: [Example] -> ListExpr -> ListExpr -> Bool
+
+-- TODO
+-- upSyntesis