implementation module RefactorX

import StdEnv

//Start = map toString [E1,E2,E3,E4,E5]
//Start = map free [E1,E2,E3,E4,E5]
//Start = map toString (map remove_unused_lets [E1,E2,E3,E4,E5])
Start = map eval [E1,E2,E3,E4,E5]
	where
		E1 = OP (LET "x" (OP (NR 42) MIN (NR 3)) (OP (VAR "x") DIV (NR 0))) PLUS (LET "y" (NR 6) (OP (VAR "y") MUL (VAR "y")))
		E2 = LET "x" (NR 42) (OP (VAR "x") PLUS (LET "x" (NR 58) (VAR "x")))
		E3 = LET "x" (NR 1) (LET "y" (NR 2) (LET "x" (NR 3) (NR 4)))
		E4 = LET "x" (NR 1) (OP (VAR "x") PLUS (VAR "y"))
		E5 = OP (LET "x" (NR 1) (VAR "x")) MUL (VAR "x")

(<+) infixl 9 :: String a -> String | toString a
(<+) str a = str +++ toString a

instance toString Operator where
	toString PLUS = "+"
	toString MIN = "-"
	toString MUL = "*"
	toString DIV = "/"
 
instance toString Expr where
	toString (NR n) = toString n
	toString (VAR v) = v
	toString (LET n e1 e2) = "(let " <+ n <+ "=" <+ e1 <+ " in " <+ e2 <+ ")"
	toString (OP e1 o e2) = bracket e1 <+ o <+ bracket e2
		where
			bracket :: Expr -> String
			bracket (OP e1 o e2) = "(" <+ (OP e1 o e2) <+ ")"
			bracket e = toString e

free:: Expr -> [Name]
free (NR n) = [] 
free (VAR v) = [v]
free (OP e1 o e2) = removeDup (free e1 ++ free e2)
free (LET n e1 e2) = removeMember n (free e2)

remove_unused_lets:: Expr -> Expr
remove_unused_lets (LET n e1 e2)
| isMember n (free e2) = (LET n (remove_unused_lets e1) (remove_unused_lets e2))
| otherwise = remove_unused_lets e2
remove_unused_lets (OP e1 o e2) = (OP (remove_unused_lets e1) o (remove_unused_lets e2))
remove_unused_lets e = e

apply:: Operator Val Val -> Val
apply _ Undef _ = Undef
apply _ _ Undef = Undef
apply DIV _ (Result 0) = Undef
apply o (Result e1) (Result e2) = Result (apply` o e1 e2)
	where 
		apply`:: Operator -> Int Int -> Int
		apply` PLUS = +
		apply` MIN = -
		apply` MUL = *
		apply` DIV = /

eval:: Expr -> Val
eval e = eval` e []
	where
		eval`:: Expr [(Name, Val)] -> Val
		eval` (NR n) _ = Result n
		eval` (VAR v) [] = Undef
		eval` (VAR v) [(n, e):xs]
		| v == n = e
		| otherwise = eval` (VAR v) xs
		eval` (OP e1 o e2) xs = apply o (eval` e1 xs) (eval` e2 xs)
		eval` (LET n e1 e2) xs = eval` e2 [(n, eval` e1 xs):xs]