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How can I simplify the below expressions using primitive recursion?

Possible duplicate:
Symbolic simplification in Haskell (using recursion?)

I have simplifications:

0*e = e*0 = 0
1*e = e*1 = 0+e = e+0 = e-0 = e

and simplification of constant subexpressions eg. Plus (Const 1) (Const 2)

will become Const 3

. I would not expect variables (or variables and constants) to be combined: Var "st"

is a great variable from Var "s"

.

for example simplify(Plus (Var "x") (Const 0))= Var "x"

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2 answers


Well, can't you apply pattern matching for individual cases?

simplify (Plus (Const 0) (Expr x)) = simplify (Expr x)
simplify (Plus (Expr x) (Const 0)) = simplify (Expr x)
simplify (Mult (Const 0) _) = Const 0
simplify (Mult _ (Const 0)) = Const 0
– … and so on


EDIT: Yes, of course ... recursion added.

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I don't know much about haskell, but essentially you want to do an expression tree traversal.

EXP tree: (statement) (EXP) (EXP) EXP: (const) EXP: (var)

then your simplification becomes heres psuedo code



simplify(Exp e)
if (e is const) return e
else if (e is var) return e
else
{//encode simplification rules
    Exp left = simplify(e.left)
    Exp right = simplify(e.right)
    if(operator is PLUS)
    {
        if(left == 0) return right;
        if(right == 0) return left;
    }
    else if(operator is MULT)
    {
        if(left == 1) return right;
        if(right == 1) return left;
        if(left == 0) return 0;
        if(right == 0) return 0;
    }
//and so on for other operators
}

It's kind of java esque, but I think the idea is there, in fact you will have to do tree traversal.

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