traversing an ast having complex conditional expression to generate linq expression

Question

I'm using Irony.net for generating a parse tree out of the source. Essentially I'm using ExpressionEvaluatorGrammer like grammer for binary expressions (arithmetic, relational and logical/conditional). I want to convert the resultant parse tree into Linq expression by traversing it. However, the tree does not seem to have a formation directly convertable to linq conditional expression. Hypothetical example of such an expression:

1 == 1 && 4 - 1 == 3

generates (pseudo xml tree for brevity):

<binary>
  <binary>
    <binary>
      <literal>1</literal>
      <op>==</op>
      <literal>1</literal>
    </binary>
    <op>&&</op>
    <binary>
      <literal>4</literal>
      <op>-</op>
      <literal>1</literal>
    </binary>
  </binary>
  <op>==</op>
  <literal>3</literal>
</binary>

In the tree above, the arithmetic expression (4 - 1) becomes the right expression to the && logical operation as the parent node closes after it. In the ideal world, it should have been a left expression of the nodes representing "== 3".

How do you traverse such a tree to generate a proper and operation? Or, is there a way to generate the tree in the form I desire?

Edit: here's the grammer (partial) definition. I have taken it from ExpressionEvaluatorGrammer that comes with Irony.interpreter.

RegisterOperators(15, "&", "&&", "|", "||");
RegisterOperators(20, "==", "<", "<=", ">", ">=", "!=");
RegisterOperators(30, "+", "-");
RegisterOperators(40, "*", "/");
Expr.Rule = Term
Term.Rule = number | ParExpr | stringLit | FunctionCall | identifier | MemberAccess | IndexedAccess;
ParExpr.Rule = "(" + Expr + ")";
BinExpr.Rule = Expr + BinOp + Expr;
BinOp.Rule = ToTerm("+") | "-" | "*" | "/" | "**" | "==" | "<" | "<=" | ">" | ">=" | "!=" | "&&" | "||" | "&" | "|";

Answer 1

Assuming the operator precedence is correct, you should walk the tree recursively using the Visitor Pattern, returning an Expression at each level:

XName xBinary = "binary";
XName xLiteral = "literal";
Expression Visit(XElement elt)
{
    if (elt.Name == xBinary)
    {
        return VisitBinary(elt);
    }
    else if (elt.Name == xLiteral)
    {
        return VisitLiteral(elt);
    } // ...

    throw new NotSupportedException();
}

Now that you have the Visit structure, you simply write each specific visitor to use your main Visit:

Expression VisitLiteral(XElement elt)
{
    Debug.Assert(elt.Name == xLiteral);
    return Expression.Constant((int)elt);
}

Expression VisitBinary(XElement elt)
{
    Debug.Assert(elt.Name == xBinary);
    Debug.Assert(elt.Elements().Count() >= 3);

    var lhs = elt.Elements().ElementAt(0);
    var op = elt.Elements().ElementAt(1);
    var rhs = elt.Elements().ElementAt(2);

    switch((string)op)
    {
    case "+":
        // by chaining LHS and RHS to Visit we allow the tree to be constructed
        // properly as Visit performs the per-element dispatch
        return Expression.Add(Visit(lhs), Visit(rhs));
    case "&&":
        return Expression.AndAlso(Visit(lhs), Visit(rhs));
    default:
        throw new NotSupportedException();
    }
}