How do you build a left-associative operator tree using PEG.js?

How do you build an AST (Abstract Syntax Tree) for left-associative operators using PEG.js?

I've tried to write some code based on the information I found on the internet, but I seem to have made a mistake.

The code I wrote generates an incorrect AST for most expressions.

Expression

12-6-4-2*1-1

Expected AST

{
    "left": {
        "left": {
            "left": {
                "left": 12,
                "operator": "-",
                "right": 6
            },
            "operator": "-",
            "right": 4
        },
        "operator": "-",
        "right": {
            "left": 2,
            "operator": "*",
            "right": 1
        }
    },
    "operator": "-",
    "right": 1
}

Generated AST

{
   "left": {
      "left": {
         "left": 12,
         "operator": "-",
         "right": 6
      },
      "operator": "-",
      "right": 4
   },
   "operator": "-",
   "right": {
      "left": 2,
      "operator": "*",
      "right": {
         "left": 1,
         "operator": "-",
         "right": 1
      }
   }
}

Code

{

    function operator(first, rest) {
        if (rest.length === 0) return first;

        return { left: first, right: rest };
    };

    function makeOperator(left, operator, right) {
        return { left: left, operator: operator[0], right: clean(right[1]) };
    };

    function clean(expression) {
        if (!expression.right) return expression;

        var result = makeOperator(expression.left, expression.right[0], expression.right[0]);

        for (var counter = 1, len = expression.right.length; counter < len; counter++) {
            result = makeOperator(result, expression.right[counter], expression.right[counter]);
        }

        return result;
    };

}

Start = E

E
  = expression:E1

    { return clean(expression); }

E1
  = expression:E2 rest:(("+" / "-") E2)*

    { return operator(expression, rest); }

E2
  = expression:Value rest:(("*" / "/") E1)*

    { return operator(expression, rest); }


Value
  = Number
  / BracketedExpression

Number
  = [1-9][0-9]*

    { return parseInt(text(), 10); }

BracketedExpression
  = "(" expression:E1 ")"

    { return expression; }

I would really appreciate any help or example code on how to build ASTs for both left-associative and right-associative operators.

Edit: As @Bergi pointed out, the problem was that E2 used E1 as the expression for the rest of the operator list instead of Value. However, the code that Bergi wrote is much simpler than mine.

Right-associative operators are relatively trivial to write, since they can be parsed "natively" recursive:

E2
  = l:Value op:("*" / "/") r:E2
    { return {left:l, operator:op, right:r}; }
  / Value

// or equivalently (but more efficiently):

E2
  = l:Value r:(("*" / "/") E2)?
    { if (!r) return l;
      return {left:l, operator:r[0], right:r[1]}
    }

We can translate the grammar for left-associative operators respectively:

// [Do not use]
E1
  = l:E1 op:("-" / "+") r:E2
    { return {left2:l, operator:op, right2:r}; }
  / E2

but all we get from this is an error Left recursion detected for rule "E1". Indeed, PEG are not capable of left recursion rules, but Wikipedia tells us how to counter this: we will need to unroll the recursion into a * loop. You already did this, but put the parenthesis differently. They should match the recursive definition above, with the single E2 on the right:

E1
  = ls:(E2 ("+" / "-"))* r:E2

so that we can build the tree from the s easily with a recursive helper function:

    { return leftAssociative(ls, r); }

    function leftAssociative(ls, r) {
        if (!ls.length) return r;
        var last = ls.pop();
        return {left:leftAssociative(ls, last[0]), operator:last[1], right:r};
    }

Alternatively, you can use a loop, which best matches the bracketing with the loop on the right side:

E1
  = l:E2 rs:(("+" / "-") E2)*
    { var e = l;
      for (var i=0; i<rs.length; i++)
          e = {left:e, operator:rs[i][0], right:rs[i][1]};
      return e;
    }

---

For reference, here is the complete parser:

{ 
    function leftAssoc(rest, val) {
        if (!rest.length) return val;
        var last = rest.pop();
        return {left:leftAssoc(rest, last[0]), operator:last[1], right:val};
    }
    function rightAssoc(val, rest) {
        if (!rest.length) return val;
        var first = rest.shift();
        return {left:val, operator:first[0], right:rightAssoc(first[1], rest)};
    }
}

Start = E1
 
E1 = rest:(E2 ("+" / "-"))* v:E2
     { return leftAssoc(rest, v); }

E2 = v:Value rest:(("*" / "/") Value)*
     { return rightAssoc(v, rest); }

Value = Number
      / BracketedExpression

Number = [1-9][0-9]*
         { return parseInt(text(), 10); }

BracketedExpression = "(" expression:E1 ")"
                      { return expression; }