Question

I’ve got a simple grammar. Actually, the grammar I’m using is more complex, but this is the smallest subset that illustrates my question.

Expr ::= Value Suffix
       | "(" Expr ")" Suffix

Suffix ::= "->" Expr
         | "<-" Expr
         | Expr
         | epsilon

Value matches identifiers, strings, numbers, et cetera. The Suffix rule is there to eliminate left-recursion. This matches expressions such as:

a -> b (c -> (d) (e))

That is, a graph where a goes to both b and the result of (c -> (d) (e)), and c goes to d and e. I’m trying to produce an abstract syntax tree for these expressions, but I’m running into difficulty because all of the operators can accept any number of operands on each side. I’d rather keep the logic for producing the AST within the recursive descent parsing methods, since it avoids having to duplicate the logic of extracting an expression. My current strategy is as follows:

1. If a Value appears, push it to the output.

2. If a From or To appears:

   1. Output a separator.

   2. Get the next Expr.

   3. Create a Link node.

   4. Pop the first set of operands from output into the Link until a separator appears.

   5. Erase the separator discovered.

   6. Pop the second set of operands into the Link until a separator.

   7. Push the Link to the output.

If I run this through without obeying steps 2.3–2.7, I get a list of values and separators. For the expression quoted above, a -> b (c -> (d) (e)), the output should be:

A sep_1 B sep_2 C sep_3 D E

Applying the To rule would then yield:

A sep_1 B sep_2 (link from C to {D, E})

And subsequently:

(link from A to {B, (link from C to {D, E})})

The important thing to note is that sep_2, crucial to delimit the left-hand operands of the second ->, does not appear, so the parser believes that the expression was actually written:

a -> (b c -> (d) (e))

In order to solve this with my current strategy, I would need a way to produce a separator between adjacent expressions, but only if the current expression is a From or To expression enclosed in parentheses. If that’s possible, then I’m just not seeing it and the answer ought to be simple. If there’s a better way to go about this, however, then please let me know!

Answer 1

I haven’t tried to analyze it in detail, but: “From or To expression enclosed in parentheses” starts to sound a lot like “context dependent”, which recursive descent can’t handle directly. To avoid context dependence you’ll probably need a separate production for a From or To in parentheses vs. a From or To without the parens.

Edit: Though it may be too late to do any good, if my understanding of what you want to match is correct, I think I’d write it more like this:

Graph := 
       | List Sep Graph
       ;

Sep := "->"
     | "<-"
     ;

List :=
      | Value List
      ;

Value := Number 
      | Identifier 
      | String 
      | '(' Graph ')'
      ;

It’s hard to be certain, but I think this should at least be close to matching (only) the inputs you want, and should make it reasonably easy to generate an AST that reflects the input correctly.