Handling rules that are both left- and right-recursive

I’m reading the literature on PEGs. This paper talks about a bug in @alexwarth’s approach to left recursion which is present in ohm:

This grammar:

MyLang {
  Expr = Expr "-" Num --a
       | Num --b  
  Num = digit+
}

… Correctly parses "1-2-3" to (((1)-2)-3). But when I change the grammar to this:

MyLang {
  Expr = Expr "-" Expr --a
       | Num --b
  Num = digit+
}

The tree is flipped to (1-(2-(3))).

Maybe this isn’t an issue in practice? Its hard to say. But I can certainly see it tripping some people up.

[alexwarth]

Hi Joseph,

I’ve known about Laurie’s paper for a while, and (to put it mildly) I violently disagree with it 😃

Who’s to say that the result of applying a rule like

expr = expr "-" expr | num

should be left-associative? Or right-associative, for that matter? PEGs don’t support left-recursion! The only “correct” result of applying this rule is non-termination. Of course that isn’t terribly useful, so researchers have proposed extensions to PEGs that enable left-recursive rules to produce useful results. The semantics of these extensions isn’t prescribed by Bryan Ford’s definition of PEGs – it’s really up to the people who created the extensions.

Ohm’s approach to left recursion happens to produce right-associative parse trees for your example. This makes sense if you think of left recursion as a kind of loop: the second application of expr in expr "-" expr is like a nested loop, which will consume as much input as it can before the “outer loop” gets a chance to consume more input. I can imagine a different semantics in which the result would be left-associative. That would be fine, too, but certainly no more correct or valid than our current semantics.

You asked if this is an issue in practice. It isn’t. I’ll go a step further and say that this kind of “ambiguous” rule definition is code smell. Do you really want people to wonder whether expr produces a left- or right-associative result? No! In a well-written grammar, it’s obvious. In this case, you want the - operator to be left-associative so you’re better off defining expr like this:

expr = expr "-" num | num

Now there’s no question about it.

We have plans to release a bunch of exciting new features and tools for Ohm. I want to prioritize that work over this, which I don’t consider to be a real issue. So I’m closing it.

Thanks!

[alexwarth]

Good idea! See #56.