如何将这个语法转换为LR（1）？

Question

I have a grammar with an LR(1) conflict which I cannot resolve; yet, the grammar should be unambiguous. I'll first demonstrate the problem on a simplified grammar with five tokens: ( , ) , {} , , and id .

The EBNF would look like this:

      args = ( id ',' )*

expression = id
           | '(' expression ')'
           | '(' args ')' '{}'

The grammar is unambiguous and requires at most two tokens of lookahead. When ( is shifted, there are only five possibilities:

1. ( → Recur.
2. ) → Reduce as '(' args ')' .
3. id ) not {} → Reduce as '(' expression ')' .
4. id ) {} → Reduce as '(' args ')' '{}'
5. id , → Reduce as '(' args ')' '{}' (eventually).

A naive translation yields the following result (and conflicts ):

   formal_arg: Ident
               {}

  formal_args: formal_arg Comma formal_args
             | formal_arg
             | /* nothing */
               {}

      primary: Ident
             | LParen formal_args Curly
             | LParen primary RParen
               {}

So, the grammar requires at most three tokens of lookahead to decide. I know that an LR(3) grammar can be transformed to LR(1) grammar.

However, I don't quite understand how to do the transformation in this particular case. Note that the simplified grammar above is an extraction from a larger body of code ; in particular, is it possible to transform primary without touching expr and everything above?

Answer 1

I provided a solution to a problem very similar to this one here: Is C#'s lambda expression grammar LALR(1)? . The basic idea was to separate out the ( id ) case from the other two possibilities ( ( expr_not_id ) and ( list_at_least_2_ids ) ). Then the decision about how to reduce ( id ) can be deferred until the lookahead token is available (in your case, { , assuming that that is sufficient).

Unfortunately, while the transformation of expr into expr_not_id is pretty straightforward and almost mechanical, it definitely touches a lot of productions. Also, it's somewhat ugly. So it fails to solve the problem you present in the last sentence. I don't actually think that it is possible to transform primary without touching expr , but I've been surprised before.

(The other obvious solution, since the grammar is in fact unambiguous, is to use a GLR parser-generator, but I don't believe the parser-generator you are using has that feature.)