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Considering the following grammar for propositional logic:

<A> ::= <B> <-> <A> | <B> 
<B> ::= <C>  -> <B> | <C> 
<C> ::= <D>  \/ <C> | <D> 
<D> ::= <E>  /\ <D> | <E> 
<E> ::= <F> | -<F>
<F> ::= <G> | <H>
<G> ::= (<A>)
<H> ::= p | q | r | ... | z

Precedence for conectives is: -, /\, /, ->, <->.

Associativity is also considered, for example p\/q\/r should be the same as p\/(q\/r). The same for the other conectives.

I pretend to make a predictive top-down parser in java. I dont see here ambiguity or direct left recursion, but not sure if thats all i need to consider this a LL(1) grammar. Maybe undirect left recursion?

If this is not a LL(1) grammar, what would be the steps required to transform it for my intentions?

Wyvern666
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    This isn't really a programming question, is it? – keyser Dec 19 '13 at 19:43
  • Please, define "programming question". – Wyvern666 Dec 19 '13 at 19:49
  • A programming question would be more concerned with the code to do what you are asking about than what you are asking about. Your question is meta if anything. – VoteCoffee Dec 19 '13 at 19:51
  • Ok, maybe this is more like a "theoretical question". – Wyvern666 Dec 19 '13 at 19:53
  • I'd file this under _Logic_ or _Math_ (the math exchange seem to have some threads on logic). No need to define it, they already did that in the help center. – keyser Dec 19 '13 at 20:01
  • I think this would be more appropriate on the [Computer Science](http://cs.stackexchange.com/) site, since it is more theoretical and doesn't include code. – Shaz Dec 19 '13 at 20:19

1 Answers1

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It's not LL(1). Here's why:

The first rule of an LL(1) grammar is:

A grammar G is LL(1) if and only if whenever A --> C | D are two distinct productions of G, the following conditions hold:

  1. For no terminal a , do both C and D derive strings beginning with a.

This rule is, so that there are no conflicts while parsing this code. When the parser encounters a (, it won't know which production to use.

Your grammar violates this first rule. All your non-terminals on the right hand of the same production , that is, all your Cs and Ds, eventually reduce to G and H, so all of them derive at least one string beginning with (.

sanjeev mk
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