If the grammar is ambiguous then there exists exactly one handle for each sentential form.?

Question

there can be two productions from which we can do the reduction. After giving precedence and associations as required there will be one handle only.so is this statement true??

Answer 1

This is partially true, a reduce/reduce conflict is usually resolved by specifying precedence or by letting the parser builder choose which rule to apply before the other.

This means that the conflict is solved but not that the parser is going to behave exactly as intended. It is convenient to study what is causing the conflict and think if a refactoring of the grammar is needed to express what you are trying to parse or if the automatic choice/precedence is enough.

Answer 2

If you have a grammar which has ambiguous rules, you get multiple interpretations. You don't have to insist that the grammar removes ambiguity; you can simply agree that something is ambiguous and parse it multiple ways:

fruit flies like an arrow.

The result of the parse is multiple interpretations.

Now, for such a language to be useful to a reader, either he has to be happy with the ambiguity, or you need to give him a way to resolve it. (In the example, I've decided for you that you are happy the ambiguity, because I haven't given you a way to resolve it!). Or, one can provide the reader of something with ambiguous parsess, a way to choose which parse make sense, and he rejects the inappropriate parses.

I can do that for the above case by telling you that I mean "fruit => watermelon".

Computer grammars are not different, but most programmers don't want ambiguous code. So in general, langauge designers like to define unambiguous grammars. In practice, they don't succeed and you get funny language rules like, "If this could be interpreted ambiguously, then interpret it this way.".