Method for Creating Any Unambiguous Grammar?

I'm in an undergraduate class where we're studying formal grammars right now. I asked my teacher if there was any known set of rules for creating context free grammars that

• Was guaranteed to produce an unambiguous grammar.

• Allows for the creation of any possible unambiguous grammar.

I am well aware that determining whether a grammar is ambiguous is undecidable. I'm not sure if the above stated idea is reducible to that, but after fiddling around with it a bit, I couldn't think of a method for making such a reduction. That said I'm really no expert at reductions or grammars. I tried googling for a while, but I only found pages about undecidability. Does anyone know?

No, and there is indeed a reduction to the undecidability of ambiguity.

First, note that ambiguity is (for context-free grammars) semi-decidable: just keep generating words by different left-derivations and say "ambiguous!" when you first find a word you've seen before.

Now, the method you are proposing allows to semi-decide unambiguity. You effectively look for a computable enumeration of all unambiguous grammars. You just generate grammars until you find your given grammar and answer "unambiguous!".

Since semi-decidability and co-semi-decidability imply decidability, this contradicts what you already know. Hence, there can be no "set of rules" as you propose.

StackExchange Computer Science Q#38314, answer score: 4