Sorry I never got back to you with a HOP-Parser example. Since Dominus said he was going to make the book available for free, I figured that eventually I could just point people to that for documentation since there's a heck of a lot to document. I do have a parsing example at Converting words to numbers with HOP::Parser. Maybe that could be a start?

Oh, and the AI::Prolog math prepocessor is pretty much "for internal use only" :)

You could also look at the code for Object::Relation::Parser. It uses the HOP::Parser internally. There's a brief explanation of it at Object::Relation::Parser::Overview. The latter documentation explains the grammar and some of the tests with that can help. Of course, I didn't write that as a tutorial, so it might not help that much :/