I ended up concieving my algorithms without thinking about Prolog's backtracking, and then coding: bending the Prolog interpreter to my will by getting the backtracking to implement the control flow called for by my algorithm. It seemed a bit indirect and a bit clumsy.

My attempts at writing a parser in Prolog were absurdly slow. Later I read that there are ways of writing parsers in Prolog that work well, and writing parsers was one of the killer apps for Prolog, so I guess I never really understood programming in Prolog properly. On the other hand it is troubling that I failed at one of the things the language is supposed to make easy. I'm in no hurry to give it a second look.