If you'd like to read more background material, here are some recommended texts and papers:
Programming with Higher-order Logic, by Dale Miller and Gopalan Nadathur, covers the key concepts of Lambda prolog. Although it's a slim little volume, it's the kind of book where you learn something new every time you open it.
"A proof procedure for the logic of Hereditary Harrop formulas", by Gopalan Nadathur. This paper covers the basics of universes, environments, and Lambda Prolog-style proof search. Quite readable.
"A new formulation of tabled resolution with delay", by Theresa Swift. This paper gives a kind of abstract treatment of the SLG formulation that is the basis for our on-demand solver.