Proof-Theoretic Foundations of Indexing in Logic Programming

Indexing is generally viewed as an implementation artifact, indispensable to speed up the execution of logic programs and theorem provers, but with little intrinsically logical about it. We show that indexing can be given a justification in proof theory on the basis of focusing and linearity. We demonstrate this approach on predicate indexing for Horn clauses and several formulations of hereditary Harrop formulas. We also show how to refine this approach to discriminate on function symbols as well.