Efficient resource management for linear logic proof search

Abstract

The design of linear logic programming languages and theorem provers opens a number of new implementation challenges not present in more traditional logic languages such as Horn clauses ( Prolog) and hereditary Harrop formulas ( λ Prolog and Elf). Among these, the problem of efficiently managing the linear context when solving a goal is of crucial importance for the use of these systems in non-trivial applications. This paper studies this problem in the case of Lolli [10], though its results have application to other systems including those based on linear type theory. We first give a proof-theoretic presentation of the operational semantics of this language as a resolution calculus. We then present a series of resource management systems designed to eliminate the non-determinism in the distribution of linear formulas that undermines the efficiency of a direct implementation of this system.