Correctness of Context-Moving Transformations for Term Rewriting Systems

摘要

Proofs by induction are often incompatible with functions in tail-recursive form as the accumulator changes in the course of unfolding the definitions. Context-moving and context-splitting (Giesl, 2000) for functional programs transform tail-recursive programs into non tail-recursive ones which are more suitable for proofs by induction and thus for verification. In this paper, we formulate context-moving and context-splitting transformations in the framework of term rewriting systems, and prove their correctness with respect to both eager evaluation semantics and initial algebra semantics under some conditions on the programs to be transformed. The conditions for the correctness with respect to initial algebra semantics can be checked by automated methods for inductive theorem proving developed in the field of term rewriting systems.