Formalizing the dependency pair criterion for innermost termination

Abstract

• Dependency pairs criterion and verification of termination of rewriting systems. • Automating termination of rewriting and functional programs. • Formalization of termination of first-order term rewriting systems. • Innermost reduction and termination of rewriting. • Formally proving the soundness of rewriting with the PVS proof assistant. Rewriting is a framework for reasoning about functional programming. The dependency pair criterion is a well-known mechanism to analyze termination of term rewriting systems. Functional specifications with an operational semantics based on evaluation are related, in the rewriting framework, to the innermost reduction relation. This paper presents a PVS formalization of the dependency pair criterion for the innermost reduction relation: a term rewriting system is innermost terminating if and only if it is terminating by the dependency pair criterion. The paper also discusses the application of this criterion to check termination of functional specifications.