Argument filterings and usable rules in higher-order rewrite systems

TL;DR

This paper extends the static dependency pair method for higher-order rewrite systems by incorporating argument filterings and usable rules, enabling more effective automated termination proofs.

Contribution

It introduces extensions of argument filterings and usable rules to higher-order rewriting, broadening the applicability of the static dependency pair method.

Findings

Extended the class of higher-order systems for static dependency pairs

Adapted argument filterings and usable rules to higher-order rewriting

Laid the groundwork for a powerful automated termination prover

Abstract

The static dependency pair method is a method for proving the termination of higher-order rewrite systems a la Nipkow. It combines the dependency pair method introduced for first-order rewrite systems with the notion of strong computability introduced for typed lambda-calculi. Argument filterings and usable rules are two important methods of the dependency pair framework used by current state-of-the-art first-order automated termination provers. In this paper, we extend the class of higher-order systems on which the static dependency pair method can be applied. Then, we extend argument filterings and usable rules to higher-order rewriting, hence providing the basis for a powerful automated termination prover for higher-order rewrite systems.