Static Dependency Pair Method based on Strong Computability for Higher-Order Rewrite Systems

TL;DR

This paper extends a powerful static dependency pair method based on strong computability from simply-typed term rewriting systems to higher-order rewrite systems, accommodating lambda abstractions without additional restrictions.

Contribution

It adapts and extends the static dependency pair method to higher-order rewrite systems, enabling termination proofs for HRSs with lambda abstractions.

Findings

Method successfully extended to HRSs

Works well without new restrictions

Handles lambda abstractions effectively

Abstract

Higher-order rewrite systems (HRSs) and simply-typed term rewriting systems (STRSs) are computational models of functional programs. We recently proposed an extremely powerful method, the static dependency pair method, which is based on the notion of strong computability, in order to prove termination in STRSs. In this paper, we extend the method to HRSs. Since HRSs include \lambda-abstraction but STRSs do not, we restructure the static dependency pair method to allow \lambda-abstraction, and show that the static dependency pair method also works well on HRSs without new restrictions.