Termination of rewrite relations on $\lambda$-terms based on Girard's notion of reducibility

Abstract

In this paper, we show how to extend the notion of reducibility introduced by Girard for proving the termination of $\beta$-reduction in the polymorphic $\lambda$-calculus, to prove the termination of various kinds of rewrite relations on $\lambda$-terms, including rewriting modulo some equational theory and rewriting with matching modulo $\beta$$\eta$, by using the notion of computability closure. This provides a powerful termination criterion for various higher-order rewriting frameworks, including Klop's Combinatory Reductions Systems with simple types and Nipkow's Higher-order Rewrite Systems.

References in corpus (2)

• The computability path ordering
• (HO)RPO Revisited

Cited by in corpus (4)

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• The unified higher-order dependency pair framework