Journal Articles Theoretical Computer Science Year : 2015

Termination of rewrite relations on λ-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 β-reduction in the polymorphic λ-calculus, to prove the termination of various kinds of rewrite relations on λ-terms, including rewriting modulo some equational theory and rewriting with matching modulo βη, 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.
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Dates and versions

hal-01191693 , version 1 (02-09-2015)

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Frédéric Blanqui. Termination of rewrite relations on λ-terms based on Girard's notion of reducibility. Theoretical Computer Science, 2015, 611 (50-86), pp.37. ⟨10.1016/j.tcs.2015.07.045⟩. ⟨hal-01191693⟩

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