Termination and Confluence of Higher-Order Rewrite SystemsReport as inadecuate

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1 LRI - Laboratoire de Recherche en Informatique

Abstract : In the last twenty years, several approaches to higher-order rewriting have been proposed, among which Klop-s Combinatory Rewrite Systems CRSs, Nipkow-s Higher-order Rewrite Systems HRSs and Jouannaud and Okada-s higher-order algebraic specification languages, of which only the last one considers typed terms. The later approach has been extended by Jouannaud, Okada and the present author into Inductive Data Type Systems IDTSs. In this paper, we extend IDTSs with the CRS higher-order pattern-matching mechanism, resulting in simply-typed CRSs. Then, we show how the termination criterion developed for IDTSs with first-order pattern-matching, called the General Schema, can be extended so as to prove the strong normalization of IDTSs with higher-order pattern-matching. Next, we compare the unified approach with HRSs. We first prove that the extended General Schema can also be applied to HRSs. Second, we show how Nipkow-s higher-order critical pair analysis technique for proving local confluence can be applied to IDTSs.

Keywords : higher-order rewriting termination confluence

Author: Frédéric Blanqui -

Source: https://hal.archives-ouvertes.fr/


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