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Termination and Confluence of Higher-Order Rewrite Systems

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Rewriting Techniques and Applications (RTA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1833))

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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.

Appendices A, B and C (proofs) are available from the web page.

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Authors and Affiliations

  1. LRI, Université de Paris-Sud, Bât. 490, 91405, Orsay, France

    Frédéric Blanqui

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  1. Frédéric Blanqui
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Editors and Affiliations

  1. Department of Computer Science, Stony Brook University, Stony Brook, P.O. Box, New York

    Leo Bachmair

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Blanqui, F. (2000). Termination and Confluence of Higher-Order Rewrite Systems. In: Bachmair, L. (eds) Rewriting Techniques and Applications. RTA 2000. Lecture Notes in Computer Science, vol 1833. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10721975_4

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  • DOI: https://doi.org/10.1007/10721975_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67778-9

  • Online ISBN: 978-3-540-44980-5

  • eBook Packages: Springer Book Archive

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