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Completeness results for basic narrowing

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

In this paper we analyze completeness results for basic narrowing. We show that basic narrowing is not complete with respect to normalizable solutions for equational theories defined by confluent term rewriting systems, contrary to what has been conjectured. By imposing syntactic restrictions on the rewrite rules we recover completeness. We refute a result of Hölldobler which states the completeness of basic conditional narrowing for complete (i.e. confluent and terminating) conditional term rewriting systems without extra variables in the conditions of the rewrite rules. In the last part of the paper we extend the completeness results of Giovannetti and Moiso for level-confluent and terminating conditional systems with extra variables in the conditions to systems that may also have extra variables in the right-hand sides of the rules.

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Authors and Affiliations

  1. Institute of Information Sciences and Electronics, University of Tsukuba, 305, Tsukuba, Japan

    Aart Middeldorp

  2. Altair Automation B.V., Weesperstraat 95, 1018, VN Amsterdam, The Netherlands

    Erik Hamoen

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  1. Aart Middeldorp
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  2. Erik Hamoen
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Additional information

An extended abstract of this paper appeared asCounterexamples to Completeness Results for Basic Narrowing (Extended Abstract) in the Proceedings of the 3rd International Conference on Algebraic and Logic Programming, Volterra, Lecture Notes in Computer Sciences 632, pp. 244–258, 1992. Most of the work reported in this paper was carried out while the first author was employed at the Department of Software Technology, CWI, Kruislaan 413, 1098 SJ Amsterdam, and the second author at the Department of Mathematics and Computer Science, Vrije Universiteit, de Boelelaan 1081a, 1081 HV Amsterdam.

Partially supported by ESPRIT Basic Research Action 3020, INTEGRATION.

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Middeldorp, A., Hamoen, E. Completeness results for basic narrowing. AAECC 5, 213–253 (1994). https://doi.org/10.1007/BF01190830

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