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Termination of narrowing via termination of rewriting

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Narrowing extends rewriting with logic capabilities by allowing logic variables in terms and by replacing matching with unification. Narrowing has been widely used in different contexts, ranging from theorem proving (e.g., protocol verification) to language design (e.g., it forms the basis of functional logic languages). Surprisingly, the termination of narrowing has been mostly overlooked. In this work, we present a novel approach for analyzing the termination of narrowing in left-linear constructor systems—a widely accepted class of systems—that allows us to reuse existing methods in the literature on termination of rewriting.

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Authors and Affiliations

  1. Graduate School of Information Science, Nagoya University, Nagoya, Japan

    Naoki Nishida

  2. MiST, DSIC, Universidad Politécnica de Valencia, Camino de Vera, S/N, 46022, Valencia, Spain

    Germán Vidal

Authors
  1. Naoki Nishida
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  2. Germán Vidal
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Correspondence to Germán Vidal.

Additional information

A preliminary short version of this paper appeared in the Proceedings of FLOPS 2008 [65].

This work has been partially supported by the Spanish Ministerio de Ciencia e Innovación under grant TIN2008-06622-C03-02, by Generalitat Valenciana under grant ACOMP/2009/017, and by UPV (programs PAID-05-08 and PAID-06-08).

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Nishida, N., Vidal, G. Termination of narrowing via termination of rewriting. AAECC 21, 177–225 (2010). https://doi.org/10.1007/s00200-010-0122-4

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