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Termination of Narrowing Using Dependency Pairs

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Logic Programming (ICLP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5366))

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Abstract

In this work, we extend the dependency pair approach for automated proofs of termination in order to prove the termination of narrowing. Our extension of the dependency pair approach generalizes the standard notion of dependency pairs by taking specifically into account the dependencies between the left-hand side of a rewrite rule and its own argument subterms. We demonstrate that the new narrowing dependency pairs exactly capture the narrowing termination behavior and provide an effective termination criterion which we prove to be sound and complete. Finally, we discuss how the problem of analyzing narrowing chains can be recast as a standard analysis problem for traditional (rewriting) chains, so that the proposed technique can be effectively mechanized by reusing the standard DP infrastructure.

This work has been partially supported by the EU (FEDER) and Spanish MEC project TIN2007-68093-C02-02, Integrated Action Hispano-Alemana HA2006-0007, and UPV-VIDI grant 3249 PAID0607.

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Author information

Authors and Affiliations

  1. Technical University of Valencia (UPV), Spain

    María Alpuente, Santiago Escobar & José Iborra

Authors
  1. María Alpuente
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  2. Santiago Escobar
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  3. José Iborra
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Editor information

Editors and Affiliations

  1. Clayton School of Information Technology, Monash University, Australia

    Maria Garcia de la Banda

  2. Department of Computer Science, New Mexico State University, NM 88003, Las Cruces, USA

    Enrico Pontelli

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Alpuente, M., Escobar, S., Iborra, J. (2008). Termination of Narrowing Using Dependency Pairs . In: Garcia de la Banda, M., Pontelli, E. (eds) Logic Programming. ICLP 2008. Lecture Notes in Computer Science, vol 5366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89982-2_31

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  • DOI: https://doi.org/10.1007/978-3-540-89982-2_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89981-5

  • Online ISBN: 978-3-540-89982-2

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