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A Complete Selection Function for Lazy Conditional Narrowing

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Functional and Logic Programming (FLOPS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2024))

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Abstract

This paper is concerned with the lazy conditional narrowing calculus LCNC. In an earlier paper we proved that this calculus is complete with respect to normalizable solutions for the class of confluent but not necessarily terminating conditional rewrite systems without so-called extra variables in the conditional parts of the rewrite rules. Unfortunately, the proof does not provide any useful complete selection function, hence in implementations we need to backtrack over the choice of equations in goals in order to guarantee that all solutions are enumerated. This is in contrast to the unconditional case where completeness with respect to the leftmost selection function is known. In this paper we close the gap by proving the completeness of lcnc with respect to the leftmost selection strategy for the above-mentioned class of conditional rewrite systems.

Acknowledgements

Taro Suzuki is partially supported by the Grant-in-Aid for Encouragement of Young Scientist 11780204. Aart Middeldorp is partially supported by the Grantin-Aids for Scientific Research B 12480066 and C(2) 11680338 of the Ministry of Education, Science, Sports and Culture of Japan.

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Author information

Authors and Affiliations

  1. Research Institute of Electrical Communication, Tohoku University, Sendai, 980-8577, Japan

    Taro Suzuki

  2. Institute of Information Sciences and Electronics, University of Tsukuba, Tsukuba, 305-8573, Japan

    Aart Middeldorp

Authors
  1. Taro Suzuki
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  2. Aart Middeldorp
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Editor information

Editors and Affiliations

  1. Institut für Wirtschaftsinformatik, WestfälischeWilhelms-Universität Münster, Steinfurter Straße 109, 48149, Münster, Germany

    Herbert Kuchen

  2. Department of Information and Computer Science, Waseda University, 4-1, Okubo 3-chome, Shinjuku-ku, Tokyo, 169-8555, Japan

    Kazunori Ueda

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© 2001 Springer-Verlag Berlin Heidelberg

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Suzuki, T., Middeldorp, A. (2001). A Complete Selection Function for Lazy Conditional Narrowing. In: Kuchen, H., Ueda, K. (eds) Functional and Logic Programming. FLOPS 2001. Lecture Notes in Computer Science, vol 2024. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44716-4_13

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  • DOI: https://doi.org/10.1007/3-540-44716-4_13

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  • Print ISBN: 978-3-540-41739-2

  • Online ISBN: 978-3-540-44716-0

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