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Higher-Order Lazy Narrowing Calculus: A Solver for Higher-Order Equations

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Computer Aided Systems Theory — EUROCAST 2001 (EUROCAST 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2178))

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Abstract

This paper introduces a higher-order lazy narrowing calculus (HOLN for short) that solves higher-order equations over the domain of simply typed λ-terms. HOLN is an extension and refinement of Prehoferés higher-order narrowing calculus LN using the techniques developed in the refinement of a first-order lazy narrowing calculus LNC. HOLN is defined to deal with both unoriented and oriented equations. It keeps track of the variables which are to be bound to normalized answers. We discuss the operating principle of HOLN, its main properties, i.e. soundness and completeness, and its further refinements. The solving capability of HOLN is illustrated with an example of program calculation.

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Author information

Authors and Affiliations

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

    Tetsuo Ida & Mircea Marin

  2. Department of Computer Software, University of Aizu, Aizu Wakamatsu, 965-8580, Japan

    Taro Suzuki

Authors
  1. Tetsuo Ida
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  2. Mircea Marin
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  3. Taro Suzuki
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Editor information

Editors and Affiliations

  1. Universidad de Las Palmas de Gran Canaria, Instituto Universitario de Ciencias y Tecnologías Cibernéticas, Campus de Tafira, 35017, Las Palmas de Gran Canaria, Spain

    Roberto Moreno-Díaz

  2. University of Linz, Research Institute for Symbolic Computation, 232, Schloss Hagenberg, Austria

    Bruno Buchberger

  3. University ofA Coruña, Facultad de Informática, LFCIA, Dpto. of Computer Science, Campus de Elviña, 15071, A Coruña, Spain

    José Luis Freire

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© 2001 Springer-Verlag Berlin Heidelberg

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Ida, T., Marin, M., Suzuki, T. (2001). Higher-Order Lazy Narrowing Calculus: A Solver for Higher-Order Equations. In: Moreno-Díaz, R., Buchberger, B., Luis Freire, J. (eds) Computer Aided Systems Theory — EUROCAST 2001. EUROCAST 2001. Lecture Notes in Computer Science, vol 2178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45654-6_38

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  • DOI: https://doi.org/10.1007/3-540-45654-6_38

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42959-3

  • Online ISBN: 978-3-540-45654-4

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