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Term Reduction Systems and Algebraic Algorithms

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GWAI-81

Part of the book series: Informatik-Fachberichte ((2252,volume 47))

Abstract

We give a short survey of results and applications of term rewriting systems. We show that common algebraic algorithms can be understood as reduction or completion procedures for equationally defined algebraic theories. Most naturally this can be done by proving algebraic reduction relations noetherian and confluent directly; however, important algebraic algorithms are instances of the Knuth Bendix completion procedure for term reduction systems.

It is the common curse of all general and abstract theories that they have to be far advanced before yielding useful results in concrete problems.

Hermann Weyl, Algebraic Theory of Numbers, Princeton University Press, 1940, p.124.

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Author information

Authors and Affiliations

  1. Institut für Informatik I, Universität Karlsruhe, Postfach 6380, D.7500, Karlsruhe 1, Germany

    Rüdiger Loos

Authors
  1. Rüdiger Loos
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Editor information

Editors and Affiliations

  1. Institut für Informatik I, Universität Karlsruhe, Postfach 6380, 7500, Karlsruhe 1, Germany

    Jörg H. Siekmann

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© 1981 Springer-Verlag Berlin Heidelberg

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Loos, R. (1981). Term Reduction Systems and Algebraic Algorithms. In: Siekmann, J.H. (eds) GWAI-81. Informatik-Fachberichte, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02328-0_20

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  • DOI: https://doi.org/10.1007/978-3-662-02328-0_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10859-7

  • Online ISBN: 978-3-662-02328-0

  • eBook Packages: Springer Book Archive

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