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A case study of completion modulo distributivity and Abelian groups

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Rewriting Techniques and Applications (RTA 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 690))

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Abstract

We propose an approach for building equational theories with the objective of improving the performance of the completion procedure, even though there exist canonical rewrite systems for these theories. As a test case of our approach, we show how to build the free Abelian groups and distributivity laws in the completion procedure. The empirical results of our experiment on proving many identities in alternative rings show clearly that the gain of this approach is substantial. More than 30 identities which are valid in any alternative ring are taken from the book “Rings that are nearly associative” by K.A. Zhevlakov et al., and include the Moufang identities and the skew-symmetry of the Kleinfeld function. The proofs of these identities are obtained by Herky, a descendent of RRL and a high-performance rewriting-based theorem prover.

Partially supported by the National Science Foundation Grants no. CCR-9202838 and INT-9016100.

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Authors and Affiliations

  1. University of Iowa, 52242, Iowa, USA

    Hantao Zhang

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  1. Hantao Zhang
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Editors and Affiliations

  1. INRIA Lorraine and CRIN, 615 Rue du Jardin Botanique, F-54602, Villers les Nancy Cedex, France

    Claude Kirchner

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© 1993 Springer-Verlag Berlin Heidelberg

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Zhang, H. (1993). A case study of completion modulo distributivity and Abelian groups. In: Kirchner, C. (eds) Rewriting Techniques and Applications. RTA 1993. Lecture Notes in Computer Science, vol 690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21551-7_4

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  • DOI: https://doi.org/10.1007/978-3-662-21551-7_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56868-1

  • Online ISBN: 978-3-662-21551-7

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