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An abstract formulation for rewrite systems

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Category Theory and Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 389))

Abstract

Herein, we describe an abstract algebraic object which can be used to discuss rewrite systems. We define then use the notion of 2-category to encapsulate some fundamental properties of rewrites. Recent developments in the general theory of 2-categories are then used to give a theorem stating conditions under which rewrite derivations exist, and to give further conditions under which there is a normal form for a derivation, hence a deterministic method to express a derivation as a composite of rewrites in a particular order. Several examples are pursued through the course of the paper in order to make clear precisely how the general theory may be applied.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Case Western Reserve University, 44106, Cleveland, Ohio, USA

    A. J. Power

Authors
  1. A. J. Power
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Editor information

David H. Pitt David E. Rydeheard Peter Dybjer Andrew M. Pitts Axel Poigné

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© 1989 Springer-Verlag Berlin Heidelberg

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Power, A.J. (1989). An abstract formulation for rewrite systems. In: Pitt, D.H., Rydeheard, D.E., Dybjer, P., Pitts, A.M., Poigné, A. (eds) Category Theory and Computer Science. Lecture Notes in Computer Science, vol 389. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018358

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  • DOI: https://doi.org/10.1007/BFb0018358

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51662-0

  • Online ISBN: 978-3-540-46740-3

  • eBook Packages: Springer Book Archive

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