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Extension orderings

  • Foundations of Programming
  • Conference paper
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Automata, Languages and Programming (ICALP 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 944))

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Abstract

In this paper we study how to extend a collection of term orderings on disjoint signatures to a single one, called an extension ordering, which preserves (part of) their properties. Apart of its own interest, e.g. in automated deduction, extension orderings turn out to be a new method to obtain simple and constructive proofs for modularity of termination of TRS. Three different schemes to define extension orderings are given. The first one to deal with reduction orderings, the second one to extend simplification orderings and the last one for total reduction orderings. This provides simpler and more constructive proofs for some known modularity results for (simple and total) termination of rewriting as well as some new results for rewriting modulo equational theories. Finally, our technique is applied to extend an ordering on a given signature to a new one on the signature enlarged with new symbols.

The author wishes to thank Hubert Comon, Jean-Pierre Jouannaud, Robert Nieuwenhuis and Aart Middeldorp for many helpful comments. Partially supported by the Esprit Working Group CCL, ref. 6028.

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Authors and Affiliations

  1. Universitat Politècnica de Catalunya, Pau Gargallo 5, 08028, Barcelona, Spain

    Albert Rubio

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  1. Albert Rubio
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Zoltán Fülöp Ferenc Gécseg

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© 1995 Springer-Verlag Berlin Heidelberg

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Rubio, A. (1995). Extension orderings. In: Fülöp, Z., Gécseg, F. (eds) Automata, Languages and Programming. ICALP 1995. Lecture Notes in Computer Science, vol 944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60084-1_101

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  • DOI: https://doi.org/10.1007/3-540-60084-1_101

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60084-8

  • Online ISBN: 978-3-540-49425-6

  • eBook Packages: Springer Book Archive

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