Advertisement

Extensions and comparison of simplification orderings

  • Joachim Steinbach
Regular Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 355)

Abstract

The effective calculation with term rewriting systems presumes termination. Orderings on terms are able to guarantee termination. This report deals with some of those term orderings: Several path and decomposition orderings and the Knuth-Bendix ordering. We pursue three aims:
  • •Known orderings will be newly defined.

  • •New ordering methods will be introduced: We will extend existing orderings by adding the principle of status (see [KL80]).

  • •The comparison of the power as well as the time behaviour of all orderings will be discussed.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AGGMS87]
    J. Avenhaus, R. Göbel, B. Gramlich, K. Madlener, J. Steinbach 1987: TRSPEC: A Term Rewriting Based System for Algebraic Specifications, Proc. 1st Int. Workshop on Conditional Rewriting Systems, LNCS 308, Orsay, 245–248Google Scholar
  2. [Da88]
    M. Dauchet 1988: Termination of rewriting is undecidable in the one rule case, Proc. 14th Mathematical foundations of computer science, LNCS 324, Carlsbad, 262–268Google Scholar
  3. [De85]
    N. Dershowitz 1985: Termination, Proc. 1st RTA, LNCS 202, Dijon, 180–224Google Scholar
  4. [De82]
    N. Dershowitz 1982: Orderings for term rewriting systems, J. Theor. Comp. Sci., Vol. 17, No. 3, 279–301Google Scholar
  5. [JLR82]
    J.-P. Jouannaud, P. Lescanne, F. Reinig: Recursive decomposition ordering, I.F.I.P. Working Conf. on Formal Description of Programming Concepts II, North Holland, Garmisch Partenkirchen, 331–348Google Scholar
  6. [KB70]
    D. E. Knuth, P. B. Bendix: Simple word problems in universal algebras, Computational problems in abstract algebra, Pergamon Press, 263–297Google Scholar
  7. [KL80]
    S. Kamin, J.-J. Lévy: Attempts for generalizing the recursive path orderings, Unpublished manuscript, Dept. of Computer Science, Univ. of IllinoisGoogle Scholar
  8. [KNS85]
    D. Kapur, P. Narendran, G. Sivakumar 1985: A path ordering for proving termination of term rewriting systems, Proc. 10th CAAP, LNCS 185, 173–187Google Scholar
  9. [La79]
    D. S. Lankford 1979: On proving term rewriting systems are noetherian, Memo MTP-3, Mathematics Dept., Louisiana Tech. Univ., RustonGoogle Scholar
  10. [La77]
    D. S. Lankford 1977: Some approaches to equality for computational logic: A survey and assessment, Report ATP-36, Depts. of Mathematics and Computer Science, Univ. of Texas, AustinGoogle Scholar
  11. [Le84]
    P. Lescanne 1984: Uniform termination of term rewriting systems — the recursive decomposition ordering with status, Proc. 9th CAAP, Cambridge University Press, Bordeaux, 182–194Google Scholar
  12. [Ma87]
    U. Martin 1987: How to choose the weights in the Knuth-Bendix ordering, Proc. 2nd RTA, LNCS 256, Bordeaux, 42–53Google Scholar
  13. [Pl78]
    D. A. Plaisted: A recursively defined ordering for proving termination of term rewriting systems, Report UIUCDCS-R-78-943, Dept. of Computer Science, Univ. of IllinoisGoogle Scholar
  14. [Ru87]
    M. Rusinowitch 1987: Path of subterms ordering and recursive decomposition ordering revisited, J. Symbolic Computation 3 (1 & 2), 117–131Google Scholar
  15. [Si87]
    C. C. Sims 1987: Verifying nilpotence, J. Symbolic Computation 3 (1 & 2), 231–247Google Scholar
  16. [St88a]
    J. Steinbach: Term orderings with status, SEKI REPORT SR-88-12, Artificial Intelligence Laboratories, Dept. of Computer Science, Univ. of KaiserslauternGoogle Scholar
  17. [St88b]
    J. Steinbach: Comparison of simplification orderings, SEKI REPORT SR-88-02. Artificial Intelligence Laboratories, Dept. of Computer Science, Univ. of KaiserslauternGoogle Scholar
  18. [St86]
    J. Steinbach: Orderings for term rewriting systems, M.S. thesis, Dept. of Computer Science, Univ. of Kaiserslautern (in German)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Joachim Steinbach
    • 1
  1. 1.Fachbereich InformatikUniversität KaiserslauternKaiserslauternFRG

Personalised recommendations