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Commutation, transformation, and termination

  • Leo Bachmair
  • Nachum Dershowitz
Term Rewriting Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 230)

Abstract

In this paper we study the use of commutation properties for proving termination of rewrite systems. Commutation properties may be used to prove termination of a combined system RS by proving termination of R and S separately. We present termination methods for ordinary and for equational rewrite systems. Commutation is also important for transformation techniques. We outline the application of transforms—mappings from terms to terms—to termination in general, and describe various specific transforms, including transforms for associative-commutative rewrite systems.

Keywords

Infinite Sequence Transformation Technique Hasse Diagram Distributivity Rule Commutation Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Bachmair, L., and Plaisted, D.A. (1985). Termination orderings for associative-commutative rewriting systems, J. of Symbolic Computation 1, 329–349.Google Scholar
  2. [2]
    Ben Cherifa, A., and Lescanne, P. (1985). A method for proving termination of rewriting systems based on elementary computations on polynomials, unpublished manuscript.Google Scholar
  3. [3]
    Dershowitz, N. (1981). Termination of linear rewriting systems, Proc. 8th EATCS Int. Colloquium on Automata, Languages and Programming, S. Even and O. Kariv, eds., Lect. Notes in Comp. Science 115, New York, Springer, 448–458.Google Scholar
  4. [4]
    Dershowitz, N. (1982). Orderings for term-rewriting systems, Theoretical Computer Science 17, 279–301.CrossRefGoogle Scholar
  5. [5]
    Dershowitz, N. (1985a). Computing with rewrite systems, Information and Control 64, 122–157.CrossRefGoogle Scholar
  6. [6]
    Dershowitz, N. (1985b). Termination. Proc. 1st Int. Conf. on Rewriting Techniques and Applications, Dijon, France, Lect. Notes in Comp. Science, Springer, 180–224.Google Scholar
  7. [7]
    Dershowitz, N., Hsiang, J., Josephson, N.A., and Plaisted, D.A. (1984). Associative-commutative rewtiting. Proc. 8th IJCAI, Karlsruhe, 940–944.Google Scholar
  8. [8]
    Guttag, J.V., Kapur, D., and Musser, D.R. (1983). On proving uniform termination and restricted termination of rewriting systems. SIAM Computing 12, 189–214.CrossRefGoogle Scholar
  9. [9]
    Hsiang, J. (1985). Refutational theorem proving using term-rewriting systems. Artificial Intelligence 25, 255–300.CrossRefGoogle Scholar
  10. [10]
    Huet, G. (1980). Confluent reductions: abstract properties and applications to term rewriting systems. J. ACM 27, 797–821.CrossRefGoogle Scholar
  11. [11]
    Huet, G. and Hullot, J.M. (1982). Proofs by induction in equational theories with constructors. J. of Comp. and System Sciences 25, 239–266.CrossRefGoogle Scholar
  12. [12]
    Jouannaud, J.-P., and Munoz, M. (1984). Termination of a set of rules modulo a set of equations, Proc. 7th Int. Conf. on Automated Deduction, R. Shostak, ed., Lect. Notes in Comp. Science 170, Berlin, Springer, 175–193.Google Scholar
  13. [13]
    Kamin, S., and Levy, J.J. (1980). Two generalizations of the recursive path ordering. Unpublished manuscript, Univ. of Illinois at Urbana-Champaign.Google Scholar
  14. [14]
    Kapur, D., and Sivakumar, G. (1984). Architecture of and experiments with RRL, a rewrite rule laboratory. Proc. NSF Workshop on the Rewrite Rule Laboratory, Rensellaerville, New York, 33–56.Google Scholar
  15. [15]
    Lankford, D.S. (1979). On proving term rewriting systems are noetherian. Memo MTP-3, Mathematics Department, Louisiana Tech. Univ., Ruston, Louisiana.Google Scholar
  16. [16]
    Manna, Z., and Ness, S. (1970). On the termination of Markov algorithms. Proc. Third Hawaii Int. Conf. on System Science, 789–792.Google Scholar
  17. [17]
    Musser, D.R. (1980). On proving inductive properties of abstract data types. Proc. 7th ACM Symp. on Principles of Programming Languages, Las Vegas, 154–162.Google Scholar
  18. [18]
    O'Donnell, M.J. (1985). Equational logic as a programming language. MIT Press, Cambridge, Massachusetts.Google Scholar
  19. [19]
    Plaisted, D.A. (1984). Associative path orderings, Proc. NSF Workshop on the Rewrite Rule Laboratory, Rensellaerville, New York, 123–126.Google Scholar
  20. [20]
    Raoult, J.C., and Vuillemin, J. (1980). Operational and semantic equivalence between recursive programs, J. ACM 27, 772–796.CrossRefGoogle Scholar
  21. [21]
    Rosen, B. (1973). Tree-manipulating systems and Church-Rosser theorems, J. ACM 20, 160–187.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Leo Bachmair
    • 1
  • Nachum Dershowitz
    • 1
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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