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Order-sorted termination: The unsorted way

  • Peter Csaba Ölveczky
  • Olav Lysne
Term Rewriting
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1139)

Abstract

We consider the problem of proving termination of order-sorted rewrite systems. The dominating method for proving termination of order-sorted systems has been to simply ignore sort information, and use the techniques developed for unsorted rewriting. The problem with this approach is that many order-sorted rewrite systems terminate because of the structure of the set of sorts. In these cases the corresponding unsorted system would not terminate.

In this paper we approach the problem of order-sorted termination by mapping the order-sorted rewrite system into an unsorted one such that termination of the latter implies termination of the former. By encoding sort information into the unsorted mapping, we are able to use general purpose termination orderings to prove termination of order-sorted rewrite systems whose termination depend on the sort hierarchy. We present a sequence of gradually stronger methods, and show that a previously published method is contained in ours as a special case.

Keywords

Order-sortedness Termination 

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References

  1. 1.
    O.-J. Dahl and O. Owe. Formal development with ABEL. In Proceedings 4th International Symposium of VDM Europe, LNCS 552, 1991.Google Scholar
  2. 2.
    N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3:69–116, 1987.Google Scholar
  3. 3.
    N. Dershowitz and C. Hoot. Natural termination. Theoretical Computer Science, 142:179–207, 1995.Google Scholar
  4. 4.
    H. Ganzinger. Order-sorted completion: the many-sorted way. Theoretical Computer Science, 89:3–32, 1991.Google Scholar
  5. 5.
    I. Gnaedig. ELIOS-OBJ: theorem proving in a specification language. In Proceedings of the 4th European Symposion on Programming, LNCS 582, pages 182–199, 1992.Google Scholar
  6. 6.
    I. Gnaedig. Termination of order-sorted rewriting. In Proceedings 3rd International Conference on Algebraic and Logic Programming, Pisa (Italy), LNCS 632, pages 37–52, 1992.Google Scholar
  7. 7.
    I. Gnaedig, C. Kirchner, and H. Kirchner. Equational completion in order-sorted algebras. Theoretical Computer Science, 72:169–202, 1990.Google Scholar
  8. 8.
    J. A. Goguen and J. Meseguer. Order-sorted algebra I: Equational deduction formultiple inheritance, overloading, exceptions and partial operators. Technical report, Programming Research Group, Oxford University Computing Laboratory, 1989.Google Scholar
  9. 9.
    J. A. Goguen and T. Winkler. Introducing OBJ3. Technical report, SRI International, Computer Science Lab, 1988.Google Scholar
  10. 10.
    S. Kamin and J.-J. Lévy. Two generalizations of the recursive path ordering. Unpublished Note, Department of Computer Science, University of Illinois, Urbana, IL, 1980.Google Scholar
  11. 11.
    D. E. Knuth and P. B. Bendix. Simple word problems in universal algebras. In J. Leech, editor, Computational Problems in Abstract Algebra, pages 263–297. Pergamon Press, Oxford, 1970.Google Scholar
  12. 12.
    P. Lescanne. Termination of rewrite systems by elementary interpretations. In Proceedings 3rd International Conference on Algebraic and Logic Programming, Pisa (Italy), LNCS 632, pages 21–36, 1992.Google Scholar
  13. 13.
    U. Waldman. Semantics of order-sorted specifications. Theoretical Computer Science, 94:1–35, 1992.Google Scholar
  14. 14.
    H. Zantema. Termination of term rewriting by semantic labelling. Fundamenta Informaticae, 24:89–105, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Peter Csaba Ölveczky
    • 1
  • Olav Lysne
    • 2
  1. 1.Department of InformaticsUniversity of Bergen, The High Technology CenterBergenNorway
  2. 2.Department of InformaticsUniversity of OsloOsloNorway

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