LSE narrowing for decreasing conditional term rewrite systems

  • Alexander Bockmayr
  • Andreas Werner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 968)


LSE narrowing is known as an optimal narrowing strategy for arbitrary unconditional canonical term rewrite systems without additional properties such as orthogonality or constructor discipline. In this paper, we extend LSE narrowing to confluent and decreasing conditional term rewrite systems.


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  1. S. Antoy, R. Echahed, and M. Hanus. A needed narrowing strategy. In 21st ACM Symposium on Principles of Programming Languages, POPL '94, Portland, pages 268–279, 1994.Google Scholar
  2. A. Bockmayr. Contributions to the Theory of Logic-Functional Programming. PhD thesis, Fakultät für Informatik, Univ. Karlsruhe, 1990. (in German).Google Scholar
  3. A. Bockmayr. Conditional narrowing modulo a set of equations. Applicable Algebra in Engineering, Communication and Computing, 4(3):147–168, 1993.Google Scholar
  4. A. Bockmayr, S. Krischer, and A. Werner. An optimal narrowing strategy for general canonical systems. In Conditional Term Rewriting Systems, CTRS'92, Pont-à-Mousson, France. Springer, LNCS 656, 1992.Google Scholar
  5. A. Bockmayr, S. Krischer, and A. Werner. Narrowing strategies for arbitrary canonical systems. Technical Report MPI-I-93-233, Max-Planck-Institut für Informatik, Saarbrücken, July 1993. To appear in Fundamenta Informaticae.Google Scholar
  6. N. Dershowitz and J.-P. Jouannaud. Rewrite systems. In Jan van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B: Formal Models and Semantics, chapter 6, pages 244–320. Elsevier, 1990.Google Scholar
  7. N. Dershowitz and D. A. Plaisted. Logic programming cum applicative programming. In Proc. Intern. Symposium on Logic Programming, Boston. IEEE, 1985.Google Scholar
  8. M. Fay. First-order unification in an equational theory. In 4th Workshop on Automated Deduction, Austin, Texas, 1979.Google Scholar
  9. E. Giovannetti and C. Moiso. A completeness result for E-unification algorithms based on conditional narrowing. In Foundations of Logic and Functional Programming, Trento. Springer LNCS 306, 1986.Google Scholar
  10. M. Hanus. The integration of functions into logic programming: From theory to practice. Journal of Logic Programming, 19&20:583–628, 1994.CrossRefGoogle Scholar
  11. A. Herold. Narrowing techniques applied to idempotent unification. SEKI-Report SR-86-16, Univ. Kaiserslautern, 1986.Google Scholar
  12. G. Huet and D. C. Oppen. Equations and rewrite rules, A survey. In R. V. Book, editor, Formal Language Theory. Academic Press, 1980.Google Scholar
  13. J. M. Hullot. Canonical forms and unification. In Proc. 5th Conference on Automated Deduction, Les Arcs. Springer, LNCS 87, 1980.Google Scholar
  14. H. Hu\mann. Unification in conditional-equational theories. Technical Report MIP-8502, Univ. Passau, Jan. 1985. Short version: EUROCAL 85, Linz, Springer, LNCS 204.Google Scholar
  15. S. Kaplan. Conditional rewrite rules. Theoretical Computer Science, 33:175–193, 1984.CrossRefGoogle Scholar
  16. S. Kaplan. Fair conditional term rewriting systems: Unification, termination and confluence. Technical Report 194, L. R. I., Univ. Paris-Sud, 1984.Google Scholar
  17. J. W. Klop. Term rewriting systems. In S. Abramski, D. M. Gabbay, and T. S. Maibaum, editors, Handbook of Logic in Computer Science, volume 2 — Background: Computational Structures, pages 1–116. Oxford Univ. Press, 1992.Google Scholar
  18. A. Middeldorp and E. Hamoen. Completeness results for basic narrowing. Applicable Algebra in Engineering, Communication and Computing, 5:213–253, 1994.Google Scholar
  19. P. Réty. Improving basic narrowing techniques. In Proc. Rewriting Techniques and Applications RTA '87, Bordeaux. Springer, LNCS 256, 1987.Google Scholar
  20. A. Werner, A. Bockmayr, and S. Krischer. How to realize LSE narrowing. Technical Report 6/93, Fakultät für Informatik, Univ. Karlsruhe, December 1993.Google Scholar
  21. A. Werner, A. Bockmayr, and S. Krischer. How to realize LSE narrowing. In Algebraic and Logic Programming, ALP'94, Madrid, pages 59–76. Springer, LNCS 850, 1994.Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Alexander Bockmayr
    • 1
  • Andreas Werner
    • 2
  1. 1.MPI InformatikSaarbrücken
  2. 2.SFB 314Univ. KarlsruheKarlsruhe

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