A Strong restriction of the inductive completion procedure

  • L. Fribourg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 226)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Au 79]
    Aubin R., "Mechanizing Structural induction", T.C.S. 9, 1979, pp 329–345 and 347–362.Google Scholar
  2. [BM 79]
    Boyer R., Moore J.S., A computational logic, Academic press, 1979.Google Scholar
  3. [Bu 69]
    Burstall R.M., "Proving properties of program by structural induction", Comput. J 12, 1969, pp 41–48.Google Scholar
  4. [Fa 79]
    Fay M., "First-Order Unification in an Equational Theory", Proc. 4th Workshop on Automated Deduction, Austin, 1979, pp 161–167.Google Scholar
  5. [Fr 82]
    Fribourg L., "Refutation par Superposition de Clauses Equationnelles", These de 3eme cycle, U. Paris 7, Sept. 1982.Google Scholar
  6. [Fr 84]
    Fribourg L., "A Narrowing Procedure for Theories with Constructors", 7th Conf. on Automated Deduction, May 1984, pp 259–281.Google Scholar
  7. [Go 80]
    Goguen J.A., "How to Prove Algebraic Inductive Hypotheses Without Induction, with Applications to the Correctness of Data Type Implementation", 5th Conf. on Automated Deduction, Les Arcs, July 1980, pp 356–373.Google Scholar
  8. [Hl 80]
    Hullot J.M., "Canonical Form and Unification", 5th Conf. on Automated Deduction, Les Arcs, July 1980, pp 318–334.Google Scholar
  9. [HH 80]
    Huet G., Hullot J.M., "Proofs by induction in equational theories with constructors", 21st FOCS, 1980, pp 96–107Google Scholar
  10. [HO 80]
    Huet G., Oppen D., "Equations and Rewrite Rules: A Survey", Formal Languages Perspective and Open Problems, Ed. Book R, Academic Press, 1980, pp 349–406Google Scholar
  11. [Hu 80a]
    Huet G., "A Complete Proof of Correctness of the Knuth-Bendix Completion Algorithm", T.R. 25, INRIA, July 1980 (also in JCSS 23:1, Aug. 1981, pp 11–21).Google Scholar
  12. [Hu 80b]
    Huet G., "Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems" J.ACM 27:4, Oct. 1980, pp 797–821.Google Scholar
  13. [JK 84]
    Jouannaud J.P., Kirchner H., "Completion of a Set of Rules Modulo a Set of Equations", Proc 11th POPL, Salt Lake City, Jan. 1984.Google Scholar
  14. [JK 85]
    Jouannaud J.P., Kounalis E., "Proofs by Induction in Equational Theories Without Constructors", Bulletin of EATCS 27, Oct. 1985, pp 49–55.Google Scholar
  15. [Ka 84a]
    Kaplan S., "Conditional Rewrite Rules", T.C.S. 33, Dec.1984, pp 175–193.Google Scholar
  16. [Ka 84b]
    Kaplan S., "Fair Conditional Term Rewriting Systems: Unification, Termination and Confluence", TR no 194, LRI, Orsay, Nov.1984.Google Scholar
  17. [KB 70]
    Knuth D., Bendix P., "Simple Word Problems in Universal Algebras", Computational Problems in Abstract Algebras, Pergamon Press, 1970, pp 263–297.Google Scholar
  18. [KL 80]
    Kamin S., Levy J.-J., "Two Generalisations of the Recursive Path Ordering", Unpublished Note, Dept of Computer Science, U. Illinois, Feb. 1980.Google Scholar
  19. [La 75]
    Lankford D, "Canonical Inference", Report ATP-32, U. of Texas, 1975.Google Scholar
  20. [MN 70]
    Manna Z., Ness N., "On the Termination of Markov Algorithms", Proc. 3rd Hawaii Intl. Conf. on Systems and Science, Jan. 1970, pp. 789–792.Google Scholar
  21. [Mu 80]
    Musser D.L., "On Proving Inductive Properties of Abstract Data Types", Proc. 7th POPL, Las Vegas, 1980, pp 154–162.Google Scholar
  22. [PS 81]
    Peterson G., Stickel M.E., "Complete Sets of Reductions for Some Equational Theories", J.ACM 28, 1981, pp 233–264.Google Scholar
  23. [Re 82]
    Remy J.L. "Etude des Systemes de Reecriture Conditionnels et Application aux Types Abstraits Algebriques", These d'Etat, Nancy, 1982.Google Scholar
  24. [RZ 84]
    Remy J.L., Zhang H., "REVEUR4: A System for Validating Conditional Algebraic Specifications of Abstract Data Types", Proc. ECAI, Pisa, 1984, pp 563–572.Google Scholar
  25. [Sl 74]
    Slagle J.R., "Automated Theorem Proving for Theories with Simplifiers, Commutativity and Associativity", J.ACM 21:4, Oct 1974, pp 622–642.Google Scholar
  26. [Sm 85]
    Smith D.R., "Reasoning by Cases and the Formation of Conditional Programs", Intl. Joint Conf. on Artificial Intelligence, Los Angeles., Aug. 1985, pp. 215–218.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • L. Fribourg
    • 1
  1. 1.Paris cedex 05France

Personalised recommendations