Matching with distributivity

  • Jalel Mzali
Unification Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 230)


We study matching problems for one-sided distributivity. A general method is presented to build up a matching algorithm in an equational theory, and illustrated by the case of one-sided distributivity. Using this algorithm, (right and left) distributivity matching is shown decidable and a method to compute distributive matches is given.

Key words

matching distributivity equational theory decomposition merging mutation 


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10. References

  1. [ArT85]
    S. Arnborg and E. Tiden, “Unification problems with one-sided distributivity”, in Proc. 1st Conf. on Rewriting Techniques and Applications, vol. 202, Springer Verlag, Dijon (France), 1985, 398–406.Google Scholar
  2. [BeK84]
    J. A. Bergstra and J. W. Klop, “The Algebra of Recursively defined Processes and the Algebra of Regular Processes”, in ICALP 84, vol. 172, 1984, 82–94.Google Scholar
  3. [Der84]
    N. Dershowitz, “Computing With Term Rewriting Systems”, Procedings of An NSF Workshop On The Rewrite Rule Laboratory, April 1984.Google Scholar
  4. [FaH83]
    F. Fages and G. Huet, “Unification and Matching in Equational Theories”, Proceedings of CAAP 83, 159, (1983), 205–220, Springer Verlag.Google Scholar
  5. [FGJ85]
    K. Futatsugi, J. A. Goguen, J. P. Jouannaud and J. Meseguer, “Principles of OBJ2”, in Proceedings, 12th ACM Symposium on Principles of Programming Languages Conference, 1985.Google Scholar
  6. [Hsi85]
    J. Hsiang, “Two Results in Term Rewriting Theorem Proving”, in Proc. 1st Conf. on Rewriting Techniques and Applications, vol. 202, Springer Verlag, Dijon (France), 1985, 301–324.Google Scholar
  7. [HuO80]
    G. Huet and D. Oppen, “Equations and Rewrite Rules: A Survey”, in Formal Languages: Perspectives And Open Problems, B. R., (ed.), Academic Press, 1980.Google Scholar
  8. [JoK84]
    J. P. Jouannaud and H. Kirchner, “Completion of a set of rules modulo a set of equations”, Proceedings 11th ACM Conference of Principles of Programming Languages, Salt Lake City (Utah, USA), 1984.Google Scholar
  9. [KaN85]
    D. Kapur and P. Narendran, “An Equational Approach to Theorem Proving in First-Order Predicate Calculus”, in Proc. Int. Joint Conf. on Artificial Intelligence, Los Angeles, 1985.Google Scholar
  10. [Kir85]
    C. Kirchner, “Méthodes et outils de conception systématique d'algorithmes d'unification dans les théories équationnelles”, Thése de doctorat d'Etat, Université de Nancy I, 1985.Google Scholar
  11. [Mza85]
    J. Mzali, “Filtrage associatif, commutatif ou idempotent”, in Proceedings of the conference Materiels et logiciels pour la 5ieme generation, AFCET, Paris (France), 1985, 243–258.Google Scholar
  12. [Sza82]
    P. Szabo, “Unificationtheorie erster Ordnung”, Doktorarbeit, Universitat Karlsruhe, 1982.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Jalel Mzali
    • 1
    • 2
  1. 1.Centre de Recherche en Informatique de NancyVandoeuvre Les Nancy Cedex
  2. 2.Greco de Programmation (C.N.R.S)France

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