Hierarchical contextual rewriting with several levels

  • Wadoud Bousdira
  • Jean-Luc Rémy
Part 1 Research Articles
Part of the Lecture Notes in Computer Science book series (LNCS, volume 308)


We present our research on conditional hierarchical specifications with several levels and we study hierarchical contextual rewriting. This relation is defined in the conditional rewriting system framework and deals with terms with two levels which support boolean contexts. Our main result is a sufficient condition for confluence on ground terms of hierarchical specifications under some hypotheses. On the other hand, because we manipulate conditional equations whose preconditions are boolean expressions with a specific syntax, we have been led to establish a result of consistency with respect to the boolean sort of hierarchical specification which guarantees the existence of initial algebras which are faithful for the boolean sort. This condition is usually assumed by the researchers working in this area.


Mutual Exclusion Critical Pair Boolean Expression Conditional Specification Ground Term 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BR87]
    W. Bousdira and J.L. Rémy. Complétion des systèmes de réécriture conditionnelle. AFCET, Actes des journées GROSPLAN, revue BIGRE+GLOBULE, 1987.Google Scholar
  2. [BR88]
    W. Bousdira and J.L. Rémy. Hierarchical contextual rewriting with several levels. In 5th Annual Symposium on Theoretical Aspects of Computer Science, Bordeaux, Lect. Notes in Comp. Sc, Springer, Berlin, 1988.Google Scholar
  3. [Gan87]
    H. Ganzinger. Ground term confluence in parametric conditional equational specifications. In F.J. Brandenburg, G. Vidal-Naquet, and M. Wirsing, editors, 4th Annual Symposium on Theoretical Aspects of Computer Science, Passau, West Germany, Lect. Notes in Comp. Sc. No 247, pages 286–298, Springer, Berlin, 1987.Google Scholar
  4. [Hsi81]
    J. Hsiang. Refutational theorem proving using term rewriting systems. Res. Report, 1981.Google Scholar
  5. [JK86]
    J.P. Jouannaud and H. Kirchner. Completion of a set of rules modulo a set of equations. SIAM J. Computing, 15:1155–1194, 1986.Google Scholar
  6. [JW86]
    J.P. Jouannaud and B. Waldmann. Reductive conditional term rewriting systems. In M. Wirsing, editor, 3rd IFIP Conf. on Formal Description of Programming Concepts, Ebberup, Denmark, Elsevier Science Publishers, Amsterdam, 1986.Google Scholar
  7. [KR87]
    S. Kaplan and J.L. Rémy. Completion algorithms for conditional rewriting systems. In H. Ait-Kaci and M. Nivat, editors, Colloquium on the Resolution of Equations in Algebraic Structures, M.C.C. and I.N.R.I.A, Austin, USA, 1987.Google Scholar
  8. [Nav87]
    M.L. Navarro. Técnicas de Reescritura para especificationes condicionales. Thèse Doctorale de l'Université Polytechnique de Catalogne, Barcelona, 1987.Google Scholar
  9. [NO84]
    M. Navarro and F. Orejas. On the equivalence of hierarchical and non-hierarchical rewriting on conditional term rewriting systems. In Eurosam Conference, Oxford, 1984.Google Scholar
  10. [RZ84]
    J.L. Rémy and H. Zhang. Reveur4: a system for validating conditional algebraic specifications of abstract data types. In 6th ECAI Conference, Pisa, Italy, 1984.Google Scholar
  11. [TW76]
    J.W. Thatcher and E.G. Wagner. Specification of abstract data types using conditional axioms. IBM T.J. Watson Res Center Rep RC-6214, 1976.Google Scholar
  12. [TW82]
    J.W. Thatcher and E.G. Wagner. Data type specification: parametrization and the power of specification techniques. In ACM TOPLAS 4,4, pages 711–732, 1982.Google Scholar
  13. [Zha84]
    H. Zhang. REVEUR4: Etude et mise en oeuvre de la réécriture conditionnelle. Thèse de 3ème cycle, Université de Nancy 1, 1984.Google Scholar
  14. [ZR85]
    H. Zhang and J.L. Rémy. Contextual rewriting. In J.P. Jouannaud, editor, 1st Conference on Rewriting Techniques and Applications, Dijon, France, Lect. Notes in Comp. Sc. No 202, pages 46–62, Springer, Berlin, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Wadoud Bousdira
    • 1
  • Jean-Luc Rémy
    • 1
  1. 1.CRIN & INRIA LorraineVandœuvre-lès-NancyFrance

Personalised recommendations