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On sufficient completeness of conditional specifications

  • Chapter 4 Combined Systems, Combined Languages And Modularity
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Book cover Conditional and Typed Rewriting Systems (CTRS 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 516))

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Abstract

We present an algorithm which, given a conditional rewriting system and a set of distinguished operators, guarantees in case of success, that the normal forms of every ground term are primitive, i.e. built only from the distinguished operators. This property is crucial for completeness of definition and very helpful in inductive proofs. It was comparatively few investigated for conditional systems. The algorithm combines structural analysis, using patterns on distinguished operators, and case analysis, using sets of preconditions involved when reducing the instances of patterns. The algorithm works for reductive systems that constitute a large class of systems, as reductivity is assumed when proving most of the properties of conditional systems. The correctness proof of the algorithm and several examples are also presented.

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References

  1. A. Bouhoula. Implantation d'un algorithme de test de complétude suffisante d'une spécification conditionnelle et d'aide à la construction de définitions structurelles complètes. Rapport de Stage de Fin d'Etudes, Centre de Recherche en Informatique de Nancy, 1990.

    Google Scholar 

  2. W. Bousdira. Etude des propriétés des systèmes de réécriture conditionnelle. Mise en œuvre de deux algorithmes de test de confluence sur les termes clos., 1990. Thèse de l'Institut National Polytechnique de Lorraine.

    Google Scholar 

  3. W. Bousdira and J-L. Rémy. Hierarchical Contextual Rewriting with Several Levels. In R. Cori and M. Wirsing, editors, Lecture Notes in Computer Science, volume 294, pages 193–206, Bordeaux, France, 1988. 5th Synposium on Theoretical Aspects of Computer Science, Springer-Verlag.

    Google Scholar 

  4. N. Dershowitz. Computing with Term Rewriting Systems. In Proceedings of An NSF Workshop On The Rewrite Rule Laboratory, 1984.

    Google Scholar 

  5. N. Dershowitz. Termination. In J-P. Jouannaud, editor, Lecture Notes in Computer Science, volume 202, Dijon, France, 1985. 1st Conference on Rewriting Techniques and Applications, Springer-Verlag. Also in Journal os jsc 3, special issue on Rewriting Techniques and Applications, 69–115, 1987.

    Google Scholar 

  6. N. Dershowitz and M. Okada. Conditional Equational Programming and the Theory of Conditional Term Rewriting. In Proceedings of the International Conference on Fifth Generation Computer Systems, pages 337–346, Tokyo, Japan, November 1988. ICOT.

    Google Scholar 

  7. J. V. Guttag and J. J. Horning. The Algebraic Specification of Abstract Data Types. Acta Informatica, 10:27–52, 1978.

    Google Scholar 

  8. J.V. Guttag. Abstract Data Types and Software Validation. Communications of the Association for Computing Machinery, 21:1048–1064, 1978.

    Google Scholar 

  9. G. Huet and J-M. Hullot. Proofs by Induction in Equational Theories with Constructors. Journal of Computer and System Sciences, 25(2):239–266, October 1982. Preliminary version in Proceedings 21st Symposium on Foundations of Computer Science, IEEE, 1980.

    Google Scholar 

  10. J-P. Jouannaud and E. Kounalis. Automatic Proofs by Induction in Theories without Constructors. Technical Report 295, Université de Paris-Sud, Centre d'Orsay, September 1986.

    Google Scholar 

  11. J-P. Jouannaud and B. Waldmann. Reductive Conditional Term Rewriting Systems. In M. Wirsing, editor, Elsevier Science Publishers, pages 223–244, Ebberup, Denmark, 1986. 3rd IFIP Working Conference on Formal Description of Programming Concepts.

    Google Scholar 

  12. S. Kaplan. Simplifying Conditional Term Rewriting Systems: Unification, Termination and Confluence. Journal of Symbolic Computation, 1987.

    Google Scholar 

  13. S. Kaplan and J-L. Rémy. Completion Algorithms for Conditional Rewriting Systems. In H. Ait-Kaci and M. Nivat, editors, Resolution of Equations in Algebraic Structures, volume 2, Austin, Texas, 1987. MCC-INRIA Colloquium, Academic Press, INC.

    Google Scholar 

  14. D. Kapur, P. Narendran, and H. Zhang. On Sufficient Completeness and Related Properties of Term Rewriting Systems. Acta Informatica, 24:395–415, 1987.

    Google Scholar 

  15. H. Kirchner. A General Inductive Algorithm and Application to Abstract Data Types. In R. Shostak, editor, Proceedings 7th International Conference on Automated Deduction, pages 282–302. Springer-Verlag, Lecture Notes in Computer Science, 1984.

    Google Scholar 

  16. E. Kounalis. Completeness in Data Type Specifications. In B. Buchberger, editor, Proceedings EUROCAL Conference, volume 204 of Lecture Notes in Computer Science, Linz (Austria), 1985. Springer-Verlag.

    Google Scholar 

  17. E. Kounalis. Validation des Spécifications Algébriques par Complétion Inductive, 1985. Thèse de l'Université de Nancy 1.

    Google Scholar 

  18. E. Kounalis. Testing for inductive (co)-reducibility. In A. Arnold, editor, Proceedings 15th CAAP, volume 431 of Lecture Notes in Computer Science, pages 221–238. Springer-Verlag, May 1990.

    Google Scholar 

  19. E. Kounalis and M. Rusinowitch. Mechanizing Inductive Reasoning. EATCS Bulletin, 41:216–226, 1990.

    Google Scholar 

  20. A. Lazrek. Etude et Réalisation de Méthodes de Preuve par Récurrence en Logique Equationnelle, décembre 1988. Thèse de l'Institut National Polytechnique de Lorraine.

    Google Scholar 

  21. A. Lazrek, P. Lescanne, and J-J. Thiel. Tools for Proving Inductive Equalities, Relative Completeness and ω-Completeness. Technical Report 88-R-131, Centre de Recherche en Informatique de Nancy, 1988. to be published in Information and Computation.

    Google Scholar 

  22. T. Nipkow and G. Weikum. A Decidability Result about Sufficient Completeness of Axiomatically Specified Abstract Data Types. In 6th GI Conference, volume 145, pages 257–268. Springer-Verlag, Lecture Notes in Computer Science, 1983.

    Google Scholar 

  23. P. Padawitz. New Results on Completeness and Consistency of Abstract Data Types. In Lecture Notes in Computer Science, volume 88, pages 460–473. Proceedings 9th Symposium on Mathematical Foundations of Computer Science, Springer-Verlag, 1980.

    Google Scholar 

  24. P. Padawitz. Correctness, Completeness and Consistency of Equational Data Type Specifications. Technical Report Bericht Nr 83-15, Technische Universitat, Berlin, West Germany, 1983.

    Google Scholar 

  25. J-L. Rémy. Etude des Systèmes de Réécriture Conditionnelle et Applications aux Types Abstraits Algébriques, 1982. Thèse d'Etat, Institut National Polytechnique de Lorraine, Nancy.

    Google Scholar 

  26. J-L. Rémy and H. Zhang. REVEUR4: a System for Validating Conditional Algebraic Specifications of Abstract Data Types. In ECAI, pages 563–572, Pisa, Italy, 1984. 6th ECAI Conference.

    Google Scholar 

  27. J-J. Thiel. Stop loosing sleep over Incomplete Data Type Specifications. In Proceeding 11th ACM Symp. on Principles of Programming Languages, pages 76–82. Association for Computing Machinery, 1984.

    Google Scholar 

  28. S. Uhrig and J-L. Rémy. An Algorithm for Testing Suffisent Completeness of a Simple Class of Conditional Specifications. Technical Report 88-R-155, Centre de Recherche en Informatique de Nancy, 1988.

    Google Scholar 

  29. H. Zhang. REVEUR4: Etude et mise en œuvre de la Réécriture Conditionnelle, 1984. Thèse de 3ème cycle, Université de Nancy 1.

    Google Scholar 

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Authors and Affiliations

  1. CRIN & INRIA Lorraine, BP 239, F54506, Vandœuvre Cedex, FRANCE

    Wadoud Bousdira & Jean-Luc Rémy

Authors
  1. Wadoud Bousdira
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  2. Jean-Luc Rémy
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S. Kaplan M. Okada

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© 1991 Springer-Verlag Berlin Heidelberg

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Bousdira, W., Rémy, JL. (1991). On sufficient completeness of conditional specifications. In: Kaplan, S., Okada, M. (eds) Conditional and Typed Rewriting Systems. CTRS 1990. Lecture Notes in Computer Science, vol 516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54317-1_97

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  • DOI: https://doi.org/10.1007/3-540-54317-1_97

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54317-6

  • Online ISBN: 978-3-540-47558-3

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