Automatic proof methods for algebraic specifications

  • Emmanuel Kounalis
  • Michaël Rusinowitch
Commanications
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 529)

Abstract

Algebraic specifications provide a formal basis for designing data-structures and reasoning about their properties. Sufficient-completeness and consistency are fundamental notions for building algebraic specifications in a modular way. We give in this paper effective methods for testing these properties for algebraic specifications including conditional axioms.

Keywords

Inference Rule Function Symbol Base Specification Critical Pair Horn Clause 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3(1 & 2):69–116, 1987.Google Scholar
  2. [2]
    H. Ehrig, H. Kreowsky, and P. Padawitz. Stepwise specifications and implementation of adt. In Proceedings International Colloquium on Automata, Languages and Programming, volume 62 of Lecture Notes in Computer Science. Springer-Verlag, 1978.Google Scholar
  3. [3]
    H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification 1. Equations and initial semantics, volume 6 of EATCS Monographs on Theorical Computer Science. Springer-Verlag, 1985.Google Scholar
  4. [4]
    J.A. Goguen, J.W. Thatcher, and E.G. Wagner. An initial algebra approach to the specification, correctness and implementation of abstract data types. In Yeh R., editor, Current Trends in Programming methodology IV: Data structuring, pages 80–144. Prentice Hall, 1978.Google Scholar
  5. [5]
    J.V. Guttag. Abstract data types and software validation. Communications of the Association for Computing Machinery, 21:1048–1064, 1978.Google Scholar
  6. [6]
    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
  7. [7]
    H. Kirchner. Proofs in parameterized specifications. RTA 91, LNCS 488, pages 174–187. Springer-Verlag, 1991.Google Scholar
  8. [8]
    D.E. Knuth and P.B. Bendix. Simple word problems in universal algebras. In J. Leech, editor, Computational Problems in Abstract Algebra, pages 263–297. Pergamon Press, Oxford, 1970.Google Scholar
  9. [9]
    E. Kounalis. Completeness in data type specifications. In B. Buchberger, editor, Proceedings EUROCAL Conference, Linz (Austria), volume 204 of Lecture Notes in Computer Science, pages 348–362. Springer-Verlag, 1985.Google Scholar
  10. [10]
    E. Kounalis and M. Rusinowitch. On word problem in Horn logic. CTRS, volume 308 of Lecture Notes in Computer Science, pages 144–160. Springer-Verlag, 1987. See also the extended version published in Journal of Symbolic Computation, 11(1 & 2), 1991.Google Scholar
  11. [11]
    E. Kounalis and M. Rusinowitch. Mechanizing inductive reasoning. In Proceedings of the AAAI Conference, pages 240–245, Boston, 1990. AAAI Press and the MIT Press.Google Scholar
  12. [12]
    D.R. Musser. On proving inductive properties of abstract data types. In Proceedings 7th ACM Symp. on Principles of Programming Languages, pages 154–162. Association for Computing Machinery, 1980.Google Scholar
  13. [13]
    P. Padawitz. New results on completeness and consistency of abstract data types. In Proceedings 9th Symposium on Mathematical Foundations of Computer Science, volume 88 of Lecture Notes in Computer Science, pages 460–473. Springer-Verlag, 1980.Google Scholar
  14. [14]
    P. Padawitz. Computing in Horn Clause Theories. Springer-Verlag, 1988.Google Scholar
  15. [15]
    D. Plaisted. Semantic confluence tests and completion methods. Information and Control, 65:182–215, 1985.Google Scholar
  16. [16]
    E.G. Wagner and H. Ehrig. Canonical constraints for parameterized data types. Elsevier Science Publishers B.V.(North-Holland), 1987.Google Scholar
  17. [17]
    H. Zhang. Reduction, Superposition and Induction: Automated Reasoning in an Equational Logic. PhD thesis, Rensselaer Polytechnic Institute, Department of Computer Science, Troy, NY, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Emmanuel Kounalis
    • 1
  • Michaël Rusinowitch
    • 1
  1. 1.Crin-InriaVandoeuvre-les-NancyFrance

Personalised recommendations