Skip to main content

Automatic proof methods for algebraic specifications

  • Commanications
  • Conference paper
  • First Online:
Fundamentals of Computation Theory (FCT 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 529))

Included in the following conference series:

  • 130 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3(1 & 2):69–116, 1987.

    Google Scholar 

  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. 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. 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. J.V. Guttag. Abstract data types and software validation. Communications of the Association for Computing Machinery, 21:1048–1064, 1978.

    Google Scholar 

  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. H. Kirchner. Proofs in parameterized specifications. RTA 91, LNCS 488, pages 174–187. Springer-Verlag, 1991.

    Google Scholar 

  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. 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. 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. 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. 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. 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. P. Padawitz. Computing in Horn Clause Theories. Springer-Verlag, 1988.

    Google Scholar 

  15. D. Plaisted. Semantic confluence tests and completion methods. Information and Control, 65:182–215, 1985.

    Google Scholar 

  16. E.G. Wagner and H. Ehrig. Canonical constraints for parameterized data types. Elsevier Science Publishers B.V.(North-Holland), 1987.

    Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

Authors

Editor information

L. Budach

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kounalis, E., Rusinowitch, M. (1991). Automatic proof methods for algebraic specifications. In: Budach, L. (eds) Fundamentals of Computation Theory. FCT 1991. Lecture Notes in Computer Science, vol 529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54458-5_75

Download citation

  • DOI: https://doi.org/10.1007/3-540-54458-5_75

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54458-6

  • Online ISBN: 978-3-540-38391-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics