Skip to main content
SpringerLink
Log in

Behavioural approaches to algebraic specifications

A comparative study

  • Published:
Acta Informatica Aims and scope Submit manuscript

Abstract

This paper focuses on observability issues in the framework of loose algebraic specifications. The main purpose of observability is to extend the model class of some given algebraic specification in order to consider not only the algebras that satisfy the axioms of the specification in order to consider not only the algebras that satisfy the axioms of the specification, but as well other ones, provided that the differences between the properties satisfied by these algebras and the properties required by the specification (i.e., the axioms) are not “observable”. We compare various behavioural approaches developed so far. We point out their respective advantages and limitations. Expressive power is our main criterion for the discussion.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bernot, G., Bidoit, M.: Proving the correctness of algebraically specified software: Modularity and observability issues. Proceedings of Second International Conference on Algebraic Methodology and Software Technology, pp. 139–161, Iowa City, May 1991

  2. Bernot, G., Gaudel, M.C., Marre, B.: Software testing based on formal specifications. Software Eng. J.6, 387–405 (1991)

    Google Scholar 

  3. van Diepen, N.W.P.: Implementation of modular algebraic specifications. In: Ganzinger, H. (ed.) ESOP 88, Nancy, March 1988. (Lect. Notes Comput Sci., vol. 300, pp. 64–78) Berlin, Heidelberg, New York: Springer 1988

    Google Scholar 

  4. Ehrig, H., Mahr, B.: Fundamentals of algebraic specifications. (EATCS Monogr. Theor. Comput. Sci., vol. 6) Berlin, Heidelberg, New York: Springer 1985

    Google Scholar 

  5. Fribourg, L.: SLOG, a logic programming language interpreter based on clausal superposition and rewriting. International Symposium on Logic Programming, Boston, July 1985

  6. Ganzinger, H.: Parameterized specifications: parameter passing and implementation with respect to observability. ACM Trans. Programm. Lang. Syst.5, 318–354 (1983)

    Google Scholar 

  7. Gaudel, M.C., Moineau, T.: A theory of software reusability. In: Ganzinger H. (ed.) ESOP 88, Nancy, March 1988. (Lect. Notes Comput. Sci., vol. 300, pp. 115–130) Berlin, Heidelberg, New York: Springer 1988

    Google Scholar 

  8. Girratana, V., Gimona, F., Montanari, U.: Observability concepts in abstract data type specification. MFCS, Gdańsk 1976 (Lect. Notes Comput. Sci., vol. 45, pp. 576–587) Berlin, Heidelberg, New York: Springer 1976

    Google Scholar 

  9. Goguen, J.A., Thatcher, J.W., Wagner, E.G.: An initial approach to the specification, correctness and implementation of abstract data types. In: Yeh, R.T. (ed.) Current trends in programming methodology, vol. 4: Data structuring, pp. 80–149. Englewood Cliffs, NJ: Prentice Hall 1978

    Google Scholar 

  10. Hennicker, R.: Observational implementation of algebraic specifications. Acta Inf. 28, 187–230 (1991)

    Google Scholar 

  11. Hennicker, R.: Context induction: a proof principle for behavioural abstractions and algebraic implementations. Formal Aspects Comput.3, 326–345 (1991)

    Google Scholar 

  12. Hennicker, R., Nickl, F.: Behavioural algebraic framework for modular system design with reuse. Institut für Informatik, Ludwig-Maximilians-Universität München, November 1992 (Internal Report 9206)

  13. Hussmann, H.: Unification in conditional-equational theories. Fakultät für Mathematik und Informatik Universität Passau, January 1985 (Internal Report MIP-8502) and short version in Proc. EUROCAL 85 Conf., Linz

  14. Kamin, S.: Final data types and their specification. ACM Trans. Programm. Lang. Syst.5, 97–123 (1983)

    Google Scholar 

  15. Knapik, T.: Spécifications algébriques observationnelles modulaires: une sémantique fondée sur une relation de satisfaction observationnelle. Thèse de l'Université de Paris-Sud, Orsay 1993

  16. Meseguer, J., Goguen, J. A.: Initiality, induction and computability. In: Nivat, M., Reynolds, J.C. (eds.), Algebraic methods in semantics, pp. 459–540. Cambridge: Cambridge University Press 1985

    Google Scholar 

  17. Moss, L.S., Meseguer, J., Goguen, J.A.: Final algebras, cosemicomputable algebras and degrees of unsolvability In: Pitt, D.H., Poigné, A., Rydeheard, D.E. (eds.) Category theory and computer science, Edinburgh, September 1987 (Lect. Notes Comput. Sci., vol. 283, pp. 158–181) Berlin, Heidelberg, New York: Springer 1987

    Google Scholar 

  18. Moss, L.S., Thatte, S.R.: Generalization of final algebra semantics by relativization. In: Main, M., Melton, A., Mislove, M., Schmidt, D. (eds.) Mathematical foundations of programming semantics. 5th Int. Conference, New Orleans, March/April 1989 (Lect. Notes Comput. Sci. vol. 442, pp. 284–300) Berlin, Heidelberg, New York: Springer 1970

    Google Scholar 

  19. Nivela, P., Orejas, F.: Initial behaviour semantics for algebraic specification. In: Sannella, D., Tarlecki, A. (eds.) Recent trends in data type specification, 5th Workshop on Specification of ADT, Gullane, September 1987 (Lect. Notes Comput. Sci, vol. 332, pp. 184–207) Berlin, Heidelberg, New York: Springer 1988

    Google Scholar 

  20. Pepper, P.: On the correctness of type transformations. Talk at 2nd Workshop on Theory and Applications of Abstract Data Types, Passau, May 1983

  21. Sannella, D., Tarlecki, A.: On observational equivalence and algebraic specification. J. Comput. Syst. Sci.34, 150–178 (1997)

    Google Scholar 

  22. Sannella, D., Tarlecki, A.: Toward formal development of programs from algebraic specifications: implementation revisited. Acta Inf.25, 233–281 (1988)

    Google Scholar 

  23. Reichel, H.: Behavioural validity of conditional equations in abstract data types contributions to general algebra 3. Proceedings of the Vienna Conference, June 1984

  24. Schoett, O.: Data abstraction and the correctness of modular programming. Ph. D. Thesis, University of Edinburgh, 1986

  25. Schoett, O.: Two impossibility theorems on behaviour specification of abstract data types. Acta Inf.29, 595–621 (1992)

    Google Scholar 

  26. Wand, M.: Final algebra semantics and data type extension. J. Comput. Syst. Sci.19, 27–44 (1979)

    Google Scholar 

  27. Wirsing, M.: Algebraic description of reusable software components. In: Milgrom, E., Wodon, P. (eds.) Proceedings of COMPEURO '88. IEEE Computer Society, vol. 843, pp. 300–312, 1988

Download references

Author information

Authors and Affiliations

  1. Ecole Normale Supérieure, L.I.E.N.S., C.N.R.S. U.R.A. 1327, 45 Rue d'Ulm, F-75230, Paris Cedex 05, France

    Gilles Bernot, Michel Bidoit & Teodor Knapik

Authors
  1. Gilles Bernot
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michel Bidoit
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Teodor Knapik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work is partially supported by ESPRIT Working Group COMPASS and C.N.R.S. GDR de Programmation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bernot, G., Bidoit, M. & Knapik, T. Behavioural approaches to algebraic specifications. Acta Informatica 31, 651–671 (1994). https://doi.org/10.1007/BF01177550

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01177550

Keywords

Search

Navigation