Observability, Connectivity, and Replay in a Sequential Calculus of Classes

  • Erika Ábrahám
  • Marcello M. Bonsangue
  • Frank S. de Boer
  • Andreas Grüner
  • Martin Steffen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3657)


Object calculi have been investigated as semantical foundation for object-oriented languages. Often, they are object-based, whereas the mainstream of object-oriented languages is class-based.

Considering classes as part of a component makes instantiation a possible interaction between component and environment. As a consequence, one needs to take connectivity information into account.

We formulate an operational semantics that incorporates the connectivity information into the scoping mechanism of the calculus. Furthermore, we formalize a notion of equivalence on traces which captures the uncertainty of observation cause by the fact that the observer may fall into separate groups of objects. We use a corresponding trace semantics for full abstraction wrt. a simple notion of observability. This requires to capture the notion of determinism for traces where classes may be instantiated into more than one instance during a run and showing thus twice an equivalent behavior (doing a “replay”), a problem absent in an object-based setting.


class-based object-oriented languages formal semantics determinism full abstraction 


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  1. 1.
    Abadi, M., Cardelli, L.: A Theory of Objects. Monographs in Computer Science. Springer, Heidelberg (1996)zbMATHGoogle Scholar
  2. 2.
    Ábrahám, E., Bonsangue, M.M., de Boer, F.S., Steffen, M.: Object connectivity and full abstraction for a concurrent calculus of classes. In: Li (ed.) [12], pp. 38–52Google Scholar
  3. 3.
    Abramsky, S.: Algorithmic game semantics: A tutorial introduction. In: Schichtenberg, Steinbruggen (eds.) [16], pp. 21–47Google Scholar
  4. 4.
    Bosangue, M., de Boer, F.S., de Roever, W.-P., Graf, S. (eds.): FMCO 2004. LNCS, vol. 3657. Springer, Heidelberg (2005)Google Scholar
  5. 5.
    de Boer, F.S., Bonsangue, M., Steffen, M., Ábrahám, E.: A fully abstract trace semantics for UML components. In: Bosangue, et al. (eds.) [4] (to appear)Google Scholar
  6. 6.
    Gordon, A.D., Hankin, P.D.: A concurrent object calculus: Reduction and typing. In: Nestmann, Pierce (eds.) [13]Google Scholar
  7. 7.
    Hennessy, M.: Algebraic Theory of Processes. MIT Press, Cambridge (1988)zbMATHGoogle Scholar
  8. 8.
    IEEE. Thirteenth Annual Symposium on Logic in Computer Science (LICS) (Indiana). Computer Society Press (July 1998)Google Scholar
  9. 9.
    IEEE. Seventeenth Annual Symposium on Logic in Computer Science (LICS), Copenhagen, Denmark, July 2002. Computer Society Press (2002)Google Scholar
  10. 10.
    Jeffrey, A., Rathke, J.: A fully abstract may testing semantics for concurrent objects. In: LICS 2002 [9] (2002)Google Scholar
  11. 11.
    Jeffrey, A., Rathke, J.: Java Jr.: A fully abstract trace semantics for a core Java language. In: Sagiv [15], pp. 423–438Google Scholar
  12. 12.
    Li, Z. (ed.): ICTAC 2004. LNCS, vol. 3407. Springer, Heidelberg (2005)Google Scholar
  13. 13.
    Nestmann, U., Pierce, B.C. (eds.): HLCL 1998: High-Level Concurrent Languages, Nice, France, September 12, 1998. Electronic Notes in Theoretical Computer Science, vol. 16(3). Elsevier Science Publishers, Amsterdam (1998)zbMATHGoogle Scholar
  14. 14.
    Rathke, J.: A fully abstract trace semantics for a core Java language (preliminary title). In: Bosangue, et al. (eds.) [4] (to appear)Google Scholar
  15. 15.
    Sagiv, M. (ed.): ESOP 2005. LNCS, vol. 3444. Springer, Heidelberg (2005)zbMATHGoogle Scholar
  16. 16.
    Schichtenberg, H., Steinbruggen, R. (eds.): Proof and System Reliability, Summer School, Marktoberdorf, Germany, NATO Advanced Study Institute. Series F: Computer and System Sciences. Kluwer Academic Publishers, Dordrecht (2001)Google Scholar
  17. 17.
    Smith, G.P.: An Object-Oriented Approach to Formal Specification. PhD thesis, Department of Computer Science, University of Queensland (October 1992)Google Scholar
  18. 18.
    Viswanathan, R.: Full abstraction for first-order objects with recursive types and subtyping. In: LICS 1998 [8] (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Erika Ábrahám
    • 2
  • Marcello M. Bonsangue
    • 3
  • Frank S. de Boer
    • 4
  • Andreas Grüner
    • 1
  • Martin Steffen
    • 1
  1. 1.Christian-Albrechts-UniversityKielGermany
  2. 2.Albert-Ludwigs-UniversityFreiburgGermany
  3. 3.University LeidenThe Netherlands
  4. 4.CWI AmsterdamThe Netherlands

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