Characterizing behavioural semantics and abstractor semantics

  • Michel Bidoit
  • Rolf Hennicker
  • Martin Wirsing
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 788)


In the literature one can distinguish two main approaches to the definition of observational semantics of algebraic specifications. On one hand, observational semantics is defined using a notion of observational satisfaction for the axioms of a specification and on the other hand one can define observational semantics of a specification by abstraction with respect to an observational equivalence relation between algebras. In this paper we present an analysis and a comparative study of the different approaches in a more general framework which subsumes not only the observational case but also other examples like the bisimulation congruence of concurrent processes. Thereby the distinction between the different concepts of observational semantics is reflected by our notions of behavioural semantics and abstractor semantics. Our main results show that behavioural semantics can be characterized by an abstractor construction and, vice versa, abstractor semantics can be characterized in terms of behavioural semantics. Hence there exists a duality between both concepts which allows to express each one by each other. As a consequence we obtain a sufficient and necessary condition under which behavioural and abstractor semantics coincide. Moreover, the semantical characterizations lead to proof-theoretic results which show that behavioural theories of specifications can be reduced to standard theories (of some classes of algebras).


  1. [Astesiano, Wirsing 89]
    E. Astesiano, M. Wirsing: Bisimulation in algebraic specifications. In: H. Ait-Kaci, M. Nivat (eds.): Resolution of Equations in Algebraic Structures, Vol. 1, Algebraic Techniques, London, Academic Press, 1–32, 1989.Google Scholar
  2. [Bernot, Bidoit 91]
    G. Bernot, M. Bidoit: Proving the correctness of algebraically specified software: modularity and observability issues. Proc. AMAST '91, Techn. Report of the University of Iowa, 139–161, 1991.Google Scholar
  3. [Bidoit, Hennicker 94]
    M. Bidoit, R. Hennicker: Proving behavioural theorems with standard first-order logic. Submitted for publication, 1994.Google Scholar
  4. [Ehrig, Mahr 85]
    H. Ehrig, B. Mahr: Fundamentals of algebraic specification 1, EATCS Monographs on Theoretical Computer Science 6, Springer, Berlin, 1985.Google Scholar
  5. [Hennicker 91]
    R. Hennicker: Context induction: a proof principle for behavioural abstractions and algebraic implementations. Formal Aspects of Computing 4 (3), 326–345, 1991.Google Scholar
  6. [Knapik 91]
    T. Knapik: Specifications with observable formulae and observational satisfaction relation. In: M. Bidoit, C. Choppy (eds.): Recent Trends in Data Type Specification, Springer LNCS 655,271–291, 1991.Google Scholar
  7. [Milner 77]
    R. Milner: Fully abstract models of typed λ-calculi. Theoretical Computer Science 4, 1–22, 1977.Google Scholar
  8. [Nivela, Orejas 88]
    P. Nivela, F. Orejas: Initial behaviour semantics for algebraic specifications. In: D. T. Sannella, A. Tarlecki (eds.): Proc. 5th Workshop on Algebraic Specifications of Abstract Data Types, Springer LNCS 332, 184–207, 1988.Google Scholar
  9. [Orejas et al. 91]
    F. Orejas, M. Navarro, A. Sanchez: Implementation and behavioural equivalence: a survey. In: M. Bidoit, C. Choppy (eds.): Recent Trends in Data Type Specification, Springer LNCS 655,93–125, 1991.Google Scholar
  10. [Reichel 81]
    H. Reichel: Behavioural equivalence — a unifying concept for initial and final specification methods. In: M. Arato, L. Varga (eds.): Math. Models in Comp. Systems, Proc. 3rd Hungarian Computer Science Conference, Budapest, 27–39, 1981.Google Scholar
  11. [Reichel 85]
    H. Reichel: Initial restrictions of behaviour. IFIP Working Conference, The Role of Abstract Models in Information Processing, 1985.Google Scholar
  12. [Sannella, Tarlecki 85]
    D. T. Sannella, A. Tarlecki: On observational equivalence and algebraic specification. Proc. TAPSOFT '85, Springer LNCS 185, 308–322, 1985.Google Scholar
  13. [Sannella, Tarlecki 88]
    D. T. Sannella, A. Tarlecki: Toward formal development of programs from algebraic specifications: implementation revisited. Acta Informatica 25, 233–281, 1988.Google Scholar
  14. [Schoett 87]
    O. Schoett: Data abstraction and correctness of modular programming. Ph. D. thesis, CST-42-87, University of Edinburgh, 1987.Google Scholar
  15. [Wirsing 86]
    M. Wirsing: Structured algebraic specifications: a kernel language. Theoretical Computer Science 42, 123–249, 1986.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Michel Bidoit
    • 1
  • Rolf Hennicker
    • 2
  • Martin Wirsing
    • 2
  1. 1.LIENS, CNRS & Ecole Normale SupérieureParis CedexFrance
  2. 2.Institut für InformatikLudwig-Maximilians-Universität MünchenMünchenGermany

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