A corrected failure-divergence model for CSP in Isabelle/HOL

  • H. Tej
  • B. Wolff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1313)


We present a failure-divergence model for CSP following the concepts of [BR 85]. Its formal representation within higher order logic in the theorem prover Isabelle/HOL [Pau 94] revealed an error in the basic definition of CSP concerning the treatment of the termination symbol tick.

A corrected model has been formally proven consistent with Isabelle/HOL. Moreover, the changed version maintains the essential algebraic properties of CSP. As a result, there is a proven correct implementation of a “CSP workbench” within Isabelle.


Fixpoint Theory High Order Logic Denotational Semantic Functional Programming Language Type Discipline 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [And 86]
    P.B. Andrews: An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof, Academic Press, 1986.Google Scholar
  2. [BH 95]
    J. P. Bowen,M. J. Hinchey: Seven more Myths of Formal Methods: Dispelling Industrial Prejudices, in FME'94: Industrial Benefit of Formal Methods, proc. 2nd Int. Symposium of Formal Methods Europe, LNCS 873, Springer Verlag 1994, pp. 105–117.Google Scholar
  3. [BR 85]
    S.D. Brookes, A.W. Roscoe: An improved failures model for communicating processes. In: S.D.Brookes (ed.): Seminar on Semantics of Concurrency. LNCS 197, Springer Verlag, pp. 281–305. 1985.Google Scholar
  4. [Cam 91]
    A.J. Camillieri: A Higher Order Logic Mechanization of the CSP Failure-Divergence Semantics. G. Birtwistle (ed): IVth Higher Order Workshop, Banff 1990. Workshops in Computing, Springer Verlag, 1991.Google Scholar
  5. [Chu 40]
    A. Church: A formulation of the simple theory of types. Journal of Symbolic Logic, 5, 1940, pp. 56–68.Google Scholar
  6. [Fis 97]
    C. Fischer: Combining CSP and Z. Submitted for publication.Google Scholar
  7. [For 95]
    Formal Systems (Europe) Ltd: Failures-Divergence Refinement: FDR2, Dec. 1995. Preliminary Manual.Google Scholar
  8. [GM 93]
    M.J.C. Gordon,T.M. Melham: Introduction to HOL: a Theorem Proving Environment for Higher order Logics, Cambridge Univ. Press, 1993.Google Scholar
  9. [Hoa 85]
    C.A.R.Hoare: Communication Sequential Processes.Prentice-Hall, 1985Google Scholar
  10. [KLMW96]
    Kolyang, C. Lüth, T. Meier, B. Wolff: Generic Interfaces for Formal Development Support Tools. In: Workshop for Verification and Validation Tools, Bremen. to appear in LNCS.Google Scholar
  11. [Kri+95]
    B. Krieg-Bruckner, J. Peleska, E.-R. Olderog, D. Balzer, A. Baer,: Uniform Workbench-Universelle Entwicklungsumgebung für formale Methoden. Technischer Bericht 8/95, Universitdt Bremen, 1995. See also the project home-page: Scholar
  12. [KSW 96a]
    Kolyang, T. Santen, B. Wolff: Correct and User-Friendly Implementations of Transformation Systems. Proc. Formal Methods Europe, Oxford. LNCS 1051, Springer Verlag, 1996.Google Scholar
  13. [KSW 96b]
    Kolyang, T. Santen, B. Wolff: A structure preserving encoding of Z in Isabelle/HOL. In J. von Wright, J. Grundy and J. Harrison (eds): Theorem Proving in Higher/Order Logics-9th International Conference, LNCS 1125, pp. 283–298, 1996.Google Scholar
  14. [Pau 94]
    L. C. Paulson: Isabelle-A Generic Theorem Prover. LNCS 828, 1994.Google Scholar
  15. [RB 89]
    A.W. Roscoe, G. Barett: Unbounded Nondeterminism in CSP. In: M. Main, A.Melton,M.Mislove,D.Schmidt (eds): 9th International Conference in Mathematical Foundations of Programming Semantics. LNCS 442,pp. 160–193, 1989.Google Scholar
  16. [Reg 94]
    F. Regensburger: HOLCF: Eine konservative Einbettung von LCF in HOL. Phd thesis, Technische Universität München. 1994.Google Scholar
  17. [Ros 88]
    A.W. Roscoe: An alternative Order for the Failures Model. In: Two Papers on CSP. Technical Monograph PRG-67, Oxford university Computer Laboratory, Programming Research Group, July 1988.Google Scholar
  18. [Ros 96]
    A.W. Roscoe, e-mail communication with the authors.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • H. Tej
    • 1
  • B. Wolff
    • 1
  1. 1.Universitat Bremen, FB3Bremen

Personalised recommendations