International Conference on Fundamentals of Software Engineering

Fundamentals of Software Engineering pp 292-307 | Cite as

An Interval-Based Approach to Modelling Time in Event-B

  • Gintautas Sulskus
  • Michael Poppleton
  • Abdolbaghi Rezazadeh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9392)


Our work was inspired by our modelling and verification of a cardiac pacemaker, which includes concurrent aspects and a set of interdependent and cyclic timing constraints. To model timing constraints in such systems, we present an approach based on the concept of timing interval. We provide a template-based timing constraint modelling scheme that could potentially be applicable to a wide range of modelling scenarios. We give a notation and Event-B semantics for the interval. The Event-B coding of the interval is decoupled from the application logic of the model, therefore a generative design of the approach is possible. We demonstrate our interval approach and its refinement through a small example. The example is verified, model-checked and animated (manually validated) with the ProB animator.


Timing Property Timing Interval Response Event Proof Obligation Property Duration 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Pacemaker Challenge (2007).
  2. 2.
    Interactive Prover Reference Manual 3.7 (2013).
  3. 3.
  4. 4.
    Abrial, J.-R.: The B-Book: Assigning Programs to Meanings. Cambridge University Press, New York (1996)Google Scholar
  5. 5.
    Abrial, J.-R.: Modeling in Event-B: System and Software Engineering, 1st edn. Cambridge University Press, New York (2010)CrossRefMATHGoogle Scholar
  6. 6.
    Abrial, J.-R., Butler, M., Hallerstede, S., Hoang, T.S., Mehta, F., Voisin, L.: Rodin: an Open Toolset for Modelling and Reasoning in Event-B. International Journal on Software Tools for Technology Transfer 12(6), 447–466 (2010)CrossRefGoogle Scholar
  7. 7.
    Back, R.-J., Kurki-Suonio, R.: Decentralization of Process Nets with Centralized Control. In: Symposium on Principles of Distributed Computing, pp. 131–142. ACM, Montreal (1983)Google Scholar
  8. 8.
    Barold, S.S., Stroobandt, R., Sinnaeve, A.F.: Cardiac Pacemakers and Resynchronization Step-by-Step: an Illustrated Guide. Wiley-Blackwell (2010)Google Scholar
  9. 9.
  10. 10.
    Bryans, J., Fitzgerald, J., Romanovsky, A., Roth, A.: Patterns for Modelling Time and Consistency in Business Information Systems, pp. 105–114. IEEE Computer Society, Oxford (2010)Google Scholar
  11. 11.
    Butler, M., Falampin, J.: An Approach to Modelling and Refining Timing Properties in B. In: Proceedings of Workshop on Refinement of Critical Systems (RCS) (January 2002)Google Scholar
  12. 12.
    Cansell, D., Méry, D., Rehm, J.: Time Constraint Patterns for Event B Development. In: Julliand, J., Kouchnarenko, O. (eds.) B 2007. LNCS, vol. 4355, pp. 140–154. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Déharbe, D., Fontaine, P., Guyot, Y., Voisin, L.: SMT Solvers for Rodin. In: Derrick, J., Fitzgerald, J., Gnesi, S., Khurshid, S., Leuschel, M., Reeves, S., Riccobene, E. (eds.) ABZ 2012. LNCS, vol. 7316, pp. 194–207. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    Gomes, A.O., Oliveira, M.: Formal Development of a Cardiac Pacemaker: From Specification to Code. In: Davies, J. (ed.) SBMF 2010. LNCS, vol. 6527, pp. 210–225. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  15. 15.
    Jee, E., Wang, S., Kim, J.K., Lee, J., Sokolsky, O., Lee, I.: A Safety-Assured Development Approach for Real-Time Software. In: The Proceedings of the 16th IEEE International Conference on Embedded and Real-Time Computing Systems and Applications, pp. 133–142 (August 2010)Google Scholar
  16. 16.
    Jiang, Z., Pajic, M., Moarref, S., Alur, R., Mangharam, R.: Modeling and Verification of a Dual Chamber Implantable Pacemaker. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 188–203. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  17. 17.
    Leuschel, M., Butler, M.: ProB: A Model Checker for B. In: Araki, K., Gnesi, S., Mandrioli, D. (eds.) FME 2003. LNCS, vol. 2805, pp. 855–874. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  18. 18.
    Macedo, H., Larsen, P., Fitzgerald, J.: Incremental Development of a Distributed Real-Time Model of a Cardiac Pacing System Using VDM. In: Cuellar, J., Sere, K. (eds.) FM 2008. LNCS, vol. 5014, pp. 181–197. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Méry, D., Singh, N.K.: Pacemaker’s Functional Behaviors in Event-B. Research Report inria-00419973 (2009)Google Scholar
  20. 20.
    Rehm, J.: From Absolute-Timer to Relative-Countdown: Patterns for Model-Checking (May 2008) (Unpublished)Google Scholar
  21. 21.
    Sarshogh, M.R.: Extending Event-B with Discrete Timing Properties. PhD thesis, University of Southampton (2013)Google Scholar
  22. 22.
    Savicks, V., Butler, M., Colley, J.: Co-simulating Event-B and Continuous Models via FMI. In: 2014 Summer Computer Simulation Conference, Society for Modeling & Simulation International (SCS) (July 2014)Google Scholar
  23. 23.
    Sulskus, G., Poppleton, M., Rezazadeh, A.: Example Event-B project (2014).
  24. 24.
    Sulskus, G., Poppleton, M., Rezazadeh, A.: An Investigation into Event-B Methodologies and Timing Constraint Modelling. Mini-Thesis, University of Southampton (2014)Google Scholar
  25. 25.
    Wang, J.: Handbook of Finite State Based Models and Applications. Discrete Mathematics and Its Applications. Chapman and Hall/CRC (2012)Google Scholar
  26. 26.
    Yang, F., Jacquot, J.-P.: Scaling Up with Event-B: A Case Study. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 438–452. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2015

Authors and Affiliations

  • Gintautas Sulskus
    • 1
  • Michael Poppleton
    • 1
  • Abdolbaghi Rezazadeh
    • 1
  1. 1.University of SouthamptonSouthamptonUK

Personalised recommendations