On Refinement and Temporal Annotations

  • Ron van der Meyden
  • Yoram Moses
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1926)


This paper introduces the semantics of a wide spectrum language with a rich compositional structure that is able to represent both temporal specifications and sequential programs. A key feature of the language is the ability to represent partial correctness annotations expressed in temporal logic. A refinement relation is presented that enables refinement steps to make use of these partial correctness assertions. It is argued by means of an example that the approach presented allows for more flexible reasoning using temporal annotations than previous approaches, and that the added .exibility has signi.cant value for program optimization.


Refinement calculus temporal logic temporal refinement calculi 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BvW98]
    R. J. Back and vonWright. Refinement Calculus: A systematic approach. Graduate Texts in Computer Science. Springer Verlag, 1998.Google Scholar
  2. [EvdMM98]
    K. Engelhardt, R. van der Meyden, and Y. Moses. Knowledge and the logic of local propositions. In I. Gilboa, editor, Proc. Conf on Theoretical Aspects of Reasoning about Knowledge, pages 29–41. Morgan Kauffman, July 1998.Google Scholar
  3. [EvdMM00]
    K. Engelhardt, R. van der Meyden, and Y. Moses. A refinement framework supporting reasoning about knowledge and time. In Proc. of FOSSACS’ 2000. Springer Verlag, March 2000.Google Scholar
  4. [FHMV95]
    R. Fagin, J. Y. Halpern, Y. Moses, and M. Y. Vardi. Reasoning about Knowledge. MIT Press, Cambridge, Mass., 1995.MATHGoogle Scholar
  5. [GS86]
    S. Graf and J. Sifakis. Alogic for the description of non-deterministic programs and their properties. Information and Control, 68(1-3):254–270, January/February/March 1986.MATHCrossRefMathSciNetGoogle Scholar
  6. [Hay98]
    I. Hayes. Separating timing and calculation in real-time refinement. In J. Grundy et al, editor, International Refinement Workshop & Formal Methods Pacific, Proc. IRW/FMP’98, Series in Discrete Mathematics and Theoretical Computer Science, 1998.Google Scholar
  7. [HL95]
    K. Havelund and K. Larsen. A refinement logic for the fork calculus. In S. T. Vuong and S. T. Chanson, editors, Protocol Specification, Testing and Verification XIV, pages 5–20. Chapman and Hall, 1995. IFIP WG 6.1 Symposium.Google Scholar
  8. [Hoa67]
    C.A.R. Hoare. An axiomatic basis for computer programming. Comm. ACM, 12:516–580, 1967.Google Scholar
  9. [Hol89]
    S. Holström. A refinement calculus for specifications in Henessy-Milner logic with recursion. Formal Aspects of Computing, 1:242–272, 1989.CrossRefGoogle Scholar
  10. [HU97]
    I. Hayes and M. Utting. A sequential real-time refinement calculus. Technical Report UQ-SVRC-97-33, Software Verification Research Centre, University of Queensland, 1997. URL http://www.svrc.it.uq.edu.au/.
  11. [Lam94]
    Leslie Lamport. The temporal logic of actions. ACM Transactions on Programming Languages and Systems, 16(3):872–923, May 1994. Also appeared as DEC SRC Research Report 79.CrossRefGoogle Scholar
  12. [MK93]
    Y. Moses and O. Kislev. Knowledge-oriented programming. In Proc. 12th ACM Symp. on Principles of Distributed Computing, pages 261–270, 1993.Google Scholar
  13. [MM98]
    R. van der Meyden and Y. Moses. Top-down considerations on distributed systems. In Proc. 12th Int. Symp. on Distributed Computing, DISC’98, pages 16–19, Andros, Greece, Sept 1998. Springer LNCS No. 1499.Google Scholar
  14. [Mor87]
    J. M. Morris. A theoretical basis for refinement and the programming calculus. Science of Computer Programming, 9(3):287–306, 1987.MATHCrossRefMathSciNetGoogle Scholar
  15. [Mor90]
    C. Morgan. Programming from Specifications. Prentice Hall, New York, 1990.MATHGoogle Scholar
  16. [UF96]
    M. Utting and C. Fidge. Areal-time refinement calculus that changes only time. In He Jifeng, editor, Proc. 7th BCS/FACS Refinement Workshop, Electronic Workshops in Computing. Springer, 1996.Google Scholar
  17. [UF97]
    M. Utting and C. Fidge. Refinement of infeasible real-time programs. In Proc. Formal Methods Pacific’ 97, Series in Discrete Mathematics and Theoretical Computer Science, pages 243–262, 1997.Google Scholar
  18. [Win86]
    G. Winskel. Acomplete proof system for SCSS with modal assertions. Fundamenta Informaticae, IX:401–419, 1986.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Ron van der Meyden
    • 1
  • Yoram Moses
    • 2
  1. 1.School of Computer Science and EngineeringThe University of New South WalesSydneyAustralia
  2. 2.Department of Electrical EngineeringTechnionHaifaIsrael

Personalised recommendations