Towards a Signal Calculus for Event-Based Synchronous Languages

  • Yongxin Zhao
  • He Jifeng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6991)

Abstract

A theory of programming is intended to support the practice of programming by relating each program to the specification of what it is intended to achieve. Our intention is to develop a signal calculus for event-based synchronous languages used for specification and programming of embedded systems. In this paper, we mainly tackle conceptually instantaneous reactions, i.e., zero-time reactions. The delay-time reactions will be investigated in the follow-up work. To explore the semantic definition of instantaneous reactions (I-calculus), a set of algebraic laws is provided, which can be used to reduce all instantaneous reactions to a normal form algebraically. The normal form, surprisingly, exposes the internal implicit dependence explicitly. Consequently, that two differently written reactions happen to mean the same thing can be proved from the equations of an algebraic presentation.

Keywords

Input Signal Operational Semantic Algebraic Semantic Instantaneous Reaction Pure Signal 
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.

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References

  1. 1.
    Goguen, J., Thatcher, J., Wagner, E., Wright, J.: Initial algebra semantics and continuous algebra. Journal of the ACM 24(1), 68–95 (1977)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Bergstra, J.A., Klop, J.W.: Algebra of communicating processes with abstraction. Theoretical Computer Science 37(1), 77–121 (1985)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Hennessy, M.C.: Algebraic Theory of Processes. MIT Press, Cambridge (1988)MATHGoogle Scholar
  4. 4.
    Roscoe, A.W., Hoare, C.A.R.: The Laws of OCCAM Programming. Theoretical Computer Science 60, 229–316 (1977/1988)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Baeten, J.C.M., Weijland, W.P.: Process Algebra. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge (1990)MATHGoogle Scholar
  6. 6.
    Libkin, L.: An elementary proof that upper and lower powerdomain constructions commute. Bulletin EATCS 48, 175–177 (1992)MATHGoogle Scholar
  7. 7.
    Berry, G., Gonthier, G.: The Esterel synchronous programming language: Design, semantics, implementation. Science of Computer Programming (SCP) 19(2), 87–152 (1992)CrossRefMATHGoogle Scholar
  8. 8.
    He, J., Hoare, C.A.R.: From Algebra to operational semantics. Information Processing Letter 46 (1993)Google Scholar
  9. 9.
    Maddux, R.D.: Fundamental study Relation-algebraic semantics. Theoretical Computer Science 160, 1–85 (1996)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Hoare, C.A.R., He, J.: Unifying Theories of Programming. Prentice Hall International Series in Computer Science. Prentice-Hall, Englewood Cliffs (1998)MATHGoogle Scholar
  11. 11.
    Lee, E.A., Sangiovanni-Vincentelli, A.: A framework for comparing models of computation. IEEE Transactions on Computer-Aided Design of Integraed Circuits and Systems 17(12), 1217–1229 (1998)CrossRefGoogle Scholar
  12. 12.
    Berry, G.: The Constructive Semantics of Pure Esterel (1999) Draft version, ftp://ftp-sop.inria.fr/meije/esterel/papers/constructiveness3.ps.gz
  13. 13.
    Tini, S: Structural Operational Semantics for Synchronous Languages. PhD thesis, Dipartimento di Informatica, Universitá degli Studi di Pisa, Pisa, Italy (2000)Google Scholar
  14. 14.
    McIver, A.K., Morgan, C.C.: Probabilistic power domains (in preparation)Google Scholar
  15. 15.
    Potop-Butucaru, D., Edwards, S.A., Berry, G.: Compiling Esterel. Springer, Heidelberg (2007)Google Scholar
  16. 16.
    Shyamasundar, R.K., Ramesh, S.: Real Time Programming: Languages, Specification and Verifcations. World Scientific Publishing, Singapore (2009)CrossRefGoogle Scholar
  17. 17.
    Mousavi, M.: Causality in the Semantics of Esterel: Revisited. Electronic Proceedings in Theoretical Computer Science 18, 32–45 (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yongxin Zhao
    • 1
  • He Jifeng
    • 1
  1. 1.Shanghai Key Laboratory of Trustworthy Computing, Software Engineer InstituteEast China Normal UniversityShanghaiChina

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