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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Goguen, J., Thatcher, J., Wagner, E., Wright, J.: Initial algebra semantics and continuous algebra. Journal of the ACM 24(1), 68–95 (1977)
Bergstra, J.A., Klop, J.W.: Algebra of communicating processes with abstraction. Theoretical Computer Science 37(1), 77–121 (1985)
Hennessy, M.C.: Algebraic Theory of Processes. MIT Press, Cambridge (1988)
Roscoe, A.W., Hoare, C.A.R.: The Laws of OCCAM Programming. Theoretical Computer Science 60, 229–316 (1977/1988)
Baeten, J.C.M., Weijland, W.P.: Process Algebra. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge (1990)
Libkin, L.: An elementary proof that upper and lower powerdomain constructions commute. Bulletin EATCS 48, 175–177 (1992)
Berry, G., Gonthier, G.: The Esterel synchronous programming language: Design, semantics, implementation. Science of Computer Programming (SCP) 19(2), 87–152 (1992)
He, J., Hoare, C.A.R.: From Algebra to operational semantics. Information Processing Letter 46 (1993)
Maddux, R.D.: Fundamental study Relation-algebraic semantics. Theoretical Computer Science 160, 1–85 (1996)
Hoare, C.A.R., He, J.: Unifying Theories of Programming. Prentice Hall International Series in Computer Science. Prentice-Hall, Englewood Cliffs (1998)
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)
Berry, G.: The Constructive Semantics of Pure Esterel (1999) Draft version, ftp://ftp-sop.inria.fr/meije/esterel/papers/constructiveness3.ps.gz
Tini, S: Structural Operational Semantics for Synchronous Languages. PhD thesis, Dipartimento di Informatica, Universitá degli Studi di Pisa, Pisa, Italy (2000)
McIver, A.K., Morgan, C.C.: Probabilistic power domains (in preparation)
Potop-Butucaru, D., Edwards, S.A., Berry, G.: Compiling Esterel. Springer, Heidelberg (2007)
Shyamasundar, R.K., Ramesh, S.: Real Time Programming: Languages, Specification and Verifcations. World Scientific Publishing, Singapore (2009)
Mousavi, M.: Causality in the Semantics of Esterel: Revisited. Electronic Proceedings in Theoretical Computer Science 18, 32–45 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhao, Y., Jifeng, H. (2011). Towards a Signal Calculus for Event-Based Synchronous Languages. In: Qin, S., Qiu, Z. (eds) Formal Methods and Software Engineering. ICFEM 2011. Lecture Notes in Computer Science, vol 6991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24559-6_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-24559-6_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24558-9
Online ISBN: 978-3-642-24559-6
eBook Packages: Computer ScienceComputer Science (R0)