Advertisement

Polarized Process Algebra and Program Equivalence

  • Jan A. Bergstra
  • Inge Bethke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2719)

Abstract

The basic polarized process algebra is completed yielding as a projective limit a cpo which also comprises infinite processes. It is shown that this model serves in a natural way as a semantics for several program algebras. In particular, the fully abstract model of the program algebra axioms of [2] is considered which results by working modulo behavioral congruence. This algebra is extended with a new basic instruction, named ‘entry instruction’ and denoted with ‘@’. Addition of @ allows many more equations and conditional equations to be stated. It becomes possible to find an axiomatization of program inequality. Technically this axiomatization is an infinite final algebra specification using conditional equations and auxiliary objects.

Keywords

Induction Hypothesis Canonical Form Basic Instruction Program Equivalence Process Algebra 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J.A. Bergstra and J.-W. Klop. Process algebra for synchronous communication. Information and Control, 60(1/3):109–137, 1984.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    J.A. Bergstra and M.E. Loots. Program algebra for component code. Formal Aspects of Computing, 12(1):1–17, 2000.zbMATHCrossRefGoogle Scholar
  3. 3.
    J.A. Bergstra and M.E. Loots. Program algebra for sequential code. Journal of Logic and Algebraic Programming, 51(2):125–156, 2002.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    J.A. Bergstra and J.V. Tucker. Equational specifications, complete rewriting systems and computable and semi-computable algebras. Journal of the ACM, 42(6):1194–1230, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    I. Bethke. Completion of equational specifications. In Terese, editors, Term Rewriting Systems, Cambridge Tracts in Theoretical Computer Science 55, pages 260–300, Cambridge University Press, 2003.Google Scholar
  6. 6.
    S.D. Brookes, C.A.R. Hoare, and A.W. Roscoe. A theory of communicating sequential processes. Journal of the ACM, 31(8):560–599, 1984.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    J.W. de Bakker and J.I. Zucker. Processes and the denotational semantics of concurreny. Information and Control, 54(1/2):70–120, 1982.zbMATHMathSciNetGoogle Scholar
  8. 8.
    W.J. Fokkink. Axiomatizations for the perpetual loop in process algebra. In P. Degano, R. Gorrieri, and A. Machetti-Spaccamela, editors, Proceedings of the 24-th ICALP, ICALP’97, Lecture Notes in Comp. Sci. 1256, pages 571–581. Springer Berlin, 1997.Google Scholar
  9. 9.
    J.-W. Klop. Term rewriting systems. In Handbook of Logic in Computer Science, volume II, pages 1–116. Oxford University Press, 1992.MathSciNetGoogle Scholar
  10. 10.
    A. Ponse. Program algebra with unit instruction operators. Journal of Logic and Algebraic Programming, 51(2):157–174, 2002.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    V. Stoltenberg-Hansen, I. Lindström, and E.R. Griffor. Mathematical Theory of Domains, Cambridge Tracts in Theoretical Computer Science 22, Cambridge University Press, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jan A. Bergstra
    • 1
    • 2
  • Inge Bethke
    • 2
  1. 1.Applied Logic Group, Department of PhilosophyUtrecht UniversityUtrechtThe Netherlands
  2. 2.Programming Research Group, Informatics Institute, Faculty of ScienceUniversity of AmsterdamAmsterdamThe Netherlands

Personalised recommendations