Abstract
The π-calculus is a relatively simple framework in which the semantics of dynamic creation and transmission of channels can be described nicely. In this paper we consider the issue of verifying mechanically the equivalence of π-terms in the context of bisimulation based semantics while relying on the general purpose theorem prover HOL. Our main contribution is the presentation of a proof method to check early equivalence between π-terms. The method is based on π-terms rewriting and an operational definition of bisimulation. The soundness of the rewriting steps relies on standard algebraic laws which are formally proved in HOL. The resulting method is implemented in HOL as an automatic tactic.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
O AÏt-Mohamed. Vérification de l'équivalence du π-calcul dans HOL. Research Report 2412, Institut National de Recherche en Informatique et Automatique, Novembre 1994.
R Amadio. On the reduction of chocs bisimulation to π-calculus bisimulation. In SLNCS 715, editor, CONCUR93, pages 112–126, 1993. Also appeared as Research Report Inria-Lorraine 1786, October 1992.
R Amadio and O AÏt-Mohamed. An analysis of π-calculus bisimulation. Technical Report 94-2, ECRC, 1994.
J A Bergstra and J W Klop. Process algebra for synchronous communication. Information and Control, 60:109–137, 1984.
J A Bergstra and J W Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 33:77–121, 1985.
A J Camilleri. Mechanizing CSP trace theory in Higher Order Logic. IEEE Transactions on Software Engineering, 16(9):993–1004, 1990.
T F Melham. Automating recursive type definitions in higher order logic. In G. Birtwistle and P. Subrahmanyam, editors, Current Trends in Hardware Verification and Automated Theorem Proving, pages 341–386. Springer-Verlag, 1989.
T F Melham. A package for inductive relation definitions in HOL. In P.J. Windly, M. Archer, K.N. Levitt, and J.J Joyce, editors, Proceedings of the 1991 International Workshop on the HOL Theorem Proving System and its Applications, pages 350–357. IEEE Computer Society Press, 1992.
T F Melham. A mechanized theory of π-calculus in HOL. Nordic Journal of Computing, 1(1):50–76, 1994.
R Milner. Communication and Concurrency. Prentice Hall, 1989.
R Milner. Functions as processes. Journal of Mathematical Structures in Computer Science, 2(2):119–141, 1992.
R Milner, J Parrow, and D Walker. A calculus of mobile process, part 1–2. Information and Computation, 100(1):1–77, 1992.
M Nesi. A formalisation of the CCS process algebra in Higher Order Logic. Technical Report 278, Computer Laboratory, University of Cambridge, December 1992.
Frederik Orava and Jaochim Parrow. An algebraic verification of a mobile network. Formal Aspects of Computing, 4(6):497–543, 1992.
D Sangiorgi. Expressing mobility in process algebras: first-order and higher order paradigms. PhD thesis, University of Edinburgh, September 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Aït Mohamed, O. (1995). Mechanizing a π-calculus equivalence in HOL. In: Thomas Schubert, E., Windley, P.J., Alves-Foss, J. (eds) Higher Order Logic Theorem Proving and Its Applications. TPHOLs 1995. Lecture Notes in Computer Science, vol 971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60275-5_53
Download citation
DOI: https://doi.org/10.1007/3-540-60275-5_53
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60275-0
Online ISBN: 978-3-540-44784-9
eBook Packages: Springer Book Archive