Abstract
We explore several ways to formalize the algebraic laws of CSP-like languages in HOL. The intent of the paper is to show how HOL can be tailored to acting as a proof assistant. The emphasis is therefore on the consequences of various choices to be made during the formalization for writing tactics. We end up with a proof assistant that allows a user to make steps of the granularity of an algebraic law. It is not the purpose of this paper to show in HOL that the algebraic laws of some CSP-like language are sound; the purpose is to show how HOL can be used to apply the algebraic laws and act as a rewrite system.
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References
M.A. Bezem and J.F. Groote. A formal verification of the alternating bit protocol in the calculus of constructions. Technical Report 88, Logic Group Preprint Series, Utrecht University, March 1993.
G. Birtwistle and B. Graham. Verifying SECD in HOL. In Proceedings of the IFIP TC10/WG10.5 Summer School on Formal Methods for VLSI Design, North Holland, 1990.
Robert S. Boyer and J Strother Moore. A Computational Logic Handbook. Academic Press, 1988.
A.J. Camilleri. A Higher Order Logic Mechanization of the CSP Failure-Divergence Semantics. In Proceedings of the 4th Banff Higher Order Workshop, G. Birtwistle (ed.), Workshops in Computing Series, Springer Verlag, 1991, pp. 123–150.
M.J.C. Gordon en T.F. Melham. Introduction to HOL. Cambridge University Press, 1993.
M. Heisel, W. Reif and W. Stephan, Tactical Theorem Proving in Program Verification, In: Conference on Automated Deduction, Siekmann (ed), LNCS 449, Spinger Verlag, 1990, pp. 117–131.
Warren A. Hunt, Jr, Microprocessor Design Verification. Journal of Automated Reasoning, Vol 5, Nr 4, December 1989, pp. 429–460.
M.B. Josephs and J.T. Udding, An Overview of DI Algebra. In: Proc. Hawaii International Conf. System Sciences, T.N. Mudge and V. Milutinovic and L. Hunter (eds), Vol. I, IEEE Computer Society Press, 1993, pp. 329–338.
P. G. Lucassen. A Denotational Model and Composition Theorems for a Calculus of Delay-Insensitive Specifications. PhD thesis, Dept. of C.S., Univ. of Groningen, The Netherlands, May 1994.
M. Nesi. A Formalization of the Process Algebra CCS in Higher Order Logic. Technical Report 278, University of Cambrigde Computer Laboratory, December 1992.
M.P.A. Sellink. Verifying Process Algebra Proofs in Type Theory, In: Proceedings of Workshop in Semantics of Specification Languages, D.J. Andrews, J.F. Groote and C.A. Middelburg (eds), October 1993, Utrecht, Springer Verlag, 1994, pp. 315–339.
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Groenboom, R., Hendriks, C., Polak, I., Terlouw, J., Udding, J.T. (1995). Algebraic proof assistants in HOL. In: Möller, B. (eds) Mathematics of Program Construction. MPC 1995. Lecture Notes in Computer Science, vol 947. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60117-1_17
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DOI: https://doi.org/10.1007/3-540-60117-1_17
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