Abstract
We show how PVS-style predicate subtyping can be simulated in HOL using predicate sets, and explain how to perform subtype checking using this model. We illustrate some applications of this to specification and verification in HOL, and also demonstrate some limits of the approach. Finally we report on the effectiveness of a subtype checker used as a condition prover in a contextual rewriter.
Supported by an EPSRC studentship.
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References
Alonzo Church. A formulation of the simple theory of types. Journal of Symbolic Logic, 5:56–68, 1940.
Adriana Compagnoni. Higher-Order Subtyping with Intersection Types. PhD thesis, Catholic University, Nigmegen, January 1995.
M. J. C. Gordon. Notes on PVS from a HOL perspective. Available from the University of Cambridge Computer Laboratory web server.
M. J. C. Gordon and T. F. Melham. Introduction to HOL (A theorem-proving environment for higher order logic). Cambridge University Press, 1993.
John Harrison. Optimizing proof search in model elimination. In M. A. McRobbie and J. K. Slaney, editors, 13th International Conference on Automated Deduction, volume 1104 of Lecture Notes in Computer Science, pages 313–327, New Brunswick, NJ, 1996. Springer-Verlag.
Joe Hurd. Verification of the Miller-Rabin probabilistic primality test. Submitted as a Category B paper to TPHOLs 2001, May 2001.
Michael D. Jones. Restricted types for HOL. In TPHOLs 1997 Category B papers, 1997.
Matt Kaufmann and J. S. Moore. Industrial strength theorem prover for a logic based on Common Lisp. IEEE Transactions on Software Engineering, 23(4):203–213, April 1997.
Leslie Lamport and Lawrence C. Paulson. Should your specification language be typed? ACM Transactions on Programming Languages and Systems, 21(3):502–526, May 1999.
Harry G. Mairson. Deciding ML typability is complete for deterministic exponential time. In Conference Record of the Seventeenth Annual ACM Symposium on Principles of Programming Languages, pages 382–401. ACM SIGACT and SIGPLAN, ACM Press, 1990.
R. Milner. A theory of type polymorphism in programming. Journal of Computer and System Sciences, 17:348–375, December 1978.
Abdel Mokkedem and Tim Leonard. Formal verification of the Alpha 21364 network protocol. In Mark Aagaard and John Harrison, editors, Theorem Proving in Higher Order Logics: 13th International Conference, TPHOLs 2000, volume 1869 of Lecture Notes in Computer Science, pages 443–461, Portland, OR, August 2000. Springer-Verlag.
S. Owre, N. Shankar, J. M. Rushby, and D. W. J. Stringer-Calvert. PVS System Guide. Computer Science Laboratory, SRI International, Menlo Park, CA, September 1999.
Sam Owre and Natarajan Shankar. The formal semantics of PVS. Technical Report SRI-CSL-97-2, Computer Science Laboratory, SRI International, Menlo Park, CA, August 1997.
J. A. Robinson. A note on mechanizing higher order logic. Machine Intelligence, 5:121–135, 1970.
Mark Saaltink. Domain checking Z specifications. In C. Michael Holloway and Kelly J. Hayhurst, editors, LFM’ 97: Fourth NASA Langley Formal Methods Workshop, pages 185–192, Hampton, VA, September 1997.
Natarajan Shankar and Sam Owre. Principles and pragmatics of subtyping in PVS. In D. Bert, C. Choppy, and P. D. Mosses, editors, Recent Trends in Algebraic Development Techniques, WADT’ 99, volume 1827 of Lecture Notes in Computer Science, pages 37–52, Toulouse, France, September 1999. Springer-Verlag.
Wai Wong. The HOL res_quan library. HOL88 documentation.
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Hurd, J. (2001). Predicate Subtyping with Predicate Sets. In: Boulton, R.J., Jackson, P.B. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2001. Lecture Notes in Computer Science, vol 2152. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44755-5_19
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DOI: https://doi.org/10.1007/3-540-44755-5_19
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