Abstract
We have developed a proof translator from HOL into a classical extension of NuPRL which is based on two lines of previous work. First, it draws on earlier work by Doug Howe, who developed a translator of theorems from HOL into a classical extension of NuPRL which is justified by a hybrid set-theoretic/computational semantics. Second, we rely on our own previous work, which investigates this mapping from a proof-theoretic viewpoint and gives a constructive meta-logical proof of its soundness. In this paper the logical foundations of the embedding of HOL into this classical extension of NuPRL as well as technical aspects of the proof translator implementation are discussed.
The first author was supported by DARPA grant F30602-98-2-0198 on the initial stage of this work that was done at Cornell University, Ithaca, NY. We furthermore gratefully acknowledge support for the work conducted at SRI by DARPA and NASA (Contract NAS2-98073), by Office of Naval Research (Contract N00014-96-C-0114), by NSF Grant (CCR-9633363), and by a DAAD grant in the scope of HSP-III.
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References
B. Barras et al. The Coq Proof Assistant Reference Manual: Version 6.1. Technical Report RT-0203, INRIA, May 1997.
S. Berghofer and T. Nipkow. Proof terms for simply typed higher order logic. In M. Aagaard and J. Harrison, editors, 13th International Conference on Theorem Proving in Higher Order Logics, volume 1869 of Lecture Notes in Computer Science, pages 38–52, Portland, Oregon, August 2000. Springer.
R.L. Constable et al. Implementing Mathematics with Nuprl Proof Development System. Prentice Hall, 1986.
T. Coquand and G. Huet. The calculus of constructions. Information and Computation, 76(2/3):95–120, 1988.
N.G. de Bruijn. Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem. Indag. Math., 34:381–392, 1972.
E. Denney. A Prototype Proof Translator from HOL to Coq. In M. Aagaard and J. Harrison, editors, The 13th International Conference on Theorem Proving in Higher Order Logics, volume 1869 of Lecture Notes in Computer Science, pages 108–125, Portland, Oregon, August 2000. Springer-Verlag.
A.P. Felty and D.J. Howe. Hybrid interactive theorem proving using Nuprl and HOL. In W. McCune, editor, Automated Deduction-CADE-14, volume 1249 of Lecture Notes in Artificial Intelligence, pages 351–365, Berlin, 1997. Springer-Verlag.
J. Goguen and R. Burstall. Institutions: Abstract model theory for specification and programming. Journal of the ACM, 39(1):95–146, 1992.
M.J.C. Gordon and T.F. Melham. Introduction to HOL-A Theorem Proving Environment for Higher Order Logic. Cambridge University Press, 1993.
D. J. Howe. A classical set-theoretic model of polymorphic extensional type theory. Manuscript.
D.J. Howe. Importing mathematics from HOL into Nuprl. In J. von Wright, J. Grundy, and J. Harrison, editors, Theorem Proving in Higher Order Logics, volume 1125 of Lecture Notes in Computer Science, pages 267–282, Berlin, 1996. Springer-Verlag.
D.J Howe. Semantics foundation for embedding HOL in Nuprl. In M. Wirsing and A. Nivat, editors, Algebraic Methodology and Software Technology, volume 1101 of Lecture Notes in Computer Science, pages 85–101, Berlin, 1996. Springer-Verlag.
P. Martin-Löf. Intuitionistic Type Theory. Bibliopolis, Napoli, 1984.
J. Meseguer. General logics. In H.-D. Ebbinghaus et al., editor, Logical Colloquium, 1987, pages 275–329. North-Holland, 1989.
R. Milner, M. Tofte, R.M. Harper, and D.B. MacQueen. The Definition of Standard ML (Revised). MIT Press, Cambridge, 1997.
G. Mints. A Short Introduction to Intuitionistic Logic. Kluwer Academic/Plenum Publishers, 2000.
P. Naumov. Importing Isabelle Formal Mathematics into NuPRL. In Supplemental proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics, Nice, France, September 1999.
P. Naumov. Formalization of Isabelle Meta Logic in NuPRL. In Supplemental proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics, pages 141–156, Portland, OR, August 2000.
L.C. Paulson. Isabelle-A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1994.
K. Petersson, J. Smith, and B. Nordstroem. Programming in Martin-Löf’s Type Theory. An Introduction. International Series of Monographs on Computer Science. Oxford: Clarendon Press, 1990.
M.-O. Stehr, P. Naumov, and J. Meseguer. A proof-theoretic approach to HOL-Nuprl connection with applications to proof translation (full version). http://cs.hbg.psu.edu/~naumov/Papers/holnuprl.ps, March 2000.
M.-O. Stehr, P. Naumov, and J. Meseguer. A proof-theoretic approach to HOL-Nuprl connection with applications to proof translation. In 15th International Workshop on Algebraic Development Techniques, Genova, Italy, April 2001. To appear. See [21] for the full version.
W. Wong. Validation of HOL proofs by proof checking. Formal Methods in System Design: An International Journal, 14(2):193–212, 1999.
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Naumov, P., Stehr, MO., Meseguer, J. (2001). The HOL/NuPRL Proof Translator. 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_23
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