Abstract
Nuprl and HOL are both tactic-based interactive theorem provers for higher-order logic, and both have been used in many substantial applications over the last decade. However, the HOL community has accumulated a much larger collection of formalized mathematics of the kind useful for hardware and software verification. Nuprl’s relative lack impedes its application to verification problems of real practical interest. This paper describes a connection we have implemented between HOL and Nuprl that gives Nuprl effective access to mathematics formalized in HOL. In designing this connection, we had to overcome a number of problems related to differences in the logics, logical infrastructures and stylistic conventions of Nuprl and HOL.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Part IIIA: SCI Coherence Overview, 1995. Unapproved draft IEEE-P1596-05Nov90-doc197-iii.
R. L. Constable, et al. Implementing Mathematics with the Nuprl Proof Development System. Prentice-Hall, Englewood Cliffs, New Jersey, 1986.
M. J. Gordon, R. Milner, and C. P. Wadsworth. Edinburgh LCF: A Mechanized Logic of Computation, volume 78 of Lecture Notes in Computer Science. Springer-Verlag, 1979.
M. J. C. Gordon and T. F. Melham. Introduction to HOL: A Theorem Proving Environment for Higher Order Logic. Cambridge University Press, Cambridge, UK, 1993.
D. J. Howe. Semantics foundations for embedding hol in nuprl. Proceedings of AMAST'96, 1996. (to appear).
P. Jackson. Nuprl 4.2 Reference Manual. Cornell University, 1995. Available from ftp://cs.cornell.edu/pub/nuprl/doc.
P. B. Jackson. Exploring abstract algebra in constructive type theory. In A. Bundy, editor, 12th Conference on Automated Deduction, Lecture Notes in Artifical Intelligence. Springer, June 1994.
B. Jacobs and T. Melham. Translating dependent type theory into higher order logic. In Proceedings of the Second International Conference on Typed Lambda Calculi and Applications, volume 664 of Lecture Notes in Computer Science, pages 209–229. Springer, 1993.
P. Martin-Löf. Constructive mathematics and computer programming. In Sixth International Congress for Logic, methodology, and Philosophy of Science, pages 153–175, Amsterdam, 1982. North Holland.
T. Melham. The HOL logic extended with quantification over type variables. Formal Methods in System Design, 3(1–2):7–24, August 1993.
R. Milner, M. Tofte, and R. Harper. The Definition of Standard ML. MIT Press, 1990.
S. Owre, S. Rajan, J. Rushby, N. Shankar, and M. Srivas. PVS: Combining specification, proof checking, and model checking. In Proceedings of CAV'96, Lecture Note in Computer Science. Springer Verlag, 1996.
M. van der Voort. Introducing well-founded function definitions in HOL. In Higher Order Logic Theorem Proving and Its Applications, volume A-20 of IFIP Transactions, pages 117–131. North-Holland, 1993.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Howe, D.J. (1996). Importing mathematics from HOL into Nuprl. In: Goos, G., Hartmanis, J., van Leeuwen, J., von Wright, J., Grundy, J., Harrison, J. (eds) Theorem Proving in Higher Order Logics. TPHOLs 1996. Lecture Notes in Computer Science, vol 1125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105410
Download citation
DOI: https://doi.org/10.1007/BFb0105410
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61587-3
Online ISBN: 978-3-540-70641-0
eBook Packages: Springer Book Archive