Abstract
This paper describes an implementation within Nuprl of mechanisms that support the use of Nuprl's type theory as a language for constructing theorem-proving procedures. The main component of the implementation is a large library of definitions, theorems and proofs. This library may be regarded as the beginning of a book of formal mathematics; it contains the formal development and explanation of a useful subset of Nuprl's metatheory, and of a mechanism for translating results established about this embedded metatheory to the object level. Nuprl's rich type theory, besides permitting the internal development of this partial reflection mechanism, allows us to make abstractions that drastically reduce the burden of establishing the correctness of new theorem-proving procedures. Our library includes a formally verified term-rewriting system.
This research was supported in part by NSF grant CCR-8616552.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Errett Bishop. Foundations of Constructive Analysis. McGraw-Hill, New York, 1967.
R. S. Boyer and J Strother Moore. Metafunctions: proving them correct and using them efficiently as new proof procedures. In R. S. Boyer and J Strother Moore, editors, The Correctness Problem in Computer Science, chapter 3, Academic Press, 1981.
Robert L. Constable and Scott F. Smith. Partial objects in constructive type theory. In Proceedings of the Second Annual Symposium on Logic in Computer Science, IEEE, 1987.
Robert L. Constable, et al. Implementing Mathematics with the Nuprl Proof Development System. Prentice-Hall, Englewood Cliffs, New Jersey, 1986.
Martin Davis and Jacob T. Schwartz. Metamathematical extensibility for theorem verifiers and proof-checkers. Computers and Mathematics with Applications, 5:217–230, 1979.
N.G. de Bruijn. The mathematical language AUTOMATH, its usage and some of its extensions. In Symposium on Automatic Demonstration, Lecture Notes in Mathematics vol. 125, pages 29–61, Springer-Verlag, New York, 1970.
Michael J. Gordon, Robin Milner, and Christopher P. Wadsworth. Edinburgh LCF: A Mechanized Logic of Computation. Volume 78 of Lecture Notes in Computer Science, Springer-Verlag, 1979.
Robert Harper, Furio Honsell, and Gordon Plotkin. A framework for defining logics. In The Second Annual Symposium on Logic in Computer Science, IEEE, 1987.
Douglas J. Howe. Automating Reasoning in an Implementation of Constructive Type Theory. PhD thesis, Cornell University, 1988.
Todd B. Knoblock. Metamathematical Extensibility in Type Theory. PhD thesis, Cornell University, 1987.
Todd B. Knoblock and Robert L. Constable. Formalized metareasoning in type theory. In Proceedings of the First Annual Symposium on Logic in Computer Science, IEEE, 1986.
Per Martin-Löf. Constructive mathematics and computer programming. In Sixth International Congress for Logic, Methodology, and Philosophy of Science, pages 153–175, North Holland, Amsterdam, 1982.
Lawrence C. Paulson. A higher-order implementation of rewriting. Science of Computer Programming, 3:119–149, 1983.
Richard W. Weyhrauch. Prolegomena to a theory of formal reasoning. Artificial Intelligence, 13:133–170, 1980.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Howe, D.J. (1988). Computational metatheory in Nuprl. In: Lusk, E., Overbeek, R. (eds) 9th International Conference on Automated Deduction. CADE 1988. Lecture Notes in Computer Science, vol 310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0012835
Download citation
DOI: https://doi.org/10.1007/BFb0012835
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19343-2
Online ISBN: 978-3-540-39216-3
eBook Packages: Springer Book Archive