The HOL logic extended with quantification over type variables
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The HOL system is an LCF-style mechanized proof assistant for conducting proofs in higher-order logic. This paper discusses a proposal to extend the primitive basis of the logic underlying the HOL system with a very simple form of quantification over types. It is shown how certain practical problems with using the definitional mechanisms of HOL would be solved by the additional expressive power gained by making this extension.
Keywordstypes higher-order logic theorem proving
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- 1.M.J.C. Gordon and T.F. Melham (eds).Introduction to HOL: A Theorem Proving Environment for Higher Order Logic. Cambridge University Press, 1993.Google Scholar
- 2.A. Church. A formulation of the simple theory of types.The Journal of Symbolic Logic, 5:56–68 (1940).Google Scholar
- 3.M.J. Gordon, A.J. Milner, and C.P. Wadsworth.Edinburgh LCF: A Mechanised Logic of Computation, Lecture Notes in Computer Science, vol. 78, Springer-Verlag, 1979.Google Scholar
- 4.J.-Y. Girard. The system F of variable types, fifteen years later.Theoretical Computer Science, 45: 159–192 (1986).Google Scholar
- 5.P.B. Andrews.A Transfinite Type Theory with Type Variables, Studies in Logic and the Foundations of Mathematics series, North-Holland, 1965.Google Scholar
- 6.T. Melham. A package for inductive relation definitions in HOL.Proceedings of the 1991 International Workshop on the HOL Theorem Proving System and its Applications, M. Archer, J.J. Joyce, K.N. Levitt, and P.J. Windley (eds) IEEE Computer Society Press, 1992, 350–357.Google Scholar
- 7.K. Slind. An Implementation of Higher Order Logic. Research Report 91/419/03, Department of Computer Science, University of Calgary, 1991.Google Scholar