Abstract
Type classes and overloading are shown to be independent concepts that can both be added to simple higher-order logics in the tradition of Church and Gordon, without demanding more logical expressiveness. In particular, model-theoretic issues are not affected. Our metalogical results may serve as a foundation of systems like Isabelle/Pure that offer the user Haskell-style order-sorted polymorphism as an extended syntactic feature. The latter can be used to describe simple abstract theories with a single carrier type and a fixed signature of operations.
Research supported by DFG SPP “Deduktion”.
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References
P. B. Andrews. An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Academic Press, 1986.
A. Church. A formulation of the simple theory of types. Journal of Symbolic Logic, pages 56–68, 1940.
M. J. C. Gordon. Set theory, higher order logic or both? In Proc. 9th TPHOLs, volume 1125 of Lecture Notes in Computer Science, pages 191–201. Springer-Verlag, 1996.
M. J. C. Gordon and T. F. Melham (editors). Introduction to HOL: A theorem proving environment for higher order logic. Cambridge University Press, 1993.
L. Henkin. Completeness in the theory of types. Journal of Symbolic Logic, 15(2):81–91, 1950.
P. Hudak, S. L. P. Jones, and P. Wadler (editors). Report on the programming language Haskell, a non-strict purely functional language (Version 1.2). SIGPLAN Notices, March, 1992.
The Isabelle library. http://www4.informatik.tu-muenchen.de/~nipkow/isabelle/.
M. P. Jones. Qualified Types: Theory and Practice. PhD thesis, University of Oxford, 1992.
T. Nipkow. Order-sorted polymorphism in Isabelle. In G. Huet and G. Plotkin, editors, Logical Environments, pages 164–188. Cambridge University Press, 1993.
T. Nipkow and C. Prehofer. Type checking type classes. In 20th ACM Symp. Principles of Programming Languages, 1993.
L. C. Paulson. The foundation of a generic theorem prover. Journal of Automated Reasoning, 5(3):363–397, 1989.
L. C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.
A. Pitts. The HOL logic. In Gordon and Melham [4], pages 191–232.
M. Schmidt-Schauß. Computational Aspects of an Order-Sorted Logic with Term Declarations, volume 395 of Lecture Notes in Artificial Intelligence. Springer-Verlag, 1989.
M. Wenzel. Using axiomatic type classes in Isabelle — a tutorial. Available at http://www4.informatik.tu-muenchen.de/~nipkow/isadist/axclass.dvi.gz.
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Wenzel, M. (1997). Type classes and overloading in higher-order logic. In: Gunter, E.L., Felty, A. (eds) Theorem Proving in Higher Order Logics. TPHOLs 1997. Lecture Notes in Computer Science, vol 1275. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028402
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DOI: https://doi.org/10.1007/BFb0028402
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