Abstract
In this paper, we show an implementation of Cantor's Diagonalization Process in the Oyster-Clam theorem proving system. To achieve that, we have extended the Oyster logic with comparison and induction on types, and developed a method and some rewrite rules. The rewrite rules deal with types, what was not supported yet in the Oyster-Clam system, and some modifications were done to make that possible.
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A. Bundy, F. van Harmelen, C. Horn, and A. Smaill. The Oyster-Clam system. In M. E. Stickel, editor, Proceedings of the 10th CADE, number 449 in LNAI, pages 647–648. Springer-Verlag, 1990.
Alan Bundy. A science of reasoning. In J. L. Lassez and G. Plotkin, editors, Computational Logic: Essays in Honor of Alan Robinson, pages 178–198. MIT Press, 1991. Also available from Edinburgh as DAI Research paper 445.
Alan Bundy, A. Stevens, F. van Harmelen, Andrew Ireland, and Alan Smaill. Rippling: A heuristic for guiding inductive proofs. Artificial Intelligence, 62:185–253, 1993. Also available from Edinburgh as DAI Research Paper No. 567.
Frank Van Harmelen and the Dream group. The Clam Proof Planner. Dept. of Artificial Intelligence, Univ. of Edinburgh, 1997. Clam is available with its manual at ftp://dream.dai.ed.ac.uk.
Christian Horn and Alan Smaill. Theorem proving with Oyster. Research Paper 505, Dept. of Artificial Intelligence, Edinburgh, 1990.
Christian Horn and Alan Smaill. From meta-level tactics to object-level programs. In S. McKee J. Johnson and A. Vella, editors, Artificial Intelligence in Mathematics, pages 135–146. Claredon Press, 1994.
Xiaorong Huang, Manfred Kerber, and Lassaad Cheikhrouhou. Adapting the diagonalization method by reformulations. In Alon Levy and Pandu Nayak, editors, Proceedings of the Symposium on Abstraction, Reformulation, and Approximation, SARA-95, Ville d'Esterel, Canada, 1995.
Xiaorong Huang, Manfred Kerber, Michael Kohlhase, Erica Melis, Dan Nesmith, Jörn Richts, and Jörg Siekmann. Ω-MKRP: A proof development environment. In Alan Bundy, editor, Automated Deduction — CADE-12, Proceedings of the 12th International Conference on Automated Deduction, pages 788–792, Nancy, France, 1994. Springer-Verlag, Berlin, Germany. LNAI 814.
Gerard Huet, Gilles Kahn, and Christine Paulin-Mohring. The coq proof assistant A tutorial: Version 6.1. Technical Report 0204, INRIA, 1997.
Per Martin-Löf. Constructive mathematics and computer programing. In 6th International Congress for Logic, Methodology and Philosophy of Science, pages 153–175, Hannover, August 1982. Published by North Holland, Amsterdam.
Lawrence C. Paulson. Introduction to Isabelle. Technical Report 280, University of Cambridge, Computer Laboratory, 1993.
Lawrence C. Paulson and Tobias Nipkow. Isabelle tutorial and user's manual. Technical Report 189, University of Cambridge, Computer Laboratory, January 1990.
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© 1997 Springer-Verlag Berlin Heidelberg
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Pellegrini, J., Wainer, J. (1997). Diagonalization and type rewriting in clam. In: Coasta, E., Cardoso, A. (eds) Progress in Artificial Intelligence. EPIA 1997. Lecture Notes in Computer Science, vol 1323. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023935
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DOI: https://doi.org/10.1007/BFb0023935
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