Abstract
This paper describes part of the formalization of Hilbert’s Grundlagen der Geometrie in the higher order logic of Isabelle/Isar, an extension of the interactive theorem prover Isabelle. Many mechanized proofs and formalization issues are discussed and the work is compared against Hilbert’s prose and also other research in the field.
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Chou, S.C., Gao, X.S., Zhang, J.Z.: Automated generation of readable proofs with geometric invariants, I. multiple and shortest proof generation. Journal of Automated Reasoning 17, 325–347 (1996)
Church, A.: A formulation of the simple theorey of type. Journal of Symbolic Logic 5, 56–68 (1940)
Dehlinger, C., Duford, J., Schreck, P.: Higher-Order Intuitionistic Formalization and Proofs in Hilbert’s Elementary Geometry. Automated deduction in Geometry, pp. 306–323. Springer, Heidelberg (2001)
Gordon, M., Melham, T.: Introduction to HOL: A theorem proving enviroment for Higher Order Logic. Cambridge University Press, Cambridge (1993)
Hilbert, D.: The Foundations of Geometry, 11th edn. The Open Court Company (2001); Translation by Leo Unger
Hilbert, D.: The Foundations of Geometry, 1st edn. The Open Court Company (1901); Translation by E. J. Townsend
Paulson, L.C. (ed.): Isabelle. LNCS, vol. 828. Springer, Heidelberg (1994)
Podnieks, K.M.: Around Goedel’s Theorem, 2nd edn. Latvian State University Press (1992)
Quaife, A.: Automated Development of Fundamental Mathematical Theories. Kluwer, Dordrecht (1992)
Wang, D.: Geometry Machines: From AI to SMC. In: Pfalzgraf, J., Calmet, J., Campbell, J. (eds.) AISMC 1996. LNCS, vol. 1138, pp. 213–239. Springer, Heidelberg (1996)
Wenzel, M.: The Isabelle/Isar Reference Manual. Technische Universität München (2002), http://isabelle.in.tum.de/dist/Isabelle2002/doc/isar-ref.pdf
Wu, W.: Basic principles of mechanical theorem proving in elementary geometries. Journal of Automated Reasoning 2, 221–252 (1986)
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Meikle, L.I., Fleuriot, J.D. (2003). Formalizing Hilbert’s Grundlagen in Isabelle/Isar. In: Basin, D., Wolff, B. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2003. Lecture Notes in Computer Science, vol 2758. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10930755_21
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DOI: https://doi.org/10.1007/10930755_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40664-8
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