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International Workshop on Automated Deduction in Geometry

ADG 2000: Automated Deduction in Geometry pp 306–323Cite as

Higher-Order Intuitionistic Formalization and Proofs in Hilbert’s Elementary Geometry

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2061))

Abstract

We propose the basis of a higher-order logical framework to axiomatize and build proofs in Hilbert’s elementary geometry in which intuitionistic aspects are emphasized. More precisely, we use the Calculus of inductive constructions and the system Coq to specify geometric concepts and to study and interactively handle proofs for the first two groups of Hilbert’s axiomatics. It is the first step to a formalization well adapted to the definition of primitive operations that are used in many different geometric algorithms.

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Author information

Authors and Affiliations

  1. Laboratoire des Sciences de l’Image, de l’Informatique et de la Télédétection (UMR CNRS 7005), Université Louis-Pasteur de Strasbourg, Pôle API, boulevard S. Brant, 67400, Illkirch, France

    Christophe Dehlinger, Jean-François Dufourd & Pascal Schreck

Authors
  1. Christophe Dehlinger
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  2. Jean-François Dufourd
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  3. Pascal Schreck
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Editor information

Editors and Affiliations

  1. Zentrum Mathematik, SB4, Technische Universität München, 80290, München, Germany

    Jürgen Richter-Gebert

  2. Laboratoire d’Informatique de Paris 6, Université Pierre et Marie Curie — CNRS, 4 place Jussieu, 75252, Paris Cedex 05, France

    Dongming Wang

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© 2001 Springer-Verlag Berlin Heidelberg

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Dehlinger, C., Dufourd, JF., Schreck, P. (2001). Higher-Order Intuitionistic Formalization and Proofs in Hilbert’s Elementary Geometry. In: Richter-Gebert, J., Wang, D. (eds) Automated Deduction in Geometry. ADG 2000. Lecture Notes in Computer Science(), vol 2061. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45410-1_17

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  • DOI: https://doi.org/10.1007/3-540-45410-1_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42598-4

  • Online ISBN: 978-3-540-45410-6

  • eBook Packages: Springer Book Archive

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