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A Formalization of Grassmann-Cayley Algebra in COQ and Its Application to Theorem Proving in Projective Geometry

  • Laurent Fuchs
  • Laurent Théry
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6877)

Abstract

This paper presents a formalization of Grassmann-Cayley algebra [6] that has been done in the COQ [2] proof assistant. The formalization is based on a data structure that represents elements of the algebra as complete binary trees. This allows to define the algebra products recursively. Using this formalization, published proofs of Pappus’ and Desargues’ theorem [7,1] are interactively derived. A method that automatically proves projective geometric theorems [11] is also translated successfully into the proposed formalization.

Keywords

Binary Tree Theorem Prove Projective Geometry Geometric Algebra Homogeneous Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Laurent Fuchs
    • 1
  • Laurent Théry
    • 2
  1. 1.XLIM-SIC UMR CNRS 6172 - Poitiers UniversityFrance
  2. 2.INRIA Sophia Antipolis - MéditerranéeFrance

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