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)


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.


Binary Tree Theorem Prove Projective Geometry Geometric Algebra Homogeneous Element 
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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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