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

Laurent Fuchs (1) , Laurent Thery (2)

1 SIC
2 MARELLE - Mathematical, Reasoning and Software

This paper presents a formalization of Grassmann-Cayley algebra that has been done in the COQ 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 are interactively derived. A method that automatically proves projective geometric theorems is also translated successfully into the proposed formalization.

Keywords: Grassmann-Cayley algebra; COQ proof assistant; Automated theorem proving; projective geometry

Domains: Formal Languages and Automata Theory [cs.FL]; Computational Geometry [cs.CG]; Commutative Algebra [math.AC]

Laurent Fuchs, Laurent Thery. A Formalization of Grassmann-Cayley Algebra in COQ and Its Application to Theorem Proving in Projective Geometry. Automated Deduction in Geometry, ADG 2010, Jul 2010, Munich, Germany. pp.51--62, ⟨10.1007/978-3-642-25070-5_3⟩. ⟨hal-00657901⟩