A formalization of grassmann-cayley algebra in COQ and its application to theorem proving in projective geometry

Authors:
Laurent Fuchs;Laurent Théry
Affiliations:
XLIM-SIC UMR CNRS 6172 - Poitiers University, France;INRIA Sophia Antipolis - Méditerranée, France
Venue:
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
Year:
2010

Citing 7
Cited 1

Algorithms in invariant theory

Algorithms in invariant theory
Geometric applications of the Grassmann-Cayley algebra

Handbook of discrete and computational geometry
Automated short proof generation for projective geometric theorems with Cayley and bracket algebras: I. incidence geometry

Journal of Symbolic Computation
Interactive Theorem Proving and Program Development

Interactive Theorem Proving and Program Development
Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry (The Morgan Kaufmann Series in Computer Graphics)

Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry (The Morgan Kaufmann Series in Computer Graphics)
Formalizing Desargues' theorem in Coq using ranks

Proceedings of the 2009 ACM symposium on Applied Computing
Formalizing projective plane geometry in Coq

ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry

Formalization of wu's simple method in coq

CPP'11 Proceedings of the First international conference on Certified Programs and Proofs

Quantified Score

Hi-index	0.00

Visualization

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.