Robustness in CAD Geometric Constructions
IV '01 Proceedings of the Fifth International Conference on Information Visualisation
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Geometric constraints solving: some tracks
Proceedings of the 2006 ACM symposium on Solid and physical modeling
On the Mechanization of the Proof of Hessenberg's Theorem in Coherent Logic
Journal of Automated Reasoning
Mechanical theorem proving in Tarski's geometry
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
Formalizing projective plane geometry in Coq
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
Using three-valued logic to specify and verify algorithms of computational geometry
ICFEM'05 Proceedings of the 7th international conference on Formal Methods and Software Engineering
CTP-based programming languages?: considerations about an experimental design
ACM Communications in Computer Algebra
Formalizing projective plane geometry in Coq
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
An investigation of hilbert's implicit reasoning through proof discovery in idle-time
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
A coherent logic based geometry theorem prover capable of producing formal and readable proofs
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
Journal of Automated Reasoning
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Formalizing geometry theorems in a proof assistant like Coq is challenging. As emphasized in the literature, the non-degeneracy conditions leads to technical proofs. In addition, when considering higher-dimensions, the amount of incidence relations (e.g. point-line, point-plane, line-plane) induce numerous technical lemmas. In this paper, we present an original approach based on the notion of rank which allows to describe incidence and non-incidence relations such as equality, collinearity and coplanarity homogeneously. It allows to carry out proofs in a more systematic way. To validate this approach, we formalize in Coq (using only ranks) one of the fundamental theorems of the projective space, namely Desargues' theorem.