Section: New Software and Platforms

Coq-Polyhedra

Keywords: Coq - Polyhedra - Automated theorem proving - Linear optimization

Scientific Description: Coq-Polyhedra is a library providing a formalization of convex polyhedra in the Coq proof assistant. While still in active development, it provides an implementation of the simplex method, and already handles the basic properties of polyhedra such as emptiness, boundedness, membership. Several fundamental results in the theory of convex polyhedra, such as Farkas Lemma, duality theorem of linear programming, and Minkowski Theorem, are also formally proved.

The formalization is based on the Mathematical Components library, and makes an extensive use of the boolean reflection methodology.

Functional Description: Coq-Polyhedra is a library which aims at formalizing convex polyhedra in Coq

• Participants: Xavier Allamigeon, Vasileios Charisopoulos and Ricardo Katz

• Partner: CIFASIS

• Contact: Xavier Allamigeon

• Publication: A Formalization of Convex Polyhedra Based on the Simplex Method

• URL: https://github.com/nhojem/Coq-Polyhedra