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A Decision Procedure for Geometry in Coq

Julien Narboux 1, 2
2 LOGICAL - Logic and computing
UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : We present in this paper the development of a decision procedure for affine plane geometry in the Coq proof assistant. Among the existing decision methods, we have chosen to implement one based on the area method developed by Chou, Gao and Zhang, which provides short and ``readable'' proofs for geometry theorems. The idea of the method is to express the goal to be proved using three geometric quantities and eliminate points in the reverse order of their construction thanks to some elimination lemmas.
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Julien Narboux. A Decision Procedure for Geometry in Coq. Theorem Proving in Higher Order Logics 2004, Jul 2004, Park City, USA, United States. pp.225-240, ⟨10.1007/b100400⟩. ⟨inria-00001035⟩



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