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Formalisation et automatisation du raisonnement géométrique en 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 : This thesis deals with the formalization and automation of geometric reasoning within the Coq proof assistant.
In the first part, we provide an overview of the main axiom systems for geometry and we present a mechanization of the geometry of Tarski. This consists in the formalization of the first eight chapters of the book of Schwabäuser, Szmielew and Tarski: Metamathematische Methoden in der Geometrie.
In the second part, we present our implementation in Coq of a decision procedure for affine plane geometry: the area method of Chou, Gao and Zhang. This method produces short and readable proofs.
In the third part, we explain the design of graphical user interface for formal proof in geometry: GeoProof. GeoProof combines a dynamic geometry software with the Coq proof assistant.
Finally, we propose a diagrammatic formal system to perform proofs in the field of abstract term rewriting. For instance, using this system we can formalize the diagrammatic proof of the Newman's lemma. The system is proved correct and complete for a class of formulas called the coherent logic.
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Contributor : Julien Narboux <>
Submitted on : Wednesday, December 6, 2006 - 3:15:21 PM
Last modification on : Wednesday, September 16, 2020 - 4:52:18 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 8:36:09 PM


  • HAL Id : tel-00118806, version 1



Julien Narboux. Formalisation et automatisation du raisonnement géométrique en Coq.. Autre [cs.OH]. Université Paris Sud - Paris XI, 2006. Français. ⟨tel-00118806⟩



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