A Coq-Based Library for Interactive and Automated Theorem Proving in Plane Geometry

  • Tuan-Minh Pham
  • Yves Bertot
  • Julien Narboux
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6785)


In this article, we present the development of a library of formal proofs for theorem proving in plane geometry in a pedagogical context. We use the Coq proof assistant [4]. This library includes the basic geometric notions to state theorems and provides a database of theorems to construct interactive proofs more easily. It is an extension of the library of F. Guilhot for interactive theorem proving at the level of high-school geometry [7], where we eliminate redundant axioms and give formalizations for the geometric concepts using a vector approach. We also enrich this library by offering an automated deduction method which can be used as a complement to interactive proof. For that purpose, we integrate the formalization of the area method [3] which was developed by J. Narboux in Coq [12, 10].


formalization automation geometry Coq teaching 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Tuan-Minh Pham
    • 1
  • Yves Bertot
    • 1
  • Julien Narboux
    • 2
  1. 1.INRIA Sophia AntipolisFrance
  2. 2.LSIIT, Université de Strasbourg, CNRSFrance

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