Skip to main content
SpringerLink
Log in

A Graphical User Interface for Formal Proofs in Geometry

  • Published:
Journal of Automated Reasoning Aims and scope Submit manuscript

Abstract

We present in this paper the design of a graphical user interface to deal with proofs in geometry. The software developed combines three tools: a dynamic geometry software to explore, measure, and invent conjectures; an automatic theorem prover to check facts; and an interactive proof system (Coq) to mechanically check proofs built interactively by the user.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ag-Almouloud, S.: L’ordinateur, outil d’aide à l’apprentissage de la démonstration et de traitement de données didactiques. Ph.D. thesis, Université de Rennes (1992)

  2. Amerkad, A., Bertot, Y., Pottier, L., Rideau, L.: Mathematics and proof presentation in Pcoq. In: Workshop Proof Transformation and Presentation and Proof Complexities in connection with IJCAR 2001 (2001)

  3. Anderson, J.R., Boyle, C.F., Yost, G.: The geometry tutor. In: IJCAI Proceedings, pp. 1–7 (1985)

  4. Aspinall, D., Lüth, C., Winterstein, D.: A framework for interactive proof. Technical report (2004)

  5. Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, New York (1998)

    Google Scholar 

  6. Balacheff, N., Pesty, S., Occello, M., Caffera, R., Webber, C., Peltier, N.: Baghera. http://www-baghera.imag.fr (1999–2002)

  7. Barwise, J., Allwein, G. (eds.): Logical Reasoning with Diagrams. Oxford University Press (1996)

  8. Bernat, P.: CHYPRE: Un logiciel d’aide au raisonnement. Technical report 10, IREM (1993)

  9. Bertot, Y., Guilhot, F., Pottier, L.: Visualizing geometrical statements with GeoView. Electronic Notes in Theoretical Computer Science 103, 49–65 (2003)

    Article  Google Scholar 

  10. Bertot, Y., Thery, L.: A generic approach to building user interfaces for theorem provers. J. Symb. Comput. 25, 161–194 (1998)

    Article  Google Scholar 

  11. Chou, S.-C.: Mechanical geometry theorem proving. Reidel (1988)

  12. Chou, S.-C., Gao, X.-S.: A class of geometry statements of constructive type and geometry theorem proving. In: Proceedings of CADE’92 (1992)

  13. Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Machine Proofs in Geometry. Singapore: World Scientific. (1994)

    MATH  Google Scholar 

  14. Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Automated generation of readable proofs with geometric invariants, theorem proving with full angle. J. Autom. Reason. 17, 325–347 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  15. Coq development team: The Coq proof assistant reference manual. Version 8.0. LogiCal Project (2004)

  16. Furinghetti, F., Domingo, P.: To produce conjectures and to prove them within a dynamic geometry environment: a case study. In: Proceedings of Psychology of Mathematics 27th International Conference, pp. 397–404 (2003)

  17. Gao, X.-S.: Geometry expert, software package. http://www.mmrc.iss.ac.cn/gex (2000)

  18. Gao, X.-S., Lin, Q.: MMP/Geometer – a software package for automated geometry reasoning. In: Winkler, F. (ed.) Proceedings of ADG 2002, pp. 44–46 (2002)

  19. Gressier, J.: Geometrix. http://perso.orange.fr/jgressier/ENGLISH/english.html (1988–1998)

  20. Guilhot, F.: Formalisation en Coq et visualisation d’un cours de géométrie pour le lycée. Revue des Sciences et Technologies de l’Information, Technique et Science Informatiques, Langages applicatifs 24, 1113–1138 (2005) Lavoisier.

  21. Harrison, J.: Automatic theorem proving examples. http://www.cl.cam.ac.uk/users/jrh/atp/index.html (2003)

  22. Jackiw, N.: The geometer’s sketchpad. http://www.keypress.com/ (1990)

  23. Jamnik, M.: Mathematical Reasoning with Diagrams: From Intuition to Automation. CSLI Press. (2001)

  24. Kortenkamp, U.: Foundations of dynamic geometry. Ph.D. thesis, ETH Zürich (1999)

  25. Kortenkamp, U., Richter-Gebert, J.: Using automatic theorem proving to improve the usability of geometry software. In: Mathematical User Interface (2004)

  26. Laborde, J.-M., Bellemain, F.: Cabri-geometry II. http://www.cabri.net (1993–1998)

  27. Luengo, V.: Cabri-Euclide: Un micromonde de Preuve intégrant la réfutation. Ph.D. thesis, Université Joseph Fourier (1997)

  28. Meikle, L., Fleuriot, J.: Formalizing Hilbert’s Grundlagen in Isabelle/Isar. In: Theorem Proving in Higher Order Logics, pp. 319–334 (2003)

  29. Miller, N.: A diagrammatic formal system for Euclidean geometry. Ph.D. thesis, Cornell University (2001)

  30. Narboux, J.: A decision procedure for geometry in Coq. In: Konrad, S., Annett, B., Ganesh, G. (eds.) Proceedings of TPHOLs’ 2004, vol. 3223 of Lecture Notes in Computer Science (2004)

  31. Narboux, J.: Formalisation et automatisation du raisonnement géométrique en Coq’. Ph.D. thesis, Université Paris Sud (2006a)

  32. Narboux, J.: A formalization of diagrammatic proofs in abstract rewriting (2006b)

  33. Narboux, J.: Mechanical theorem proving in Tarski’s geometry. In: Proceedings of Automatic Deduction in Geometry 06 (2006c)

  34. Narboux, J.: The user manual of GeoProof. http://home.gna.org/geoproof/documentation.html (2006d)

  35. Py, D.: Reconnaissance de plan pour l’aide à la démonstration dans un tuteur intelligent de la géométrie. Ph.D. thesis, Université de Rennes (1990)

  36. Richter-Gebert, J., Kortenkamp, U.: Die interaktive Geometrie software Cinderella Book and CD-ROM. German school-edition of the Cinderella software. http://cinderella.de (1999)

  37. Schwartz, J. T.: Probabilistic algorithms for verification of polynomial identities. In: Symbolic and Algebraic Computation, vol. 72. Lecture Notes in Computer Science. Marseille, pp. 200–215 (1979)

  38. Wilson, S., Fleuriot, J.: Combining dynamic geometry, automated geometry theorem proving and diagrammatic proofs. In: ETAPS Satellite Workshop on User Interfaces for Theorem Provers (UITP). Edinburgh (2005)

  39. Winterstein, D.: Dr. Doodle: A diagrammatic theorem prover. In: Proceedings of IJCAR 2004 (2004a)

  40. Winterstein, D.: Using diagrammatic reasoning for theorem proving in continous domain. Ph.D. thesis, The University of Edinburgh (2004b)

  41. Winterstein, D., Aspinall, D., Lüth, C.: PG/Eclipse: A generic interface for interactive proof. Technical report (2004)

  42. Wu, W.-T.: On the decision problem and the mechanization of theorem proving in elementary geometry. In: Scientia Sinica, vol. 21. pp. 157–179 (1978)

  43. Yevdokimov, O.: About a constructivist approach for stimulating students’ thinking to produce conjectures and their proving in active learning of geometry. In: Fourth Congress of the European Society for Research in Mathematics Education (2004)

Download references

Author information

Authors and Affiliations

  1. Project PCRI Pôle Commun de Recherche en Informatique du plateau de Saclay, CNRS, École Polytechnique, INRIA, Université Paris-Sud, Paris, France

    Julien Narboux

Authors
  1. Julien Narboux
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Julien Narboux.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Narboux, J. A Graphical User Interface for Formal Proofs in Geometry. J Autom Reasoning 39, 161–180 (2007). https://doi.org/10.1007/s10817-007-9071-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10817-007-9071-4

Keywords

Search

Navigation