Skip to main content

Formalization of Wu’s Simple Method in Coq

  • Conference paper
Certified Programs and Proofs (CPP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7086))

Included in the following conference series:

Abstract

We present in this paper the integration within the Coq proof assistant, of a method for automatic theorem proving in geometry. We use an approach based on the validation of a certificate. The certificate is generated by an implementation in Ocaml  of a simple version of Wu’s method.

This work is partially supported by the ANR project Galapagos.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Boespflug, M., Dénès, M., Grégoire, B.: Full Reduction at Full Throttle. In: Jouannaud, J.-P., Shao, Z. (eds.) CPP 2011. LNCS, vol. 7086, pp. 357–372. Springer, Heidelberg (2011)

    Google Scholar 

  2. Chou, S.-C., Gao, X.-S.: Ritt-Wu’s Decomposition Algorithm and Geometry Theorem Proving. In: Stickel, M.E. (ed.) CADE 1990. LNCS, vol. 449, pp. 207–220. Springer, Heidelberg (1990)

    Chapter  Google Scholar 

  3. Chou, S.-C., Gao, X.-S.: A Class of Geometry Statements of Constructive Type and Geometry Theorem Proving. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 20–34. Springer, Heidelberg (1992)

    Google Scholar 

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

    Book  MATH  Google Scholar 

  5. Chou, S.-C.: Mechanical Geometry Theorem Proving. D. Reidel Publishing Company (1988)

    Google Scholar 

  6. Coq development team. The Coq proof assistant reference manual, Version 8.3. LogiCal Project (2010)

    Google Scholar 

  7. Chaieb, A., Wenzel, M.: Context Aware Calculation and Deduction. In: Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds.) MKM/CALCULEMUS 2007. LNCS (LNAI), vol. 4573, pp. 27–39. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Fuchs, L., Théry, L.: A Formalization of Grassmann-Cayley Algebra in Coq and its Application to Theorems Proving in Projective Geometry. In: Schreck, P., Narboux, J., Richter-Gebert, J. (eds.) ADG 2010. LNCS (LNAI), vol. 6877, pp. 51–67. Springer, Heidelberg (2011)

    Google Scholar 

  9. Gao, X.-S.: Geometry expert, software package (2000)

    Google Scholar 

  10. Gao, X.-S., Chou, S.-C.: Solving geometric constraint systems. I. A global propagation approach. Computer Aided Design 30(1), 47–54 (1998)

    Article  Google Scholar 

  11. Gao, X.-S., Chou, S.-C.: Solving geometric constraint systems. II. A symbolic approach and decision of Rc-constructibility. Computer Aided Design 30(2), 115–122 (1998)

    Article  Google Scholar 

  12. Gao, X.-S., Lin, Q.: MMP/Geometer – A Software Package for Automated Geometric Reasoning. In: Winkler, F. (ed.) ADG 2002. LNCS (LNAI), vol. 2930, pp. 44–66. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  13. Grégoire, B., Mahboubi, A.: Proving Equalities in a Commutative Ring Done Right in Coq. In: Hurd, J., Melham, T. (eds.) TPHOLs 2005. LNCS, vol. 3603, pp. 98–113. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  14. Grégoire, B., Pottier, L., Théry, L.: Proof Certificates for Algebra and Their Application to Automatic Geometry Theorem Proving. In: Sturm, T., Zengler, C. (eds.) ADG 2008. LNCS (LNAI), vol. 6301, pp. 42–59. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  15. Harrison, J.: Automating Elementary Number-Theoretic Proofs Using Gröbner Bases. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 51–66. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  16. Harrison, J.: Without Loss of Generality. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 43–59. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  17. Janičić, P., Narboux, J., Quaresma, P.: The Area Method: a Recapitulation. Journal of Automated Reasoning (2010)

    Google Scholar 

  18. Janičić, P., Quaresma, P.: System Description: GCLCprover + Geothms. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 145–150. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  19. Kapur, D.: Geometry Theorem Proving using Hilbert’s Nullstellensatz. In: SYMSAC 1986: Proceedings of the fifth ACM Symposium on Symbolic and Algebraic Computation, New York, NY, USA, pp. 202–208. ACM Press (1986)

    Google Scholar 

  20. Mahboubi, A.: Contributions à la certification des calculs dans R: théorie, preuves, programmation. PhD thesis, Université de Nice Sophia-Antipolis (November 2006)

    Google Scholar 

  21. Narboux, J.: A Decision Procedure for Geometry in Coq. In: Slind, K., Bunker, A., Gopalakrishnan, G.C. (eds.) TPHOLs 2004. LNCS, vol. 3223, pp. 225–240. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  22. Narboux, J.: A graphical user interface for formal proofs in geometry. J. Autom. Reasoning 39(2), 161–180 (2007)

    Article  MATH  Google Scholar 

  23. Pham, T.-M., Bertot, Y., Narboux, J.: A Coq-Based Library for Interactive and Automated Theorem Proving in Plane Geometry. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds.) ICCSA 2011, Part IV. LNCS, vol. 6785, pp. 368–383. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  24. Pham, T.M.: An Additional Tool About the Orientation for Theorem Proving in the Coq Proof Assitant. In: Proceedings of Automated Deduction in Geometry, ADG 2010 (2010)

    Google Scholar 

  25. Pottier, L.: Connecting Gröbner Bases Programs with Coq to do Proofs in Algebra, Geometry and Arithmetics. In: Sutcliffe, G., Rudnicki, P., Schmidt, R., Konev, B., Schulz, S. (eds.) Knowledge Exchange: Automated Provers and Proof Assistants. CEUR Workshop Proceedings, Doha, Qatar p. 418 (2008)

    Google Scholar 

  26. Robu, J.: Geometry Theorem Proving in the Frame of the Theorema Project. PhD thesis, Johannes Kepler Universitt, Linz (September 2002)

    Google Scholar 

  27. Wang, D.: A new theorem discovered by computer prover. Journal of Geometry 36, 173–182 (1989), doi:10.1007/BF01231031

    Article  MathSciNet  MATH  Google Scholar 

  28. Wang, D.: Elimination Method. Springer, Heidelberg (2001)

    Book  Google Scholar 

  29. Wang, D.: GEOTHER 1.1: Handling and Proving Geometric Theorems Automatically. In: Winkler, F. (ed.) ADG 2002. LNCS (LNAI), vol. 2930, pp. 194–215. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  30. Wang, D.: Elimination Practice. Springer, Heidelberg (2004)

    Book  Google Scholar 

  31. Wu, W.-T.: On the Decision Problem and the Mechanization of Theorem Proving in Elementary Geometry. Scientia Sinica 21, 157–179 (1978)

    MathSciNet  Google Scholar 

  32. Ye, Z., Chou, S.-C., Gao, X.-S.: An Introduction to Java Geometry Expert. In: Sturm, T., Zengler, C. (eds.) ADG 2008. LNCS, vol. 6301, pp. 189–195. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Génevaux, JD., Narboux, J., Schreck, P. (2011). Formalization of Wu’s Simple Method in Coq. In: Jouannaud, JP., Shao, Z. (eds) Certified Programs and Proofs. CPP 2011. Lecture Notes in Computer Science, vol 7086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25379-9_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-25379-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25378-2

  • Online ISBN: 978-3-642-25379-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics