Skip to main content
SpringerLink
Log in

Certified version of Buchberger's algorithm

  • Conference paper
  • First Online:
Automated Deduction — CADE-15 (CADE 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1421))

Included in the following conference series:

Abstract

We present a proof of Buchberger's algorithm that has been developed in the Coq proof assistant. The formulation of the algorithm in Coq can then be efficiently compiled and used to do computation.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Jacques Calmet and Karsten Homann. Classification of communication and cooperation mechanisms for logical and symbolic computation systems. In First International Workshop ‘Frontiers of Combining Systems’ (FroCoS'96), Kluwer Series on Applied Logic, pages 133–146. Springer-Verlag, 1996.

    Google Scholar 

  2. Bruce W. Char, Keith O. Geddes, and Gaston H. Gonnet. First leaves: a tutorial introduction to Maple V. Springer-Verlag, 1992.

    Google Scholar 

  3. Edmund Clarke and Xudong Zhao. Analytica — a theorem prover for Mathematica. Research report, Carnegie Mellon University, 1991.

    Google Scholar 

  4. Robert L. Constable, Stuart P. Allen, H.M. Bromley, Walter R. Cleaveland, James F. Cremer, Robert W. Harper, Douglas J. Howe, Todd B. Knoblock, Nax P. Mendier, Prakash Panangaden, James T. Sasaki, and Scott F. Smith. Implementing mathematics with the Nuprl proof development system. Prentice Hall, 1986.

    Google Scholar 

  5. Yann Coscoy, Gilles Kahn, and Laurent Théry. Extracting text from proofs. In Typed Lambda Calculus and its Applications, volume 902 of LNCS, pages 109–123. Springer-Verlag, 1995.

    Google Scholar 

  6. William M. Farmer, Joshua D. Guttman, and F. Javier Thayer. Little theories. In D. Kapur, editor, Automated Deduction—CADE-11, volume 607 of LNCS, pages 567–581. Springer-Verlag, 1992.

    Google Scholar 

  7. Keith O. Geddes, Stephen R. Czapor, and George Labahn. Algorithms for computer algebra. Kluwer, 1992.

    Google Scholar 

  8. Michael Gordon and Thomas Melham. Introduction to HOL: a theorem proving environment for higher order logic. Cambridge University Press, 1993.

    Google Scholar 

  9. John R. Harrison. Theorem proving with the real numbers. Technical Report 408, University of Cambridge Computer Laboratory, 1996. PhD thesis.

    Google Scholar 

  10. John R. Harrison and Laurent Théry. Extending the HOL theorem prover with a computer algebra system to reason about the reals. In Higher Order Logic Theorem Proving and Its Applications, volume 780 of LNCS. Springer-Verlag, August 1995.

    Google Scholar 

  11. Doug Howe. Reasoning About Functional Programs in Nuprl. In Functional Programming, Concurrency, Simulation and Automated Reasoning, volume 693 of LNCS, pages 144–164. Springer-Verlag, 1993.

    Google Scholar 

  12. Gérard Huet, Gilles Kahn, and Christine Paulin-Mohring. The Coq proof assistant: A tutorial: Version 6.1. Technical Report 204, INRIA, 1997.

    Google Scholar 

  13. Paul B. Jackson. Enhancing the Nuprl proof development system and applying it to computational abstract algebra. Technical Report TR95-1509, Cornell University, 1995.

    Google Scholar 

  14. Xavier Leroy. Objective Caml. Available at http: //pauillac.inria.fr/ocaml/, 1997.

    Google Scholar 

  15. Rob P. Nederpelt, J. Herman Geuvers, and Roel C. De Vrijer, editors. Selected papers on Automath. North-Holland, 1994.

    Google Scholar 

  16. Christine Paulin-Mohring and Benjamin Werner. Synthesis of ML programs in the system Coq. Journal of Symbolic Computation, 15(5–6):607–640, May–June 1993.

    MathSciNet  MATH  Google Scholar 

  17. Lawdrence C. Paulson. Constructing Recursion Operators in Intuitionistic Type Theory. Journal of Symbolic Computation, 2(4):325–355, December 1986.

    Article  MATH  MathSciNet  Google Scholar 

  18. Lawrence C. Paulson. Isabelle: a generic theorem prover, volume 828 of LNCS. Springer-Verlag, 1994.

    Google Scholar 

  19. LoÏc Pottier. Dixon's lemma. Available at ftp://www.inria.fr/safir/pottier/MON/, 1996.

    Google Scholar 

  20. Piotr Rudnicki. An overview of the MIZAR projet. In Workshop on Types and Proofs for Programs. Available by ftp at pub/csreports/Bastad92/proc.ps.Z onftp.cs.chalmers.se, June 1992.

    Google Scholar 

  21. John M. Rushby, Natajaran Shankar, and Mandayam Srivas. PVS: Combining specification, proof checking, and model checking. In CAV '96, volume 1102 of LNCS. Springer-Verlag, July 1996.

    Google Scholar 

  22. Daniela Vasaru, Tudor Jebelean, and Bruno Buchberger. Theorema: A system for formal scientific training in natural language presentation. Technical Report 97-34, Risc-Linz, 1997.

    Google Scholar 

  23. Stephen Wolfram. Mathematica: a system for doing mathematics by computer. Addison-Wesley, 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. INRIA, 2004 route des Lucioles, 06902, Sophia Antipolis, France

    Laurent Théry

Authors
  1. Laurent Théry
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Claude Kirchner Hélène Kirchner

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Théry, L. (1998). Certified version of Buchberger's algorithm. In: Kirchner, C., Kirchner, H. (eds) Automated Deduction — CADE-15. CADE 1998. Lecture Notes in Computer Science, vol 1421. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054271

Download citation

  • DOI: https://doi.org/10.1007/BFb0054271

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64675-4

  • Online ISBN: 978-3-540-69110-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation