A Refinement-Based Approach to Computational Algebra in Coq

  • Maxime Dénès
  • Anders Mörtberg
  • Vincent Siles
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7406)


We describe a step-by-step approach to the implementation and formal verification of efficient algebraic algorithms. Formal specifications are expressed on rich data types which are suitable for deriving essential theoretical properties. These specifications are then refined to concrete implementations on more efficient data structures and linked to their abstract counterparts. We illustrate this methodology on key applications: matrix rank computation, Winograd’s fast matrix product, Karatsuba’s polynomial multiplication, and the gcd of multivariate polynomials.


Polynomial Multiplication Proof Assistant Canonical Structure Multivariate Polynomial Concrete Implementation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Maxime Dénès
    • 1
  • Anders Mörtberg
    • 2
  • Vincent Siles
    • 2
  1. 1.INRIA Sophia Antipolis – MéditerranéeFrance
  2. 2.University of GothenburgSweden

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