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Erschienen in:
2012 | OriginalPaper | Buchkapitel
A Refinement-Based Approach to Computational Algebra in Coq
verfasst von : Maxime Dénès, Anders Mörtberg, Vincent Siles
Erschienen in: Interactive Theorem Proving
Verlag: Springer Berlin Heidelberg
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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.