Canonical Big Operators

  • Yves Bertot
  • Georges Gonthier
  • Sidi Ould Biha
  • Ioana Pasca
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5170)

Abstract

In this paper, we present an approach to describe uniformly iterated “big” operations, like \(\sum_{i=0}^n f(i)\) or max i ∈ If(i) and to provide lemmas that encapsulate all the commonly used reasoning steps on these constructs.

We show that these iterated operations can be handled generically using the syntactic notation and canonical structure facilities provided by the Coq system. We then show how these canonical big operations played a crucial enabling role in the study of various parts of linear algebra and multi-dimensional real analysis, as illustrated by the formal proofs of the properties of determinants, of the Cayley-Hamilton theorem and of Kantorovitch’s theorem.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Yves Bertot
    • 1
  • Georges Gonthier
    • 2
  • Sidi Ould Biha
    • 1
  • Ioana Pasca
    • 1
  1. 1.INRIAFrance
  2. 2.Microsoft ResearchUSA

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