Canonical Big Operators (original) (raw)

Abstract

In this paper, we present an approach to describe uniformly iterated “big” operations, like \(\sum_{i=0}^n f(i)\) or max i ∈ I f(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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Authors and Affiliations

  1. INRIA, France
    Yves Bertot, Sidi Ould Biha & Ioana Pasca
  2. Microsoft Research, USA
    Georges Gonthier

Authors

  1. Yves Bertot
  2. Georges Gonthier
  3. Sidi Ould Biha
  4. Ioana Pasca

Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, Concordia University, 1455 de Maisonneuve Blvd. W, H3G 1M8, Montreal, Quebec, Canada
    Otmane Ait Mohamed
  2. National Institute of Aerospace, 100 Exploration Way, VA 23666, Hampton, USA
    César Muñoz
  3. Dept. of Electrical & Computer Engineering, Concordia University, 1455 de Maisonette W, H3G 1M8, Montreal, Quebec, Canada
    Sofiène Tahar

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Bertot, Y., Gonthier, G., Ould Biha, S., Pasca, I. (2008). Canonical Big Operators. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2008. Lecture Notes in Computer Science, vol 5170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71067-7\_11

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