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A Formal Proof of Cauchy’s Residue Theorem

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Interactive Theorem Proving (ITP 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9807))

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Abstract

We present a formalization of Cauchy’s residue theorem and two of its corollaries: the argument principle and Rouché’s theorem. These results have applications to verify algorithms in computer algebra and demonstrate Isabelle/HOL’s complex analysis library.

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Notes

  1. 1.

    Source is available from https://bitbucket.org/liwenda1990/src_itp_2016/src.

  2. 2.

    Our formalization is based on a proof by Brosowski and Deutsch [7].

  3. 3.

    Holomorphic except for isolated poles.

  4. 4.

    The existence proof of such is ported from HOL Light, while we have shown the uniqueness of on our own.

  5. 5.

    Either the lemma or the lemma suffices in this place.

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Acknowledgements

We are grateful to John Harrison for his insightful suggestions about mathematical formalization, and also to the anonymous reviewers for their useful comments on the first version of this paper. The first author was funded by the China Scholarship Council, via the CSC Cambridge Scholarship programme.

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Authors and Affiliations

  1. Computer Laboratory, University of Cambridge, Cambridge, UK

    Wenda Li & Lawrence C. Paulson

Authors
  1. Wenda Li
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  2. Lawrence C. Paulson
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Correspondence to Wenda Li .

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Editors and Affiliations

  1. Inria Nancy – Grand Est, Villers-lès-Nancy, France

    Jasmin Christian Blanchette

  2. Inria Nancy – Grand Est, Villers-lès-Nancy, France

    Stephan Merz

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Li, W., Paulson, L.C. (2016). A Formal Proof of Cauchy’s Residue Theorem. In: Blanchette, J., Merz, S. (eds) Interactive Theorem Proving. ITP 2016. Lecture Notes in Computer Science(), vol 9807. Springer, Cham. https://doi.org/10.1007/978-3-319-43144-4_15

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  • DOI: https://doi.org/10.1007/978-3-319-43144-4_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-43143-7

  • Online ISBN: 978-3-319-43144-4

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