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Formal Power Series

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Abstract

We present a formalization of the topological ring of formal power series in Isabelle/HOL. We also formalize formal derivatives, division, radicals, composition and reverses. As an application, we show how formal elementary and hyper-geometric series yield elegant proofs for some combinatorial identities. We easily derive a basic theory of polynomials. Then, using a generic formalization of the fraction field of an integral domain, we obtain formal Laurent series and rational functions for free.

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Authors and Affiliations

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

    Amine Chaieb

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  1. Amine Chaieb
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Correspondence to Amine Chaieb.

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The research was supported by the Engineering and Physical Sciences Research Council [grant number EP/G002290/1].

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Chaieb, A. Formal Power Series. J Autom Reasoning 47, 291–318 (2011). https://doi.org/10.1007/s10817-010-9195-9

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  • DOI: https://doi.org/10.1007/s10817-010-9195-9

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