Article

Journal of Automated Reasoning

, Volume 47, Issue 3, pp 291-318

Formal Power Series

  • Amine ChaiebAffiliated withComputer Laboratory, University of Cambridge Email author 

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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.

Keywords

Formalization of mathematics Theorem proving Formal power series Generating functions