, Volume 47, Issue 3, pp 291-318
Date: 06 Aug 2010

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.

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