Journal of Automated Reasoning

, Volume 47, Issue 3, pp 291–318

Formal Power Series


DOI: 10.1007/s10817-010-9195-9

Cite this article as:
Chaieb, A. J Autom Reasoning (2011) 47: 291. doi:10.1007/s10817-010-9195-9


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.


Formalization of mathematicsTheorem provingFormal power seriesGenerating functions

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Computer LaboratoryUniversity of CambridgeCambridgeUK