Computer-Assisted Proofs in Analysis and Programming in Logic: A case Study

In this paper we present a computer{assisted proof of the existence of a solution for the Feigenbaum equation '(x) = 1 '('( x)): There exist by now various such proofs in the literature. Although the one presented here is new, the main purpose of this paper is not to provide yet another version, but to give an easy{to{read and self contained introduction to the technique of computer{assisted proofs in analysis. Our proof is written in Prolog (Programming in logic), a programming language which we found to be well suited for this purpose. In this paper we also give an introduction to Prolog, so that even a reader without prior exposure to programming should be able to verify the correctness of the proof. 1 Supported in Part by the National Science Foundation under Grant No. DMS{9103590, and by the Texas Advanced Research Program under Grant No. ARP{035. 2 Supported in Part by the Swiss National Science Foundation.