, Volume 24, Issue 3, pp 191-206,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 01 Jun 2012

A proof of Moessner’s theorem by coinduction

Abstract

We present a coinductive proof of Moessner’s theorem. This theorem describes the construction of the stream (1 n ,2 n ,3 n ,…) (for n≥1) out of the stream of positive natural numbers by repeatedly dropping and summing elements. Our formalisation consists of a direct translation of the operational description of Moessner’s procedure into the equivalence of—in essence—two functional programs. Our proof fully exploits the circularity that is implicitly present in Moessner’s procedure, and it is more elementary than existing proofs. As such, it serves as a non-trivial illustration of the relevance and power of coinduction.

The research of Milad Niqui was supported by the Netherlands Organisation for Scientific Research (NWO).