Ackermann's Function in Iterative Form: A Proof Assistant Experiment

Abstract

Ackermann's function can be expressed using an iterative algorithm, which essentially takes the form of a term rewriting system. Although the termination of this algorithm is far from obvious, its equivalence to the traditional recursive formulation--and therefore its totality--has a simple proof in Isabelle/HOL. This is a small example of formalising mathematics using a proof assistant, with a focus on the treatment of difficult recursions.