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

04/22/2021

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by   Lawrence C. Paulson, et al.

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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.