Notes on higher-dimensional tarai functions

TL;DR

This paper proves that higher-dimensional tarai functions terminate under call-by-need evaluation and confirms the correctness of a proposed closed-form solution for these functions.

Contribution

It establishes termination for all n-dimensional tarai functions and verifies the accuracy of a previously suggested closed-form expression.

Findings

Higher-dimensional tarai functions terminate with call-by-need.

The closed form for the n-dimensional tarai function is correct.

The results extend understanding of recursive function termination.

Abstract

We proved that for every $n\geq 3$, the $n$-dimensional tarai function terminates with call-by-need. It was also shown that the closed form for the function suggested by T. Bailey and J. Cowles is correct.