Six Ways to Implement Divisibility by Three in miniKanren

This paper explores options for implementing the relation $n\equiv 0(\text{mod }3)$ within miniKanren using miniKanren numbers and its arithmetic suite. We examine different approaches starting from straightforward implementations to more optimized versions. The implementations discussed include brute-force arithmetic methods, divisibility tricks, and derivation from a finite automaton. Our contributions include an in-depth look at the process of implementing a miniKanren relation and observations on benchmarking $\mathtt{\text{defrel}}$s. This study aims to provide practical insights for miniKanren programmers on both performance and implementation techniques.