Six Ways to Implement Divisibility by Three in miniKanren

Abstract

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 \texttt{defrel}s. This study aims to provide practical insights for miniKanren programmers on both performance and implementation techniques.