Six Ways to Implement Divisibility by Three in miniKanren

TL;DR

This paper investigates six different methods to implement divisibility by three in miniKanren, comparing their performance and practicality for programmers using miniKanren's relational programming approach.

Contribution

It provides a comprehensive analysis of various implementation strategies for divisibility in miniKanren, including optimized and automaton-based methods.

Findings

Automated benchmarks compare different implementations.

Optimized methods outperform brute-force approaches.

Finite automaton derivation offers a novel implementation technique.

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.