Understanding the Expressive Power of Unhygienic Substitution in Metaprogramming via Combinatory Logic

TL;DR

This paper explores how unhygienic substitution in metaprogramming systems enhances expressive power, using combinatory logic to analyze open term semantics and compare with hygienic approaches.

Contribution

It extends combinatory logic translation techniques to metaprogramming systems, providing evidence that unhygienic substitution offers greater expressive capabilities.

Findings

Unhygienic substitution is more expressive than hygienic substitution.

Quantitative evidence supports increased power of unhygienic approaches.

The study bridges combinatory logic and metaprogramming semantics.

Abstract

Recent work on combinatory logic demonstrates a compositional translation from lambda calculus that gives meaning to open terms. As the meaning of open terms is a key difficulty in the study of metaprogramming, we investigate whether this idea can be extended to metaprogramming systems with hygienic and unhygienic substitution, specifically $\lambda_{e}^{\rightarrow \Box}$ and $\lambda_{\mathcal{S}}$. We conclude that there is quantitative evidence to support the claim that metaprogramming with unhygienic substitution is more powerful than metaprogramming with hygienic substitution.