An ML-Style Module System for Cross-Stage Type Abstraction in Multi-stage Programming

We propose MetaFM, a novel ML-style module system that enables users to decompose multi-stage programs (i.e., programs written in a typed multi-stage programming language) into loosely coupled components in a manner natural with respect to type abstraction. The distinctive aspect of MetaFM is that it allows values at different stages to be bound in a single structure (i.e., \( \textbf{struct} \ \cdots \ \textbf{end} \) ). This feature is crucial, for example, for defining a function and a macro that use one abstract type in common, without revealing the implementation detail of that type. MetaFM also accommodates functors, higher-kinded types, the \(\textbf{with} \ \textbf{type} \) -construct, etc. with staging features. For defining semantics and proving type safety, we employ an elaboration technique, i.e., type-directed translation to a target language, inspired by the formalization of F-ing Modules. Specifically, we give a set of elaboration rules for converting MetaFM programs into System F \(\omega ^{\langle \rangle }\) , a multi-stage extension of System F \(\omega \) , and prove that the elaboration preserves typing. Additionally, our language supports cross-stage persistence (CSP), a feature for code reuse spanning more than one stage, without breaking type safety.