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

• Published in: Functional and Logic Programming pp. 237 - 272
• Main Authors: Suwa, Takashi, Igarashi, Atsushi
• Format: Book Chapter
• Language: English
• Published: Singapore Springer Nature Singapore 2024
• Series: Lecture Notes in Computer Science
• Subjects: Code generation; Macros; Module systems; Staging
• ISBN: 9819722993; 9789819722990
• ISSN: 0302-9743; 1611-3349; 1611-3349
• DOI: 10.1007/978-981-97-2300-3_13

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., struct⋯end $$ \textbf{struct} \ \cdots \ \textbf{end} $$ ). 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 withtype $$\textbf{with} \ \textbf{type} $$ -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 Fω⟨⟩ $$\omega ^{\langle \rangle }$$ , a multi-stage extension of System Fω $$\omega $$ , 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.