Path resolution for recursive modules

The ML module system enables flexible development of large software systems by its support of nested structures, functors and signatures. In spite of this flexibility, however, recursion between modules is prohibited, since dependencies between modules must accord with the order of definitions. As a result of this constraint, programmers may have to consolidate conceptually separate components into a single module, intruding on modular programming. Recently much work has been devoted to extending the module system with recursion, and developing a type system for recursive modules is one of the main subjects of study. Since recursion is an essential mechanism, one is to face several non-trivial issues to be considered for designing a practical type system. Our goal is to make recursive modules an ordinary construct of the module language for ML programmers. We want to use them easily in everyday programming, possibly combining with other constructs of the core and the module languages. With this goal, we are to develop a type system for recursive modules, which is practical and useful from the programmer’s perspective. In this paper, we present a decidable type system which can reconstruct the necessary type information during type checking of recursive modules. In particular, we develop algorithms for resolving forward references in recursive modules, by confining ourselves to first-order functors. The type system is provably sound for a call-by-value operational semantics.