True Higher-Order Modules, Separate Compilation, and Signature Calculi∗

In the past three decades, the ML module system has been the focal point of tremendous interest in the research community. The combination of parameterized modules and fine-grain data abstraction control have proven to be quite powerful in practice. Mainstream languages have slowly adopted features inspired by the ML module system. However, programmers have run into various limitations and complexities in implementations of the ML module system. In the presence of common extensions such as true higher-order modules, true separate compilation becomes a problem. This conflict reflects a fundamental tension in module system design. Module systems should both propagate as much type information across module boundaries as is unconstrained by the programmer and be able to separately typecheck modules.