Recursive structures for standard ML

Standard ML is a statically typed programming language that is suited for the construction of both small and large programs. "Programming in the small" is captured by Standard ML's Core language. "Programming in the large" is captured by Standard ML's Modules language that provides constructs for organizing related Core language definitions into self-contained modules with descriptive interfaces. While the Core is used to express details of algorithms and data structures, Modules is used to express the overall architecture of a software system. In Standard ML, modular programs must have a strictly hierarchical structure: the dependency between modules can never be cyclic. In particular, definitions of mutually recursive Core types and values, that arise frequently in practice, can never span module boundaries. This limitation compromises modular programming, forcing the programmer to merge conceptually (i.e. architecturally) distinct modules. We propose a practical and simple extension of the Modules language that caters for cyclic dependencies between both types and terms defined in separate modules. Our design leverages existing features of the language, supports separate compilation of mutually recursive modules and is easy to implement.