A simple implementation of an SML-like module system is presented as a module parameterized by a base language and its type-checker. This implementation is useful both as a detailed tutorial on the Harper-Lillibridge-Leroy module system and its implementation, and as a constructive demonstration of the applicability of that module system to a wide range of programming languages.

Several proof-assistants rely on the very formal basis of Pure Type Systems (PTS) as their foundations. We are concerned with the issues involved in the development of large proofs in these provers such as namespace management, development of reusable proof libraries and separate verification. Although actual implementations offer many features to address them, few theoretical foundations have been laid for them up to now.