Abstract: Equational Reasoning for Linking with First-Class Primitive Modules

Modules and linking are usually formalized by encodings which use the lambda-calculus, records (possibly dependent), and possibly some construct for recursion. In contrast, we introduce the m-calculus, a calculus where the primitive constructs are modules, linking, and the selection and hiding of module components. The m-calculus supports smooth encodings of software structuring tools such as functions (lambda-calculus), records, objects (varsigma-calculus), and mutually recursive definitions. The m-calculus can also express widely varying kinds of module systems as used in languages like C, Haskell, and ML. The m-calculus has been proven confluent, thereby showing that equational reasoning via the m-calculus is sensible and well behaved.