Application of Category-Theory Methods to the Design of a System of Modules for a Functional Programming Language

Module systems embed elements of methodologies, formalisms and tools for programming-in-the-large into programming languages. In our thesis we design a module system, its categorical model and a constructive semantics of the system in the model. The categorical model is simple and general, built using elementary categorical notions, admitting many variants and extensions of the module system. Our module system features programming mechanisms inspired by category theory and enables fine-grained modular programming, as witnessed by the case studies presented. We show how to extend our categorical model with data types expressible as adjunctions, as well as with (co)inductive constructions and with fully parameterized exponents. We analyze and compare alternative axiomatizations of the extensions and demonstrate a series of properties concerning rewriting of terms denoting morphisms of 2-categories; in particular, the terms expressing general adjunctions. On the basis of the extended model and without introducing recursive types we define the mechanism of mutual dependency among modules, in the form of (co)inductive module construction. The extended module system contains the essential mechanisms of modular programming, such as type sharing, transparent as well as non-transparent functor application and grouping of related modules. Conventional modular idioms are expressible in new, original ways, enabling modular programming with no headers, no explicit module applications and no global modular errors.