Thesis Proposal: Effective Type Theory for Modularity

The programming language Standard ML (SML) draws much of its expressive power from advanced concepts in type theory. In addition, unlike other HOT (Higher-Order Typed) languages, SML has the distinction of being formally defined. Unfortunately, the Definition of SML is not type-theoretic, making it difficult to analyze and extend. Much work in the last decade has thus been devoted to better understanding the type-theoretic underpinnings of SML, particularly with respect to its module system. In my thesis work I plan to study several extensions to SML that would enhance its support for modular programming even further. My methodology for formalizing these extensions follows the approach advocated by Harper and Stone, who gave an interpretation of SML that involves elaborating SML programs into type theory. This approach allows me to design my extensions at the level of the underlying type theory, which is the ideal setting for language design, but provides the option to fall back on elaboration techniques when type inference or syntactic sugar is key to making a language feature palatable. I will incorporate my extensions into the TILT compiler for SML, whose front-end is a suitable testbed for implementation as it is based on the Harper-Stone framework. This proposal describes my work thus far on extending SML with higher-order modules, modules as firstclass values, and recursive modules. A running theme in my type theory for modules is the importance of effects. The design of my type system for the first two extensions is driven by the intuition that the creation of abstract data types should be thought of as an effect. My type system is more expressive than previous systems because it distinguishes type abstraction (a compile-time effect) from type generativity (a run-time effect). While my proposal for recursive modules relies more heavily on elaboration techniques, its success hinges critically on the introduction of a type of lazy memoized modules, used to encapsulate term-level computational effects.