Regular Types for Active Objects

Previous work on type-theoretic foundations for object-oriented programming languages has mostly focused on applying or extending functional type theory to functional "objects." This approach, while benefiting from a vast body of existing literature, has the disadvantage of dealing with state change either in a roundabout way or not at all, and completely sidestepping issues of concurrency. In particular, dynamic issues of non-uniform service availability and conformance to protocols are not addressed by functional types. We propose a new type framework that characterizes objects as regular (finite state) processes that provide guarantees of service along public channels. We also propose a new notion of subtyping for active objects, based on Brinksma's notion of extension, that extends Wegner and Zdonik's "principle of substitutability" to non-uniform service availability. Finally, we formalize what it means to "satisfy a client's expectations," and we show how regular types can be used to tell when sequential or concurrent clients are satisfied.