The notion of types is an important concept in both the design of programming languages and in the theoretical investigations of programming languages. While a significant understanding of type theoretic issues in a programming language context exists, fairly basic questions remain open. Similarly, while it has been suggested that sophisticated type systems enhance the expressive power of languages, very little has been done to set-up a formal work to investigate this idea. Two related issues form the core of this work: language expressiveness, and types and operational semantics. A notion of expressiveness for typed programming languages is described. The expressive power of a language relative to another is measured by comparing the sets of abstract data types implementable in the two languages. Preliminary results suggest that the resulting expressiveness hierarchy of programming languages in non-trivial. This research conducts a detailed investigation into the relationship between this notion of expressiveness, and various type disciplines and language mechanisms. Answers to these questions have a definite impact on the design of programming languages. The research investigates some questions about types in an operational semantics context; these are related to questions studied in the context of lambda calculus and type theory. Two specific classes of questions that are addressed follow: (1) orthogonal extension questions: does type system A, when added to a languages based on type system B, invalidate any existing observational equivalences; and (2) type isomorphism questions: given a pair of types in a programming language is there a pair of definable functions (from one to the other) which are observationally inverse. These lead to further questions about axiomatization of observational equivalence in fragments of typed programming languages.
