An Interpretation of Typed Objects Into Typed $\pi$-calculus

An interpretation of Abadi and Cardelli's first-order functional {\em Object Calculus\/} \cite{AbCa94a} into a typed $\pi$-calculus is presented. The interpretation validates the subtyping relation and the typing judgements of the Object Calculus, and is computationally adequate. The type language for the $\pi$-calculus is that in \cite{PiSa93} --- a development of Milner's sorting discipline \cite{Mil91} with I/O annotations to separate the capabilities of reading and writing on a channel --- but with {\em variants} in place of tuples. Types are necessary to justify certain algebraic laws for the $\pi$-calculus which are important in the proof of computational adequacy of the translation. The study intends to offer a contribution to understanding, on the one hand, the relationship between $\pi$-calculus types and conventional types of programming languages and, on the other hand, the usefulness of the $\pi$-calculus as a metalanguage for the semantics of typed ØbO languages.