On Behavioural Interpretation of Types in Name Passing Calculi (extended Abstract)

We introduce a theory of behavioural types as a semantic foundation of typed-calculi. In this theory, a type is a set of behaviours, represented by early name passing synchronisation trees, which conform to a certain behavioural constraint. Operations on typed processes are derived from typed variants of well-known process-theoretic operations for mobile processes, and each model of typed-calculi in a typed universe induces a compositional theory of typed bisimilarities. The construction is simple and intuitive, yet ooers a rich class of typed universes of name passing interactive behaviours, which contain, among others, models of known typed-calculi and universes of game semantics. As a simple but non-trivial application, we show how the sorting by Milner can be given a sound model in a basic universe of types. The soundness states not only that the interpretation is sound in the standard sense, but also that the untyped interactive behaviour of typed terms is justiiable on the semantic ground.