Behavioural Subtyping in Name Passing Synchronisation Trees

We present a general theory of behavioural subtyping for name passing interactive behaviours using early name-passing synchronisation trees. In this theory types are collections of name passing synchronisation trees organised by typed variants of process-theoretic operations, and a simple behavioural notion of subtyping speciies when one type denotes more constrained behaviours than another, ooering a semantic basis for diverse instances of subtyping in sequential and concurrent computation through their representation in name passing. The robustness of the notion is shown by a few equivalent characterisa-tions, including the one based on the subset inclusion with respect to inhabitants of types and another concerning a basic substitutability property. As an application, we show how the subtyping in the-calculus with constant data domains is soundly embeddable into the present theory, illuminating the functional notion of subtyping from a behavioural viewpoint. 1. Introduction The present paper introduces a general theory of subtyping for the class of name-passing syn-chronisation trees in which only part of possible values are instantiated in input actions. The restricted instantiation for input naturally arises in diverse classes of \typed" name passing