Control in the π-calculus

Abstract

This paper presents a type-preserving translation from the call-by-value -calculus ( v-calculus) into a typed -calculus, and shows full abstraction up to maximally consistent observational congruences in both calculi. The -calculus has a particularly simple representation as typed mobile processes where a unique stateless replicated input is associated to each name. The corresponding -calculus is a proper subset of the linear -calculus, the latter being able to embed the simplytyped -calculus fully abstractly. Strong normalisability of the v-calculus is an immediate consequence of this correspondence and the strong normalisability of the linear -calculus, using the standard argument based on simulation between the v-calculus and its translation. Full abstraction, our main result, is proved via an inverse transformation from the typed -terms which inhabit the encoded v-types into the v-calculus (the so-called de nability argument), using proof techniques from games semantics and process calculi. A tight operational correspondence assisted by the de nability result opens a possibility to use typed -calculi as a tool to investigate and analyse behaviours of various control operators and associated calculi in a uniform setting, possibly integrated with other language primitives and operational structures.