Typing Composite Subjects

TL;DR

This paper introduces a novel type system capable of handling composite subjects in pi-calculus variants like epi, including proofs of correctness and an encoding of an object-oriented language to demonstrate its applicability.

Contribution

It proposes a general type system for composite subjects in pi-calculus with proofs of correctness and relates it to conventional OO types through encoding.

Findings

Proves subject reduction and type safety for the proposed type system.

Provides an encoding of a minimal OO language into epi matching the type system.

Establishes a relationship between the new type system and traditional object-oriented types.

Abstract

Many type systems have been presented in the literature for variants of the pi-calculus, but none of them are able to handle composite subjects such as those found in the language epi, which features polyadic synchronisation. The purpose of this paper is to address the question of how to type composite subjects in a general fashion. We assess the validity of our proposal by first proving the standard correctness results for a type system (i.e., subject reduction and type safety). Then, we follow the path opened by Sangiorgi in 1998 and show an encoding in epi of a minimal OO language called WC (While with \Classes) whose ``expectable'' type system exactly corresponds to the one induced by ours via the encoding. This comparison contributes to understanding the relationship between our types and conventional types for OO languages.