Compositional Constructor Interpretation over Coalgebraic Models for the π—Calculus

Abstract

The π-calculus and its variants are one of the most important subjects in the field of process algebra. Researchers in the coalgebra community have taken account of that by developing a family of related final coalgebra models for the π-calculus. None of these models has, however, been given with interpretations of the π-calculus constructors as operations on semantic domains. The present paper introduces such interpretations over final coalgebra models for the π-calculus. These models do not exactly belong to the realm of the already existing work. Rather, we emphasise the distinction between a a ground model and a full model: The ground model is fully abstract with respect to a form of π-calculus ground bisimulation; the full model is built on top of the ground model and is fully abstract with respect to the congruence derived from that ground bisimulation. Also, every semantic object is a 3-tuple with a direct representation of its transformation under renamings. A straightforward adaption of Rutten and Turi's mixed terms technique then yields compositional interpretations of most constructors of the π-calculus on the ground level. These interpretations can be lifted to the full level, again yielding compositionality.Because input prefixing does not preserve ground bisimilarity, this π-calculus constructor cannot be interpreted compositionally strictly on the ground level. It is therefore given an independent interpretation over the full model.