Relationally Staged Computations in Calculi of Mobile Processes

Abstract

We apply the recently developed techniques of higher order abstract syntax and functorial operational semantics to give a compositional and fully abstract semantics for the π-calculus equipped with open bisimulation. The key novelty in our work is the realisation that the sophistication of open bisimulation requires us to move from the usual semantic domain of presheaves over subcategories of Set to presheaves over subcategories of Rel. This extra structure is crucial in controlling the renaming of extruded names and in providing a variety of different dynamic allocation operators to model the different binders of the π-calculus.

Relating coalgebraic notions of bisimulation

“…More sophisticated models of process calculi are found by taking presheaves over more elaborate categories (see e.g. [10,11,22,49]). …”

“…1.4] have observed. The counterexample of [27] is easily adapted to the settings of the presheaf categories for name passing, correcting oversights in [19,22,48].…”

“…For instance: transition systems for name and value passing process calculi have been studied in terms of coalgebras in categories of presheaves (e.g. [19,22,48]); probabilistic transition systems have been modelled by coalgebras for a probabilitydistribution monad (e.g. [6,53]); descriptive frames and concepts from modal logic have been studied in terms of coalgebras over Stone spaces (e.g.…”

Modelling Fusion Calculus using HD-Automata

“…Open semantics of π-calculus is complicated because extruded names need to be recorded and kept distinct from all other names under renaming. On the theoretical side, it would be interesting to study how this work is related to a presheaf model of open semantics of π-calculus as in [14] and other approaches as in [12,13].…”

A Class of Automata for the Verification of Infinite, Resource-Allocating Behaviours

“…For instance, they have ad-hoc notions of bisimulation, which cannot be captured by standard set-theoretic models. Transition structures that correctly model name allocation have been proposed in various forms, including coalgebras over presheaf categories [6,7,8,9,10], history-dependent automata [11], and automata over nominal sets [12]. Equivalence of these models has been established both at the level of base categories [13,14,15] and of coalgebras [16].…”