An intensionally fully-abstract sheaf model for $\pi$ (expanded version)

Abstract

Following previous work on CCS, we propose a compositional model for the$\pi$-calculus in which processes are interpreted as sheaves on certain simplesites. Such sheaves are a concurrent form of innocent strategies, in the senseof Hyland-Ong/Nickau game semantics. We define an analogue of fair testingequivalence in the model and show that our interpretation is intensionallyfully abstract for it. That is, the interpretation preserves and reflects fairtesting equivalence; and furthermore, any innocent strategy is fair testingequivalent to the interpretation of some process. The central part of our workis the construction of our sites, relying on a combinatorial presentation of$\pi$-calculus traces in the spirit of string diagrams