A resource analysis of the pi-calculus

We give a new treatment of the pi-calculus based on the semantic theory of separation logic, continuing a research program begun by Hoare and O’Hearn. Using a novel resource model that distinguishes between public and private ownership, we refactor the operational semantics so that sending, receiving, and allocating are commands that influence owned resources. These ideas lead naturally to two denotational models: one for safety and one for liveness. Both models are fully abstract for the corresponding observables, but more importantly both are very simple. The close connections with the model theory of separation logic (in particular, with Brookes’s action trace model) give rise to a logic of processes and resources.

💡 Research Summary

The paper presents a novel treatment of the π‑calculus grounded in the semantic framework of separation logic. The authors introduce a resource model that distinguishes between public and private ownership of channels, turning the traditional lexical scope mechanism into an explicit, imperative allocation operation. In this model a resource is a function σ from channel names to the atoms {pub, pri}, indicating whether a channel is publicly usable or exclusively owned.

Operational semantics are defined in two layers. The first layer generates all conceivable labeled transitions (send, receive, name extrusion, internal τ, and a fault label ⊥) without regard to global feasibility. The second layer interprets each label as a deterministic resource transformer LαM : Σ → Σ ⊎ ⊥ ⊓ ⊤, filtering out implausible steps. For example, a send c!c on a privately owned channel yields Lc!cM(