Comparing session type systems derived from linear logic

Session types are a typed approach to message-passing concurrency, where types describe sequences of intended exchanges over channels. Session type systems have been given strong logical foundations via Curry-Howard correspondences with linear logic, a resource-aware logic that naturally captures structured interactions. These logical foundations provide an elegant framework to specify and (statically) verify message-passing processes.

In this paper, we rigorously compare different type systems for concurrency derived from the Curry-Howard correspondence between linear logic and session types. We address the main divide between these type systems: the classical and intuitionistic presentations of linear logic. Over the years, these presentations have given rise to separate research strands on logical foundations for concurrency; the differences between their derived type systems have only been addressed informally.

To formally assess these differences, we develop $\pi \mathrm{ULL}$, a session type system that encompasses type systems derived from classical and intuitionistic interpretations of linear logic. Based on a fragment of Girard's Logic of Unity, $\pi \mathrm{ULL}$ provides a basic reference framework: we compare existing session type systems by characterizing fragments of $\pi \mathrm{ULL}$ that coincide with classical and intuitionistic formulations. We analyze the significance of our characterizations by considering the locality principle (enforced by intuitionistic interpretations but not by classical ones) and forms of process composition induced by the interpretations.