A Subexponential View of Domains in Session Types

Abstract

Linear logic (LL) has inspired the design of many computational systems, offering reasoning techniques built on top of its meta-theory. Since its inception, several connections between concurrent systems and LL have emerged from different perspectives. In the last decade, the seminal work of Caires and Pfenning showed that formulas in LL can be interpreted as session types and processes in the pi-calculus as proof terms. This leads to a Curry-Howard interpretation where proof reductions in the cut-elimination procedure correspond to process reductions/interactions. The subexponentials in LL have also played an important role in concurrent systems since they can be interpreted in different ways, including timed, spatial and even epistemic modalities in distributed systems. In this paper we address the question: What is the meaning of the subexponentials from the point of view of a session type interpretation? Our answer is a pi-like process calculus where agents reside in locations/sites and they make it explicit how the communication among the different sites should happen. The design of this language relies completely on the proof theory of the subexponentials in LL, thus extending the Caires-Pfenning interpretation in an elegant way.