Session Type Systems based on Linear Logic: Classical versus Intuitionistic

Bas van den Heuvel
(University of Groningen)
Jorge A. Pérez
(University of Groningen)

Session type systems have been given logical foundations via Curry-Howard correspondences based on both intuitionistic and classical linear logic. The type systems derived from the two logics enforce communication correctness on the same class of pi-calculus processes, but they are significantly different. Caires, Pfenning and Toninho informally observed that, unlike the classical type system, the intuitionistic type system enforces locality for shared channels, i.e. received channels cannot be used for replicated input. In this paper, we revisit this observation from a formal standpoint. We develop United Linear Logic (ULL), a logic encompassing both classical and intuitionistic linear logic. Then, following the Curry-Howard correspondences for session types, we define piULL, a session type system for the pi-calculus based on ULL. Using piULL we can formally assess the difference between the intuitionistic and classical type systems, and justify the role of locality and symmetry therein.

In Stephanie Balzer and Luca Padovani: Proceedings of the 12th International Workshop on Programming Language Approaches to Concurrency- and Communication-cEntric Software (PLACES 2020), Dublin, Ireland, 26th April 2020, Electronic Proceedings in Theoretical Computer Science 314, pp. 1–11.
Published: 3rd April 2020.

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