Separating Sessions Smoothly

This paper introduces Hypersequent GV (HGV), a modular and extensible core calculus for functional programming with session types that enjoys deadlock freedom, confluence, strong normalisation. HGV exploits hyper-environments, which are collections of type environments, to ensure structural congruence is preserving. As consequence we obtain an operational correspondence between HCP -- process based on hypersequents in propositions-as-types classical linear logic (CLL). Our translations from vice-versa both preserve reflect reduction. scales smoothly support Girard's Mix rule, crucial ingredient channel forwarding exceptions.