Cut Reduction in Linear Logic as Asynchronous Session-Typed Communication

Prior work has shown that intuitionistic linear logic can be seen as a session-type discipline for the π-calculus, where cut reduction in the sequent calculus corresponds to synchronous process reductions. In this paper, we exhibit a new process assignment from the asynchronous, polyadic π-calculus to exactly the same proof rules. Proof-theoretically, the difference between these interpretations can be understood through permutations of inference rules that preserve observational equivalence of closed processes in the synchronous case. We also show that, under this new asynchronous interpretation, cut reductions correspond to a natural asynchronous buffered session semantics, where each session is allocated a separate communication buffer.