Synchronous Forwarders

Abstract: Session types are types for specifying protocols that processes must follow when communicating with each other. Session types are in a propositions-as-types correspondence with linear logic. Previous work has shown that a multiparty session type, a generalisation of session types to protocols of two or more parties, can be modelled as a proof of coherence, a generalisation of linear logic duality. And, protocols expressed as coherence can be simulated by arbiters, processes that act as a middleware by forwarding messages according to the given protocol. In this paper, we generalise the concept of arbiter to that of synchronous forwarder, that is a processes that implements the behaviour of an arbiter in several different ways. In a propositions-as-types fashion, synchronous forwarders form a logic equipped with cut elimination which is a special restriction of classical linear logic. Our main result shows that synchronous forwarders are a characterisation of coherence, i.e., coherence proofs can be transformed into synchronous forwarders and, viceversa, every synchronous forwarder corresponds to a coherence proofs.