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.

中文翻译：

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同步转发器

会话类型是用于指定进程之间相互通信时必须遵循的协议的类型。会话类型与线性逻辑处于命题即类型对应。先前的工作表明，多方会话类型，即会话类型对两个或更多方协议的一般化，可以建模为一致性证明，即线性逻辑对偶性的一般化。而且，表示为一致性的协议可以由仲裁器模拟，仲裁器通过根据给定协议转发消息来充当中间件。在本文中，我们将仲裁器的概念概括为同步转发器的概念，即以多种不同方式实现仲裁器行为的过程。以命题形式，同步转发器形成了一种配备了消除消除功能的逻辑，这是对经典线性逻辑的特殊限制。我们的主要结果表明，同步转发器是一致性的表征，即，一致性证明可以转换为同步转发器，反之，每个同步转发器都对应于一致性证明。