In multiparty session types, interconnection networks identify which roles in a session engage in communication (i.e., two roles are connected if they exchange a message). In session-based interpretations of linear logic the analogue notion corresponds to determining which processes are composed, or cut, using compatible channels typed by linear propositions. In this work, we show that well-formed interactions represented in a session-based interpretation of classical linear logic (CLL) form strictly less-expressive interconnection networks than those of a multiparty session calculus. To achieve this result, we introduce a new compositional synthesis property dubbed partial multiparty compatibility (PMC), enabling us to build a global type denoting the interactions obtained by iterated composition of well-typed CLL threads. We then show that CLL composition induces PMC global types without circular interconnections between three (or more) participants. PMC is then used to define a new CLL composition rule that can form circular interconnections but preserves the deadlock-freedom of CLL.

中文翻译：

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基于会话的逻辑进程的互连性

在多方会话类型中，互连网络识别会话中的哪些角色参与通信（即，如果两个角色交换消息，则它们被连接）。在基于会话的线性逻辑解释中，类比概念对应于确定使用由线性命题类型的兼容通道组成或切割哪些过程。在这项工作中，我们表明，与多方会话演算相比，在基于会话的经典线性逻辑 (CLL) 解释中表示的格式良好的交互形成了严格来说表达性较低的互连网络。为了实现这一结果，我们引入了一种称为部分多方兼容性（PMC）的新组合合成属性，使我们能够构建一个全局类型，表示通过良好类型 CLL 线程的迭代组合获得的交互。然后，我们表明 CLL 组合诱导 PMC 全局类型，而三个（或更多）参与者之间没有循环互连。然后使用 PMC 定义一个新的 CLL 组合规则，该规则可以形成循环互连但保持 CLL 的无死锁。