Session-types specify communication protocols for communicating processes, and session-typed languages are often specified using substructural operational semantics given by multiset rewriting systems. We give an observed communication semantics for a session-typed language with recursion, where a process's observation is given by its external communications. To do so, we introduce fair executions for multiset rewriting systems, and extract observed communications from fair process executions. This semantics induces an intuitively reasonable notion of observational equivalence that we conjecture coincides with semantic equivalences induced by denotational semantics, bisimulations, and barbed congruences for these languages.

中文翻译：

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子结构观察通信语义

会话类型指定用于通信进程的通信协议，并且会话类型语言通常使用由多集重写系统给出的子结构操作语义来指定。我们为具有递归的会话类型语言提供了观察到的通信语义，其中进程的观察由其外部通信给出。为此，我们为多集重写系统引入了公平执行，并从公平进程执行中提取观察到的通信。这种语义引发了一个直观合理的观察等价概念，我们推测该概念与由这些语言的指称语义、互模拟和倒钩同余引起的语义等价一致。