Session type systems have been given logical foundations via Curry-Howard correspondences based on both intuitionistic and classical linear logic. The type systems derived from the two logics enforce communication correctness on the same class of pi-calculus processes, but they are significantly different. Caires, Pfenning and Toninho informally observed that, unlike the classical type system, the intuitionistic type system enforces locality for shared channels, i.e. received channels cannot be used for replicated input. In this paper, we revisit this observation from a formal standpoint. We develop United Linear Logic (ULL), a logic encompassing both classical and intuitionistic linear logic. Then, following the Curry-Howard correspondences for session types, we define piULL, a session type system for the pi-calculus based on ULL. Using piULL we can formally assess the difference between the intuitionistic and classical type systems, and justify the role of locality and symmetry therein.

中文翻译：

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基于线性逻辑的会话类型系统：经典与直觉

会话类型系统已经通过基于直觉和经典线性逻辑的 Curry-Howard 对应关系获得了逻辑基础。从这两种逻辑派生的类型系统在同一类 pi 演算过程中强制执行通信正确性，但它们有显着差异。Caires、Pfenning 和 Toninho 非正式地观察到，与经典类型系统不同，直觉类型系统强制共享通道的局部性，即接收通道不能用于复制输入。在本文中，我们从正式的角度重新审视这一观察结果。我们开发了联合线性逻辑 (ULL)，一种包含经典和直觉线性逻辑的逻辑。然后，根据会话类型的 Curry-Howard 对应关系，我们定义了 piULL，这是一个基于 ULL 的 pi 演算的会话类型系统。