论文标题
基于线性逻辑的会话类型系统：经典和直觉
Session Type Systems based on Linear Logic: Classical versus Intuitionistic
论文作者
论文摘要
会话类型系统通过基于直觉和经典线性逻辑的咖喱 - 霍德对应关系为逻辑基础。从两种逻辑中得出的类型系统在同一类Pi-Calculus过程上执行了通信正确性，但它们却大不相同。 Caires，Pfenning和Toninho非正式地观察到，与经典类型系统不同，直觉类型系统可以为共享通道执行局部性，即无法将接收的通道用于复制输入。在本文中，我们从正式的角度重新审视了这一观察结果。我们开发了联合线性逻辑（ULL），这是一种逻辑，涵盖了古典和直觉的线性逻辑。然后，遵循会话类型的咖喱 - 霍德对应关系，我们定义了基于ULL的PI-Calculus的会话类型系统。使用Piull，我们可以正式评估直觉和经典类型系统之间的差异，并证明其中局部性和对称性的作用是合理的。
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.
