This work exploits the logical foundation of session types to determine what kind of type discipline for the Λ-calculus can exactly capture, and is captured by, Λ-calculus behaviours. Leveraging the proof theoretic content of the soundness and completeness of sequent calculus and natural deduction presentations of linear logic, we develop the first mutually inverse and fully abstract processes-as-functions and functions-as-processes encodings between a polymorphic session π-calculus and a linear formulation of System F. We are then able to derive results of the session calculus from the theory of the Λ-calculus: (1) we obtain a characterisation of inductive and coinductive session types via their algebraic representations in System F; and (2) we extend our results to account for value and process passing, entailing strong normalisation.

中文翻译：

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关于多态会话和函数

这项工作利用会话类型的逻辑基础来确定 Λ 演算的哪种类型规则可以准确地捕获并被 Λ 演算行为捕获。利用级数演算的健全性和完整性的证明理论内容和线性逻辑的自然演绎表示，我们开发了第一个互逆和完全抽象的多态会话 π 演算和系统 F 的线性公式之间的过程作为函数和函数作为过程编码。然后我们能够从 Λ 演算的理论中推导出会话演算的结果： (1)我们通过它们在系统 F 中的代数表示获得了归纳和共归纳会话类型的特征；(2) 我们扩展我们的结果来解释价值和过程通过，需要强大的正常化。