This paper studies typed translations of $\lambda$-calculi into $\pi$-calculi, both with non-determinism, informed by the Curry-Howard isomorphism between linear logic and session types (propositions-as-sessions). Prior work considered calculi with non-collapsing non-determinism, a non-committal form of choice in which all alternatives are preserved, ensuring confluence. A question left open is whether there is a correct translation for calculi with the more traditional (and non-confluent) collapsing non-determinism, which commits to one single alternative and discards the rest. A session-typed $\pi$-calculi with collapsing non-determinism is proposed. Next, (i) the key meta-theoretical properties of typed processes (type preservation and deadlock-freedom) are proven following propositions-as-sessions, and (ii) a correct translation of a resource $\lambda$-calculus with non-determinism is given. An alternative semantics for non-determinism is then shown to unlock stronger correctness results for the translation.

翻译：本文研究将 $\ lambda$- calculi 打印成 $\ pi$- calculi, 两者均以非确定性的方式, 在线性逻辑类型和会话类型(Proposs-as-sessions)之间的Curry-Howard 线性逻辑和会话类型(Propositions-as-sessions)之间, 参考Corculi 的不确定性( proposed) 。 先前的工作认为, Calculi 是非确定性的非确定性, 是一种非确定性的非承诺, 是一种非确定性的非确定性, 是一种非确定性的非确定性选择。 下一步, (i) 类型保存和僵局- 解锁性的所有替代方法的关键元理论性特征在提出主张后得到证明, 以及 (ii) 将资源 $\ lambda- calluus 崩溃的非确定性非确定性非确定性非确定性解释正确翻译, 显示非确定性后的非确定性矫正性结果。