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 转换成 spi} calculi, 两者均以非确定性的方式, 在线性逻辑类型和会话类型( Propositions- as- sessions) 之间由 Curry- Howard 线性逻辑和会话类型( Propositions- as- sessions) 之间, 以非确定性( Propositions- assessions) 提供信息。 本文先前的工作被视为计算非确定性非确定性非确定性( 一种非承诺形式的非确定性选择), 一种保存所有替代方法的非承诺性选择形式, 并确保相互融合 。 一个尚未解决的问题是, 是否正确翻译 Calculi 与较传统性( 和非确定性) 的不确定性( lambda), 以及 (ii) 正确翻译资源 和不确定性( lambda) 的不确定性( lambda) 等非确定性( ) 非确定性( ) 非确定性) 的替代的解说 。