We study encodings of the lambda-calculus into the pi-calculus in the unexplored case of calculi with non-determinism and failures. On the sequential side, we consider lambdafail, a new non-deterministic calculus in which intersection types control resources (terms); on the concurrent side, we consider spi, a pi-calculus in which non-determinism and failure rest upon a Curry-Howard correspondence between linear logic and session types. We present a typed encoding of lambdafail into spi and establish its correctness. Our encoding precisely explains the interplay of non-deterministic and fail-prone evaluation in lambdafail via typed processes in spi. In particular, it shows how failures in sequential evaluation (absence/excess of resources) can be neatly codified as interaction protocols.

中文翻译：

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非确定性函数作为非确定性过程（扩展版本）

我们在未确定的结石具有不确定性和失败的情况下研究了λ演算到pi演算的编码。在顺序方面，我们考虑lambdafail，这是一种新的非确定性演算，其中交集类型控制资源（项）；在并发方面，我们考虑spi，一种pi演算，其中非确定性和失败取决于线性逻辑和会话类型之间的Curry-Howard对应关系。我们将lambdafail的类型化编码呈现为spi并建立其正确性。我们的编码通过spi中的类型化过程精确地解释了lambdafail中不确定性和易失败评估的相互作用。特别是，它显示了如何将顺序评估中的失败（资源的缺乏/过多）如何巧妙地编码为交互协议。