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arXiv · 2104.14759

Non-Deterministic Functions as Non-Deterministic Processes (Extended Version)

Joseph W. N. Paulus·Daniele Nantes-Sobrinho·Jorge A. Pérez
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Abstract

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.

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Joseph W. N. Paulus, Daniele Nantes-Sobrinho, Jorge A. Pérez. 2021-04-30. Non-Deterministic Functions as Non-Deterministic Processes (Extended Version). https://doi.org/10.46298/lmcs-19(4%3A1)2023

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