Types and Terms Translated: Unrestricted Resources in Encoding Functions as Processes (Extended Version)

Abstract

Type-preserving translations are effective rigorous tools in the study of core programming calculi. In this paper, we develop a new typed translation that connects sequential and concurrent calculi; it is governed by type systems that control resource consumption. Our main contribution is the source language, a new resource $\lambda$-calculus with non-determinism and failures, dubbed \ulamf. In \ulamf, resources are split into linear and unrestricted; failures are explicit and arise from this distinction. We define a type system based on intersection types to control resources and fail-prone computation. The target language is \spi, an existing session-typed $\pi$-calculus that results from a Curry-Howard correspondence between linear logic and session types. Our typed translation subsumes our prior work; interestingly, it treats unrestricted resources in \lamrfailunres as client-server session behaviours in \spi.