Types and Terms Translated: Unrestricted Resources in Encoding Functions as Processes

Authors Joseph W. N. Paulus , Daniele Nantes-Sobrinho , Jorge A. Pérez



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Author Details

Joseph W. N. Paulus
  • University of Groningen, The Netherlands
Daniele Nantes-Sobrinho
  • University of Brasília, Brazil
  • Imperial College London, UK
Jorge A. Pérez
  • University of Groningen, The Netherlands

Acknowledgements

We are grateful to the anonymous reviewers for their constructive feedback.

Cite AsGet BibTex

Joseph W. N. Paulus, Daniele Nantes-Sobrinho, and Jorge A. Pérez. Types and Terms Translated: Unrestricted Resources in Encoding Functions as Processes. In 27th International Conference on Types for Proofs and Programs (TYPES 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 239, pp. 11:1-11:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.TYPES.2021.11

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 λ-calculus with non-collapsing non-determinism and failures, dubbed uλ^{↯}_{⊕}. In uλ^{↯}_{⊕}, 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 𝗌π, an existing session-typed π-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 uλ^{↯}_{⊕} as client-server session behaviours in 𝗌π.

Subject Classification

ACM Subject Classification
  • Theory of computation → Type structures
  • Theory of computation → Process calculi
Keywords
  • Resource λ-calculus
  • intersection types
  • session types
  • process calculi

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References

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