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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

Funding

Research partially supported by the Dutch Research Council (NWO) under project No. 016.Vidi.189.046 (Unifying Correctness for Communicating Software).

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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