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Games, Mobile Processes, and Functions

Authors Guilhem Jaber, Davide Sangiorgi

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Author Details

Guilhem Jaber
  • Université de Nantes, France
Davide Sangiorgi
  • Università di Bologna, Italy
  • Inria Sophia Antipolis, France

Funding

  • Sangiorgi, Davide: supported by the MIUR-PRIN project "Analysis of Program Analyses" (ASPRA, ID 201784YSZ5_004).

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Guilhem Jaber and Davide Sangiorgi. Games, Mobile Processes, and Functions. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 25:1-25:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.CSL.2022.25

Abstract

We establish a tight connection between two models of the λ-calculus, namely Milner’s encoding into the π-calculus (precisely, the Internal π-calculus), and operational game semantics (OGS). We first investigate the operational correspondence between the behaviours of the encoding provided by π and OGS. 
We do so for various LTSs: the standard LTS for π and a new "concurrent" LTS for OGS; an "output-prioritised" LTS for π and the standard alternating LTS for OGS. We then show that the equivalences induced on λ-terms by all these LTSs (for π and OGS) coincide. 
These connections allow us to transfer results and techniques between π and OGS. In particular we import up-to techniques from π onto OGS and we derive congruence and compositionality results for OGS from those of π. The study is illustrated for call-by-value; similar results hold for call-by-name.

Subject Classification

ACM Subject Classification
  • Theory of computation → Program semantics
Keywords
  • λ-calculus
  • π-calculus
  • game semantics

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