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Justified Sequences in String Diagrams: a Comparison Between Two Approaches to Concurrent Game Semantics

Authors Clovis Eberhart, Tom Hirschowitz

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Clovis Eberhart
Tom Hirschowitz

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Clovis Eberhart and Tom Hirschowitz. Justified Sequences in String Diagrams: a Comparison Between Two Approaches to Concurrent Game Semantics. In 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 72, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.CALCO.2017.10

Abstract

Recent developments of game semantics have given rise to new models of concurrent languages.  On the one hand, an approach based on string diagrams has given models of CCS and the pi-calculus, and on the other hand, Tsukada and Ong have designed a games model for a non-deterministic lambda-calculus. There is an obvious, shallow relationship between the two approaches, as they both define innocent strategies as sheaves for a Grothendieck topology embedding     
"views" into "plays". However, the notions of views and plays differ greatly between the approaches: Tsukada and Ong use notions from standard game semantics, while the authors of this paper use string diagrams. We here aim to bridge this gap by showing that even though the notions of plays, views, and innocent strategies differ, it is mostly a matter of presentation.

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Keywords
  • Concurrency
  • Sheaves
  • Presheaf models
  • Game Semantics

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References

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