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Output Without Delay: A π-Calculus Compatible with Categorical Semantics

Authors Ken Sakayori , Takeshi Tsukada



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Ken Sakayori
  • The University of Tokyo, Japan
Takeshi Tsukada
  • Chiba University, Japan

Acknowledgements

We would like to thank anonymous referees for useful comments.

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Ken Sakayori and Takeshi Tsukada. Output Without Delay: A π-Calculus Compatible with Categorical Semantics. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 32:1-32:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.FSCD.2021.32

Abstract

The quest for logical or categorical foundations of the π-calculus (not limited to session-typed variants) remains an important challenge. A categorical type theory correspondence for a variant of the i/o-typed π-calculus was recently revealed by Sakayori and Tsukada, but, at the same time, they exposed that this categorical semantics contradicts with most of the behavioural equivalences. This paper diagnoses the nature of this problem and attempts to fill the gap between categorical and operational semantics. We first identify the source of the problem to be the mismatch between the operational and categorical interpretation of a process called the forwarder. From the operational viewpoint, a forwarder may add an arbitrary delay when forwarding a message, whereas, from the categorical viewpoint, a forwarder must not add any delay when forwarding a message. Led by this observation, we introduce a calculus that can express forwarders that do not introduce delay. More specifically, the calculus we introduce is a variant of the π-calculus with a new operational semantics in which output actions are forced to happen as soon as they get unguarded. We show that this calculus (i) is compatible with the categorical semantics and (ii) can encode the standard π-calculus.

Subject Classification

ACM Subject Classification
  • Theory of computation → Concurrency
  • Theory of computation → Process calculi
  • Theory of computation → Denotational semantics
Keywords
  • π-calculus
  • categorical semantics
  • linear approximation

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