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Coherence Generalises Duality: A Logical Explanation of Multiparty Session Types

Authors Marco Carbone, Sam Lindley, Fabrizio Montesi, Carsten Schürmann, Philip Wadler

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Keywords
  • Multiparty Session Types
  • Linear Logic
  • Propositions as Types

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Abstract

Wadler introduced Classical Processes (CP), a calculus based on a propositions-as-types correspondence between propositions of classical linear logic and session types. Carbone et al. introduced Multiparty Classical Processes, a calculus that generalises CP to multiparty session types, by replacing the duality of classical linear logic (relating two types) with a more general notion of coherence (relating an arbitrary number of types). This paper introduces variants of CP and MCP, plus a new intermediate calculus of Globally-governed Classical Processes (GCP). We show a tight relation between these three calculi, giving semantics-preserving translations from GCP to CP and from MCP to GCP. The translation from GCP to CP interprets a coherence proof as an arbiter process that mediates communications in a session, while MCP adds annotations that permit processes to communicate directly without centralised control.

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Marco Carbone, Sam Lindley, Fabrizio Montesi, Carsten Schürmann, and Philip Wadler. Coherence Generalises Duality: A Logical Explanation of Multiparty Session Types. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 33:1-33:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.CONCUR.2016.33

Author Details

Marco Carbone
Sam Lindley
Fabrizio Montesi
Carsten Schürmann
Philip Wadler

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