Multiparty Session Types as Coherence Proofs

Marco Carbone, Fabrizio Montesi, Carsten Schürmann, Nobuko Yoshida

Research output: Conference Article in Proceeding or Book/Report chapterArticle in proceedingsResearchpeer-review


We propose a Curry-Howard correspondence between a language for programming multiparty sessions and a generalisation of Classical Linear Logic (CLL). In this framework, propositions correspond to the local behaviour of a participant in a multiparty session type, proofs to processes, and proof normalisation to executing communications. Our key contribution is generalising duality, from CLL, to a new notion of n-ary compatibility, called coherence. Building on coherence as a principle of compositionality, we generalise the cut rule of CLL to a new rule for composing many processes communicating in a multiparty session. We prove the soundness of our model by showing the admissibility of our new rule, which entails deadlock-freedom via our correspondence.
Original languageEnglish
Title of host publication26th International Conference on Concurrency Theory (CONCUR 2015) : Leibniz International Proceedings in Informatics
Number of pages15
PublisherSchloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH
Publication date2015
ISBN (Electronic)978-3-939897-91-0
Publication statusPublished - 2015


  • Curry-Howard Correspondence
  • Multiparty Session Types
  • Classical Linear Logic
  • Proof Normalisation
  • Deadlock-Freedom


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