Multiparty session types as coherence proofs

Marco Carbone, Fabrizio Montesi, Carsten Schürmann, Nobuko Yoshida [2017].
In Acta Informatica 54.

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.
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  author       = {Marco Carbone and
                  Fabrizio Montesi and
                  Carsten Sch{\"{u}}rmann and
                  Nobuko Yoshida},
  title        = {Multiparty session types as coherence proofs},
  journal      = {Acta Informatica},
  volume       = {54},
  number       = {3},
  pages        = {243--269},
  year         = {2017},
  url          = {},
  doi          = {10.1007/s00236-016-0285-y},
  timestamp    = {Sun, 21 Jun 2020 17:38:23 +0200},
  biburl       = {},
  bibsource    = {dblp computer science bibliography,}

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