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π-calculus, Session Types research at Imperial College

Multiparty session types as coherence proofs
Marco CARBONE , Fabrizio MONTESI , Carsten SCHÜRMANN , Nobuko YOSHIDA
Acta Informatica

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.

@article{CMSY2017,
  author = {Marco Carbone and Fabrizio Montesi and Carsten Schürmann and Nobuko Yoshida},
  title = {{Multiparty session types as coherence proofs}},
  journal = {Acta Inf.},
  pages = {1--27},
  publisher = {Springer},
  year = 2017
}
@article{CMSY2017,
  author = {Marco Carbone and Fabrizio Montesi and Carsten Schürmann and Nobuko Yoshida},
  title = {{Multiparty session types as coherence proofs}},
  journal = {Acta Informatica},
  pages = {1--27},
  publisher = {Springer},
  doi = "10.1007/s00236-016-0285-y",
  year = 2017
}