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.
|Title of host publication||26th International Conference on Concurrency Theory (CONCUR 2015) : Leibniz International Proceedings in Informatics|
|Number of pages||15|
|Publisher||Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH|
|Publication status||Published - 2015|