On the Fair Termination of Client-Server Sessions

Author Luca Padovani

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Luca Padovani
  • University of Camerino, Italy


The author is grateful to the anonymous reviewers of the TYPES'22 post-proceedings for their helpful comments, observations and suggestions of related work.

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Luca Padovani. On the Fair Termination of Client-Server Sessions. In 28th International Conference on Types for Proofs and Programs (TYPES 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 269, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Client-server sessions are based on a variation of the traditional interpretation of linear logic propositions as session types in which non-linear channels (those regulating the interaction between a pool of clients and a single server) are typed by coexponentials instead of the usual exponentials. Coexponentials enable the modeling of racing interactions, whereby clients compete to interact with a single server whose internal state (and thus the offered service) may change as the server processes requests sequentially. In this work we present a fair termination result for CSLL^∞, a core calculus of client-server sessions. We design a type system such that every well-typed term corresponds to a valid derivation in μMALL^∞, the infinitary proof theory of linear logic with least and greatest fixed points. We then establish a correspondence between reductions in the calculus and principal reductions in μMALL^∞. Fair termination in CSLL^∞ follows from cut elimination in μMALL^∞.

Subject Classification

ACM Subject Classification
  • Theory of computation → Linear logic
  • Theory of computation → Process calculi
  • Theory of computation → Program analysis
  • client-server sessions
  • linear logic
  • fixed points
  • fair termination
  • cut elimination


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