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Linear logic propositions as session types

Published online by Cambridge University Press:  10 November 2014

LUÍS CAIRES ,
FRANK PFENNING  and
BERNARDO TONINHO
LUÍS CAIRES
Affiliation:
Faculdade de Ciências e Tecnologia and CITI, Universidade Nova de Lisboa, Lisboa, Portugal Emails: btoninho@gmail.com and luis.caires@fct.unl.pt
FRANK PFENNING
Affiliation:
Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA Email: fp@cs.cmu.edu
BERNARDO TONINHO
Affiliation:
Faculdade de Ciências e Tecnologia and CITI, Universidade Nova de Lisboa, Lisboa, Portugal Emails: btoninho@gmail.com and luis.caires@fct.unl.pt Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA Email: fp@cs.cmu.edu
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Abstract

Throughout the years, several typing disciplines for the π-calculus have been proposed. Arguably, the most widespread of these typing disciplines consists of session types. Session types describe the input/output behaviour of processes and traditionally provide strong guarantees about this behaviour (i.e. deadlock-freedom and fidelity). While these systems exploit a fundamental notion of linearity, the precise connection between linear logic and session types has not been well understood.

This paper proposes a type system for the π-calculus that corresponds to a standard sequent calculus presentation of intuitionistic linear logic, interpreting linear propositions as session types and thus providing a purely logical account of all key features and properties of session types. We show the deep correspondence between linear logic and session types by exhibiting a tight operational correspondence between cut-elimination steps and process reductions. We also discuss an alternative presentation of linear session types based on classical linear logic, and compare our development with other more traditional session type systems.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 26 , Special Issue 3: Special Issue: Behavioural Types Part 2 , March 2016 , pp. 367 - 423
Copyright
Copyright © Cambridge University Press 2014 

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