The Different Shades of Infinite Session Types

Gay, S. J. , Pocas, D. and Vasconcelos, V. T. (2022) The Different Shades of Infinite Session Types. In: 25th International Conference on Foundations of Software Science and Computation Structures (FoSSaCS 2022), Munich, Germany, 02-07 Apr 2022, pp. 347-367. ISBN 9783030992521 (doi: 10.1007/978-3-030-99253-8_18)

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Many type systems include infinite types. In session type systems, infinite types are important because they specify communication protocols that are unbounded in time. Usually infinite session types are introduced as simple finite-state expressions rec X.T or by nonparametric equational definitions X .= T. Alternatively, some systems of label- or value-dependent session types go beyond simple recursive types. However, leaving dependent types aside, there is a much richer world of infinite session types, ranging through various forms of parametric equational definitions, to arbitrary infinite types in a coinductively defined space. We study infinite session types across a spectrum of shades of grey on the way to the bright light of general infinite types. We identify four points on the spectrum, characterised by different styles of equational definitions, and show that they form a strict hierarchy by establishing bidirectional correspondences with classes of automata: finite-state, 1- counter, pushdown and 2-counter. This allows us to establish decidability and undecidability results for type formation, type equivalence and duality in each class of types. We also consider previous work on context-free session types (and extend it to higher-order) and nested session types, and locate them on our spectrum of infinite types.

Item Type:Conference Proceedings
Glasgow Author(s) Enlighten ID:Gay, Professor Simon
Authors: Gay, S. J., Pocas, D., and Vasconcelos, V. T.
Subjects:Q Science > QA Mathematics > QA75 Electronic computers. Computer science
College/School:College of Science and Engineering > School of Computing Science
Published Online:29 March 2022
Copyright Holders:Copyright © 2022 The Authors
First Published:First published in Lecture Notes in Computer Science 13242: 347-367
Publisher Policy:Reproduced under a Creative Commons License
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
306912Session Types for Reliable Distributed SystemsSimon GayEngineering and Physical Sciences Research Council (EPSRC)EP/T014628/1Computing Science