Proof-relevant π-calculus: a constructive account of concurrency and causality

Perera, R. and Cheney, J. (2018) Proof-relevant π-calculus: a constructive account of concurrency and causality. Mathematical Structures in Computer Science, 28(9), pp. 1541-1577. (doi:10.1017/S096012951700010X)

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Abstract

We present a formalisation in Agda of the theory of concurrent transitions, residuation and causal equivalence of traces for the π-calculus. Our formalisation employs de Bruijn indices and dependently typed syntax, and aligns the ‘proved transitions’ proposed by Boudol and Castellani in the context of CCS with the proof terms naturally present in Agda's representation of the labelled transition relation. Our main contributions are proofs of the ‘diamond lemma’ for the residuals of concurrent transitions and a formal definition of equivalence of traces up to permutation of transitions. In the π-calculus, transitions represent propagating binders whenever their actions involve bound names. To accommodate these cases, we require a more general diamond lemma where the target states of equivalent traces are no longer identical, but are related by a braiding that rewires the bound and free names to reflect the particular interleaving of events involving binders. Our approach may be useful for modelling concurrency in other languages where transitions carry meta-data sensitive to particular interleavings, such as dynamically allocated memory addresses.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Perera, Dr Roland
Authors: Perera, R., and Cheney, J.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Mathematical Structures in Computer Science
Publisher:Cambridge University Press
ISSN:0960-1295
ISSN (Online):1469-8072
Published Online:04 May 2017
Copyright Holders:Copyright © 2017 Cambridge University Press
First Published:First published in Mathematical Structures in Computer Science 28(9):1541-1577
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
612411From Data Types to Session Types - A Basis for Concurrency and Distribution.Simon GayEngineering & Physical Sciences Research Council (EPSRC)EP/K034413/1COM - COMPUTING SCIENCE