Proof-Relevant π-Calculus

Perera, R. and Cheney, J. (2015) Proof-Relevant π-Calculus. In: Tenth International Workshop on Logical Frameworks and Meta Languages: Theory and Practice (LFMTP 2015), Berlin, Germany, 1 Aug 2015, pp. 46-70. (doi:10.4204/EPTCS.185.4)

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Formalising the π-calculus is an illuminating test of the expressiveness of logical frameworks and mechanised metatheory systems, because of the presence of name binding, labelled transitions with name extrusion, bisimulation, and structural congruence. Formalisations have been undertaken in a variety of systems, primarily focusing on well-studied (and challenging) properties such as the theory of process bisimulation. We present a formalisation in Agda that instead explores the theory of concurrent transitions, residuation, and causal equivalence of traces, which has not previously been formalised for the π-calculus. Our formalisation employs de Bruijn indices and dependentlytyped 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 residuation of concurrent transitions and a formal definition of equivalence of traces up to permutation of transitions.

Item Type:Conference Proceedings
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
Copyright Holders:Copyright © 2016 The Authors
Publisher Policy:Reproduced under a Creative Commons License
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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