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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