Bonchi, F;
Holland, J;
Piedeleu, R;
Sobocinski, P;
Zanasi, F;
(2019)
Diagrammatic Algebra: from Linear to Concurrent Systems.
In:
Proceedings of the ACM on Programming Languages.
ACM: New York, NY, USA.
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Abstract
We introduce the resource calculus, a string diagrammatic language for concurrent systems. Significantly, it uses the same syntax and operational semantics as the signal flow calculus — an algebraic formalism for signal flow graphs, which is a combinatorial model of computation of interest in control theory. Indeed, our approach stems from the simple but fruitful observation that, by replacing real numbers (modelling signals) with natural numbers (modelling resources) in the operational semantics, concurrent behaviour patterns emerge. The resource calculus is canonical: we equip it and its stateful extension with equational theories that characterise the underlying space of definable behaviours—a convex algebraic universe of additive relations— via isomorphisms of categories. Finally, we demonstrate that our calculus is sufficiently expressive to capture behaviour definable by classical Petri nets
| Type: | Proceedings paper |
|---|---|
| Title: | Diagrammatic Algebra: from Linear to Concurrent Systems |
| Event: | 46th ACM SIGPLAN Symposium on Principles of Programming Languages, 13- 19 January 2019, Cascais, Lisbon, Portugal |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1145/3290338 |
| Publisher version: | https://doi.org/10.1145/3290338 |
| Language: | English |
| Additional information: | © 2019 Copyright held by the owner/author(s). This work is licensed under a Creative Commons Attribution 4.0 International License. http://creativecommons.org/licenses/by/4.0/ |
| Keywords: | String Diagrams, props, Completeness, Petri nets, Category Theory, Concurrency |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10062540 |
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