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Diagrammatic algebra: From linear to concurrent system

Diagrammatic algebra: From linear to concurrent system
Diagrammatic algebra: From linear to concurrent system
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.
ACM
Bonchi, Filippo
3c53e89d-d280-4911-9938-eb861553d04e
Holland, Joshua
69af19f5-c3dc-42b3-a2c5-4848f98b19e0
Piedeleu, Robin
84e8d041-a00a-44d5-9d7f-101cffd71ee2
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd
Zanasi, Fabio
5bc03cd7-0fb6-4e14-bae8-8bf0d5d4be38
Bonchi, Filippo
3c53e89d-d280-4911-9938-eb861553d04e
Holland, Joshua
69af19f5-c3dc-42b3-a2c5-4848f98b19e0
Piedeleu, Robin
84e8d041-a00a-44d5-9d7f-101cffd71ee2
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd
Zanasi, Fabio
5bc03cd7-0fb6-4e14-bae8-8bf0d5d4be38

Bonchi, Filippo, Holland, Joshua, Piedeleu, Robin, Sobocinski, Pawel and Zanasi, Fabio (2019) Diagrammatic algebra: From linear to concurrent system. In Proceedings of the ACM on Programming Languages: POPL. vol. 3, ACM.. (doi:10.1145/3290338).

Record type: Conference or Workshop Item (Paper)

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.

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Published date: 12 January 2019

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Local EPrints ID: 429551
URI: https://eprints.soton.ac.uk/id/eprint/429551
PURE UUID: fea6a2f8-f227-42e9-89ab-58c91bceae3e

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Date deposited: 29 Mar 2019 17:30
Last modified: 29 Mar 2019 17:30

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Contributors

Author: Filippo Bonchi
Author: Joshua Holland
Author: Robin Piedeleu
Author: Pawel Sobocinski
Author: Fabio Zanasi

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