一句话：提出资源演算，一种图表式并发语言，用自然数替换信号流演算中的实数，并以等式理论刻画其可定义行为。
论文关注如何以统一的图解代数框架刻画并发系统行为。作者提出资源演算，一种弦图式语言，其语法与操作语义继承自信号流演算；关键观察是，将操作语义中的实数（表示信号）替换为自然数（表示资源），即可涌现并发行为模式。作者为资源演算及其带状态扩展建立等式理论，并通过范畴同构精确刻画可定义行为空间，即加法关系的凸代数宇宙。最后证明该演算足以捕获经典 Petri 网可定义的行为。
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.
@article{paperbot632,
title = {Diagrammatic algebra: from linear to concurrent systems},
author = {Filippo Bonchi and Joshua Holland and Robin Piedeleu and Paweł Sobociński and Fabio Zanasi},
journal = {Proceedings of the ACM on Programming Languages},
volume = {3},
number = {POPL},
year = {2019},
doi = {10.1145/3290338}
}