Graphical Affine Algebra

Graphical linear algebra is a diagrammatic language allowing to reason compositionally about different types of linear computing devices. In this paper, we extend this formalism with a connector for affine behaviour. The extension, which we call graphical affine algebra, is simple but remarkably pow...

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Published in2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) pp. 1 - 12
Main Authors Bonchi, Filippo, Piedeleu, Robin, Sobocinski, Pawel, Zanasi, Fabio
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.06.2019
Subjects
Algebra
Calculus
Connectors
Gallium arsenide
Semantics
Syntactics
Wires
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DOI10.1109/LICS.2019.8785877

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Summary:Graphical linear algebra is a diagrammatic language allowing to reason compositionally about different types of linear computing devices. In this paper, we extend this formalism with a connector for affine behaviour. The extension, which we call graphical affine algebra, is simple but remarkably powerful: it can model systems with richer patterns of behaviour such as mutual exclusion-with modules over the natural numbers as semantic domain-or non-passive electrical components-when considering modules over a certain field. Our main technical contribution is a complete axiomatisation for graphical affine algebra over these two interpretations. We also show, as case studies, how graphical affine algebra captures electrical circuits and the calculus of stateless connectors-a coordination language for distributed systems.
DOI:10.1109/LICS.2019.8785877