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
Online AccessGet full text
DOI10.1109/LICS.2019.8785877

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Abstract 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.
AbstractList 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.
Author Bonchi, Filippo
Sobocinski, Pawel
Piedeleu, Robin
Zanasi, Fabio
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  fullname: Piedeleu, Robin
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  fullname: Sobocinski, Pawel
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  givenname: Fabio
  surname: Zanasi
  fullname: Zanasi, Fabio
  organization: University College London London, United Kingdom
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Snippet Graphical linear algebra is a diagrammatic language allowing to reason compositionally about different types of linear computing devices. In this paper, we...
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SubjectTerms Algebra
Calculus
Connectors
Gallium arsenide
Semantics
Syntactics
Wires
Title Graphical Affine Algebra
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