%X 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
%A F Bonchi
%A R Piedeleu
%A P Sobocinski
%A F Zanasi
%O This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
%D 2019
%T Graphical affine algebra
%L discovery10081075
%C Vancouver, BC, Canada
%J Proceedings - Symposium on Logic in Computer Science
%I IEEE
%B Proceedings of the 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)