%0 Generic
%A Bonchi, F
%A Piedeleu, R
%A Sobocinski, P
%A Zanasi, F
%C Vancouver, BC, Canada
%D 2019
%F discovery:10081075
%I IEEE
%T Graphical affine algebra
%U https://discovery.ucl.ac.uk/id/eprint/10081075/
%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
%Z This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.