'Institute of Electrical and Electronics Engineers (IEEE)'
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 system
