Abstract

We introduce a general diagrammatic theory of digital circuits, based on connections between monoidal cate- gories and graph rewriting. The main achievement of the paper is conceptual, filling a foundational gap in reasoning syntac- tically and symbolically about a large class of digital circuits (discrete values, discrete delays, feedback). This complements the dominant approach to circuit modelling, which relies on simulation. The main advantage of our symbolic approach is the enabling of automated reasoning about parametrised circuits, with a potentially interesting new application to partial evaluation of digital circuits. Relative to the recent interest and activity in categorical and diagrammatic methods, our work makes several new contributions. The most important is establishing that categories of digital circuits are Cartesian and form, in the presence of feedback, so-called dataflow categories, which have expressive iteration axioms. The second is producing a general yet simple graph-rewrite framework for reasoning about such categories in which the rewrite rules are computationally efficient, opening the way for practical applications.

Joint work with Achim Jung and Aliaume Lopez