Premonoidal categories and flow graphs

Abstract We give two presentations of the semantics of programs: a categorical semantics based on Power and Robinson's symmetric premonoidal categories and Joyal, Street and Verity's traced monoidal categories, and a graphical semantics based on mixed control flow and data flow graphs. We show how these semantics are related, and sketch how the 2-categorical versions could be used to give an operational semantics for programs. The semantics is similar to Hasegawa's presentation of Milner and Gardner's name-free action calculi.