Control Structures

Action calculi are a class of action structures with added structure. Each action calculus AC(K) is determined by a set K of controls, equipped with reaction rules; calculi such as Petri nets, the typed lambda calculus and the pi calculus are obtained by varying K. This paper defines for each K a category CS(K), characterized by equational axioms, of action structures with added structure; they are called control structures and provide models of the calculus AC(K), which is initial in the category. The surface of an action is defined; it is an abstract correlate of the syntactic notion of free name. Three equational characterizations of surface are found equivalent. It permits a non-syntactic treatment of the linkage among the components of an interactive system. Finally, control structures and their morphisms offer a means of classifying the variety of dynamic disciplines in models of concurrency, such as the mobility present in the pi calculus but absent in other calculi.