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 λ-calculus and the π-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; this is an abstract correlate of the syntactic notion of `free name´. Three equational characterizations of the surface are found to be equivalent. This 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 π-calculus but absent in other calculi