Control structures
Adrian Mifsud, R. Milner, John Power · Logic in Computer Science · 1995
'Action calculi' are a class of action structures with added structure. Each action calculus AC(/spl Kscr/) is determined by a set /spl Kscr/ of controls, equipped with reaction rules; calculi such as Petri nets, the typed /spl lambda/-calculus and the /spl pi/-calculus are obtained by varying /spl Kscr/. This paper defines for each /spl Kscr/ a category CS(/spl Kscr/), characterized by equational axioms, of action structures with added structure; they are called 'control structures' and provide models of the calculus AC(/spl Kscr/), 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 /spl pi/-calculus but absent in other calculi.