Higher-Order Action Calculi

Action calculi are a broad class of algebraic structures, including a formulation of Petri nets as well as a formulation of the π-calculus. Each action calculus HAC(K) is generated by a particular set K of operators called controls. The purpose of this paper is to extend action calculi in a uniform manner to higher-order. A special case is essentially the extension of the π-calculus to higher order by Sangiorgi. To establish a link between the interactive and functional paradigms of computation, a variety of the λ-calculus is obtained as the extension of the smallest action calculus HAC(θ).