A fully abstract denotational model for higher-order processes

A higher-order process calculus is defined in which one can describe processes which transmit as messages other processes; it may be viewed as a generalization of the lazy λ-calculus. The authors present a denotational model for the language, obtained by generalizing the domain equation for S. Abramsky´s (1990) model of the lazy λ-calculus. It is shown to be fully abstract with respect to three different behavioural preorders. The first is based on observing the ability of processes to perform an action in all contexts, the second on testing, and the final one on satisfying certain kinds of modal formulae