On parameterization of higher-order processes

Parameterization provides an effective way to improve on the expressiveness of process-passing. In this paper, we study two kinds of parameterization: name parameterization and process parameterization. Firstly, we show that process parameterization retains the characterization of context bisimulation in terms of the far simpler normal bisimulation, in which universal quantifiers are eliminated. Secondly, we prove that name parameterization is at least as expressive as process parameterization by giving an encoding from the higher-order calculus with process parameterization into the higher-order calculus with name parameterization. These results clarify further the theoretical framework of higher-order processes, and shed light on the relationship between the two kinds of parameterization.