On the Expressiveness of Parameterization in Process-Passing

This paper studies higher-order processes with the capability of parameterization (or abstraction), which has been proven to be an effective measure of lifting the mere process-passing in expressiveness. We contribute to the understanding of two kinds of parameterization: nameparameterization and process-parameterization, particularly in a secondorder setting (no currying of parameterization). Firstly, we show that in the expressiveness hierarchy of process-parameterization, n-ary parameterization can faithfully translate (n+1)-ary parameterization in a linear setting where each received process can be used only once. Secondly, the two kinds of parameterization are compared. We prove that nameparameterization is more basic than process-parameterization, i.e. the former can encode the union of them. As a result, name-parameterization can strictly promote the expressiveness of mere process-passing.