First-Order Store and Visibility in Name-Passing Calculi

The π-calculus is the paradigmatical name-passing calculus. While being purely name-passing, it allows the representation of higher-order functions and store. We study how π-calculus processes can be controlled so that computations can only involve storage of first-order values. The discipline is enforced by a type system that is based on the notion of visibility, coming from game semantics. We discuss the impact of visibility on the behavioural theory. We propose characterisations of may-testing and barbed equivalence, based on (variants of) trace equivalence and labelled bisimilarity, in the case where computation is sequential, and in the case where computation is well-bracketed.