Symmetries and Dualities in Name-Passing Process Calculi

We study symmetries and duality between input and output in the \(\pi \)-calculus. We show that in dualisable versions of \(\pi \), including \(\pi \) and fusions, duality breaks with the addition of ordinary input/output types. We illustrate two proposals of calculi that overcome these problems. One approach is based on a modification of fusion calculi in which the name equivalences produced by fusions are replaced by name preorders, and with a distinction between positive and negative occurrences of names. The resulting calculus allows us to import subtype systems, and related results, from the pi-calculus. The second approach consists in taking the minimal symmetrical conservative extension of \(\pi \) with input/output types.