Modelling Calculi with Name Mobility using Graphs with Equivalences

In the theory of graph rewriting, the use of coalescing rules, i.e., of rules which besides deleting and generating graph items, can coalesce some parts of the graph, turns out to be quite useful for modelling purposes, but, at the same time, problematic for the development of a satisfactory partial order concurrent semantics for rewrites. Rewriting over graphs with equivalences, i.e., (typed hyper)-graphs equipped with an equivalence over nodes provides a technically convenient replacement of graph rewriting with coalescing rules, for which a truly concurrent semantics can be easily defined. The expressivity of such a formalism is tested in a setting where coalescing rules typically play a basic role: the encoding of calculi with name passing as graph rewriting systems. Specifically, we show how the (monadic fragment) of the solo calculus, one of the dialect of those calculi whose distinctive feature is name fusion, can be encoded as a rewriting system over graph with equivalences.