A linear metalanguage for concurrency

Abstract

A metalanguage for concurrent process languages is introduced. Within it a range of process languages can be defined, including higher-order process languages where processes are passed and received as arguments. The metalanguage is provided with two interpretations both of which can be understood as categorical models of a variant of linear logic. One interpretation is in a simple category of nondeterministic domains; here a process will denote its set of traces. The other interpretation, obtained by direct analogy with the nondeterministic domains, is in a category of presheaf categories; the nondeterministic branching behaviour of a process is captured in its denotation as a presheaf. Every presheaf category possesses a notion of (open-map) bisimulation, preserved by terms of the metalanguage. The conclusion summarises open problems and lines of future work.