Name generation and linearity

A path-based domain theory for higher-order processes is extended to allow name generation. The original domain theory is built around the monoidal-closed category Lin consisting of path orders with join-preserving functions between their domains of path sets. Name generation is adjoined by forming the functor category [I, Lin], where I consists of finite sets of names and injections. The functor category [I, Lin] is no longer monoidal-closed w.r.t. the tensor inherited pointwise from Lin. However, conditions are given under which function spaces exist. The conditions are preserved by a rich discipline of linear types, including those of new-HOPLA, a recent powerful language for higher-order processes with name generation.