Modal μ-types for processes

We introduce a new paradigm for concurrency, called behaviours-as-types. In this paradigm, types are used to convey information about the behaviour of processes: while terms corresponds to processes, types correspond to behaviours. We apply this paradigm to Winskel's Process Algebra. Its types are similar to Kozen's modal μ-calculus; hence, they are called modal μ-types. We prove that two terms having the same type denote two processes which behave in the same way, that is, they are bisimilar. We give a sound and complete compositional typing system for this language. Such a system naturally recovers the notion of bisimulation also on open terms, allowing us to deal with processes with undefined parts in a compositional manner