Towards an algebraic theory of typed mobile processes

The impact of types on the algebraic theory of the π-calculus is studied. The type system has capability types. They allow one to distinguish between the ability to read from a channel, to write to a channel, and both to read and to write. They also give rise to a natural and powerful subtyping relation. Two variants of typed bisimilarity are considered, both in their late and in their early version. For both of them, proof systems that are sound and complete on the closed finite terms are given. For one of the two variants, a complete axiomatisation for the open finite terms is also presented.