Linearity, session types and the Pi calculus

We present a reconstruction of session types in a conventional pi calculus. Our session types are qualified as linear or unrestricted. Linearly typed communication channels are guaranteed to occur in exactly one thread, possibly multiple times; afterwards they evolve to unrestricted channels. We equip types with a constructor that describes the two ends of a same communication channel, and propose a type system that is sound with respect to the reduction relation. We then introduce an algorithmic type system which we prove sound and complete with respect to original system. We assess the expressivity of our typing system by providing three distinct encodings (from the pi calculus with polarized variables, from the pi calculus with accept and request primitives, and from the linear pi calculus) into our system. For each language we present operational and typing correspondences, showing that our system e↵ectively subsumes the linear pi calculus as well as foregoing works on session types. In the case of the linear pi calculus we also provide a completeness result, thus proving that linear pi is a sublanguage of ours.