A Linear Account of Session Types in the Pi Calculus

We present a reconstruction of session types in a conventional pi calculus where types are qualified as linear or unrestricted. Linearly typed communication channels are guaranteed to occur in exactly one thread, possibly multiple times. We equip types with a constructor that denotes the two ends of a same communication channel. In order to assess the flexibility of the new type system, we provide three distinct encodings (from the linear lambda calculus, from the linear pi calculus, and from the pi calculus with polarized variables) into our system. For each language we present operational and typing correspondences, showing that our system effectively subsumes the linear pi calculus as well as foregoing works on session types.