Principal Typing Schemes in a Polyadic pi-Calculus

The present paper introduces a typing system for a version of Milner's polyadic π-calculus, and a typing inference algorithm linear on the size of the input. The central concept underlying the typing system is the notion of type assignment, where each free name in a term is assigned a type, the term itself being given multiple nametype pairs. This observation leads to a clean typing system for Milner's sorting, and induces an efficient algorithm to infer the typing of a term. The typing system enjoys a subject-reduction property and possesses a notion of principal typing scheme. The algorithm to reconstruct the principal typing scheme of a process, or to detect its inexistence, is proved correct with respect to the typing system.