Instant Polymorphic Type Systems for Mobile Process Calculi: Just Add Reduction Rules and Close

Many different mobile process calculi have been invented, and for each some number of type systems has been developed. Soundness and other properties must be proved separately for each calculus and type system. We present the generic polymorphic type system Poly* which works for a wide range of mobile process calculi, including the π-calculus and Mobile Ambients. For any calculus satisfying some general syntactic conditions, well-formedness rules for types are derived automatically from the reduction rules and Poly* works otherwise unchanged. The derived type system is automatically sound (i.e., has subject reduction) and often more precise than previous type systems for the calculus, due to Poly*'s spatial polymorphism. We present an implemented type inference algorithm for Poly* which automatically constructs a typing given a set of reduction rules and a term to be typed. The generated typings are principal with respect to certain natural type shape constraints.