Encoding CDuce in the Cπ-calculus?

CDuce is a functional programming language featuring overloaded functions and a rich type system with recursive types, subtyping, union, negation and intersection types. The boolean constructors have a set-theoretic behaviour defined via a semantic interpretation of the types. The Cπ-calculus is an extension of the π-calculus that enriches Pierce and Sangiorgi π-calculus subtyping with union, intersection, and negation types. It is based on the same set-theoretic interpretation as CDuce. In this work we present a type faithful encoding of the CDuce into the Cπ-calculus. This encoding is a modification of the Milner-Turner encoding of the λ-calculus with subtyping into the π-calculus with subtyping. The main difficulty to overcome was to find an encoding of the types that respects the subtyping relation. Besides the technical challenge, this effort is interesting because it sheds new light on the Milner-Turner encoding and on the relations between sequential and remote execution of functions/services, in particular in the presence of type-driven semantics. It also confirms the validity of the equational laws for union and intersection types in π-calculus.