Predicative Polymorphism in - Calculus

We present a formulation of the polyadic-calculus featuring a syntactic category for agents, together with a typing system assigning polymorphic types to agents. The new presentation introduces an operator to express recursion, and an ML-style let-constructor allowing to associate an agent to an agent-variable, and use the latter several times in a program. The essence of the monomorphic type system is the assignment of types to names, and multiple name-type pairs to programs 14]. The polymorphic type system incorporates a form of abstraction over types, and inference rules allowing to introduce and eliminate the abstraction operator. The extended system preserves most of the syntactic properties of the monomorphic system, including subject-reduction and computability of principal typings. We present an algorithm to extract the principal typing of a process, and prove it correct with respect to the typing system. We also study, in the context of-calculus, some well-known properties of the let-constructor.