A Note on a Typing System for the Higher-order -calculus

We study a typing assignment system for the higher-order-calculus. The system proposed is a straightforward extension of the typing system for the polyadic-calculus proposed by Kohei Honda and the author 6], by introducing a new type constructor for agents (i.e., processes abstracted on some sequence of names and variables.) We also present an eecient typing reconstruction algorithm to extract the most general typing of an agent or to detect its inexistence, and prove its correctness with respect to the typing system. Finally we show that well-sorted agents are typable, and that typable agents are well-sorted, thus establishing the correspondence between Sangiorgi's sorting system 4] and the typing assignment system.