On the Relative Expressiveness of Higher-Order Session Processes

By integrating constructs from the λ-calculus and the π-calculus, in higher-order process calculi exchanged values may contain processes. This paper studies the relative expressiveness of HOπ, the higher-order π-calculus in which communications are governed by session types. Our main discovery is that HO, a subcalculus of HOπ which lacks name-passing and recursion, can serve as a new core calculus for session-typed higher-order concurrency. By exploring a new bisimulation for HO, we show that HO can encode HOπ fully abstractly (up to typed contextual congruence) more precisely and efficiently than the first-order session π-calculus (π). Overall, under session types, HOπ, HO, and π are equally expressive; but HOπ and HO are more tightly related than HOπ and π.