On the Relative Expressiveness of Higher-Order Session Processes

By integrating constructs from the $$\lambda $$λ-calculus and the $$\pi $$π-calculus, in higher-order process calculi exchanged values may contain processes. This paper studies the relative expressiveness of $$\mathsf {HO}\pi $$HOπ, the higher-order $$\pi $$π-calculus in which communications are governed by session types. Our main discovery is that $$\mathsf {HO}$$HO, a subcalculus of $$\mathsf {HO}\pi $$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 $$\mathsf {HO}$$HO, we show that $$\mathsf {HO}$$HO can encode $$\mathsf {HO}\pi $$HOπ fully abstractly upi¾?to typed contextual equivalence more precisely and efficiently than the first-order session $$\pi $$π-calculus $$\pi $$π. Overall, under session types, $$\mathsf {HO}\pi $$HOπ, $$\mathsf {HO} $$HO, and $$\pi $$π are equally expressive; however, $$\mathsf {HO}\pi $$HOπ and $$\mathsf {HO} $$HO are more tightly related than $$\mathsf {HO}\pi $$HOπ and $$\pi $$π.