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This work proposes tractable bisimulations for the higher-order pi-calculuswith session primitives (HOpi) and offers a complete study of the expressivityof its most significant subcalculi. First we develop three typed bisimulations,which are shown to coincide with contextual equivalence. Thesecharacterisations demonstrate that observing as inputs only a specific finiteset of higher-order values (which inhabit session types) suffices to reasonabout HOp} processes. Next, we identify HO, a minimal, second-order subcalculusof HOpi in which higher-order applications/abstractions, name-passing, andrecursion are absent. We show that HO can encode HOpi extended withhigher-order applications and abstractions and that a first-order sessionpi-calculus can encode HOpi. Both encodings are fully abstract. We also provethat the session pi-calculus with passing of shared names cannot be encodedinto HOpi without shared names. We show that HOpi, HO, and pi are equallyexpressive; the expressivity of HO enables effective reasoning about typedequivalences for higher-order processes.

Core Higher-Order Session Processes: Tractable Equivalences and Relative Expressiveness