Core Higher-Order Session Processes: Tractable Equivalences and Relative Expressiveness.
Dimitrios Kouzapas (University of Glasgow / Imperial College London) 
Jorge A. Pérez (University of Groningen)
Nobuko Yoshida (Imperial College London)

This work proposes tractable bisimulations for the higher- order π-calculus with session primitives (HOπ) and offers a complete study of the expressivity of its most significant subcalculi. 

First we develop three typed bisimulations, which are shown to coincide with contextual equivalence. These characterisations demonstrate that observing as inputs only a specific finite set of higher-order values (which inhabit session types) suffices to reason about HOπ processes. Next, we identify HO, a minimal, second-order subcalculus of HOπ in which higher-order applications/abstractions, name-passing, and recursion are absent. We show that HO can encode HOπ extended with higher-order applications and abstractions and that a first-order session π-calculus can encode HOπ. Both encodings are fully abstract. We also prove that the session π-calculus with passing of shared names cannot be encoded into HOπ without shared names. We show that HOπ, HO, and π are equally expressive; the expressivity of HO enables effective reasoning about typed equivalences for higher-order processes. 

Short Version (31 pages - Last update: 01/19/2015) Download [PDF
Long Version, with proofs (90 pages - Last update: 09/02/2015) Download [PDF] [arXiv] (also Imperial College DoC TechReport [DTR15-1])

The first part of this work, on typed behavioral equivalences, appears in the Proceedings of CONCUR 2015 [PDF].
The second part of this work, on relative expressiveness, will appear in the Proceedings of ESOP 2016 [PDF].