Characteristic bisimulation for higher-order session processes

Abstract

For higher-order (process) languages, characterising contextual equivalence is a long-standing issue. In the setting of a higher-order π-calculus with session types, we develop characteristic bisimilarity, a typed bisimilarity which fully characterises contextual equivalence. To our knowledge, ours is the first characterisation of its kind. Using simple values inhabiting (session) types, our approach distinguishes from untyped methods for characterising contextual equivalence in higher-order processes: we show that observing as inputs only a precise finite set of higher-order values suffices to reason about higher-order session processes. We demonstrate how characteristic bisimilarity can be used to justify optimisations in session protocols with mobile code communication.

On the Relative Expressiveness of Higher-Order Session Processes

“…HOπ it is a subcalculus of the language studied in [22]. It is also a variant of the language that we investigated in [14], which includes higher-order value applications. Names a, b, c, .…”

“…In [14] we have characterised reduction-closed, barbed congruence for HOπ via a typed relation called characteristic bisimilarity. Its definition uses a typed labelled transition system (LTS) informed by session types.…”

“…We show that HO can encode HOπ precisely and efficiently. Requiring type preservation makes this encoding far from trivial: we crucially exploit advances on session type duality [2,3] and recent characterisations of typed contextual equivalence [14]. We develop a full hierarchy of variants of HOπ based on precise encodings: our encodings are type-preserving and fully abstract up to typed behavioural equalities.…”

“…15), which extends encodability criteria for untyped processes with full abstraction. Full abstraction results are stated up to two behavioural equalities that characterise barbed congruence: characteristic bisimilarity (≈ C , defined in [14]) and higher-order bisimilarity (≈ H ), introduced in this work. It turns out that ≈ H offers more direct reasoning than ≈ C .…”

“…§ 3 presents HOπ and its subcalculi (HO and π); § 4 summarises their session type system. § 5 presents behavioural equalities for HOπ: we recall definitions of barbed congruence and characteristic bisimilarity [14], and introduce higher-order bisimilarity. We show that these three typed relations coincide (Thm.…”