On the Expressiveness of Polyadic and Synchronous Communication in Higher-Order Process Calculi

Abstract

Abstract. Higher-order process calculi are calculi in which processes can be communicated. We study the expressiveness of strictly higher-order process calculi, and focus on two issues well-understood for first-order calculi but not in the higher-order setting: synchronous vs. asynchronous communication and polyadic vs. monadic communication. First, and similarly to the first-order setting, synchronous process-passing is shown to be encodable into asynchronous processpassing. Then, the absence of name-passing is shown to induce a hierarchy of higher-order process calculi based on the arity of polyadic communication, thus revealing a striking point of contrast with respect to first-order calculi. Finally, the passing of abstractions (i.e., functions from processes to processes) is shown to be more expressive than process-passing alone.

On the Relative Expressiveness of Higher-Order Session Processes

“…We define the formal notion of encoding by extending to a typed setting existing criteria for untyped processes (as in, e.g., [24,26,27,10,16,8,41,30]). We first define a typed calculus parametrised by a syntax, operational semantics, and typing.…”

“…Compositionality wrt restriction is also supported by typing and is useful in our encodability results ( § 7). The name invariance criterion follows [10,16].…”

“…The work [16] extends this core calculus with restriction, output prefix, and polyadicity; it shows that synchronous communication can encode asynchronous communication, and that process passing polyadicity induces an expressiveness hierarchy. The paper [43] complements [16] by studying the expressivity of second-order process abstractions. Polyadicity is shown to induce an expressiveness hierarchy; also, by adapting the encoding in [32], process abstractions are encoded into name abstractions.…”

“…Polyadicity is shown to induce an expressiveness hierarchy; also, by adapting the encoding in [32], process abstractions are encoded into name abstractions. In contrast, here we give a fully abstract encoding of HO π + into HO that preserves session types; this improves [16,43] by enforcing linearity disciplines on process behaviour. The focus of [16,42,43,44] is on untyped, higher-order processes; they do not address communication disciplined by (session) type systems.…”

“…A vast literature on expressiveness in concurrency theory also studies compilations (or encodings) [26,10,8,16,31]: they are used to transfer reasoning techniques across calculi, and to implement process constructs using simpler ones. In this work, we study relative expressiveness via type-preserving encodings for HOπ, a higher-order process language that integrates message-passing concurrency with functional features.…”