On the Computation Power of Name Parameterization in Higher-order Processes

Abstract

Parameterization extends higher-order processes with the capability of abstraction (akin to that in lambda-calculus), and is known to be able to enhance the expressiveness. This paper focuses on the parameterization of names, i.e. a construct that maps a name to a process, in the higher-order setting. We provide two results concerning its computation capacity. First, name parameterization brings up a complete model, in the sense that it can express an elementary interactive model with built-in recursive functions. Second, we compare name parameterization with the well-known pi-calculus, and provide two encodings between them.

On the Relative Expressiveness of Higher-Order Session Processes

“…This encoding is quite different from the one in § 7.1: in [44] names are encoded using polyadic name abstractions (called pipes); guarded replication enables infinite behaviours. While our encoding satisfies full abstraction, the encoding in [44] does not: only divergencereflection and operational correspondence (soundness and completeness) properties are established. Soundness is stated up-to pipe-bisimilarity, an equivalence tailored to the encoding strategy; the authors of [44] describe this result as "weak".…”

“…While our encoding satisfies full abstraction, the encoding in [44] does not: only divergencereflection and operational correspondence (soundness and completeness) properties are established. Soundness is stated up-to pipe-bisimilarity, an equivalence tailored to the encoding strategy; the authors of [44] describe this result as "weak".…”

“…Building upon [40], the work [42] studies the (non)encodability of the untyped π-calculus into a higher-order π-calculus with a powerful name relabelling operator, which is essential to encode name-passing. The paper [44] defines an encoding of the (untyped) π-calculus without relabeling. This encoding is quite different from the one in § 7.1: in [44] names are encoded using polyadic name abstractions (called pipes); guarded replication enables infinite behaviours.…”

“…The paper [44] defines an encoding of the (untyped) π-calculus without relabeling. This encoding is quite different from the one in § 7.1: in [44] names are encoded using polyadic name abstractions (called pipes); guarded replication enables infinite behaviours. While our encoding satisfies full abstraction, the encoding in [44] does not: only divergencereflection and operational correspondence (soundness and completeness) properties are established.…”

“…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.…”