Parameterizing higher-order processes on names and processes

• Published in: RAIRO. Informatique théorique et applications Vol. 53; no. 3-4; pp. 153 - 206
• Main Author: Xu, Xian
• Format: Journal Article
• Language: English
• Published: Paris EDP Sciences 01.07.2019
• Subjects: 68Q05; 68Q10; 68Q85; Context; context bisimulation; encoding; first-order; higher-order; normal bisimulation; Parameterization; processes
• ISSN: 0988-3754; 1290-385X
• DOI: 10.1051/ita/2019005

Parameterization extends higher-order processes with the capability of abstraction and application (like those in lambda-calculus). As is well-known, this extension is strict, meaning that higher-order processes equipped with parameterization are strictly more expressive than those without parameterization. This paper studies strictly higher-order processes (i.e., no name-passing) with two kinds of parameterization: one on names and the other on processes themselves. We present two main results. One is that in presence of parameterization, higher-order processes can interpret first-order (name-passing) processes in a quite elegant fashion, in contrast to the fact that higher-order processes without parameterization cannot encode first-order processes at all. We present two such encodings and analyze their properties in depth, particularly full abstraction. In the other result, we provide a simpler characterization of the standard context bisimilarity for higher-order processes with parameterization, in terms of the normal bisimilarity that stems from the well-known normal characterization for higher-order calculus. As a spinoff, we show that the bisimulation up-to context technique is sound in the higher-order setting with parameterization.