Precise subtyping for synchronous multiparty sessions

• Published in: Journal of logical and algebraic methods in programming Vol. 104; pp. 127 - 173
• Main Authors: Ghilezan, Silvia, Jakšić, Svetlana, Pantović, Jovanka, Scalas, Alceste, Yoshida, Nobuko
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.04.2019
• Subjects: Concurrency; Multiparty session types; Process calculi; Subtyping; Multiparty session types; Subtyping; Concurrency; Process calculi
• ISSN: 2352-2208
• DOI: 10.1016/j.jlamp.2018.12.002

This paper proves the soundness and completeness, together referred to as preciseness, of the subtyping relation for a synchronous multiparty session calculus. We address preciseness from operational and denotational viewpoints. The operational preciseness has been recently developed with respect to type safety, i.e., the safe replacement of a process of a smaller type in a context where a process of a bigger type is expected. The denotational preciseness is based on the denotation of a type: a mathematical object describing the meaning of the type, in accordance with the denotations of other expressions from the language. The main technical contribution of this paper is a novel proof strategy for the operational completeness of subtyping. We develop the notion of characteristic global type of a session type T, which describes a deadlock-free circular communication protocol involving all participants appearing in T. We prove operational completeness by showing that, if we place a process not conforming to a subtype of T in a context that matches the characteristic global type of T, then we obtain a deadlock. The denotational preciseness is proved as a corollary of the operational preciseness.