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
, which describes a deadlock-free circular communication protocol involving all participants appearing in . We prove operational completeness by showing that, if we place a process not conforming to a subtype of in a context that matches the characteristic global type of , then we obtain a deadlock. The denotational preciseness is proved as a corollary of the operational preciseness.