In this paper we explore the structure and applicability of the Distributed Measurement Calculus (DMC), a formal assembly language for distributed measurement-based quantum computations. We describe its syntax and semantics, both operational and denotational, and state several properties that are crucial to the practical usability of our language, such as equivalence of our semantics, as well as compositionality and context-freeness of DMC programs. We show how to put these properties to use by constructing a composite program that implements distributed controlled operations, and demonstrate that the semantics of this program does not change under the various composition operations. Our formal model is meant to be the basis of a virtual machine for distributed quantum computations, where programming execution no longer needs to be analysed by hand, while at the same time formal properties may be relied upon. Several insights on how to move towards this virtual level are given.
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