This is the first in a series of papers dealing with the implementation of an extended term graph rewriting model of computation (described by the DACTL language) on a distributed store architecture. In this paper we set out the high level model, and under some simple restrictions, prove an abstract packet store implementation correct modulo garbage. The abstract packet store model is compared to a more realistic and finegrained packet store model, more closely related to the properties of a genuine distributed store architecture, and the differences are used to inspire the definition of the MONSTR sublanguage of DACTL, intended for direct execution on the machine. Various alternative operational semantics for MONSTR are proposed to reflect more closely the finegrained packet store model, and the prospects for establishing correctness are discussed. The detailed treatment of the alternative models, in the context of suitable sublanguages of MONSTR where appropriate, are subjects for subsequent papers.