The development, certification and evolution of dependable software requires the ability to analyze software artifacts in all their extensive detail. This, in turn, is contingent upon availability of reliable, certified tools that can rigorously analyze the behavior and properties of software artifacts. One of the most difficult challenges in the development of such a tool is the ability to derive the function of a loop from a static analysis of its source code. In this paper, we discuss the

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... n tenets of our approach to this problem, based on a relation-theoretic refinement calculus, and outline its results, insights, and prospects.