Abstract
We show here how to formalize different kinds of loop constructs within the refinement calculus, and how to use this formalization to derive general loop transformation rules. The emphasis is on using algebraic methods for reasoning about equivalence and refinement of loops, rather than looking at operational ways of reasoning about loops in terms of their execution sequences. We apply the algebraic reasoning techniques to derive a collection of different loop transformation rules that have been found important in practical program derivations: merging and reordering of loops, data refinement of loops with stuttering transitions and atomicity refinement of loops.
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