Hoare Logic and Auxiliary Variables

Thomas Kleymann


Auxiliary variables are essential for specifying programs in Hoare Logic. They are required to relate the value of variables in different states. However, the axioms and rules of Hoare Logic turn a blind eye to the role of auxiliary variables. We stipulate a new structural rule for adjusting auxiliary variables when strengthening preconditions and weakening postconditions. Courtesy of this new rule, Hoare Logic is adaptation complete, which benefits software re-use. This property is responsible for a number of improvements. Relative completeness follows uniformly from the Most General Formula property. Moreover, contrary to common belief, one can show that Hoare Logic subsumes VDM's operation decomposition rules in that every derivation in VDM can be naturally embedded in Hoare Logic. Furthermore, the new treatment leads to a significant simplification in the presentation for verification calculi dealing with more interesting features such as recursion or concurrency.


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