Dexter Kozen. On Hoare Logic, Kleene Algebra, and Types. In P. Gärdenfors, J. Wolenski, and K. Kijania-Placek, editors, In the Scope of Logic, Methodology, and Philosophy of Science: Volume 1 of the 11th Int. Congress Logic, Methodology and Philosophy of Science, Cracow, August 1999, volume 315 of Studies in Epistemology, Logic, Methodology, and Philosophy of Science, pages 119-133. Kluwer, 2002.

We show that propositional Hoare logic is subsumed by the type calculus of typed Kleene algebra augmented with subtypes and typecasting. Assertions are interpreted as typecast operators. Thus Hoare-style reasoning with partial correctness assertions reduces to typechecking in this system.