An Algebraic Formulation for Data Refinement

We analyze recent work on an algebraic formulation for data refinement. Hoare's principal mathematical constructions are reviewed. Then, they are mildly reformulated and unified in terms of two principal category theoretic notions: those of an enriched category and monad, also known as a triple. The requisite definitions and theory are given, together with several examples to illustrate precisely how Hoare's work, including his main theorem may be seen in this light.