Refinement Calculus, Lattices and Higher Order Logic

We show how to describe refinement calculus in a lattice theoretic framework. The predicate transformer lattice is built by pointwise extensions from the truth value lattice. A simple but very powerful statement language characterizes the monotonic predicate transformer lattice. We show how to formalize the calculus in higher order logic. We also show how to express data refinement in this framework. A theorem of data refinement with stuttering is proved, to illustrate the algebraic nature of reasoning in this framework.