Unifying theories of healthiness condition

Abstract

A theory of programming starts with a complete Boolean algebra of specifications, and defines healthiness conditions which exclude infeasibility of implementation. These are expressed as algebraic laws useful for transformation and optimisation of designs. Programming notations and languages must be restricted to those preserving all the healthiness conditions. We have explored a wide range of programming paradigms, including nondeterministic, sequential, parallel, logical and probabilistic. In all cases, we have found a single healthiness condition, formalised by constructions due to Karoubi and to Kleisli. The uniformity maintains for all paradigms a single notion of correctness throughout the chain that leads from specification through designs to programs that are proved to meet the original specification.