The Refinement Calculus Hierarchy

Abstract

The predicate transformers that we use to model contracts are constructed from other predicate transformers or from simpler elements, like state predicates, state transformers, or state relations. The predicate transformer constructors can thus be seen as functions that map elements in one domain to the domain itself or to another domain. The basic question that we investigate in this chapter is to what extent the lattice and category structure is preserved by these constructors, i.e., to what extent the constructors are monotonic and homomorphic.