4. A Relational View of Refinement

In Chap. 1 we introduced differing notions of refinement in the LTS setting - each one based upon a different notion of observation. In Chap. 2 we focused on simulations as a means to verify trace refinements in an Automata context, and we discussed both finite trace refinement as well as trace refinement in the presence of infinite traces. In Chap. 3 we developed a basic refinement model that looked at states in the first place, and constructed a relational semantics for it. We ended with sketching how labels on transitions could be added to that and how we could apply abstraction to state spaces, in preparation for the model in the current chapter. In this chapter we will look at a semantic model that is entirely based on relations and abstract state as a model of computation. In this context programs will be finite relational compositions of operations together with a finalisation which makes explicit the observations made of that program. As in Chap. 1 and ever since refinement will be the consistency of observations. We will then explore, without fixing the exact observations to be made, how simulations can be used to verify the refinement in a way similar to that found in Chap. 2.