Relational Concurrent Refinement with Internal Operations

Data refinement in a state-based language such as Z is defined using a relational model in terms of the input-output behaviour of abstract programs. Downward and upward simulations form a sound and jointly complete methodology for verifying relational data refinements. Refinement in a concurrent context, for example, as found in a process semantics, takes a number of different forms. Typically this is based on a notion of observation, for example, which events a system is prepared to accept or refuse. Concurrent refinement relations include trace refinement, failures-divergences refinement, readiness refinement and bisimulation. In this paper we survey recent results linking the relational model of refinement to the process algebraic models. Specifically, we detail how variations in the relational framework lead to relational data refinement being in correspondence with traces-divergences, singleton failures and failures-divergences refinement in a process semantics. We then extend these results by showing how the effect of internal operations can be incorporated into the relational model. As a consequence simulation rules for failures-divergences refinement can be derived.