ASM refinement and generalizations of forward simulation in data refinement: a comparison

In [1], we have formalized Börger’s refinement notion for Abstract State Machines (ASMs). The formalization was based on transition systems, and verification conditions were expressed in Dynamic Logic. In this paper, the relation between ASM refinement and data refinement is explored. Data refinement expresses operations and verification conditions using relational calculus. We show how to bridge the gap between the different notations, and that forward simulation in the behavioral approach to data refinement can be viewed as a specific instance of ASM refinement with 1:1 diagrams, where control structure is not refined. We also prove that two recent generalizations of data refinement, weak refinement and coupled refinement can be derived from ASM refinement.