On Teaching the Concept of Refinement with B

The concept of refinement is central to the development of software. It appears in various forms in the different methodologies taught to students. A key point in the B method is the validation of the refinement step. The B methodology exhibits mathematical properties of correct refinements, and also automatically checkable conditions that ensure those properties. Some of the main pedagogical difficulties that the present authors found in teaching B centered around the notions linked to refinement, at the conceptual level, and at the tool level. Many papers have been published on the general benefits of the B method. This paper will focus on the specific concepts linked to refinements, and on the ones which need special care. We argue that, although B presents a complete mathematical analysis, it is beneficial to put the concept of refinement in perspective with other theories that come from formal methods, namely, in this paper, coalgebra and bisimulation.