Automatic refactoring of conditions and substitutions for B state transition models

The automation of programming, which lies at the intersection of software engineering and artificial intelligence, enables machines to automatically generate programs that satisfy given requirements. In the context of B formal design modeling, one of the challenges is the refactoring of substitutions in design specifications, which often uses state transitions to describe how program or system statuses change during execution. This paper proposes a condition and substitution refactoring algorithm for the B formal specification language. The aim of the work is to automatically derive B operational predicates based on given transitions. The work has been extremely useful to machine-driven formal design model repair as well as automated design specification generation. Given a set of state transitions, common relations of their state variables can be discovered and clustered into a number of classes. These relations can be further used to synthesize substitutions that derive new states from existing states. To restrict application domains of the synthesized substitutions, conditions that guard these substitutions are generated using first-order logic. We have implemented the proposed algorithm as an extension to the ProB model checker. Experiments were conducted based on the B model public dataset. The evaluation results demonstrated that our solution is able to synthesize conditions and substitutions for various sets of state transitions in a wide range of B models.