Guarded Transitions in Evolving Specifications

We represent state machines in the category of speci cations, where assignment statements correspond exactly to interpretations between theories [7, 8]. However, the guards on an assignment require a special construction. In this paper we raise guards to the same level as assignments by treating each as a distinct category over a shared set of objects. A guarded assignment is represented as a pair of arrows, a guard arrow and an assignment arrow. We give a general construction for combining arrows over a factorization system, and show its specialization to the category of speci cations. This construction allows us to de ne the ne structure of state machine morphisms with respect to guards. Guards de ne the ow of control in a computation, and how they may be translated under re nement is central to the formal treatment of safety, liveness, concurrency, and determinism.