FOUNDATIONS OF A THEORY OF SYNCHRONOUS SYSTEMS

A semantic algebra construction is introduced to model the stepwise behavior of synchronous systems in an arbitrary pointed algebraic theory T The theory T is extended to a feedback theory F(infinity)T in which the bottom morphism is the designated point of T The feedback theory F(infinity)T is obtained as the inverse limit of the theories n-res T that describe the stepwise behavior of systems in T restricted to the first n clock cycles. It is shown that in F(infinity)T, iteration satisfies the functorial dagger condition. Some suggestions are made about how to generalize the construction to handle infinite systems.