Formal Methods Unifying Computing Science and Systems Theory

Computing Science and Systems Theory can gain much from unified mathematical models and methodology, in particular formal reasoning (“letting the symbols do the work”). This is achieved by a wide-spectrum formalism. The language uses just four constructs, yet suffices to synthesize familiar notations (minus the defects) as well as new ones. It supports formal calculation rules convenient for hand calculation and amenable to automation. The basic framework has two main elements. First, a functional predicate calculus makes formal logic practical for engineers, allowing them to calculate with predicates and quantifiers as easily as with derivatives and integrals. Second, concrete generic functionals support smooth transition between pointwise and point-free formulations, facilitating calculation with functionals and exploiting formal commonalities between CS and Systems Theory. Elaborating a few small but representative examples shows how formal calculational reasoning about diverse topics such as mathematical analysis, program semantics, transform methods, systems properties (causality, LTI), data types and automata provides a unified methodology.