Towards a design calculus for CSP

The algebra of relations has been very successful for reasoning about possibly non-deterministic programs, provided their behaviour can be fully characterized by just their initial and final states. We use a slight generalization, called sequential algebra, to extend the scope of relation-algebraic methods to reactive systems, where the behaviour between initiation and termination is also important. The sequential calculus is clearly differentiated from the relational one by the absence of a general converse operation. As a consequence, the past can be distinguished from the future, so that we can define the temporal operators and mix them freely with executable programs. We use a subset of CSP in this paper, but the sequential calculus can also be instantiated to different theories of programming. In several examples we demonstrate the use of the calculus for specification, derivation and verification.