Representability and program construction within fork algebras

The representational theorem for fork algebras was always misunderstood regarding its applications in program construction. Its application was always described as 'the portability of properties of the problem domain into the abstract calculus of fork algebras'. In this paper we show that the results provided by the representation theorem are by far more important. We show that not only the heuristic power coming from concrete binary relations is captured inside the abstract calculus, but also design strategies for the program development can be successfully expressed. This result makes fork algebras a programming calculus by far more powerful than it was previously thought.