The Case for Total Programming

This paper considers total functions, which are uniformly defined, total procedures (or batch programs), which terminate uniformly, and total processes, which consist of a UNITY-like set of total procedures, so that they never terminate. This collection is shown to be Turing-complete. It can also appropriate for interactive programming. The paper argues from a software engineering viewpoint that total programming improves the reliability of programs, and makes them easier to reason about, with only a minor sacrifice of expressiveness. In particular, considering only total programs allows definitions and laws to be simplified. Formal derivations of total procedures are given using a novel combination of the Z-style termination convention combined with partial correctness reasoning. The derivations, it is claimed, are at least as clear and simple as those produced by other methods of formal operational refinement.