Tabular Expressions and Total Functional Programming

Tabular expressions are a multidimensional structured notation for complex mathematical definitions of relations or functions. They have been found useful for documenting imperative programs by stating the function or relation that describes the black-box behaviour of those programs. Tools are needed to increase the practicality of this approach to documentation. In order to create tools to check and evaluate tabular expressions, we have investigated functional programming as an implementation paradigm that reflects the semantics of these mathematical expressions faithfully. We explain why and how the restriction to total functions improves the semantic correspondence substantially, and describe the basic design and capabilities of our total functional programming tools for tabular expressions. We demonstrate the practical advantages of totality by giving examples for the especially easy and effective application of well-known code transformation techniques to total functional programs.