First Steps in Pointfree Functional Dependency Theory

When software designers refer to the relational calculus, what they usually mean is the set-theoretic kernel of relational database design “à la Codd” and not the calculus of binary relations which was initiated by De Morgan in the 1860s an eventually became the core of the algebra of programming. Contrary to the intuition that a binary relation is just a particular case of -ary relation, this paper shows the effectiveness of the former in “explaining” and reasoning about the latter. The theory of functional dependencies, which is central to such database design techniques, is addressed in a pointfree style instead of reasoning in the standard set-theoretic model “à la Codd”. It turns out that the theory becomes more general and considerably simpler. Elegant expressions replace lengthy formulæ and easy-to-follow calculations replace pointwise proofs with lots of “ ” notation, case analyses and natural language explanations for “obvious” steps.