Weak Functional Dependencies in Higher-Order Datamodels - The Case of the Union Constructor -

We present an axiomatisation for weak functional depen- dencies, i.e. disjunctions of functional dependencies, in the presence of several constructors for complex values. These constructors are the tu- ple constructor, the set-constructor, an optionality constructor, and a union constructor. The theory is smooth and rather uniform, if the union- constructor is absent. Its presence, however, complicates all results and proofs significantly. The reason for this is that the union-constructor comes alomg with non-trivial restructuring rules. In particular, if the union-constructor is absent, a subset of the rules is complete for the im- plication of ordinary functional dependencies, but this does not hold, if the union constructor is present.