Calculating constraints on relational expression

This paper deals with the problem of determining which of a certain class of constraints hold on a given relational algebra expression where the base relations come from a given schema. The class of constraints includes functional dependencies, equality of domains, and constancy of domains. The relational algebra consists of projection, selection, restriction, cross product, union, and difference. The problem as given is undecidable, but if set difference is removed from the algebra, there is a solution. Operators specifying a closure function (similar to functional dependency closure on one relation) are defined; these will generate exactly the set of constraints valid on the given relational algebra expression. We prove that the operators are sound and complete.