Heterogeneous Relation Algebra

So far, relational algebra has been presented in its classical form. Relations are often conceived as something that might be called quadratic or homogeneous; a relation over a set. It is interpreted as a subset R ⊂ U × U of a Cartesian product of the universe U with itself. If relations between two or more sets are considered, this may easily be subsumed under this view, uniting all the sets in question into one huge set and calling this set the universe U. On the other hand, a variant of the theory has evolved that treats relations from the very beginning as heterogeneous or rectangular, i.e. as relations where the normal case is that they are relations between two different sets. The present chapter is devoted to this variant form.