The theta-join as a join with theta

We present an algebra for the classical database operators. Contrary to most approaches we use (inner) join and projection as the basic operators. Theta joins result by representing theta as a database table itself and defining theta-join as a join with that table. The same technique works for selection. With this, (point-free) proofs of the standard optimisation laws become very simple and uniform. The approach also applies to proving join/projection laws for preference queries. Extending the earlier approach of [16], we replace disjointness assumptions on the table types by suitable consistency conditions. Selected results have been machine-verified using the CALCCHECK tool