Transforming queries into canonical forms

A canonical form is defined for the relational algebra (RA) queries, which is a selection followed by a projection. We show that each RA query not containing the difference operator can be equivalently expressed by some union of canonical forms queries. Two classes of canonical are also introduced (called respectively D - and DO_canonical form), both of them satidfying some restrictions on the form of predicate in the selection. The relationship among the canonical form, the D_canonical form and the DO_canonical form queries are studied. In particular, each canonical form query is shown to have an equivalent D canonical form query. And each D_canonical form query is shown to be equivalent to some union of DO_canonical form queries.