Table Comparison - SQL

The following definitions for relation comparisons:

Let r1 and r2 be relations having the same heading. Then:

r1 ⊆ r2 is true if every tuple of r1 is also a tuple of r2, otherwise false.

r1 ⊇ r2 is equivalent to r2 ⊆ r1

r1 = r2 is equivalent to r1 ⊆ r2 AND r2 ⊆ r1

The question arises as to whether SQL tables can be similarly compared. SQL does not have direct counterparts of ⊆ and ⊇. It does of course have =, but table expressions cannot be used as comparands. However, as we have seen in Examples et seq., the operator TABLE has been available since SQL: 2003 to derive from a given table expression a value of a multiset type whose element type is a row type. In other words, (SELECT * FROM t1) = (SELECT * FROM t2) is illegal but we can obtain the required effect by writing TABLE (SELECT * FROM t1) = TABLE (SELECT * FROM t2). So, to compare two tables, we have to use an operator named TABLE to "convert" them from tables into multisets of rows!

To test for every row of t1 being also a row of t2 we could write, for example, NOT EXISTS (SELECT * FROM t1 EXCEPT SELECT * FROM t2). In fact, SQL's NOT EXISTS is an exact counterpart of Tutorial D's IS_EMPTY operator. However, note carefully that the case where every row in t1 appears in t2 and every row of t2 appears in t1 does not guarantee that t1 and t2 are the same table. Row r might appear twice in t1 but only once in t2, for example.