Proving SQL query equivalency

Question

How would you go about proving that two queries are functionally equivalent, eg they will always both return the same result set.

---

As I had a specific query in

Answer 1

CAREFUL! Functional "equivalence" is often based on the data, and you may "prove" equivalence of 2 queries by comparing results for many cases and still be wrong once the data changes in a certain way.

For example:

SQL> create table test_tabA
(
col1 number
)

Table created.

SQL> create table test_tabB
(
col1 number
)

Table created.

SQL> -- insert 1 row

SQL> insert into test_tabA values (1)

1 row created.

SQL> commit

Commit complete.

SQL> -- Not exists query:

SQL> select * from test_tabA a
where not exists
(select 'x' from test_tabB b
where b.col1 = a.col1)

      COL1

----------

         1

1 row selected.

SQL> -- Not IN query:

SQL> select * from test_tabA a
where col1 not in
(select col1
from test_tabB b)

      COL1

----------

         1

1 row selected.


-- THEY MUST BE THE SAME!!! (or maybe not...)


SQL> -- insert a NULL to test_tabB

SQL> insert into test_tabB values (null)

1 row created.

SQL> commit

Commit complete.

SQL> -- Not exists query:

SQL> select * from test_tabA a
where not exists
(select 'x' from test_tabB b
where b.col1 = a.col1)


      COL1

----------

         1

1 row selected.

SQL> -- Not IN query:

SQL> select * from test_tabA a
where col1 not in
(select col1
from test_tabB b)

**no rows selected.**