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

The best you can do is compare the 2 query outputs based on a given set of inputs looking for any differences. To say that they will always return the same results for all inputs really depends on the data.

For Oracle one of the better if not best approaches (very efficient) is here (Ctrl+F Comparing the Contents of Two Tables):
http://www.oracle.com/technetwork/issue-archive/2005/05-jan/o15asktom-084959.html

Which boils down to:

select c1,c2,c3, 
       count(src1) CNT1, 
       count(src2) CNT2
  from (select a.*, 
               1 src1, 
               to_number(null) src2 
          from a
        union all
        select b.*, 
               to_number(null) src1, 
               2 src2 
          from b
       )
group by c1,c2,c3
having count(src1) <> count(src2);