How do you show two SQL query statements are equivalent (SQL server, development)?

 To show that two SQL queries are equivalent in SQL Server, you can follow several approaches to compare their behavior, performance, and results. Here’s a structured way to demonstrate equivalence:

1. Compare the Results of Both Queries

The most direct way to show two SQL queries are equivalent is to compare their outputs. You can do this by running both queries and ensuring they return identical results.

Method:

• Run the queries side by side and check that the result sets (including rows, columns, and data) are exactly the same. You can do this manually or automate it by saving results in a temporary table.

Example:

-- Query 1
SELECT column1, column2
FROM my_table
WHERE column1 = 'value';

-- Query 2
SELECT column1, column2
FROM my_table
WHERE column2 = 'value'
  AND column1 = 'value';

Steps to Compare:

1. Run both queries separately and examine the results.
2. Use EXCEPT or INTERSECT to compare the results.

   -- Check if Query 1 results are the same as Query 2
   SELECT column1, column2
   FROM my_table
   WHERE column1 = 'value'
   EXCEPT
   SELECT column1, column2
   FROM my_table
   WHERE column2 = 'value'
     AND column1 = 'value';
   
   -- Check if Query 2 results are the same as Query 1
   SELECT column1, column2
   FROM my_table
   WHERE column2 = 'value'
     AND column1 = 'value'
   EXCEPT
   SELECT column1, column2
   FROM my_table
   WHERE column1 = 'value';
   

If both of these queries return no rows, it indicates that the result sets of the two queries are equivalent.

2. Check Execution Plans

SQL Server generates an execution plan for every query, which shows how the SQL Server engine will execute the query. You can compare the execution plans of the two queries to see if they perform similarly.

Steps:

1. Generate Execution Plans for both queries:
   • In SQL Server Management Studio (SSMS), press Ctrl+M to include the actual execution plan.
   • Run each query and examine the execution plan tab that is generated.
2. Compare the Execution Plans:
   • Look for similar operations (e.g., index scans, table scans, joins).
   • Check the cost (in terms of CPU, I/O, etc.).
   • If the execution plans are nearly identical, the queries are likely equivalent in performance.

3. Check Query Performance and Execution Time

If the queries are syntactically different but you suspect they might be logically equivalent, comparing their performance is another good indicator of equivalence.

Steps:

1. Run both queries and measure their execution times using the SET STATISTICS TIME command:

   SET STATISTICS TIME ON;
   
   -- Query 1
   SELECT column1, column2
   FROM my_table
   WHERE column1 = 'value';
   
   -- Query 2
   SELECT column1, column2
   FROM my_table
   WHERE column2 = 'value'
     AND column1 = 'value';
   
   SET STATISTICS TIME OFF;
   

2. Compare the execution time and other statistics (such as logical reads, CPU time). If both queries execute with similar performance metrics, they are likely optimized in a similar manner and thus are equivalent.

4. Consider Set Theory and Algebra

Mathematically, SQL queries can be analyzed using set theory, as SQL queries typically return sets of results. By analyzing the underlying set operations (e.g., selections, joins, projections), you can prove that the two queries are logically equivalent, though this approach is often more theoretical.

For example:

• If two queries return the same rows under all conditions (ignoring order unless ORDER BY is specified), then they are equivalent.
• If the queries use different operations but are logically consistent, such as one using an INNER JOIN and another using WHERE clauses, they may still return the same result.

5. Check for Equivalent Logic

If one query is more complicated than another (e.g., uses JOIN vs WHERE), you can attempt to break down each query logically and show that the conditions or transformations applied are equivalent.

Example:

-- Query 1 (using JOIN)
SELECT a.column1, b.column2
FROM table1 a
JOIN table2 b ON a.id = b.id
WHERE a.column1 = 'value';

-- Query 2 (using WHERE)
SELECT a.column1, b.column2
FROM table1 a, table2 b
WHERE a.id = b.id AND a.column1 = 'value';

• In this case, both queries are logically equivalent despite using different syntax (explicit join vs implicit join).

6. Review SQL Server Query Optimizer's Transformations

Sometimes SQL Server’s query optimizer might transform one query into another (e.g., rewriting subqueries as joins). Even though the queries are written differently, the optimizer might transform them into equivalent plans.

To check this:

• Review the execution plan and see if SQL Server rewrites the query during optimization.
• Use the QUERY TRACE option to see detailed transformations.

Conclusion

To prove that two SQL queries are equivalent:

1. Compare the result sets.
2. Compare the execution plans.
3. Compare performance metrics.
4. Analyze the logical transformations or algebraic structure behind the queries.

If these comparisons yield identical or near-identical outcomes, the queries can be considered equivalent.