CTE with UNION ALL not working as expected

Question

The query below seems simple and straightforward, yet it produces unexpected results.

CREATE TABLE #NUMBERS
(
    N BIGINT
);
INSERT INTO #NUMBERS VALUES
(1),
(2),
(3),
(4),
(5),
(6),
(7),
(8),
(9)
;
WITH
A AS
(

    -- CHOOSE A ROW AT RANDOM
    SELECT   TOP 1 *
    FROM     #NUMBERS

    ORDER BY NewID()

),
B AS
(
    SELECT A.N AS QUANTITY, 'METERS' AS UNIT FROM A
UNION ALL

SELECT A.N*100 AS QUANTITY, 'CENTIMETERS' AS UNIT FROM A

UNION ALL

SELECT A.N*1000 AS QUANTITY, 'MILLIMETERS' AS UNIT FROM A

UNION ALL

SELECT A.N*1000000 AS QUANTITY, 'MICRONS' AS UNIT FROM A

UNION ALL

SELECT A.N*1000000000 AS QUANTITY, 'NANOMETERS' AS UNIT FROM A

)
SELECT   *
FROM     B
ORDER BY B.QUANTITY
;

I would expect it to execute CTE A once, and then carry those results into CTE B to produce results something like this:

QUANTITY	UNIT
4	METERS
400	CENTIMETERS
4000	MILLIMETERS
4000000	MICRONS
4000000000	NANOMETERS

However, it produces results like this:

QUANTITY	UNIT
8	METERS
700	CENTIMETERS
1000	MILLIMETERS
6000000	MICRONS
3000000000	NANOMETERS

It means it is going back and executing CTE A five times, once for every mention of A in CTE B. Not only is this unwanted and unintuitive, but it also seems unnecessarily inefficient.

What is going on, and how would a CTE genius rewrite it to produce the desired results?

BTW, the Microsoft documentation pages on CTEs contain this cryptic statement which might or might not be related:

If more than one CTE_query_definition is defined, the query definitions must be joined by one of these set operators: UNION ALL, UNION, EXCEPT, or INTERSECT.

Finally, rewriting the query to eliminate CTE B didn't help:

WITH
A AS
(   
    -- CHOOSE A ROW AT RANDOM
    SELECT   TOP 1 *
    FROM     #NUMBERS            
    ORDER BY NewID()           
)
SELECT   *
FROM     (
          SELECT A.N AS QUANTITY, 'METERS' AS UNIT FROM A
      UNION ALL

      SELECT A.N*100 AS QUANTITY, 'CENTIMETERS' AS UNIT FROM A

      UNION ALL

      SELECT A.N*1000 AS QUANTITY, 'MILLIMETERS' AS UNIT FROM A

      UNION ALL

      SELECT A.N*1000000 AS QUANTITY, 'MICRONS' AS UNIT FROM A

      UNION ALL

      SELECT A.N*1000000000 AS QUANTITY, 'NANOMETERS' AS UNIT FROM A

     ) AS B

ORDER BY B.QUANTITY
;

Answer 1

It's helpful to think of common table expressions more like expressions and less like (permanent) tables. Each time you reference a common table expression, it must re-express itself.

Here's a simple example:

DECLARE
    @t table(id int);
INSERT 
    @t
(
    id
)
SELECT
    id = 1
SET STATISTICS XML ON;
WITH
    t AS
(
    SELECT
        t.id
    FROM @t AS t
)
SELECT
    t.*
FROM t 
JOIN t AS t1
  ON t1.id = t.id
JOIN t AS t2
  ON t2.id = t.id;

The query plan will look something like this, with a join to the base table variable for each join between to the common table expression:

Likewise, UNION (ALL) will produce a reference each time as well:

WITH
    t AS
(
    SELECT
        t.id
    FROM @t AS t
)
SELECT
    t.*
FROM t 
UNION ALL
SELECT
    t.*
FROM @t AS t
UNION ALL
SELECT
    t.*
FROM @t AS t;

If you need to stabilize a result, you need to use a:

• #temp table
• @table variable
• Permanent table

Answer 2

Other answers have explained the reason for the issue happening: basically, a CTE is just an expression that evaluates as many times as it is referenced, thus causing A to return a different value at each evaluation.

What I would like to address in my answer is this part of the question:

how would a CTE genius rewrite it to produce the desired results?

Hanging around some of the places where CTE geniuses gather to discuss their CTE-related business may have taught me a few tricks that I would like to share.

What I think would be very useful here in resolving the issue at hand are two things:

• the CROSS APPLY operator;
• the VALUES row constructor.

Using those two, I would rewrite specifically the B CTE like this:

B AS
(
    SELECT   X.*
    FROM     A
    CROSS APPLY
    (
        VALUES
        (A.N, 'METERS'),
        (A.N*100, 'CENTIMETERS'),
        (A.N*1000, 'MILLIMETERS'),
        (A.N*1000000, 'MICRONS'),
        (A.N*1000000000, 'NANOMETERS')
    ) AS X (QUANTITY, UNIT)
)

leaving the rest of the query intact.

The way B is defined above, A is referenced (and evaluated) only once. It still produces a rowset rather than a single row because it replaces (with the help of CROSS APPLY) the row returned by A with a rowset, and the rowset (constructed by VALUES) essentially takes A.N as an argument, producing the desired set of values.

You can test the full query at dbfiddle.uk.

Answer 3

CTEs are not always materialized as many people believe.