Using IS NULL or IS NOT NULL on join conditions - Theory question

Example with tables A and B:

 A (parent)       B (child)    
============    =============
 id | name        pid | name 
------------    -------------
  1 | Alex         1  | Kate
  2 | Bill         1  | Lia
  3 | Cath         3  | Mary
  4 | Dale       NULL | Pan
  5 | Evan  

If you want to find parents and their kids, you do an INNER JOIN:

SELECT id,  parent.name AS parent
     , pid, child.name  AS child

FROM
        parent  INNER JOIN  child
  ON   parent.id     =    child.pid

Result is that every match of a parent's id from the left table and a child's pid from the second table will show as a row in the result:

+----+--------+------+-------+
| id | parent | pid  | child | 
+----+--------+------+-------+
|  1 | Alex   |   1  | Kate  |
|  1 | Alex   |   1  | Lia   |
|  3 | Cath   |   3  | Mary  |
+----+--------+------+-------+

Now, the above does not show parents without kids (because their ids do not have a match in child's ids, so what do you do? You do an outer join instead. There are three types of outer joins, the left, the right and the full outer join. We need the left one as we want the "extra" rows from the left table (parent):

SELECT id,  parent.name AS parent
     , pid, child.name  AS child

FROM
        parent  LEFT JOIN  child
  ON   parent.id    =    child.pid

Result is that besides previous matches, all parents that do not have a match (read: do not have a kid) are shown too:

+----+--------+------+-------+
| id | parent | pid  | child | 
+----+--------+------+-------+
|  1 | Alex   |   1  | Kate  |
|  1 | Alex   |   1  | Lia   |
|  3 | Cath   |   3  | Mary  |
|  2 | Bill   | NULL | NULL  |
|  4 | Dale   | NULL | NULL  |
|  5 | Evan   | NULL | NULL  |
+----+--------+------+-------+

Where did all those NULL come from? Well, MySQL (or any other RDBMS you may use) will not know what to put there as these parents have no match (kid), so there is no pid nor child.name to match with those parents. So, it puts this special non-value called NULL.

My point is that these NULLs are created (in the result set) during the LEFT OUTER JOIN.

So, if we want to show only the parents that do NOT have a kid, we can add a WHERE child.pid IS NULL to the LEFT JOIN above. The WHERE clause is evaluated (checked) after the JOIN is done. So, it's clear from the above result that only the last three rows where the pid is NULL will be shown:

SELECT id,  parent.name AS parent
     , pid, child.name  AS child

FROM
        parent  LEFT JOIN  child
  ON   parent.id    =    child.pid

WHERE child.pid IS NULL

Result:

+----+--------+------+-------+
| id | parent | pid  | child | 
+----+--------+------+-------+
|  2 | Bill   | NULL | NULL  |
|  4 | Dale   | NULL | NULL  |
|  5 | Evan   | NULL | NULL  |
+----+--------+------+-------+

Now, what happens if we move that IS NULL check from the WHERE to the joining ON clause?

SELECT id,  parent.name AS parent
     , pid, child.name  AS child

FROM
        parent  LEFT JOIN  child
  ON   parent.id    =    child.pid
  AND  child.pid IS NULL

In this case the database tries to find rows from the two tables that match these conditions. That is, rows where parent.id = child.pid AND child.pid IN NULL. But it can find no such match because no child.pid can be equal to something (1, 2, 3, 4 or 5) and be NULL at the same time!

So, the condition:

ON   parent.id    =    child.pid
AND  child.pid IS NULL

is equivalent to:

ON   1 = 0

which is always False.

So, why does it return ALL rows from the left table? Because it's a LEFT JOIN! And left joins return rows that match (none in this case) and also rows from the left table that do not match the check (all in this case):

+----+--------+------+-------+
| id | parent | pid  | child | 
+----+--------+------+-------+
|  1 | Alex   | NULL | NULL  |
|  2 | Bill   | NULL | NULL  |
|  3 | Cath   | NULL | NULL  |
|  4 | Dale   | NULL | NULL  |
|  5 | Evan   | NULL | NULL  |
+----+--------+------+-------+

I hope the above explanation is clear.

Sidenote (not directly related to your question): Why on earth doesn't Pan show up in none of our JOINs? Because his pid is NULL and NULL in the (not common) logic of SQL is not equal to anything so it can't match with any of the parent ids (which are 1,2,3,4 and 5). Even if there was a NULL there, it still wouldn't match because NULL does not equal anything, not even NULL itself (it's a very strange logic, indeed!). That's why we use the special check IS NULL and not a = NULL check.

So, will Pan show up if we do a RIGHT JOIN ? Yes, it will! Because a RIGHT JOIN will show all results that match (the first INNER JOIN we did) plus all rows from the RIGHT table that don't match (which in our case is one, the (NULL, 'Pan') row.

SELECT id,  parent.name AS parent
     , pid, child.name  AS child

FROM
        parent  RIGHT JOIN  child
  ON   parent.id     =    child.pid

Result:

+------+--------+------+-------+
| id   | parent | pid  | child | 
+---------------+------+-------+
|   1  | Alex   |   1  | Kate  |
|   1  | Alex   |   1  | Lia   |
|   3  | Cath   |   3  | Mary  |
| NULL | NULL   | NULL | Pan   |
+------+--------+------+-------+

Unfortunately, MySQL does not have FULL JOIN. You can try it in other RDBMSs, and it will show:

+------+--------+------+-------+
|  id  | parent | pid  | child | 
+------+--------+------+-------+
|   1  | Alex   |   1  | Kate  |
|   1  | Alex   |   1  | Lia   |
|   3  | Cath   |   3  | Mary  |
|   2  | Bill   | NULL | NULL  |
|   4  | Dale   | NULL | NULL  |
|   5  | Evan   | NULL | NULL  |
| NULL | NULL   | NULL | Pan   |
+------+--------+------+-------+

The NULL part is calculated AFTER the actual join, so that is why it needs to be in the where clause.