Advanced SQL: Relational division in jOOQ

Posted on by lukaseder

Relational algebra has its treats. One of the most academic features is the relational division. It is hardly ever used, but comes in handy every now and then. And when you need it, you’ll probably hate yourself for having slept during the relevant classes at the university.

What is relational division?

Relational division is the inverse of a cross join operation. The following is an approximate definition of a relational division:

Assume the following cross join / cartesian product 
C = A × B 

Then it can be said that 
A = C ÷ B 
B = C ÷ A

What does it mean, typically?

Let’s have a look at the sample provided on Wikipedia:

Wikipedia example of a relational division
Wikipedia example of a relational division

This looks sensible. The division of Completed ÷ DBProject leads to a list of students that have completed all projects.

Now how to phrase that in SQL??

That’s not so simple as it looks. The most commonly documented solution involves a doubly-nested select statement using anti-joins. In human language (using double negative), it is like Fred and Sarah saying “there is no DBProject that we have not Completed“. Or in SQL:

SELECT DISTINCT "c1".Student FROM Completed "c1"
WHERE NOT EXISTS (
  SELECT 1 FROM DBProject
  WHERE NOT EXISTS (
    SELECT 1 FROM Completed "c2"
    WHERE "c2".Student = "c1".Student
    AND "c2".Task = DBProject.Task
  )
)

Now, no one sane wants to remember this just for the 1-2 times in a SQL developer’s life that they actually need it. So they use jOOQ, which wraps up the above monster in a concise syntax:

create.select().from(
  Completed.divideBy(DBProject)
           .on(Completed.Task.equal(DBProject.Task))
           .returning(Completed.Student)
);

Note that from the above SQL statement, it is immediately clear that proper indexing is of the essence. Be sure to have indexes on all columns referenced from the on(…) and returning(…) clauses.

More information

For more information about relational division and some nice, real-life examples, see

Published by lukaseder

I made jOOQ

2 thoughts on “Advanced SQL: Relational division in jOOQ”

  1. Nice article. I was wondering if this is a valid alternate query:

    SELECT DISTINCT c1.student
FROM completed c1
WHERE (
    SELECT *
    FROM dbproject EXCEPT (
        SELECT task
        FROM completed c2
        WHERE c2.student = c1.student 
        INTERSECT 
        SELECT *
        FROM dbproject)) IS NULL

    Obviously yours is more succinct.

    Reply

    1. I think your query is a bit informal? E.g. the INTERSECT assumes DBProject only has a task column? And the IS NULL predicate will raise an exception if the subquery produces more than 1 row.

      Reply

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