Relational databases define the term “Functional Dependency” as such (from Wikipedia):

In relational database theory, a functional dependency is a constraint between two sets of attributes in a relation from a database. In other words, functional dependency is a constraint that describes the relationship between attributes in a relation.

In SQL, functional dependencies appear whenever there is a unique constraint (e.g. a primary key constraint). Let’s assume the following:

CREATE TABLE actor (
  actor_id BIGINT NOT NULL PRIMARY KEY,
  first_name VARCHAR(50) NOT NULL,
  last_name VARCHAR(50) NOT NULL
);

It can be said that both FIRST_NAME and LAST_NAME each have a functional dependency on the ACTOR_ID column.

Nice. So What?

This isn’t just some mathematical statement that can be applied to unique constraints. It’s extremely useful for SQL. It means that for every ACTOR_ID value, there can be only one (functionally dependent) FIRST_NAME and LAST_NAME value. The other way around, this isn’t true. For any given FIRST_NAME and/or LAST_NAME value, we can have multiple ACTOR_ID values, as we can have multiple actors by the same names.

Because there can be only one corresponding FIRST_NAME and LAST_NAME value for any given ACTOR_ID value, we can omit those columns in the GROUP BY clause. Let’s assume also:

CREATE TABLE film_actor (
  actor_id BIGINT NOT NULL,
  film_id BIGINT NOT NULL,

  PRIMARY KEY (actor_id, film_id),
  FOREIGN KEY (actor_id) REFERENCS actor (actor_id),
  FOREIGN KEY (film_id) REFERENCS film (film_id)
);

Now, if we want to count the number of films per actor, we can write:

SELECT
  actor_id, first_name, last_name, COUNT(*)
FROM actor
JOIN film_actor USING (actor_id)
GROUP BY actor_id
ORDER BY COUNT(*) DESC

This is extremely useful as it saves us from a lot of typing. In fact, the way GROUP BY semantics is defined, we can put all sorts of column references in the SELECT clause, which are any of:

• Column expressions that appear in the GROUP BY clause
• Column expressions that are functionally dependent on the set of column expressions in the GROUP BY clause
• Aggregate functions

Unfortunately, Not Everyone Supports This

If you’re using Oracle, for instance, you can’t make use of the above. You’ll need to write the classic, equivalent version where all the non-aggregate column expressions appearing in the SELECT clause must also appear in the GROUP BY clause

SELECT
  actor_id, first_name, last_name, COUNT(*)
FROM actor
JOIN film_actor USING (actor_id)
GROUP BY actor_id, first_name, last_name
--                 ^^^^^^^^^^  ^^^^^^^^^ unnecessary
ORDER BY COUNT(*) DESC

Further reading:

• Wikipedia article on functional dependency
• How SQL GROUP BY Should Have Been Designed – Like Neo4j’s Implicit GROUP BY
• Do You Really Understand SQL’s GROUP BY and HAVING clauses?
• How to Translate SQL GROUP BY and Aggregations to Java 8
• GROUP BY ROLLUP / CUBE