MySQL 8.0 Release Notes
MySQL 8.0 Source Code Documentation
The following discussion provides several examples of the ways in which MySQL detects functional dependencies. The examples use this notation:
{X} -> {Y}
Understand this as “X uniquely
determines Y,” which also
means that Y is functionally
dependent on X.
The examples use the world database, which
can be downloaded from
https://dev.mysql.com/doc/index-other.html. You can find details
on how to install the database on the same page.
The following query selects, for each country, a count of spoken languages:
SELECT co.Name, COUNT(*)
FROM countrylanguage cl, country co
WHERE cl.CountryCode = co.Code
GROUP BY co.Code;
co.Code is a primary key of
co, so all columns of co
are functionally dependent on it, as expressed using this
notation:
{co.Code} -> {co.*}
Thus, co.name is functionally dependent on
GROUP BY columns and the query is valid.
A UNIQUE index over a NOT
NULL column could be used instead of a primary key
and the same functional dependence would apply. (This is not
true for a UNIQUE index that permits
NULL values because it permits multiple
NULL values and in that case uniqueness is
lost.)
This query selects, for each country, a list of all spoken languages and how many people speak them:
SELECT co.Name, cl.Language,
cl.Percentage * co.Population / 100.0 AS SpokenBy
FROM countrylanguage cl, country co
WHERE cl.CountryCode = co.Code
GROUP BY cl.CountryCode, cl.Language;
The pair (cl.CountryCode,
cl.Language) is a two-column composite
primary key of cl, so that column pair
uniquely determines all columns of cl:
{cl.CountryCode, cl.Language} -> {cl.*}
Moreover, because of the equality in the
WHERE clause:
{cl.CountryCode} -> {co.Code}
And, because co.Code is primary key of
co:
{co.Code} -> {co.*}“Uniquely determines” relationships are transitive, therefore:
{cl.CountryCode, cl.Language} -> {cl.*,co.*}As a result, the query is valid.
As with the previous example, a UNIQUE key
over NOT NULL columns could be used instead
of a primary key.
An INNER JOIN condition can be used instead
of WHERE. The same functional dependencies
apply:
SELECT co.Name, cl.Language,
cl.Percentage * co.Population/100.0 AS SpokenBy
FROM countrylanguage cl INNER JOIN country co
ON cl.CountryCode = co.Code
GROUP BY cl.CountryCode, cl.Language;
Whereas an equality test in a WHERE
condition or INNER JOIN condition is
symmetric, an equality test in an outer join condition is not,
because tables play different roles.
Assume that referential integrity has been accidentally broken
and there exists a row of countrylanguage
without a corresponding row in country.
Consider the same query as in the previous example, but with a
LEFT JOIN:
SELECT co.Name, cl.Language,
cl.Percentage * co.Population/100.0 AS SpokenBy
FROM countrylanguage cl LEFT JOIN country co
ON cl.CountryCode = co.Code
GROUP BY cl.CountryCode, cl.Language;
For a given value of cl.CountryCode, the
value of co.Code in the join result is
either found in a matching row (determined by
cl.CountryCode) or is
NULL-complemented if there is no match
(also determined by cl.CountryCode). In
each case, this relationship applies:
{cl.CountryCode} -> {co.Code}
cl.CountryCode is itself functionally
dependent on {cl.CountryCode,
cl.Language} which is a primary key.
If in the join result co.Code is
NULL-complemented,
co.Name is as well. If
co.Code is not
NULL-complemented, then because
co.Code is a primary key, it determines
co.Name. Therefore, in all cases:
{co.Code} -> {co.Name}Which yields:
{cl.CountryCode, cl.Language} -> {cl.*,co.*}As a result, the query is valid.
However, suppose that the tables are swapped, as in this query:
SELECT co.Name, cl.Language,
cl.Percentage * co.Population/100.0 AS SpokenBy
FROM country co LEFT JOIN countrylanguage cl
ON cl.CountryCode = co.Code
GROUP BY cl.CountryCode, cl.Language;Now this relationship does not apply:
{cl.CountryCode, cl.Language} -> {cl.*,co.*}
Indeed, all NULL-complemented rows made for
cl is put into a single group (they have
both GROUP BY columns equal to
NULL), and inside this group the value of
co.Name can vary. The query is invalid and
MySQL rejects it.
Functional dependence in outer joins is thus linked to whether
determinant columns belong to the left or right side of the
LEFT JOIN. Determination of functional
dependence becomes more complex if there are nested outer
joins or the join condition does not consist entirely of
equality comparisons.
Suppose that a view on countries produces their code, their name in uppercase, and how many different official languages they have:
CREATE VIEW country2 AS
SELECT co.Code, UPPER(co.Name) AS UpperName,
COUNT(cl.Language) AS OfficialLanguages
FROM country AS co JOIN countrylanguage AS cl
ON cl.CountryCode = co.Code
WHERE cl.isOfficial = 'T'
GROUP BY co.Code;This definition is valid because:
{co.Code} -> {co.*}
In the view result, the first selected column is
co.Code, which is also the group column and
thus determines all other selected expressions:
{country2.Code} -> {country2.*}MySQL understands this and uses this information, as described following.
This query displays countries, how many different official
languages they have, and how many cities they have, by joining
the view with the city table:
SELECT co2.Code, co2.UpperName, co2.OfficialLanguages,
COUNT(*) AS Cities
FROM country2 AS co2 JOIN city ci
ON ci.CountryCode = co2.Code
GROUP BY co2.Code;This query is valid because, as seen previously:
{co2.Code} -> {co2.*}
MySQL is able to discover a functional dependency in the
result of a view and use that to validate a query which uses
the view. The same would be true if
country2 were a derived table (or common
table expression), as in:
SELECT co2.Code, co2.UpperName, co2.OfficialLanguages,
COUNT(*) AS Cities
FROM
(
SELECT co.Code, UPPER(co.Name) AS UpperName,
COUNT(cl.Language) AS OfficialLanguages
FROM country AS co JOIN countrylanguage AS cl
ON cl.CountryCode=co.Code
WHERE cl.isOfficial='T'
GROUP BY co.Code
) AS co2
JOIN city ci ON ci.CountryCode = co2.Code
GROUP BY co2.Code;