Null (SQL) - Check Constraints and Foreign Keys

Check Constraints and Foreign Keys

The primary place in which SQL three-valued logic intersects with SQL Data Definition Language (DDL) is in the form of check constraints. A check constraint placed on a column operates under a slightly different set of rules than those for the DML WHERE clause. While a DML WHERE clause must evaluate to True for a row, a check constraint must not evaluate to False. (From a logic perspective, the designated values are True and Unknown.) This means that a check constraint will succeed if the result of the check is either True or Unknown. The following example table with a check constraint will prohibit any integer values from being inserted into column i, but will allow Null to be inserted since the result of the check will always evaluate to Unknown for Nulls.

CREATE TABLE t ( i INTEGER, CONSTRAINT ck_i CHECK ( i < 0 AND i = 0 AND i > 0 ) );

Because of the change in designated values relative to the WHERE clause, from a logic perspective the law of excluded middle is a tautology for CHECK constraints, meaning CHECK (p OR NOT p) always succeeds. Furthermore, assuming Nulls are to be interpreted as existing but unknown values, some pathological CHECKs like the one above allow insertion of Nulls that could never be replaced by any non-null value.

In order to constrain a column to reject Nulls, the NOT NULL constraint can be applied, as shown in the example below. The NOT NULL constraint is semantically equivalent to a check constraint with an IS NOT NULL predicate.

CREATE TABLE t ( i INTEGER NOT NULL );

By default check constraints against foreign keys succeed if any of the fields in such keys are Null. For example the table

CREATE TABLE Books ( title VARCHAR(100), author_last VARCHAR(20), author_first VARCHAR(20), FOREIGN KEY (author_last, author_first) REFERENCES Authors(last_name, first_name));

would allow insertion of rows where author_last or author_first are NULL irrespective of how the table Authors is defined or what it contains. More precisely, a null in any of these fields would allow any value in the other one, even on that is not found in Authors table. For example if Authors contained only ('Doe', 'John'), then ('Smith', NULL) would satisfy the foreign key constraint. SQL-92 added two extra options for narrowing down the matches in such cases. If MATCH PARTIAL is added after the REFERENCES declaration then any non-null must match the foreign key, e. g. ('Doe', NULL) would still match, but ('Smith', NULL) would not. Finally, if MATCH FULL is added then ('Smith', NULL) would not match the constraint either, but (NULL, NULL) would still match it.