as Escher’s cube
There have been endless discussions already if NULL should be implemented in relational databases, and if it should even be included in the relational theory. My favourite quote on this subject is from the person who helped Ted Codd to divulgate – and probably refine – his relational algebra:
I hate NULL.
Chris Date
I tend to hate it too, except that sometimes it is necessary. But my point is totally different from Date’s. I have nothing against the idea of NULL, I just think that it is wrong by design in SQL.
Because NULL has two incompatible meanings, and depending from the context, the SQL standard and implementations randomly choose one of them.
Note: SQL:2011 (and probably other SQL standard versions) defines NULL as the absence of any data value. But this definition is not consistent with the semantics specified in the document itself.
The theory
Ted Codd didn’t propose anything corresponding to NULL in his fist version of the relational algebra. In a later document, he proposed two markers. A marker is something that is placed where you’d expect a value, but is not a regular value. These markers were:
- I-MARKER: Non-applicable, absent value;
- A-MARKER: Applicable but unknown value.
This idea was later abandoned by Codd. Anyway, it has very little to do with SQL design choice of merging these markers into one.
Personally, I tend to believe that Codd’s idea would be a bit overcomplicated for most common practical cases. But it is consistent – actually, his purpose was to elaborate a mathematically consistent system, and he did.
SQL doesn’t have the original theory’s consistency, but it is more practical. Yet, about NULL, I think it should have chosen one of the following: implementing both these markers, implementing only one of them with consistent semantics, or implementing none.
SQL’s inconsistency
Again: my point is that SQL merged two ideas into one, and mixed their semantics in an inconsistent way, so the meaning of NULL depends on the context. I will describe the behaviors of NULL in different contexts.
Comparisons
NULL = NULL returns NULL. In a previous article I explained how to properly compare values that could be NULL.
This makes perfectly sense if NULL is unknown. Is an unknown value equal to an unknown value? The answer is unknown: they could be the same value or not.
But if NULL is a missing value, this is puzzling. Is a missing value identical to another missing value? The answer in my opinion should be yes. But for sure, the answer shouldn’t be a missing value itself.
However, consider this expression:
null_column >= 100 OR null_columns < 100
It returns NULL. This defies the idea that comparisons make sense if NULL is an unknown value. Comparisons are simply inconsistent in all cases.
NULL and UNKNOWN
For NULL-safe comparisons, the IS NULL and IS NOT NULL operators can be used. They are synonyms for IS UNKNOWN and IS NOT UNKNOWN, which suggests that NULL is an unknown value.
Scalar expressions
Scalar expressions seem to consider NULL as an unknown value. Scalar subqueries are a different matter, see below. For example:
1 + NULL = NULL
If NULL was a missing value, it would behave exactly as 0, so the above expression would return 1.
Aggregate functions
Aggregate functions are those that accept any number of 1-column rows and return exactly one value.
COUNT(*) returns the number of rows. If a row only contains NULLs, it still counts as one. So, in this context, NULL is considered as an unknown existing value.
COUNT(column) ignores NULLs. This means that, in this context, NULL is considered as a missing value.
For a funny fact about COUNT() and NULL, see this old article by Baron Schwartz.
Other aggregate functions consider NULL as a missing value – so it is ignored by MIN(), MAX(), AVG(), etc.
GROUP BY, DISTINCT
GROUP BY and DISTINCT treat NULL as a regular value.
This could be consistent with both interpretations of NULL.
ORDER BY
Some DBMSs return NULLs before values, others return values first. I’d like to see more consistency, but in both cases it is just a practical choice that does not contradict any interpretation of NULL.
Outer joins
Left, right and full outer can return rows that have no match in the other table. When this happens, columns from the other table are populated with NULLs.
This behaviour treats NULLs as absent values.
It is interesting to note that, while in most cases this is just fine, sometimes this behaviour is ambiguous. Consider the following query:
SELECT t1.a, t2.b
FROM t1 LEFT JOIN t2
ON t1.a = t2.b OR t2.b IS NULL;In the results, it is impossible to distinguish an absent match in t2 from a match in t2 where the b column is NULL.
This shows that, even if NULL represents an absent value, this is not enough to answer joins properly, as it doesn’t say anything about why the value is missing.
Scalar subqueries
Scalar subqueries are nested queries that return one row consisting of one column. In practice, they return a single value, or NULL in case no value was found. And this is the trap: normally, you don’t know if a subquery returned NULL because it found it in a table, or because it found nothing.
As mentioned for joins, at least one more marker would be needed to eliminate ambiguity.
Unicity
SELECT DISTINCT always treats NULL as a normal value. This seems to me coherent with considering NULL as a missing value (someone could disagree). But it is incoherent with the idea of treating it as an unknown value.
Primary keys don’t allow NULL columns. Primary keys logically identify each row, this is one of the pillars of relational algebra. So this is consistent with treating NULL as an unknown value. But if the primary key consists of multiple columns, it should be allowed to store NULL markers – as long as no row only consists of NULLs and unicity is certain. Of course this is just a theoretical objection, since a practical implementation would probably be not desirable.
Most DBMSs allow to insert any number of NULLs in a UNIQUE index. This is consistent with treating NULL as a missing value: an absence doesn’t duplicate another absence.
Other DBMSs only allow one NULL per duplicate index. This is not consistent for any NULL interpretations. Not with absences, as mentioned earlier. And not with unknown values: an unknown value could duplicate another unknown value, but it could also duplicate any known value – the chances are exactly the same. So NULL shouldn’t be allowed if the table contains more than one row.
Some DBMSs, like Db2, don’t allow any NULL value in UNIQUE indexes. This can be a good idea for any interpretation of NULL, as it’s the only way to be sure that no constraint is violated.
Other meanings of NULL
NULL also has a couple of additional meanings:
- Any value;
- Default value.
Default
The meaning is default when we create a sort of “default row”. For example, we could have a table user_setting, with the columns user_id, setting_name and setting_value. When a user changes a preference, a row is created. But all preferences have a default value, which is used by all users who didn’t change it. The rows with the default values will have a user_id set to NULL.
This technique is not particularly efficient. With many DBMSs, this event prevents us to create a primary key on (user_setting, setting_name). It’s usually better to use a special value, like 0 or -1 – which is not special for the DBMS, but it’s special for us.
We can also use NULL with meaning in stored procedures. When NULL is passed as an argument, the procedure will assign a default value.
Another example is variables. In most DBMSs that support some type of variables, an unset variable is NULL.
Any value
Sometimes a row represents a fact that is true for any value. You can translate it into English as “any object”, which is usually equivalent to “all objects”.
For example, your website may have contents that appear on multiple pages. You may have a table for those contents, which has a page_id column. Where this columns is set to NULL, the content is included in all pages.
NULL and DML
The way NULL is used in CREATE TABLE and ALTER TABLE statements is quite strange. This does not directly affect the semantics meaning of NULL, but it is worth mentioning here.
NULL and NOT NULL
It is possible to specify NULL or NOT NULL to determine if a columns should allow NULLs or not. This is absolutely reasonable.
What I consider less reasonable is that, if we don’t specify this clause, NULLs will be permitted. Whichever meaning you associate to NULL, it doesn’t make sense for most columns.
Even worse, there is an exception: for columns that are part of the primary key, NOT NULL is the default. This is surely confusing for whoever is not familiar with DML.
In my opinion, NULL or NOT NULL should always be specified.
[NOT] NULL and DEFAULT clauses
Columns may have DEFAULT values or not. The DEFAULT value applies if no value was specified in the INSERT statement, while it has no effect during an UPDATE. I have absolutely nothing against this.
But what happens if no value is specified on INSERT for a column that doesn’t have a DEFAULT value? Here’s the funny part: it depends if the column can contain NULLs or not.
If it is allowed, NULL is inserted. If it is not, the client will receive an error. In my opinion, this difference is confusing. It is also error prone: if a column is not specified, it is possible that the author of the query simply forgot it. The only exceptions should be the ones for which a DEFAULT was defined.
About specific implementations
Every SQL implementation is different, and none of them reflects a big portion of the standard. A couple of them deserve some words.
All of the below oddities is documented and should be considered as a design choice, not a bug.
PostgreSQL
PostgreSQL has several markers, or special values. NULL is special even between them.
SELECT FLOAT8 'Infinity' = FLOAT8 'Infinity';This expression returns true, but this is wrong. Some infinities are bigger than others. PostgreSQL allows us to talk about infinity, but it treats is like a regular number.
If you consider NULL as an absence, the result is funny. The number of points in a plane is the number of points in a straight line, but two absences are not equal.
Oracle
Oracle is fantastic in this respect. Sometimes it treats NULL as inconsistently as standard SQL. Sometimes it treats it as… an empty string! Despite this, the documentation says:
Do not use null to represent a value of zero, because they are not equivalent.
I’m not going to dig more into this absurdity, so for more info see Oracle documentation.
SQLite
SQLite is kind enough to let us decide if NULL should be treated as one value in SELECT DISTINCT or not. By default it is. To change this behaviour, we can change the NULL_ALWAYS_DISTINCT macro and recompile the code.
Federico Razzoli