Firebird Null Guide | Predicates | EXISTS And SINGULAR

`SINGULAR`

SINGULAR is an InterBase/Firebird extension to the SQL standard.It is often described as returning true if exactly one row in the subquery meets the search condition.By analogy with EXISTS this would make you expect that SINGULAR too will only ever return true or false.After all, a result set has either exactly 1 row or a different number of rows.Unfortunately, all versions of Firebird up to and including 2.0 have a bug that causes NULL results in a number of cases.The behaviour is pretty inconsistent, but at the same time fully reproducible.For instance, on a column A containing (1, NULL, 1), a SINGULAR test with subselect “A=1” returns NULL, but the same test on a column with (1, 1, NULL) returns false.Notice that only the insertion order is different here!

To make matters worse, all versions prior to 2.0 sometimes return NULL for NOT SINGULAR where false or true is returned for SINGULAR.In 2.0, this at least doesn’t happen anymore: it’s either false vs. true or twice NULL.

The code has been fixed for Firebird 2.1; from that version onward SINGULAR will return:

false if the search condition is never true (this includes the empty-set case);
true if the search condition is true for exactly 1 row;
false if the search condition is true for more than 1 row.

Whether the other rows yield false, NULL or a combination thereof, is irrelevant.

NOT SINGULAR will always return the opposite of SINGULAR (as is already the case in 2.0).

In the meantime, if there’s any chance that the search condition may evolve to NULL for one or more rows, you should always add an IS NOT NULL condition to your [NOT] SINGULAR clauses, e.g.like this:

... SINGULAR( SELECT * from MyTable
              WHERE MyField > 38
              AND MyField IS NOT NULL )

Searches

If the search condition of a SELECT, UPDATE or DELETE statement resolves to NULL for a certain row, the effect is the same as if it had been false.Put another way: if the search expression is NULL, the condition is not met, and consequently the row is not included in the output set (or is not updated/deleted).

Note	The search condition or search expression is the `WHERE` clause minus the `WHERE` keyword itself.

Some examples (with the search condition in boldface):

SELECT Farmer, Cows FROM Farms WHERE Cows > 0 ORDER BY Cows

The above statement will return the rows for farmers that are known to possess at least one cow.Farmers with an unknown (NULL) number of cows will not be included, because the expression “NULL > 0” returns NULL.

SELECT Farmer, Cows FROM Farms WHERE NOT (Cows > 0) ORDER BY Cows

Now, it’s tempting to think that this will return “all the other records” from the Farms table, right?But it won’t — not if the Cows column contains any NULLs.Remember that not(NULL) is itself NULL.So for any row where Cows is NULL, “Cows > 0” will be NULL, and “NOT (Cows > 0)” will be NULL as well.

SELECT Farmer, Cows, Sheep FROM Farms WHERE Cows + Sheep > 0

On the surface, this looks like a query returning all the farms that have at least one cow and/or sheep (assuming that neither Cows nor Sheep can be a negative number).However, if farmer Fred has 30 cows and an unknown number of sheep, the sum Cows + Sheep becomes NULL, and the entire search expression boils down to “NULL > 0”, which is… you got it.So despite his 30 cows, our friend Fred won’t make it into the result set.

As a last example, we shall rewrite the previous statement so that it will return any farm which has at least one animal of a known kind, even if the other number is NULL.To do that, we exploit the fact that “NULL or true” returns true — one of the rare occasions where a NULL operand doesn’t render the entire expression NULL:

SELECT Farmer, Cows, Sheep FROM Farms WHERE Cows > 0 OR Sheep > 0

This time, Fred’s thirty cows will make the first comparison true, while the sheep bit is still NULL.So we have “true or NULL”, which is true, and the row will be included in the output set.

Caution

If your search condition contains one or more IN predicates, there is the additional complication that some of the list elements (or subselect results) may be NULL.The implications of this are discussed in [nullguide-pred-in].

Sorts

In Firebird 2, NULLs are considered “smaller” than anything else when it comes to sorting.Consequently, they come first in ascending sorts and last in descending sorts.You can override this default placement by adding a NULLS FIRST or NULLS LAST directive to the ORDER BY clause.

In earlier versions, NULLs were always placed at the end of a sorted set, no matter whether the order was ascending or descending.For Firebird 1.0, that was the end of the story: NULLs would always come last in any sorted set, period.Firebird 1.5 introduced the NULLS FIRST/LAST syntax, so you could force them to the top or bottom.

To sum it all up:

Table 1. `NULL`s placement in ordered columns
Ordering	`NULL`s placement
Ordering	Firebird 1	Firebird 1.5	Firebird 2
`order by Field [asc]`	bottom	bottom	top
`order by Field desc`	bottom	bottom	bottom
`order by Field [asc \| desc] nulls first`	—	top	top
`order by Field [asc \| desc] nulls last`	—	bottom	bottom

Specifying NULLS FIRST on an ascending or NULLS LAST on a descending sort in Firebird 2 is of course rather pointless, but perfectly legal.The same is true for NULLS LAST on any sort in Firebird 1.5.

Note

If you override the default NULLs placement, no index will be used for sorting.In Firebird 1.5, that is the case with NULLS FIRST.In 2.0 and higher, with NULLS LAST on ascending and NULLS FIRST on descending sorts.
If you open a pre-2.0 database with Firebird 2, it will show the old NULL ordering behaviour (that is: at the bottom, unless overridden by NULLS FIRST).A backup-restore cycle will fix this, provided that at least the restore is executed with Firebird 2’s gbak!
Firebird 2.0 has a bug that causes the NULLS FIRST|LAST directive to fail under certain circumstances with SELECT DISTINCT.See the bugs list for more details.

Warning

Don’t be tempted into thinking that, because NULL is now the “smallest thing” in sorts, an expression like “NULL < 3” will return true in Firebird 2 and up.It won’t.Using NULL in this kind of expression will always give a NULL outcome.

Aggregate functions

The aggregate functions — COUNT, SUM, AVG, MAX, MIN and LIST — don’t handle NULL in the same way as ordinary functions and operators.Instead of returning NULL as soon as a NULL operand is encountered, they only take non-NULL fields into consideration while computing the outcome.That is, if you have this table:

MyTable
ID	Name	Amount
1	John	37
2	Jack	`NULL`
3	Jim	5
4	Joe	12
5	Josh	`NULL`

...the statement select sum(Amount) from MyTable returns 54, which is 37 + 5 + 12.Had all five fields been summed, the result would have been NULL.For AVG, the non-NULL fields are summed and the sum divided by the number of non-NULL fields.

There is one exception to this rule: COUNT(*) returns the count of all rows, even rows whose fields are all NULL.But COUNT(FieldName) behaves like the other aggregate functions in that it only counts rows where the specified field is not NULL.

Another thing worth knowing is that COUNT(*) and COUNT(FieldName) never return NULL: if there are no rows in the set, both functions return 0.COUNT(FieldName) also returns 0 if all FieldName fields in the set are NULL.The other aggregate functions return NULL in such cases.Be warned that SUM even returns NULL if used on an empty set, which is contrary to common logic (if there are no rows, the average, maximum and minimum are undefined, but the sum is known to be zero).

Now let’s put all that knowledge in a table for your easy reference:

Table 1. Aggregate function results with different column states
Function	Results
Function	Empty set	All-`NULL` set or column	Other sets or columns
`COUNT(*)`	0	Total number of rows	Total number of rows
`COUNT(Field)`	0	0	Number of rows where `Field` is not `NULL`
`MAX`, `MIN`	`NULL`	`NULL`	Max or min value found in the column
`SUM`	`NULL`	`NULL`	Sum of non-`NULL` values in the column
`AVG`	`NULL`	`NULL`	Average of non-`NULL` values in the column.This equals `SUM(Field) / COUNT(Field)`.^[1]
`LIST`^[2]	`NULL`	`NULL`	Comma-separated string concatenation of non-`NULL` values in the column

1. If Field is of an integer type, AVG is always rounded towards 0. For instance, 6 non-null INT records with a sum of -11 yield an average of -1, not -2.

2. LIST was added in Firebird 2.1

The `GROUP BY` clause

A GROUP BY clause doesn’t change the aggregate function logic described above, except that it is now applied to each group individually rather than to the result set as a whole.Suppose you have a table Employee, with fields Dept and Salary which both allow NULLs, and you run this query:

SELECT Dept, SUM(Salary) FROM Employee GROUP BY Dept

The result may look like this (the row where Dept is <null> may be at the top or bottom, depending on your Firebird version):

DEPT                     SUM

=====================

<null> 219465.19000 266643.00100 155262.50110 130442.81115 13480000.00120 <null>121 110000.00123 390500.00

First notice that the people whose department is unknown (`NULL`) are grouped together, although you can't say that they have the same _value_ in the Dept field.
But the alternative would have been to give each of those records a "`group`" of their own.
Not only would this possibly add a huge number of lines to the output, but it would also defeat the purpose of __group__ing: those lines wouldn't be aggregates, but simple "```SELECT Dept, Salary```" rows.
So it makes sense to group the `NULL` depts by their state and the rest by their value.

Anyway, the `Dept` field is not what interests us most.
What does the aggregate `SUM` column tell us?
That all salaries are non-`NULL`, except in department 120?
No.
All we can say is that in every department except 120, there is at least one employee with a known salary in the database.
Each department _may_ contain `NULL` salaries;
in dept. 120 _all_ the salaries are `NULL`.

You can find out more by throwing in one or more `COUNT()` columns.
For instance, if you want to know the number of `NULL` salaries in each group, add a column "```COUNT({asterisk}) – COUNT(Salary)```".

Counting frequencies

A GROUP BY clause can be used to report the frequencies with which values occur in a table.In that case you use the same field name several times in the query statement.Let’s say you have a table TT with a column A whose contents are { 3, 8, NULL, 6, 8, -1, NULL, 3, 1 }.To get a frequencies report, you could use:

SELECT A, COUNT(A) FROM TT GROUP BY A

which would give you this result:

A            COUNT
============ ============
          -1            1
           1            1
           3            2
           6            1
           8            2
      <null>            0

Oops — something went wrong with the NULL count, but what? Remember that COUNT(FieldName) skips all NULL fields, so with COUNT(A) the count of the <null> group can only ever be 0.Reformulate your query like this:

SELECT A, COUNT(*) FROM TT GROUP BY A

and the correct value will be returned (in casu 2).

The `HAVING` clause

HAVING clauses can place extra restrictions on the output rows of an aggregate query — just like WHERE clauses do in record-by-record queries.A HAVING clause can impose conditions on any output column or combination of columns, aggregate or not.

As far as NULL is concerned, the following two facts are worth knowing (and hardly surprising, I would guess):

Rows for which the HAVING condition evaluates to NULL won’t be included in the result set.(“Only true is good enough.”)
“HAVING <col> IS [NOT] NULL” is a legal and often useful condition, whether <col> is aggregate or not.(But if <col> is non-aggregate, you may save the engine some work by changing HAVING to WHERE and placing the condition before the “GROUP BY” clause.This goes for any condition on non-aggregate columns.)

For instance, adding the following clause to the example query from the “GROUP BY” paragraph:

...HAVING Dept IS NOT NULL

will prevent the first row from being output, whereas this one:

...HAVING SUM(Salary) IS NOT NULL

suppresses the sixth row (the one with Dept = 120).

Conditional statements and loops

`IF` statements

If the test expression of an IF statement resolves to NULL, the THEN clause is skipped and the ELSE clause — if present — executed.In other words, NULL and false have the same effect in this context.So in situations where you would logically expect false but NULL is returned, no harm will be done.However, we’ve already seen examples of NULL being returned where you would expect true, and that does affect the flow of the code!

Below are some examples of the seemingly paradoxical (but perfectly correct) results you can get if NULLs creep into your IF statements.

Tip	If you use Firebird 2 or higher, you can avoid all the pitfalls discussed here, simply by using `[NOT] DISTINCT` instead of the ‘`=`’ and “`<>`” operators!

Equals (‘=’)
```
if (a = b) then
  MyVariable = 'Equal';
else
  MyVariable = 'Not equal';
```
If a and b are both NULL, MyVariable will yet be “Not equal” after executing this code.The reason is that the expression “a = b” yields NULL if at least one of them is NULL.With a NULL test expression, the THEN block is skipped and the ELSE block executed.
Not equals (‘<>’)
```
if (a <> b) then
  MyVariable = 'Not equal';
else
  MyVariable = 'Equal';
```
Here, MyVariable will be “Equal” if a is NULL and b isn’t, or vice versa.The explanation is analogous to that of the previous example.

So how should you set up equality tests that do give the logical result under all circumstances, even with NULL operands?In Firebird 2 you can use DISTINCT, as already shown (see Testing DISTINCTness). With earlier versions, you’ll have to write some more code.This is discussed in the section [nullguide-testing-equality], later on in this guide.For now, just remember that you have to be very careful with IF conditions that may resolve to NULL.

Another aspect you shouldn’t forget is the following: a NULL test expression may behave like false in an IF condition, but it doesn’t have the value false.It’s still NULL, and that means that its inverse will also be NULL — not “true”.As a consequence, inverting the test expression and swapping the THEN and ELSE blocks may change the behaviour of the IF statement.In binary logic, where only true and false can occur, such a thing could never happen.

To illustrate this, let’s refactor the last example:

Not not equals (“not (.. <> ..)”)
```
if (not (a <> b)) then
  MyVariable = 'Equal';
else
  MyVariable = 'Not equal';
```
In the original version, if one operand was NULL and the other wasn’t (so they were intuitively unequal), the result was “Equal”.Here, it’s “Not equal”.The explanation: one operand is NULL, therefore “a <> b” is NULL, therefore “not(a <> b)” is NULL, therefore ELSE is executed.While this result is correct where the original had it wrong, there’s no reason to rejoice: in the refactored version, the result is also “Not equal” if both operands are NULL — something that the original version “got right”.

Of course, as long as no operand in the test expression can ever be NULL, you can happily formulate your IF statements like above.Also, refactoring by inverting the test expression and swapping the THEN and ELSE blocks will always preserve the functionality, regardless of the complexity of the expressions — as long as they aren’t NULL.What’s especially treacherous is when the operands are almost always non-NULL, so in the vast majority of cases the results will be correct.In such a situation those rare NULL cases may go unnoticed for a long time, silently corrupting your data.

`CASE` expression

Firebird introduced the CASE construct in version 1.5, with two syntactic variants.The first one is called the simple syntax:

case <expression>
  when <exp1> then <result1>
  when <exp2> then <result2>
  ...
  [else <defaultresult>]
end

This one works more or less like a Pascal case or a C switch construct: <expression> is compared to <exp1>, <exp2> etc., until a match is found, in which case the corresponding result is returned.If there is no match and there is an ELSE clause, <defaultresult> is returned.If there is no match and no ELSE clause, NULL is returned.

It is important to know that the comparisons are done with the ‘=’ operator, so a null <expression> will not match a null <expN>.If <expression> is NULL, the only way to get a non-NULL result is via the ELSE clause.

It is OK to specify NULL (or any other valid NULL expression) as a result.

The second, or searched syntax is:

case
  when <condition1> then <result1>
  when <condition2> then <result2>
  ...
  [else <defaultresult>]
end

Here, the <conditionN>s are tests that give a ternary boolean result: true, false, or NULL.Once again, only true is good enough, so a condition like “A = 3” — or even “A = null” — is not satisfied when A is NULL.Remember though that “IS [NOT] NULL” never returns NULL: if A is NULL, the condition “A is null” returns true and the corresponding <resultN> will be returned.In Firebird 2+ you can also use “IS [NOT] DISTINCT FROM” in your conditions — this operator too will never return NULL.

`WHILE` loops

When evaluating the condition of a WHILE loop, NULL has the same effect as in an IF statement: if the condition resolves to NULL, the loop is not (re)entered — just as if it were false.Again, watch out with inversion using NOT: a condition like

while ( Counter > 12 ) do

will skip the loop block if Counter is NULL, which is probably what you want, but:

while ( not Counter > 12 ) do

will also skip if Counter is NULL.Maybe this is also exactly what you want — just be aware that these seemingly complementary tests both exclude NULL counters.

`FOR` loops

To avoid any possible confusion, let us emphasise here that FOR loops in Firebird PSQL have a totally different function than WHILE loops, or for loops in general programming languages.Firebird FOR loops have the form:

for <select-statement> into <var-list> do <code-block>

and they will keep executing the code block until all the rows from the result set have been retrieved, unless an exception occurs or a BREAK, LEAVE or EXIT statement is encountered.Fetching a NULL, or even row after row filled with NULLs, does not terminate the loop!

SINGULAR