4.2. Value Expressions

4.2.1. Column References

A column can be referenced in the form:

correlation.columnname

correlation is the name of a table (possibly qualified with a schema name), or an alias for a table defined by means of a FROM clause. The correlation name and separating dot can be omitted if the column name is unique across all the tables being used in the current query. (See also Chapter 7.)

4.2.2. Positional Parameters

A positional parameter reference is used to indicate a value that is supplied externally to an SQL statement. Parameters are used in SQL function definitions and in prepared queries. Some client libraries also support specifying data values separately from the SQL command string, in which case parameters are used to refer to the out-of-line data values. The form of a parameter reference is:

$number

For example, consider the definition of a function, dept, as:

CREATE FUNCTION dept(text) RETURNS dept
    AS $$ SELECT * FROM dept WHERE name = $1 $$
    LANGUAGE SQL;

Here the $1 references the value of the first function argument whenever the function is invoked.

4.2.3. Subscripts

If an expression yields a value of an array type, then a specific element of the array value can be extracted by writing

expression[subscript]

or multiple adjacent elements (an "array slice") can be extracted by writing

expression[lower_subscript:upper_subscript]

(Here, the brackets [ ] are meant to appear literally.) Each subscript is itself an expression, which must yield an integer value.

In general the array expression must be parenthesized, but the parentheses can be omitted when the expression to be subscripted is just a column reference or positional parameter. Also, multiple subscripts can be concatenated when the original array is multidimensional. For example:

mytable.arraycolumn[4]
mytable.two_d_column[17][34]
$1[10:42]
(arrayfunction(a,b))[42]

The parentheses in the last example are required. See Section 8.15 for more about arrays.

4.2.4. Field Selection

If an expression yields a value of a composite type (row type), then a specific field of the row can be extracted by writing

expression.fieldname

In general the row expression must be parenthesized, but the parentheses can be omitted when the expression to be selected from is just a table reference or positional parameter. For example:

mytable.mycolumn
$1.somecolumn
(rowfunction(a,b)).col3

(Thus, a qualified column reference is actually just a special case of the field selection syntax.) An important special case is extracting a field from a table column that is of a composite type:

(compositecol).somefield
(mytable.compositecol).somefield

The parentheses are required here to show that compositecol is a column name not a table name, or that mytable is a table name not a schema name in the second case.

In a select list (see Section 7.3), you can ask for all fields of a composite value by writing .*:

(compositecol).*

4.2.5. Operator Invocations

There are three possible syntaxes for an operator invocation:

OPERATOR(schema.operatorname)

Which particular operators exist and whether they are unary or binary depends on what operators have been defined by the system or the user. Chapter 9 describes the built-in operators.

4.2.6. Function Calls

The syntax for a function call is the name of a function (possibly qualified with a schema name), followed by its argument list enclosed in parentheses:

function_name ([expression [, expression ... ]] )

For example, the following computes the square root of 2:

sqrt(2)

The list of built-in functions is in Chapter 9. Other functions can be added by the user.

The arguments can optionally have names attached. See Section 4.3 for details.

4.2.7. Aggregate Expressions

An aggregate expression represents the application of an aggregate function across the rows selected by a query. An aggregate function reduces multiple inputs to a single output value, such as the sum or average of the inputs. The syntax of an aggregate expression is one of the following:

aggregate_name (expression [ , ... ] [ order_by_clause ] ) [ FILTER ( WHERE filter_clause ) ]
aggregate_name (ALL expression [ , ... ] [ order_by_clause ] ) [ FILTER ( WHERE filter_clause ) ]
aggregate_name (DISTINCT expression [ , ... ] [ order_by_clause ] ) [ FILTER ( WHERE filter_clause ) ]
aggregate_name ( * ) [ FILTER ( WHERE filter_clause ) ]
aggregate_name ( [ expression [ , ... ] ] ) WITHIN GROUP ( order_by_clause ) [ FILTER ( WHERE filter_clause ) ]

where aggregate_name is a previously defined aggregate (possibly qualified with a schema name) and expression is any value expression that does not itself contain an aggregate expression or a window function call. The optional order_by_clause and filter_clause are described below.

The first form of aggregate expression invokes the aggregate once for each input row. The second form is the same as the first, since ALL is the default. The third form invokes the aggregate once for each distinct value of the expression (or distinct set of values, for multiple expressions) found in the input rows. The fourth form invokes the aggregate once for each input row; since no particular input value is specified, it is generally only useful for the count(*) aggregate function. The last form is used with ordered-set aggregate functions, which are described below.

Most aggregate functions ignore null inputs, so that rows in which one or more of the expression(s) yield null are discarded. This can be assumed to be true, unless otherwise specified, for all built-in aggregates.

For example, count(*) yields the total number of input rows; count(f1) yields the number of input rows in which f1 is non-null, since count ignores nulls; and count(distinct f1) yields the number of distinct non-null values of f1.

Ordinarily, the input rows are fed to the aggregate function in an unspecified order. In many cases this does not matter; for example, min produces the same result no matter what order it receives the inputs in. However, some aggregate functions (such as array_agg and string_agg) produce results that depend on the ordering of the input rows. When using such an aggregate, the optional order_by_clause can be used to specify the desired ordering. The order_by_clause has the same syntax as for a query-level ORDER BY clause, as described in Section 7.5, except that its expressions are always just expressions and cannot be output-column names or numbers. For example:

SELECT array_agg(a ORDER BY b DESC) FROM table;

When dealing with multiple-argument aggregate functions, note that the ORDER BY clause goes after all the aggregate arguments. For example, write this:

SELECT string_agg(a, ',' ORDER BY a) FROM table;

not this:

SELECT string_agg(a ORDER BY a, ',') FROM table;  -- incorrect

The latter is syntactically valid, but it represents a call of a single-argument aggregate function with two ORDER BY keys (the second one being rather useless since it's a constant).

If DISTINCT is specified in addition to an order_by_clause, then all the ORDER BY expressions must match regular arguments of the aggregate; that is, you cannot sort on an expression that is not included in the DISTINCT list.

Placing ORDER BY within the aggregate's regular argument list, as described so far, is used when ordering the input rows for a "normal" aggregate for which ordering is optional. There is a subclass of aggregate functions called ordered-set aggregates for which an order_by_clause is required, usually because the aggregate's computation is only sensible in terms of a specific ordering of its input rows. Typical examples of ordered-set aggregates include rank and percentile calculations. For an ordered-set aggregate, the order_by_clause is written inside WITHIN GROUP (...), as shown in the final syntax alternative above. The expressions in the order_by_clause are evaluated once per input row just like normal aggregate arguments, sorted as per the order_by_clause's requirements, and fed to the aggregate function as input arguments. (This is unlike the case for a non-WITHIN GROUP order_by_clause, which is not treated as argument(s) to the aggregate function.) The argument expressions preceding WITHIN GROUP, if any, are called direct arguments to distinguish them from the aggregated arguments listed in the order_by_clause. Unlike normal aggregate arguments, direct arguments are evaluated only once per aggregate call, not once per input row. This means that they can contain variables only if those variables are grouped by GROUP BY; this restriction is the same as if the direct arguments were not inside an aggregate expression at all. Direct arguments are typically used for things like percentile fractions, which only make sense as a single value per aggregation calculation. The direct argument list can be empty; in this case, write just () not (*). (PostgreSQL will actually accept either spelling, but only the first way conforms to the SQL standard.) An example of an ordered-set aggregate call is:

SELECT percentile_disc(0.5) WITHIN GROUP (ORDER BY income) FROM households;
 percentile_disc
-----------------
           50489

which obtains the 50th percentile, or median, value of the income column from table households. Here, 0.5 is a direct argument; it would make no sense for the percentile fraction to be a value varying across rows.

If FILTER is specified, then only the input rows for which the filter_clause evaluates to true are fed to the aggregate function; other rows are discarded. For example:

SELECT
    count(*) AS unfiltered,
    count(*) FILTER (WHERE i < 5) AS filtered
FROM generate_series(1,10) AS s(i);
 unfiltered | filtered
------------+----------
         10 |        4
(1 row)

The predefined aggregate functions are described in Section 9.20. Other aggregate functions can be added by the user.

An aggregate expression can only appear in the result list or HAVING clause of a SELECT command. It is forbidden in other clauses, such as WHERE, because those clauses are logically evaluated before the results of aggregates are formed.

When an aggregate expression appears in a subquery (see Section 4.2.11 and Section 9.22), the aggregate is normally evaluated over the rows of the subquery. But an exception occurs if the aggregate's arguments (and filter_clause if any) contain only outer-level variables: the aggregate then belongs to the nearest such outer level, and is evaluated over the rows of that query. The aggregate expression as a whole is then an outer reference for the subquery it appears in, and acts as a constant over any one evaluation of that subquery. The restriction about appearing only in the result list or HAVING clause applies with respect to the query level that the aggregate belongs to.

4.2.8. Window Function Calls

A window function call represents the application of an aggregate-like function over some portion of the rows selected by a query. Unlike regular aggregate function calls, this is not tied to grouping of the selected rows into a single output row — each row remains separate in the query output. However the window function is able to scan all the rows that would be part of the current row's group according to the grouping specification (PARTITION BY list) of the window function call. The syntax of a window function call is one of the following:

function_name ([expression [, expression ... ]]) [ FILTER ( WHERE filter_clause ) ] OVER window_name
function_name ([expression [, expression ... ]]) [ FILTER ( WHERE filter_clause ) ] OVER ( window_definition )
function_name ( * ) [ FILTER ( WHERE filter_clause ) ] OVER window_name
function_name ( * ) [ FILTER ( WHERE filter_clause ) ] OVER ( window_definition )

where window_definition has the syntax

[ existing_window_name ]
[ PARTITION BY expression [, ...] ]
[ ORDER BY expression [ ASC | DESC | USING operator ] [ NULLS { FIRST | LAST } ] [, ...] ]
[ frame_clause ]

and the optional frame_clause can be one of

{ RANGE | ROWS } frame_start
{ RANGE | ROWS } BETWEEN frame_start AND frame_end

where frame_start and frame_end can be one of

UNBOUNDED PRECEDING
value PRECEDING
CURRENT ROW
value FOLLOWING
UNBOUNDED FOLLOWING

Here, expression represents any value expression that does not itself contain window function calls.

window_name is a reference to a named window specification defined in the query's WINDOW clause. Alternatively, a full window_definition can be given within parentheses, using the same syntax as for defining a named window in the WINDOW clause; see the SELECT reference page for details. It's worth pointing out that OVER wname is not exactly equivalent to OVER (wname); the latter implies copying and modifying the window definition, and will be rejected if the referenced window specification includes a frame clause.

The PARTITION BY option groups the rows of the query into partitions, which are processed separately by the window function. PARTITION BY works similarly to a query-level GROUP BY clause, except that its expressions are always just expressions and cannot be output-column names or numbers. Without PARTITION BY, all rows produced by the query are treated as a single partition. The ORDER BY option determines the order in which the rows of a partition are processed by the window function. It works similarly to a query-level ORDER BY clause, but likewise cannot use output-column names or numbers. Without ORDER BY, rows are processed in an unspecified order.

The frame_clause specifies the set of rows constituting the window frame, which is a subset of the current partition, for those window functions that act on the frame instead of the whole partition. The frame can be specified in either RANGE or ROWS mode; in either case, it runs from the frame_start to the frame_end. If frame_end is omitted, it defaults to CURRENT ROW.

A frame_start of UNBOUNDED PRECEDING means that the frame starts with the first row of the partition, and similarly a frame_end of UNBOUNDED FOLLOWING means that the frame ends with the last row of the partition.

In RANGE mode, a frame_start of CURRENT ROW means the frame starts with the current row's first peer row (a row that ORDER BY considers equivalent to the current row), while a frame_end of CURRENT ROW means the frame ends with the last equivalent ORDER BY peer. In ROWS mode, CURRENT ROW simply means the current row.

The value PRECEDING and value FOLLOWING cases are currently only allowed in ROWS mode. They indicate that the frame starts or ends the specified number of rows before or after the current row. value must be an integer expression not containing any variables, aggregate functions, or window functions. The value must not be null or negative; but it can be zero, which just selects the current row.

The default framing option is RANGE UNBOUNDED PRECEDING, which is the same as RANGE BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW. With ORDER BY, this sets the frame to be all rows from the partition start up through the current row's last ORDER BY peer. Without ORDER BY, all rows of the partition are included in the window frame, since all rows become peers of the current row.

Restrictions are that frame_start cannot be UNBOUNDED FOLLOWING, frame_end cannot be UNBOUNDED PRECEDING, and the frame_end choice cannot appear earlier in the above list than the frame_start choice — for example RANGE BETWEEN CURRENT ROW AND value PRECEDING is not allowed.

If FILTER is specified, then only the input rows for which the filter_clause evaluates to true are fed to the window function; other rows are discarded. Only window functions that are aggregates accept a FILTER clause.

The built-in window functions are described in Table 9-56. Other window functions can be added by the user. Also, any built-in or user-defined normal aggregate function can be used as a window function. Ordered-set aggregates presently cannot be used as window functions, however.

The syntaxes using * are used for calling parameter-less aggregate functions as window functions, for example count(*) OVER (PARTITION BY x ORDER BY y). The asterisk (*) is customarily not used for non-aggregate window functions. Aggregate window functions, unlike normal aggregate functions, do not allow DISTINCT or ORDER BY to be used within the function argument list.

Window function calls are permitted only in the SELECT list and the ORDER BY clause of the query.

More information about window functions can be found in Section 3.5, Section 9.21, and Section 7.2.5.

4.2.9. Type Casts

A type cast specifies a conversion from one data type to another. PostgreSQL accepts two equivalent syntaxes for type casts:

CAST ( expression AS type )
expression::type

The CAST syntax conforms to SQL; the syntax with :: is historical PostgreSQL usage.

When a cast is applied to a value expression of a known type, it represents a run-time type conversion. The cast will succeed only if a suitable type conversion operation has been defined. Notice that this is subtly different from the use of casts with constants, as shown in Section 4.1.2.7. A cast applied to an unadorned string literal represents the initial assignment of a type to a literal constant value, and so it will succeed for any type (if the contents of the string literal are acceptable input syntax for the data type).

An explicit type cast can usually be omitted if there is no ambiguity as to the type that a value expression must produce (for example, when it is assigned to a table column); the system will automatically apply a type cast in such cases. However, automatic casting is only done for casts that are marked "OK to apply implicitly" in the system catalogs. Other casts must be invoked with explicit casting syntax. This restriction is intended to prevent surprising conversions from being applied silently.

It is also possible to specify a type cast using a function-like syntax:

typename ( expression )

However, this only works for types whose names are also valid as function names. For example, double precision cannot be used this way, but the equivalent float8 can. Also, the names interval, time, and timestamp can only be used in this fashion if they are double-quoted, because of syntactic conflicts. Therefore, the use of the function-like cast syntax leads to inconsistencies and should probably be avoided.

4.2.10. Collation Expressions

The COLLATE clause overrides the collation of an expression. It is appended to the expression it applies to:

expr COLLATE collation

where collation is a possibly schema-qualified identifier. The COLLATE clause binds tighter than operators; parentheses can be used when necessary.

If no collation is explicitly specified, the database system either derives a collation from the columns involved in the expression, or it defaults to the default collation of the database if no column is involved in the expression.

The two common uses of the COLLATE clause are overriding the sort order in an ORDER BY clause, for example:

SELECT a, b, c FROM tbl WHERE ... ORDER BY a COLLATE "C";

and overriding the collation of a function or operator call that has locale-sensitive results, for example:

SELECT * FROM tbl WHERE a > 'foo' COLLATE "C";

Note that in the latter case the COLLATE clause is attached to an input argument of the operator we wish to affect. It doesn't matter which argument of the operator or function call the COLLATE clause is attached to, because the collation that is applied by the operator or function is derived by considering all arguments, and an explicit COLLATE clause will override the collations of all other arguments. (Attaching non-matching COLLATE clauses to more than one argument, however, is an error. For more details see Section 23.2.) Thus, this gives the same result as the previous example:

SELECT * FROM tbl WHERE a COLLATE "C" > 'foo';

But this is an error:

SELECT * FROM tbl WHERE (a > 'foo') COLLATE "C";

because it attempts to apply a collation to the result of the > operator, which is of the non-collatable data type boolean.

4.2.11. Scalar Subqueries

A scalar subquery is an ordinary SELECT query in parentheses that returns exactly one row with one column. (See Chapter 7 for information about writing queries.) The SELECT query is executed and the single returned value is used in the surrounding value expression. It is an error to use a query that returns more than one row or more than one column as a scalar subquery. (But if, during a particular execution, the subquery returns no rows, there is no error; the scalar result is taken to be null.) The subquery can refer to variables from the surrounding query, which will act as constants during any one evaluation of the subquery. See also Section 9.22 for other expressions involving subqueries.

For example, the following finds the largest city population in each state:

SELECT name, (SELECT max(pop) FROM cities WHERE cities.state = states.name)
    FROM states;

4.2.12. Array Constructors

An array constructor is an expression that builds an array value using values for its member elements. A simple array constructor consists of the key word ARRAY, a left square bracket [, a list of expressions (separated by commas) for the array element values, and finally a right square bracket ]. For example:

SELECT ARRAY[1,2,3+4];
  array
---------
 {1,2,7}
(1 row)

By default, the array element type is the common type of the member expressions, determined using the same rules as for UNION or CASE constructs (see Section 10.5). You can override this by explicitly casting the array constructor to the desired type, for example:

SELECT ARRAY[1,2,22.7]::integer[];
  array
----------
 {1,2,23}
(1 row)

This has the same effect as casting each expression to the array element type individually. For more on casting, see Section 4.2.9.

Multidimensional array values can be built by nesting array constructors. In the inner constructors, the key word ARRAY can be omitted. For example, these produce the same result:

SELECT ARRAY[ARRAY[1,2], ARRAY[3,4]];
     array
---------------
 {{1,2},{3,4}}
(1 row)

SELECT ARRAY[[1,2],[3,4]];
     array
---------------
 {{1,2},{3,4}}
(1 row)

Since multidimensional arrays must be rectangular, inner constructors at the same level must produce sub-arrays of identical dimensions. Any cast applied to the outer ARRAY constructor propagates automatically to all the inner constructors.

Multidimensional array constructor elements can be anything yielding an array of the proper kind, not only a sub-ARRAY construct. For example:

CREATE TABLE arr(f1 int[], f2 int[]);

INSERT INTO arr VALUES (ARRAY[[1,2],[3,4]], ARRAY[[5,6],[7,8]]);

SELECT ARRAY[f1, f2, '{{9,10},{11,12}}'::int[]] FROM arr;
                     array
------------------------------------------------
 {{{1,2},{3,4}},{{5,6},{7,8}},{{9,10},{11,12}}}
(1 row)

You can construct an empty array, but since it's impossible to have an array with no type, you must explicitly cast your empty array to the desired type. For example:

SELECT ARRAY[]::integer[];
 array
-------
 {}
(1 row)

It is also possible to construct an array from the results of a subquery. In this form, the array constructor is written with the key word ARRAY followed by a parenthesized (not bracketed) subquery. For example:

SELECT ARRAY(SELECT oid FROM pg_proc WHERE proname LIKE 'bytea%');
                                 array
-----------------------------------------------------------------------
 {2011,1954,1948,1952,1951,1244,1950,2005,1949,1953,2006,31,2412,2413}
(1 row)

SELECT ARRAY(SELECT ARRAY[i, i*2] FROM generate_series(1,5) AS a(i));
              array
----------------------------------
 {{1,2},{2,4},{3,6},{4,8},{5,10}}
(1 row)

The subquery must return a single column. If the subquery's output column is of a non-array type, the resulting one-dimensional array will have an element for each row in the subquery result, with an element type matching that of the subquery's output column. If the subquery's output column is of an array type, the result will be an array of the same type but one higher dimension; in this case all the subquery rows must yield arrays of identical dimensionality, else the result would not be rectangular.

The subscripts of an array value built with ARRAY always begin with one. For more information about arrays, see Section 8.15.

4.2.13. Row Constructors

A row constructor is an expression that builds a row value (also called a composite value) using values for its member fields. A row constructor consists of the key word ROW, a left parenthesis, zero or more expressions (separated by commas) for the row field values, and finally a right parenthesis. For example:

SELECT ROW(1,2.5,'this is a test');

The key word ROW is optional when there is more than one expression in the list.

A row constructor can include the syntax rowvalue.*, which will be expanded to a list of the elements of the row value, just as occurs when the .* syntax is used at the top level of a SELECT list. For example, if table t has columns f1 and f2, these are the same:

SELECT ROW(t.*, 42) FROM t;
SELECT ROW(t.f1, t.f2, 42) FROM t;

By default, the value created by a ROW expression is of an anonymous record type. If necessary, it can be cast to a named composite type — either the row type of a table, or a composite type created with CREATE TYPE AS. An explicit cast might be needed to avoid ambiguity. For example:

CREATE TABLE mytable(f1 int, f2 float, f3 text);

CREATE FUNCTION getf1(mytable) RETURNS int AS 'SELECT $1.f1' LANGUAGE SQL;

-- No cast needed since only one getf1() exists
SELECT getf1(ROW(1,2.5,'this is a test'));
 getf1
-------
     1
(1 row)

CREATE TYPE myrowtype AS (f1 int, f2 text, f3 numeric);

CREATE FUNCTION getf1(myrowtype) RETURNS int AS 'SELECT $1.f1' LANGUAGE SQL;

-- Now we need a cast to indicate which function to call:
SELECT getf1(ROW(1,2.5,'this is a test'));
ERROR:  function getf1(record) is not unique

SELECT getf1(ROW(1,2.5,'this is a test')::mytable);
 getf1
-------
     1
(1 row)

SELECT getf1(CAST(ROW(11,'this is a test',2.5) AS myrowtype));
 getf1
-------
    11
(1 row)

Row constructors can be used to build composite values to be stored in a composite-type table column, or to be passed to a function that accepts a composite parameter. Also, it is possible to compare two row values or test a row with IS NULL or IS NOT NULL, for example:

SELECT ROW(1,2.5,'this is a test') = ROW(1, 3, 'not the same');

SELECT ROW(table.*) IS NULL FROM table;  -- detect all-null rows

For more detail see Section 9.23. Row constructors can also be used in connection with subqueries, as discussed in Section 9.22.

4.2.14. Expression Evaluation Rules

The order of evaluation of subexpressions is not defined. In particular, the inputs of an operator or function are not necessarily evaluated left-to-right or in any other fixed order.

Furthermore, if the result of an expression can be determined by evaluating only some parts of it, then other subexpressions might not be evaluated at all. For instance, if one wrote:

SELECT true OR somefunc();

then somefunc() would (probably) not be called at all. The same would be the case if one wrote:

SELECT somefunc() OR true;

Note that this is not the same as the left-to-right "short-circuiting" of Boolean operators that is found in some programming languages.

As a consequence, it is unwise to use functions with side effects as part of complex expressions. It is particularly dangerous to rely on side effects or evaluation order in WHERE and HAVING clauses, since those clauses are extensively reprocessed as part of developing an execution plan. Boolean expressions (AND/OR/NOT combinations) in those clauses can be reorganized in any manner allowed by the laws of Boolean algebra.

When it is essential to force evaluation order, a CASE construct (see Section 9.17) can be used. For example, this is an untrustworthy way of trying to avoid division by zero in a WHERE clause:

SELECT ... WHERE x > 0 AND y/x > 1.5;

But this is safe:

SELECT ... WHERE CASE WHEN x > 0 THEN y/x > 1.5 ELSE false END;

A CASE construct used in this fashion will defeat optimization attempts, so it should only be done when necessary. (In this particular example, it would be better to sidestep the problem by writing y > 1.5*x instead.)

CASE is not a cure-all for such issues, however. One limitation of the technique illustrated above is that it does not prevent early evaluation of constant subexpressions. As described in Section 36.6, functions and operators marked IMMUTABLE can be evaluated when the query is planned rather than when it is executed. Thus for example

SELECT CASE WHEN x > 0 THEN x ELSE 1/0 END FROM tab;

is likely to result in a division-by-zero failure due to the planner trying to simplify the constant subexpression, even if every row in the table has x > 0 so that the ELSE arm would never be entered at run time.

While that particular example might seem silly, related cases that don't obviously involve constants can occur in queries executed within functions, since the values of function arguments and local variables can be inserted into queries as constants for planning purposes. Within PL/pgSQL functions, for example, using an IF-THEN-ELSE statement to protect a risky computation is much safer than just nesting it in a CASE expression.

Another limitation of the same kind is that a CASE cannot prevent evaluation of an aggregate expression contained within it, because aggregate expressions are computed before other expressions in a SELECT list or HAVING clause are considered. For example, the following query can cause a division-by-zero error despite seemingly having protected against it:

SELECT CASE WHEN min(employees) > 0
            THEN avg(expenses / employees)
       END
    FROM departments;

The min() and avg() aggregates are computed concurrently over all the input rows, so if any row has employees equal to zero, the division-by-zero error will occur before there is any opportunity to test the result of min(). Instead, use a WHERE or FILTER clause to prevent problematic input rows from reaching an aggregate function in the first place.