Every function has a volatility classification, with the possibilities being VOLATILE, STABLE, or IMMUTABLE. VOLATILE is the default if the CREATE FUNCTION command does not specify a category. The volatility category is a promise to the optimizer about the behavior of the function:
A VOLATILE function can do anything, including modifying the database. It can return different results on successive calls with the same arguments. The optimizer makes no assumptions about the behavior of such functions. A query using a volatile function will re-evaluate the function at every row where its value is needed.
A STABLE function cannot modify the database and is guaranteed to return the same results given the same arguments for all rows within a single statement. This category allows the optimizer to optimize multiple calls of the function to a single call. In particular, it is safe to use an expression containing such a function in an index scan condition. (Since an index scan will evaluate the comparison value only once, not once at each row, it is not valid to use a VOLATILE function in an index scan condition.)
An IMMUTABLE function cannot modify the database and is guaranteed to return the same results given the same arguments forever. This category allows the optimizer to pre-evaluate the function when a query calls it with constant arguments. For example, a query like SELECT ... WHERE x = 2 + 2 can be simplified on sight to SELECT ... WHERE x = 4, because the function underlying the integer addition operator is marked IMMUTABLE.
For best optimization results, you should label your functions with the strictest volatility category that is valid for them.
Any function with side-effects must be labeled VOLATILE, so that calls to it cannot be optimized away. Even a function with no side-effects needs to be labeled VOLATILE if its value can change within a single query; some examples are random(), currval(), timeofday().
Another important example is that the current_timestamp family of functions qualify as STABLE, since their values do not change within a transaction.
There is relatively little difference between STABLE and IMMUTABLE categories when considering simple interactive queries that are planned and immediately executed: it doesn't matter a lot whether a function is executed once during planning or once during query execution startup. But there is a big difference if the plan is saved and reused later. Labeling a function IMMUTABLE when it really isn't might allow it to be prematurely folded to a constant during planning, resulting in a stale value being re-used during subsequent uses of the plan. This is a hazard when using prepared statements or when using function languages that cache plans (such as PL/pgSQL).
For functions written in SQL or in any of the standard procedural languages, there is a second important property determined by the volatility category, namely the visibility of any data changes that have been made by the SQL command that is calling the function. A VOLATILE function will see such changes, a STABLE or IMMUTABLE function will not. This behavior is implemented using the snapshotting behavior of MVCC (see Chapter 13): STABLE and IMMUTABLE functions use a snapshot established as of the start of the calling query, whereas VOLATILE functions obtain a fresh snapshot at the start of each query they execute.
Functions written in C can manage snapshots however they want, but it's usually a good idea to make C functions work this way too.
Because of this snapshotting behavior, a function containing only SELECT commands can safely be marked STABLE, even if it selects from tables that might be undergoing modifications by concurrent queries. PostgreSQL will execute all commands of a STABLE function using the snapshot established for the calling query, and so it will see a fixed view of the database throughout that query.
The same snapshotting behavior is used for SELECT commands within IMMUTABLE functions. It is generally unwise to select from database tables within an IMMUTABLE function at all, since the immutability will be broken if the table contents ever change. However, PostgreSQL does not enforce that you do not do that.
A common error is to label a function IMMUTABLE when its results depend on a configuration parameter. For example, a function that manipulates timestamps might well have results that depend on the TimeZone setting. For safety, such functions should be labeled STABLE instead.
PostgreSQL requires that STABLE and IMMUTABLE functions contain no SQL commands other than SELECT to prevent data modification. (This is not a completely bulletproof test, since such functions could still call VOLATILE functions that modify the database. If you do that, you will find that the STABLE or IMMUTABLE function does not notice the database changes applied by the called function, since they are hidden from its snapshot.)