PostgreSQL: Immutable, Volatile, Stable I'm unclear about the true meaning in the definitions for IMMUTABLE, VOLATILE and STABLE functions.

I read the documentation, specifically the definitions of each.  


  IMMUTABLE indicates that the function cannot modify the database and
  always returns the same result when given the same argument values; that is, it does not do database lookups or otherwise use
  information not directly present in its argument list. If this option
  is given, any call of the function with all-constant arguments can be
  immediately replaced with the function value.
  
  STABLE indicates that the function cannot modify the database, and
  that within a single table scan it will consistently return the same
  result for the same argument values, but that its result could change
  across SQL statements. This is the appropriate selection for functions
  whose results depend on database lookups, parameter variables (such as
  the current time zone), etc. (It is inappropriate for AFTER triggers
  that wish to query rows modified by the current command.) Also note
  that the current_timestamp family of functions qualify as stable,
  since their values do not change within a transaction.
  
  VOLATILE indicates that the function value can change even within a
  single table scan, so no optimizations can be made. Relatively few
  database functions are volatile in this sense; some examples are
  random(), currval(), timeofday(). But note that any function that has
  side-effects must be classified volatile, even if its result is quite
  predictable, to prevent calls from being optimized away; an example is
  setval().


My confusion comes in with the condition for IMMUTABLE and STABLE that the function ALWAYS or CONSISTENTLY returns the same result given the same arguments.  

The IMMUTABLE definition states that the function does not database lookups or otherwise use information not directly present in its argument list.  So, to me, that means such functions are used to manipulate data provided by the client, and should not have SELECT statements...although that just sounds a bit odd to me.

With STABLE, the definition is similar in that it says it should consistently return the same result.  So, to me, that means that everytime the function is called with the same arguments, it should return the same results (same exact rows, every single time).

So, to me...that means that any function that performs a SELECT on a table or tables that can be updated, should only be volatile.

But, again...that doesn't sound right to me.

Bringing this back to my use-case, I am writing functions that perform SELECT statements with multiple JOIN's on tables that are constantly being added to, so the function calls would be expected to return different results each time it's called, even with the same arguments.

So, does that mean that my functions should be VOLATILE?  Even though the documentation indicates relatively few database functions are volatile in this sense?

Thank you!
IMMUTABLE must be a pure function, whose results depend only on its inputs. This is a very strict requirement; they cannot call other non-immutable functions, they cannot access tables, they cannot access the value of configuration properties, etc.
STABLE can use any inputs that are themselves STABLE: other STABLE or IMMUTABLE functions, and SELECT queries of tables. It's safe to query tables because the function's view of those tables will not change within the query's current snapshot. You can access GUC values (current_setting(...)) so long as you know they won't also be assigned to within the current statement.
VOLATILE functions are everything that doesn't fit the above:

Anything with side-effects
Anything that does writes
Anything that queries external data not managed by the PostgreSQL snapshot
...

In general, just leave everything VOLATILE unless you have a good reason not to.
The main reason to use IMMUTABLE is when writing functions that are to be used as part of index expressions.