Actually, despite tilly's response, these are exactly like some of what Postgresql calls "window functions" which are exactly the same thing that Oracle calls "analytic functions" (Oracle uses "window functions" to refer to a subset of the "analytic functions").

One difference between my user-defined aggregate functions above and the standard window functions first_value() and last_value(), is that my aggregates can be used as simple aggregates (such as with just "GROUP BY") while first_value() and last_value() must have a window defined (via "OVER"). That is, my aggregates can be used with OVER or without OVER.

But the main reason I am responding is to note that my third attempt at defining first() and last() was much simpler. It is just like the _nonnull versions except you drop the word 'strict'.

create function first( one anyelement, two anyelement )
    returns anyelement
as $$ begin return one; end $$ language plpgsql;

create function last( one anyelement, two anyelement )
    returns anyelement
as $$ begin return two; end $$ language plpgsql;

create aggregate first( anyelement )(
    stype = anyelement
  , sfunc = first
);

create aggregate last( anyelement )(
    stype = anyelement
  , sfunc = last
);
[download]

Which makes me wonder what my first try (that didn't work) looked like.

I'm now working with newer Postgresql that supports window functions. But this version's first_value() doesn't support the standard "IGNORE NULLS" option which looked like the best solution for a problem I was working on today. So I asked google where my implementations were so I could just use them.

Swapping in these details again made me suspect that the first() and last() implementations could be as simple as the first_nonnull() and last_nonnull() implementations. Testing on this newer version of Postgresql showed that they could be.