Using only closures you can build an OO system, with what looks like an OO syntax.
I believe that Smalltalk's OO system
works like this. Definitely Lisp's CLOS does.
I'm not so sure that I'd say that CLOS needs to use
closures to quite the extent you imply. Take a look for
example at the
found in The Art of the Metaobject Protocol.
I think it's an exaggeration to say that this uses only
(or even primarily) closures to do its work.
In reply to tilly's update :-) (Let me first qualify that
IANALI - I am not a Lisp implementor - take me with the
appropriate grain of salt.) Certainly it's possible to do
the same thing with closures. And I cheated a little bit -
the Closette implementation is a simple one that has a few
problems which AMOP suggests are probably overcome using
closures. But I'd be surprised if any widely used CLOS
implementation is largely in terms of closures - I'd expect
it to be more the melange of imperative, OO, and
functional programming that is Common Lisp (and that
is evidenced in Closette). It wouldn't
surprise me, though, if some of the Scheme object systems out there
were a little more functional, and if anyone around here knows,
it'd be interesting to know how its done in OCaml,
which is a much more functional language than CL.