Cartesian closed without products

[Richard Garner <rhgg2@hermes.cam.ac.uk>]

Dear categorists,

A small category C has finite products just when the
representables in [C^op, Set] are closed under finite
products. It is cartesian closed just when the representables
are closed under finite products and internal hom.

It seems natural, therefore, to consider a notion of
"cartesian closedness without finite products": categories in
which the representables are closed in [C^op, Set] under
internal hom but not necessarily under finite products. This
amounts to giving, for each pair of objects X and Y, an
object [X, Y] together with a universal natural
transformation C(-, [X, Y]) x C(-, X) -> C(-, Y). Such
categories will be closed in the sense of Eilenberg-Kelly
without necessarily being monoidal: let us call them
"universally closed" for now.

Obviously, any cartesian closed category is universally
closed; and categorical proof theory gives us a class of
non-degenerate examples built from the syntax of (classical)
sequent calculi with implication but no product.

The question now arises as to whether there are any
non-syntactic examples of universally closed categories which
are not cartesian closed. The most likely place seems to me
to be domain theory, but I have been unable to track anything
down. Does anyone have any pointers?

Thanks,

Richard.