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One might want (TYPE-OF 2) => (INTEGER 2 2), or perhaps just (INTEGER 2)
and define (INTEGER x) <=> (integer x x).  But this does not seem to
generalize nicely to other data types.

If the goal is that TYPE-OF should return the most specific possible
type, then clearly when applied to object x it should return (MEMBER x),
as that is the most specific type that contains x.  But this is not
very useful, and therefore this goal is not what we really want.