I think it's a stretch to say this, itself, provides any notion of identity. You could certainly implement identity with any of the myriad ways of maintaining references with state, of course.
Of course you're right, but I think a function like
Complex -> Radian -> Complex
offers two points of view. You can see it as a function which transforms complex numbers or a function representing an update to the internal state of a Complex object. The second highlights the need to keep track of identity. Throwing an STRef into the mix just gives you a particular kind of history—one which only retains the "now".
Which is all sort of obvious and meaningless, but I still think it's interesting to think about. I think coalgebras tend to force thinking in terms of identity in this kind of way.
