Earlier quoted context omitted.
I feel like the nearest thing to OO in Haskell in common use is the records-of-closures pattern. Still doesn't have persistent identity, of course.
Records-of-closures is pretty much what I'm talking about. There is a notion of identity when those records are recursive, though the state management is still manual (as you'd expect). data Complex = { rotate :: Degrees -> Complex } -- thus -- rotate :: Complex -> Degrees -> Complex where `rotate` is a state transformer and thus produces a notion of identity.
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.