Specific denotations for pure types

I just learned on #haskell that Int has implementation/machine-dependent semantics. I'd always assumed that pure (non-imperative) types have specific denotational models, so that for instance the denotation of something of type Int is either bottom or a (smallish) integer. Since precise & simple denotation is at the heart of how I think about programming, and Haskell is my favorite language, I'm startled and disappointed. I knew we didn't have a denotational semantics for Haskell, but I'd previously assumed it was just a matter of working out the details. Has implementation-independent denotation been discussed for Haskell' ? Thanks, - Conal