Patrick,
It seems that I need to distinguish between a theory for Haskell and a given implementation (GHCi).
What do you mean by this?
Obviously I get two different types Wrong. You get exactly the same type, it's just that GHCi detected that you have a fancy name for this type, so it gives you that name. It's not type system, it's just GHCi.
Are you saying there is just one type? (not two isomorphic types because there is only one of them with two names)
Indeed. To create a new type isomorphic to an existing type, have a look at newtype declarations. (http://www.haskell.org/onlinereport/decls.html , ยง4.2).
Why are the GHCi commands :t "ww" and :t getName("ww") not a valid type checks?
I am not sure what you mean by this. Cheers, Stefan