From the user's point of view, there is little difference between a class method and a class-constrained polymorphic function when the
I had looked into the source code of IArray a bit. Like you have found, (!) is not a class method. In fact, none of the claimed class methods in the doc is a class method, and no class method of IArray is documented. Instead, IArray class methods seem to pertain to implementation details (I mean, "unsafeAt"!), and user operations such as (!) are constrained polymorphic functions, e.g., (!) :: (IArray a e, Ix ix) => a ix e -> ix -> e provided instances are abstract types. So the documentation is telling a white lie. Of course, you see the difference when you roll your own IArray instance. I think the white lie is a balance between exposition simplicity and implementation tuning.