[Haskell-cafe] Re: Why does the class called "Real" support only rationals, and not all reals?

[DavidA]

Yes, I'm afraid that you are understanding correctly. Annoying isn't it.

It is well-known (among Haskell mathematicians at least) that the numeric type 
classes in the prelude are broken.

Here's one proposal for a small step in the right direction:
http://hackage.haskell.org/trac/haskell-prime/ticket/112

But it really needs a mathematician to sit down and sort it out properly.