Extensible Haskell Type Classes

Question

I am reading a paper on dependently-typed programming and came across the following quote:

"[...] in contrast to Haskell's type classes, the data type [...] is closed", in the sense that one cannot add new types to the universe without extending the data type.

My newbie question is: in what sense are Haskell type classes open? How are they extensible? Also, what are the type-theoretical consequences of having this property (open vs closed)?

Thank you!

Answer 1

Type classes are open, because you can make arbitrary type an instance of it. When you create type class you specify interface, but not the types which belong to it. Then in any code which includes typeclass definition you can make your type instance of it providing necessary functions from interface using instance TypeClass type of syntax.