2009/1/23 Brent Yorgey
AbstractInterface a = new ConcreteClass();
In Java, if a variable has type AbstractInterface, it is *existentially* quantified: it means, this variable references a value of *some* type, and all you know about it is that it is an instance of AbstractInterface. Whatever code sets the value of the variable gets to choose its concrete type; any code that uses the variable cannot choose what type it should be, but can only use AbstractInterface methods on it (since that's all that is known).
However, a Haskell variable with type
var :: AbstractInterface a => a
is *universally* quantified: it means, this variable has a polymorphic value, which can be used as a value of any type which is an instance of AbstractInterface. Here, it is the code which *uses* var that gets to choose its type (and indeed, different choices can be made for different uses); the definition of var cannot choose, and must work for any type which is an instance of AbstractInterface (hence it must only use methods of the AbstractInterface type class).
Writing
a :: Num n => n a = 3 :: Integer
is trying to define a universally quantified value as if it were existentially quantified.
Now, it *is* possible to have existentially quantification in Haskell; I can show you how if you like, but I think I'll stop here for now.
Does this help?
Yes thanks.
From other answers, I also got the essence of it, but now I know the exact terminology: I met the terms 'existentially quantification' and 'universal quantification' before, but did not have any idea of their meaning. I did not now than embarking in studying haskell I had to study phylosophy too :-)
Joking apart, I believe something like your explanation should be reported in tutorials helping to learn haskell, especially the ones for people coming from other languages. As I said in my initial post the analogy 'type class are like interfaces' is a good starting point, but carried too far it is misleading. Thanks again to all the posters that replied to my question. This seems a lively forum: expect to see soon other questions from me :-). Ciao ------ FB