On Fri, Oct 25, 2013 at 12:44:06PM +0900, KwangYul Seo wrote:
Hello,
It seems there are three different ways to declare an empty type in Haskell.
http://www.haskell.org/haskellwiki/Empty_type
1) data E0 = E0
This one is not empty, as others have pointed out. It is inhabited by _|_ and E0.
2) newtype Void = Void Void
This one is in fact empty (that is, only inhabited by _|_), but it depends on the fact that newtype constructors do not add any laziness. The same thing done with 'data', data NotVoid = NotVoid NotVoid is not empty, because it is inhabited by _|_, NotVoid _|_, NotVoid (NotVoid _|_), ... With the data declaration, these are all different. With the newtype, they are all equal to _|_. This is a bit of a technical point, however; if I were you I wouldn't worry about it at this point. It sounds like the most important thing for you to understand is below:
I'd like to know how the second trick works. Is it possible to create a new type from itself? How should I interpret this?
Yes, it is possible to create a new type from itself! This is called a "recursive data type", and they are the bread and butter of Haskell programming. For some other less silly/trivial examples, consider data IntList = Nil | Cons Int IntList data BTree a = Empty | Node a (BTree a) (BTree a) both of which are recursive types. -Brent