[Haskell-beginners] Empty type

[Ben Gamari]

KwangYul Seo <skyul at company100.com> writes:

> 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
>
Perhaps this is a bit nit-picky, but is this truly empty? I would
actually argue that the type is inhabited by precisely one element,
`E0` (note that we aren't counting _|_).

> 2) newtype Void = Void Void
>
> 3) data Void
>
> 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?
>
I'll try to answer as far as I understand it but someone please correct
any mistruths below.

Consider your type,

    newtype Void = Void Void

There are only two ways we could construct a value of type `Void`,

    a = Void _|_

and,

    b = Void b

However, `b` is a non-terminating recursion, making it equivalent to
`a`. By this reasoning, since both of these constructions evaluate to
_|_, `Void` must be empty.

Cheers,

- Ben
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