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Today's Topics:
1. Re: Empty type (Nicholas Vanderweit)
2. Re: Empty type (Kim-Ee Yeoh)
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Message: 1
Date: Fri, 25 Oct 2013 11:26:28 -0600
From: Nicholas Vanderweit <[email protected]>
To: The Haskell-Beginners Mailing List - Discussion of primarily
beginner-level topics related to Haskell <[email protected]>
Subject: Re: [Haskell-beginners] Empty type
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Not sure if this is haskell-beginners material, but it's possible in a lazy
language like Haskell to define an inhabitant of NotVoid recursively:
let x = NotVoid x in x
Or, alternatively, using fix from Data.Function:
fix NotVoid
This gives NotVoid (NotVoid (NotVoid (...)))
Nick
On Fri, Oct 25, 2013 at 5:54 AM, Brent Yorgey <[email protected]>wrote:
> 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
> _______________________________________________
> Beginners mailing list
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> http://www.haskell.org/mailman/listinfo/beginners
>
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Message: 2
Date: Sat, 26 Oct 2013 03:12:36 +0700
From: Kim-Ee Yeoh <[email protected]>
To: The Haskell-Beginners Mailing List - Discussion of primarily
beginner-level topics related to Haskell <[email protected]>
Subject: Re: [Haskell-beginners] Empty type
Message-ID:
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On Sat, Oct 26, 2013 at 12:26 AM, Nicholas Vanderweit <
[email protected]> wrote:
> Or, alternatively, using fix from Data.Function:
>
> fix NotVoid
>
Yes, and all of them are indistinguishable from bottom or 'undefined ::
forall a. a', the ghost that inhabits all types, including the empty one:
Void.
What trips up beginners is the interpretation of indistinguishable-ness. At
the level of denotational design, 'undefined' and 'error "(sadface)"' are
to be treated as equal, although beginners would point out: "hey look, I
get different output!"
Call it denotational design, or call it beautiful FP modelling, this stuff
is really where it's at.
-- Kim-Ee
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