[Haskell-cafe] Re: Wikipedia on first-class object

[Cristian Baboi]

On Thu, 27 Dec 2007 20:46:24 +0200, Jonathan Cast  
<jonathanccast at fastmail.fm> wrote:

> Preference doesn't come into it.  By definition, the denotations of  
> Haskell functions are monotone continous functions on pointed complete  
> partial orders.

> You seem to think that _|_ is defined in terms of operational  
> semantics.  Haskell hasn't got an operational semantics, just a  
> denotational semantics that implementations must produce an operational  
> semantics to match with.  _|_ is a denotational idea, defined in terms  
> of partial orders and least upper bounds.  An infinite list is the least  
> upper bound of an infinite set of partial lists, and the value of any  
> function (such as \x -> x == x) applied to it is the least upper bound  
> of the values of that function applied to those partial lists.
>
> By definition.
>


Questions:

The fact that Haskell functions are monotone continous functions on  
pointed complete partial orders imply this ?

- every domain in Haskell is a "pointed complete partial order", including  
domains of functions ?
- the "structure" of a domain is preserved in the result when you apply a  
Haskell function to it ?
- every domain can be enumerated ?

Thank you.



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