[Haskell-cafe] Re: Wikipedia on first-class object
Jonathan Cast
jonathanccast at fastmail.fm
Fri Dec 28 18:57:49 EST 2007
On 28 Dec 2007, at 2:08 AM, Cristian Baboi wrote:
> 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 ?
Yes.
> - the "structure" of a domain is preserved in the result when you
> apply a Haskell function to it ?
The structure is preserved by every function, but that's a global
property, not really something that applies to a particular
application f x.
> - every domain can be enumerated ?
There exist models of Haskell where the domain representing every
type is recursively enumerable, yes. But the critical thing for
finding a printing function is enumerating each value /once/, which
is harder to do. (I'm not aware of a way to do it).
jcc
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