[Haskell-cafe] Re: Wikipedia on first-class object
Cristian Baboi
cristi at ot.onrc.ro
Fri Dec 28 03:08:17 EST 2007
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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