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

On 28 Dec 2007, at 2:08 AM, Cristian Baboi wrote:

On Thu, 27 Dec 2007 20:46:24 +0200, Jonathan Cast 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