[Haskell-cafe] Basic question concerning the category Hask (was: concerning data constructors)

Yitzchak Gale gale at sefer.org
Thu Jan 3 09:32:44 EST 2008

Jonathan Cast wrote:
>>> The normal view taken by Haskellers is that the denotations of
>>> Haskell types are CPPOs.

I wrote:
>> CPPO?

>>> (1) Must be monotone
>>> (2) Must be continuous

>> Could you please define what you mean by those terms
>> in this context?

Jens Blanck wrote:
> The extra P would stand for "pointed" (has a least element, bottom), this is
> common in some communities. To me though, a cpo (complete partial order) is
> closed under directed suprema and the empty set is directed so bottom is
> already required. The category of cpos in not cartesian closed. For
> denotational semantics I believe the subcategory of Scott domains are what
> is usually considered.
> Continuous functions on cpos are by definition monotone and they respect
> directed suprema.


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