On 3 Jan 2008, at 3:40 AM, Jens Blanck wrote:

> The normal view taken by Haskellers is that the denotations of > Haskell types are CPPOs.CPPO? > So: > > (1) Must be monotone > (2) Must be continuous Could you please define what you mean by those terms in this context?> (Needn't be strict, even though that messes up the resultingcategory> substantially). I'm not convinced that the category is all that "messed up".

`Well, no coproducts (Haskell uses a lifted version of the coproduct`

`from CPO). Of course, Haskell makes things even worse by lifting the`

`product and exponential objects, as well, which come to think of it`

`is unnecessary even in the category of CPPOs and not necessarily`

`strict continuous functions.`

`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.`

`Not so. A set is directed iff every finite subset has an upper bound`

`in the set; {} is finite, so it must have an upper bound in the set.`

`So directed sets must be non-empty. (So CPOs needn't be pointed).`

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