[Haskell-cafe] Re: Haskell-Cafe Digest, Vol 53, Issue 2

[Jens Blanck]

> 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 resulting category
> > substantially).
>
> I'm not convinced that the category is all that "messed up".
>
> 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.

Jens
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