On Tue, Jul 8, 2008 at 8:54 PM, Bill Page wrote:
> ...
> It seems less mysterious to me. I think almost:
>
>  Category():Domain  == SubDomain Domain
>

Oops. Sorry for sending prematurely.

Since 'Type' is the category of 'Domain', perhaps one should write:

  Type():Category == SetCategory with ...

  Domain():Type == add ...

Then

   Category():Type with ... == SubDomain Domain

In other words Category is a Domain with additional exports.

> 'SubDomain' is like the domain constructor 'Set' except of course
> unlike 'Set Domain', on coerce to OutputForm the objects of 'Category'
> have names (the category name). But the result of 'members' would be
> List(Domain):
>
>  members: % -> List Domain
>
> implemented by a database query. One might also expect more reflections such 
> as:
>
>  exports: % -> List Record(name:Symbol, body:Tuple Domain -> Domain)
>  parents: % -> List %
>
> etc.

Regards,
Bill Page.

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