> Bill Page <bill.p...@newsynthesis.org> writes:
>
> | On Thu, Dec 3, 2009 at 9:12 PM, Waldek Hebisch wrote:
> | > I just commited a patch which replaces uses of 'Domain' in interpreter
> | > by 'Type'.  Similarely, it replaces uses of 'Subdomain(Domain)'
> | > by 'Category'.  This makes interpreter and compiler more consistent.
> | > Additionally this patch allows limited (should be comparable to
> | > what OpenAxiom allows) use of type valued functions in interpeter.
> | >
> |
> | I rather strongly dislike this change. It seems to me that the
> | interpreter (almost) got it right and the older notions built in to
> | Spad were not.  Consistency is a good thing but I would have much
> | preferred that Type be replaced with Domain and Category (as a type)
> | be replaced with Subdomain(Domain) - since that is what a category is
> | according to the original published intentions of the Axiom designers.
> |  For what its worth, I also think OpenAxiom did the wrong thing here
> | (at least in part), although OpenAxiom does at least define Domain as
> | a Domain in the the library.
>

On Fri, Dec 4, 2009 at 11:30 AM, Gabriel Dos Reis wrote:
>
> I'm unconvinced that there is a Single One True Answer here.  The design
> space is huge -- to have a glimpse, have a look at the lambda cube.

E.g.

http://en.wikipedia.org/wiki/Lambda_cube

and references therein. Perhaps you can suggest others?

> Consequently, I would encourage people to explore other choices, and in
> case they find a choice to be wrong, I encourage them -- for the benefits
> of scientific discourse -- to provide logical arguments as to why.
> 'original published intentions' does not make it.
>

In general I agree that citing original design documents for Axiom
does not constitute a logical argument. Nonetheless I do think that
the view of categories as subdomains of the domain of all domains as
exposed by Stephen Watt is logically consistent and could be
implemented consistently by some future version of Axiom.

Such  subtyping however

  http://en.wikipedia.org/wiki/Subtyping

is not usually included in the usual "lambda cube". So the design
space that I would like to consider is even larger.

Regards,
Bill Page.

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