> But in this case unless we assert it, not every domain has Domain.

That's true, but the only thing that must be extended is a few basic 
categories like, for example SetCategory.

> Declaring X:Domain or X:Domain with ..., or X:Join(Domain, ...) is
> just making this assertion. It does not provide X with the
> characteristics of an "object", which by definition is an instance of
> some domain.

> That category that plays this role in Axiom is called Type

> (1) -> )sh Type
>  Type  is a category constructor

Hmmm, maybe I mix again Aldor and SPAD...

See section 7.7 AUG:
Type: A type S satisfies the language-defined type Type if S is the type
of a domain or category. In other words, all domains and categories
are types.

Is this really different for SPAD? (I am not saying anything about the 
interpreter.) Is there a definition for SPAD somewhere besides the one 
given by ")sh Type"?

> But the structure of Type is quite different than the structure of a domain.

Sorry I don't know about the internals.

Ralf

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