Bill,

On Jan 16, 2013, at 1:31 PM, Bill Richter <rich...@math.northwestern.edu> wrote:

> 
> …
> And as Rob says that eventually we should modify HOL to allow type 
> quantification

You make me sound more definite about this than I actually feel. In fact it has 
already been done (for HOL4) in the shape of Peter Homeier's HOL-Omega. But 
Peter has gone quite a bit further than I expected.

> maybe we should ask if we shouldn't allow terms to show up it types, so we 
> could define real^3 where 3 has type num, as it normally does, rather than 
> being a type that somehow satisfies dimindex (:3) = 3.  

You are now entering the world of dependent types - where the extent of a type 
can depend on the value of a term.  This introduces a whole new set of 
complications. I don't recall how far down this path HOL-Omega goes.

Regards,

Rob.



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