[Haskell-cafe] type universes (was Re: MPTC inheritance

[Larry Evans]

On 02/24/09 13:41, Paul Johnson wrote:
> Derek Gladding wrote:
>> Please forgive me if I'm still mentally contaminated by the OO way of 
>> seeing (and discussing) the universe, but I'm trying to figure out how 
>> to "inherit an interface" from a multi-parameter type class.
>> [...]
>> but this isn't allowed (kind mismatch).
>>
> Kinds are a meta-type system for types.  Because Haskell has such a rich 
> type system, the types themselves need a type-like system.  These are 
> "kinds".  You never declare kinds (apart from certain language 
> extensions not in use here): the compiler infers them.

Is a kind sorta like a type universe as in nuprl:

http://www.cs.cornell.edu/home/sfa/Nuprl/NuprlPrimitives/Xuniverse_doc.html

Except that a kind sounds like a universe at level 2 or 3.
IOW, I guess haskell types are at level 1, and kines at level 2?
Then I guess values would be at level 0?

Is there some version of haskell that has more levels in its
type universe.  If not, it there some reason for that
limitation?  Is there some reference explaining the relationship
of haskell types to nuprl type universes?


TIA.

-Larry