Qi does include facilities for handling dependent types see

http://groups.google.co.uk/group/qilang/browse_thread/thread/96892fbdfd312c97/8db8cdb3dfeba0fd?hl=en&lnk=gst&q=dependent+types#8db8cdb3dfeba0fd

The type notation is actually Turing equivalent, as asserted here

http://www.lambdassociates.org/studies/study01.htm

and demonstrated formally here

http://groups.google.co.uk/group/qilang/browse_thread/thread/f9dadc73d3ccafcd/085df0b43ab86f3a?hl=en&lnk=gst&q=combinator#085df0b43ab86f3a

Qi II includes lazy evaluation on demand

http://www.lambdassociates.org/Book/page153.htm

Shen has one important innovation not found in Qi II, which is the
ability to extend the resident type checker with type secure *tactics*
in the manner of LCF etc.  This enables advanced techniques form
algebra and formal methods to be programmed into Shen.  This feature
has not yet been discussed in this group, but will be when Shen
appears later this spring.

Mark

On 9 Apr, 16:23, "Serge D. Mechveliani" <mech...@botik.ru> wrote:
> Dear Qi team and community,
>
> I have a large computer algebra library called  DoCon  written in  
> Haskell  (both tools are available on the Web).
>
> Also I have formulated certain main requirements for an universal
> functional language. This is described in the manuscripts
>
>   "What should be an universal functional language" (2003)
>  http://www.botik.ru/pub/local/Mechveliani/otherPapers/whatsh.ps.zip
> and
>   "Haskell and computer algebra" (2001)
>  http://www.botik.ru/pub/local/Mechveliani/basAlgPropos/haskellInCA2.p...
>
> The first main point is
>   how to add to Haskell the  dependent types  feature?
>   (the possibility to define a domain computed at runtime dependently
>   on its parameters).
>
> Due to absence of dependent types, the DoCon library has too complex
> architecture for an algebraic domain and its instances
> (see about the "sample argument approach" in DoCon and in the above
> two manuscripts).
>
> It is difficult to reliably implement categories (classes) with
> dynamic instances.
>
> The  Cayenne  language tried dependent types. But its project has
> stopped long ago, so far as I know.
> The  Aldor  language has dynamic domains, but it is not functional,
> it stands too far from Haskell. Also I never tried the implementation.
>
> Can  Qi  be considered as an improvement of  Haskell  in what it
> concerns computer algebra?
>
> With kind regards,
>
> -----------------
> Serge Mechveliani
> mech...@botik.ru
>
> (for any occasion, copy the reply to  mech...@botik.ru)