[Haskell-cafe] Re: Proposal for Number classes

[Serge D. Mechveliani]

Dylan Thurston <dthurston at barnard.edu> wrote on 17 Apr 2006 


> On Sat, Apr 08, 2006 at 10:16:53PM +0400, Serge D. Mechveliani wrote:
>> I think that without  dependent types  for a Haskell-like language, 
>> it is impossible to propose any adequate and in the same time plainly
>> looking algebraic class system.

> Agreed.  Is there anything really wrong with the Kiselyov-Shan
> approach to dependent types?  Does it look too bizarre?
>
> http://okmij.org/ftp/Haskell/types.html#Prepose
> http://okmij.org/ftp/Haskell/number-parameterized-types.html


I am out of this field since about 2001.

The first paper mentions the foreign function interface, and 
transmitting integer by means of tricks with types (I recall 
difficulties with existential types), and so on.

It also mentions passing vocabularies (maybe, via foreign interface
extension).
Of course, if a language extension allows to express the constructs 
like

  if  isPrime n  
  then  
         (pass  inv  (the inversion operation) to the vocabulary
          of  (ResidueDomain Integer n),
          with this implementation ...
         )
  else   do not pass it
,
then this is what is needed: an equivalent of a dynamic conditional 
instance. 
In this example, passing  inv  expresses actially dynamic and 
conditional definition of the  Field  instance.
Field a  <==>  (CommutativeRing a,  `inv' is in vocabulary of a).

In  Magma  system,  and in  Aldor,  it can be, probably, written 
plainly.
But these systems are not functional, nor lazy, have not pattern
matching, etc.

Currently I am out of this field, have not time to study all this.

For example, if Dylan Thurston tries to implement the Basic Algebra 
proposal basing on the approach of `configurations' of
http://okmij.org/ftp/Haskell/types.html#Prepose,

and with the functionality as of the BAL proposal, then we could 
observe whether the thing looks natural enough.

I could also think of doing an attentive investigation on this 
subject, maybe, together with some qualified people, if I have 
this project as somehow a visiting research job, and paid.
And there is no guarantee that the result occurs positive.

-----------------
Serge Mechveliani
mechvel at botik.ru