[Haskell-cafe] Re: Positive integers

[Henning Thielemann]

On Fri, 24 Mar 2006, Aaron Denney wrote:

> Basically, my big objection is that it's hard to define many useful
> operations on them that are statically safe.

Why not defining the Torsor class you suggested?

>  Any definition of Num a for instance leaves a whole bunch of unsafe 
> methods, or just plain inapplicable methods, such as "negate".

Yes Num class is quite inappropriate.

> Now granted, the numeric hierarchy should be broken up a bit (hmm, I
> should finish my strawman proposal for Haskell'), but even then I see
> problems.

Hm, is there something going on? Without breaking compatibility? But class 
instances become invalid if the hierarchy is modified. If there is some 
progress towards a refined numeric class hierarchy I want to point again 
to
  http://cvs.haskell.org/darcs/numericprelude/
  http://cvs.haskell.org/darcs/numericprelude/src/Algebra/Core.lhs
   I hope I don't annoy you. :-)