[Haskell-cafe] ANNOUNCE: yap-0.0 - yet another prelude

[Henning Thielemann]

On Thu, 11 Aug 2011, Sebastian Fischer wrote:

> [switched to Cafe]
>
> On Wed, Aug 10, 2011 at 11:46 PM, Henning Thielemann
> <lemming at henning-thielemann.de> wrote:
>>
>> On Wed, 10 Aug 2011, Paterson, Ross wrote:
>>
>>> Yet another restructuring of the Prelude numeric classes on algebraic
>>> lines, proposed for a revision of the Haskell Prelude:
>>>
>>> http://hackage.haskell.org/package/yap-0.0
>>
>> A nice lightweight design, both in terms of the use of type extensions and
>> import dependencies, that should people encourage to use it, when they are
>> afraid of changing to a more radical approach like numeric-prelude. I would
>> have prefered the name AdditiveGroup to AbelianGroup, since with '+' and '-'
>> and '0' I associate more than just the laws of an Abelian group. The
>> multiplicative group of rational numbers is abelian, too.
>
> I'm curious: what laws do you have in mind for '+', '-', and '0' that
> do not hold in the multiplicative group of rational numbers with
>
>    (+) = (*); (-) = (/); 0 = 1
>
> ?

  I do not associate more laws, but I expect to use zero for things that 
are somehow related to numbers. And I also do not want to use (+) and (-), 
say, for rational numbers to mean (*) and (/). That's not an algebraical 
reason, but a matter of error prevention and expectations.
  It's the same reason, why I would not want to define an Ord instance for 
Complex numbers. Complex numbers can be ordered, but a < (b::Complex 
Rational) will be a mistake in many cases, I guess.