Break `abs` into two aspects

[Carter Schonwald]

Andrew: could you explain the algebra notation you were using for short
hand?  I think I followed, but for people the libraries list might be their
first exposure to advanced / graduate abstract algebra (which winds up
being simpler than most folks expect ;) )

On Fri, Jan 31, 2020 at 4:36 PM Carter Schonwald <carter.schonwald at gmail.com>
wrote:

> that actually sounds pretty sane. I think!
>
> On Fri, Jan 31, 2020 at 3:38 PM Andrew Lelechenko <
> andrew.lelechenko at gmail.com> wrote:
>
>> On Tue, 28 Jan 2020, Dannyu NDos wrote:
>>
>> > Second, I suggest to move `abs` and `signum` from `Num` to `Floating`
>>
>> I can fully relate your frustration with `abs` and `signum` (and numeric
>> type classes in Haskell altogether). But IMO breaking both in `Num` and in
>> `Floating` at once is not a promising way to make things proper.
>>
>> I would rather follow the beaten track of Applicative Monad and Semigroup
>> Monoid proposals and - as a first step - introduce a superclass (probably,
>> borrowing the design from `semirings` package):
>>
>> class Semiring a where
>>   zero  :: a
>>   plus  :: a -> a -> a
>>   one   :: a
>>   times :: a -> a -> a
>>   fromNatural :: Natural -> a
>> class Semiring a => Num a where ...
>>
>> Tangible benefits in `base` include:
>> a) instance Semiring Bool,
>> b) a total instance Semiring Natural (in contrast to a partial instance
>> Num Natural),
>> c) instance Num a => Semiring (Complex a) (in contrast to instance
>> RealFloat a => Num (Complex a)),
>> d) newtypes Sum and Product would require only Semiring constraint
>> instead of Num.
>>
>> Best regards,
>> Andrew
>>
>>
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>
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