Break `abs` into two aspects

[Zemyla]

Should we move the Semiring discussion to a new proposal?

On Fri, Feb 7, 2020, 09:01 Carter Schonwald <carter.schonwald at gmail.com>
wrote:

> Derp. :)
>
> On Wed, Feb 5, 2020 at 9:08 PM Zemyla <zemyla at gmail.com> wrote:
>
>> "i" is an Integer there, which has an Ord instance.
>>
>> On Wed, Feb 5, 2020, 19:20 Carter Schonwald <carter.schonwald at gmail.com>
>> wrote:
>>
>>> Num doesn't have Ord as a parent constraint any more ... Though i
>>> suppose that works as a default signature instance?
>>>
>>> On Wed, Feb 5, 2020 at 3:19 PM Mario Blažević <mblazevic at stilo.com>
>>> wrote:
>>>
>>>> On 2020-02-04 11:32 a.m., Zemyla wrote:
>>>> > It really doesn't matter if it's not "interesting" or not surjective
>>>> for
>>>> > some Semirings. It should be included, because:
>>>>
>>>>         I fully agree, and I'll add another reason you left out. The
>>>> presence
>>>> of fromNatural would allow defaulting of Num's fromInteger as
>>>>
>>>>  > fromInteger i
>>>>  >     | i >= 0 = fromNatural (fromInteger i)
>>>>  >     | otherwise = negate . fromInteger . negate $ i
>>>>
>>>>
>>>> > (a) Even for semirings where it is "interesting", it's not surjective
>>>> > (for instance, Rational or Double)
>>>> > (b) It's a method with a default definition, so you don't have to
>>>> expend
>>>> > any mental effort on it
>>>> > (c) A lot of instances have uninteresting methods: for instance, (*>)
>>>> > and (<*) for Applicative ((->) e) are const id and const
>>>> respectively.
>>>> > Haskell adds methods to classes when they're always possible and
>>>> > sometimes useful/interesting/faster, rather than when they're always
>>>> > interesting.
>>>> > (d) It's useful for Semiring-generic methods and instances.
>>>> > (e) It can achieve an asymptotic speedup on some instances. Like, if
>>>> you
>>>> > have Semiring a => Semiring (f a) for some type f, then you can have
>>>> > fromNatural n = pure (fromNatural n) instead of doing the whole O(log
>>>> n)
>>>> > song and dance with the default definition. Also, your example admits
>>>> a
>>>> > simple definition:
>>>> >    fromNatural n = if n == 0 then S.empty else S.singleton True
>>>> > (f) "zero" and "one" can be defined in terms of fromNatural, for
>>>> > programmers who only need to define that:
>>>> >    zero = fromNatural 0
>>>> >    one = fromNatural 1
>>>> > This leads to the MINIMAL pragma on Semiring being {-# MINIMAL plus,
>>>> > times, (zero, one | fromNatural) #-}
>>>> > (g) If it's not included in the class, but in some subclass
>>>> > (NaturalSemiring, you proposed), but it's possible from the class,
>>>> then
>>>> > people will just define and use the O(log n) version instead of
>>>> > requiring the subclass, leading to wasted effort and duplicated code.
>>>>
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