Re: Break `abs` into two aspects

6 Feb 2020


      "i" is an Integer there, which has an Ord instance.

On Wed, Feb 5, 2020, 19:20 Carter Schonwald 
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  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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