popCount is a method of Bits, not a FiniteBits

[Oleg Grenrus]

I'd refine the documentation of `Bits` class to say that it's a class 
for integral types with finite count of bits toggled, i.e. finite popCount.
Than many things work out, except complementInteger is actually used.

It's not a big change codewise: 
https://gitlab.haskell.org/ghc/ghc/merge_requests/2261 (GHC actually 
uses complementInteger for something itself).

Without complement, Bits Natural would total instance, without partial 
methods. If complement for Integer is very important, then I'd propose 
to introduce classes to form diamond shape:

-- instance can be defined for Integer
class Bits b => Complement b where
     complement :: b -> b

-- instance can be defined for Natural
class Bits b => PopCount b where
     popCount :: b -> b

class Complement b => FiniteBits b where
     ...

I think this is worth the trouble, this wart should been fixed when 
Natural was brought to base. And in fact, because of complement is in 
Bits, clearBit :: Natural -> Natural is broken in base-4.9.0.0 bundled 
with GHC-8.0: It went unnoticed, because there were default 
implementation using complement. If Haskell2020 will happen, it really 
should explain what the complement :: Natural -> Natural does otherwise. 
Haskell2010 just mentions that there is Bits Integer. For the report 
defense, popCount isn't in its Bits version.

So, we made warts by both adding popCount to Bits and adding Natural 
Bits instance. Let's just fix them.

- Oleg

On 1.12.2019 5.21, Brent Yorgey wrote:
> A few points:
>
> 1. The Bits instance for Integer essentially already behaves as if 
> they are the 2-adic numbers.  For example, if you use testBit you can 
> discover that (-2 :: Integer) is treated as if it were an infinite 
> sequence of 1's followed by a single 0.
> 2. However, because testBit takes an Int index, instances of Bits 
> actually can't have an infinite number of 1 bits---at least not in 
> practice---since you cannot observe anything past the (maxBound :: 
> Int)th bit.
> 3. Currently, popCount on negative Integer values satisfies popCount 
> (-x) = -(popCount x)  which does not seem very well motivated and does 
> not match the way negative values are presented via testBit.
>
> I am strongly -1 on moving popCount to FiniteBits. popCount on 
> positive Integers is useful and well-defined.  I am mildly +1 on 
> Zemlya's proposal to change the behavior of popCount for negative 
> Integer values, though I am not sure it is really worth the trouble.
>
> -Brent
>
> On Sat, Nov 30, 2019 at 10:10 AM Zemyla <zemyla at gmail.com 
> <mailto:zemyla at gmail.com>> wrote:
>
>     popCount is a perfectly sensible method for Natural, and it could
>     theoretically become one for Integer as well if we say that,
>     whenever there's an infinite number of 1s and a finite number of
>     0s, then the result is -(1 + count of 0s), as though it were
>     maxBound :: Word bits in size and merely converted to an Int (a
>     sensible assumption, considering memory limits). The results for
>     types where there can be both infinite 0s and 1s should still be
>     an error.
>
>     On Sat, Nov 30, 2019, 09:21 Oleg Grenrus <oleg.grenrus at iki.fi
>     <mailto:oleg.grenrus at iki.fi>> wrote:
>
>         Although, popCount for Integer/Natural kind of makes sense, as
>         they
>         aren't infinite list of [Bit]s, but smarter structure.
>
>         On 30.11.2019 17.17, Oleg Grenrus wrote:
>         > I propose to change it to be member of FiniteBits
>         >
>         > I recall, there was a proposal to remove bitSize from Bits,
>         so it's an
>         > opportunity to introduce another small, yet breaking change
>         at the
>         > same time.
>         >
>         > Discussion time 2 week.
>         >
>         > - Oleg
>         >
>         > _______________________________________________
>         > Libraries mailing list
>         > Libraries at haskell.org <mailto:Libraries at haskell.org>
>         > http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries
>         _______________________________________________
>         Libraries mailing list
>         Libraries at haskell.org <mailto:Libraries at haskell.org>
>         http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries
>
>     _______________________________________________
>     Libraries mailing list
>     Libraries at haskell.org <mailto:Libraries at haskell.org>
>     http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mail.haskell.org/pipermail/libraries/attachments/20191202/b731e5f4/attachment.html>