PROPOSAL: Add 'Natural' type to base:Data.Word

[Daniel Díaz]

I am +1 on having Natural in base, I don't really mind the place 
(although I also admit that Data.Word seems odd to me).

About subtraction. For the Num instance of Natural, I'd prefer (x - y) 
where (y > x) to fail with an error call. This is
consistent with the behavior we already have for division. The type 
`(-):: Natural ->Natural -> Natural` forces us to return
a value for any pair of naturals. However, subtraction is not defined 
for every pair, so it makes sense to me for the function
to be partial.

That being said, I consider myself an enemy of partial functions (head, 
tail, and family), and I'd probably prefer to use subtraction
with the following type:

safeSubtract :: Natural -> Natural -> Maybe Natural

With this type, we are not forced to return a value for every pair, 
returning Nothing instead for those cases where subtraction does not make
sense. This is, IMHO, the best way to subtract naturals.

Best regards,
Daniel Díaz.

On 11/13/2014 01:03 AM, Sean Leather wrote:
> Iavor laid out the options nicely, so I'm building off of his response.
>
> On Wed, Nov 12, 2014 at 9:16 PM, Iavor Diatchki wrote:
>
>     1. I like the idea of having a `Natual` type similar to `Integer`,
>     so +1 from me.
>
>
> A definite +1 from me, too.
>
>     2. I am a bit worried about the partiality of some of the
>     operations, but I don't see an appealing alternative... I guess we
>     should just throw some informative exceptions.
>
>
> I agree, but see my response to John Lato below.
>
>     3. I don't mind where it lives, although `Data.Word` does seem a
>     little odd.
>
>
> Agreed with this, too, but I'm not sure of a better place. Would it be 
> worth exporting Integer from Data.Int to have symmetry? Or is that silly?
>
> On Thu, Nov 13, 2014 at 2:51 AM, John Lato wrote:
>
>     +0.9 for saturated subtraction.
>     Playing devil's advocate, the downside is that if a user forgets
>     to check the subtraction preconditions, saturated subtraction will
>     silently give the wrong answer instead of calling error.  So for a
>     (relatively common?) mistake, the consequences will be worse
>     (exceptions are better than wrong values).
>
>     However, this is balanced by several use cases for which saturated
>     subtraction is the desired behavior. Furthermore there's no
>     existing code to break, so now is the time to make this choice (it
>     would be easier to go to a partial function in the future than
>     vice versa).
>
>
> I'm not sure how it would be “easier to go to a partial function” if 
> your code expects saturation.
>
> Here's another option: Provide total (or partial) functions by default 
> in the Num and other instances, and provide supplementary partial 
> (total) functions for those who want the other semantics.
>
> Regards,
> Sean
>
>
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