Enum and bounded instances for (,) and Either

[Carter Schonwald]

isnt there also the issue that while we good provide newtypes for various
choices of product of enum instance => enum of products, there literally
quite easily 3 valid instances we could concoct (and  many more besides)

"row by row"
"column by column"
"diagonalization"
etc?
that is: each of these is just as valid?

On Wed, May 12, 2021 at 5:46 PM Edward Kmett <ekmett at gmail.com> wrote:

> Nothing indicates that minBound is >= 0.
>
> So if you want to deal with a modulus properly you need to deal with a
> modulus of something like maxBound - minBound + 1 (after appropriately
> upcasting intermediate results to a large enough type to contain that
> range).
>
> You also run into range issues pretty early on, and then scenarios like
> the instances for Float that are even wonkier.
>
> If toEnum/fromEnum went to a larger type (Integer or Natural) and we
> didn't have the wonkier Float instances and the like this would be a much
> easier sell. As it is I find myself rather uncomfortable with the shakiness
> of the foundations this thing rests upon.
>
> Sent from my iPhone
>
> On May 12, 2021, at 10:53 AM, Sandy Maguire <sandy at sandymaguire.me> wrote:
>
> 
> Hi all,
>
> Found myself puzzled the other day when I wanted an (Enum a, Enum b) =>
> Enum (a, b) instance, and was distraught that it didn't exist.
>
> The following is a reasonable implementation:
>
>
> instance (Bounded b, Enum a, Enum b) => Enum (a, b) where
>   fromEnum (a, b) = (fromEnum (maxBound @b) + 1) * fromEnum a + fromEnum b
>   toEnum n =
>     let bound = fromEnum (maxBound @b) + 1
>         b = n `rem` bound
>         a = n `div` bound
>      in (toEnum a, toEnum b)
>
> And, while we're at it, might as well add canonical instances for Either:
>
>
> instance (Bounded a, Bounded b) => Bounded (Either a b) where
>   minBound = Left minBound
>   maxBound = Right maxBound
>
> instance (Bounded a, Enum a, Enum b) => Enum (Either a b) where
>   toEnum i =
>     let bound = fromEnum (maxBound @a) + 1
>      in case i < bound of
>           True -> Left $ toEnum i
>           False -> Right $ toEnum $ i - bound
>   fromEnum (Left a) = fromEnum a
>   fromEnum (Right b) = fromEnum b + fromEnum (maxBound @a) + 1
>
> Are there any reasons these instances are missing from base?
>
> Cheers,
> Sandy
>
>>
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