Enum and bounded instances for (,) and Either

[Carter Schonwald]

This raises a good point: enum as it currently exists is pretty bad and not
well behaved !

On Sat, May 15, 2021 at 10:54 AM Zemyla <zemyla at gmail.com> wrote:

> We can't write instances of Enum for (,) and Either until we have total
> versions of pred and succ.
>
> On Wed, May 12, 2021, 20:11 Carter Schonwald <carter.schonwald at gmail.com>
> wrote:
>
>> *while we could
>>
>> Perhaps we should provide these flavors via new types and thus folks
>> could still benefit from these instances by way of deriving via ?
>>
>> On Wed, May 12, 2021 at 6:38 PM Carter Schonwald <
>> carter.schonwald at gmail.com> wrote:
>>
>>> 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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