# Enum and bounded instances for (,) and Either

Edward Kmett ekmett at gmail.com
Wed May 12 21:46:18 UTC 2021

```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
>   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
>
> Are there any reasons these instances are missing from base?
>
> Cheers,
> Sandy
>>
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