Question

Could Ord and Enum be one typeclass? Why doesn’t Enum require Eq?

Answer 1

Enum represents types that can be mapped to/from integers. This doesn’t say anything about how those types should be sorted, merely that you can represent them with integers.

Ord represents ordered types. This is different than types that can be mapped to integers. For example, you can’t map arbitrary-precision floating point values to integers, but you can order them. And while you technically could try and map Floats to integers, nobody in their right mind would do so.

As for Eq, Ord requires this because it doesn’t make sense to have a totally ordered datatype that doesn’t support equality. However, Enum has no need for Eq. Since Enum doesn’t provide any ordering guarantees, it doesn’t provide equality guarantees either.