Are Ord and Enum sometimes incompatible in Haskell?

Question

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

Answer 1

There are things that can be enumerated without an order. For example:

data Color = Red | Green | Blue deriving Enum

Which order should colors have? There is no inherent order, even though the colors can be enuemrated.

There are also things that can be enumerated but not compared for equality. Floats, for example, have a NaN value that isn't equal to anything. Floats can be enumerated, however.

Answer 2

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.