如何在 Haskell 中实现代数数据类型的“Ord”？

Question

Imagine you have a rating like

Rating = OneStar | TwoStars | ThreeStars | FourStars | FiveStars

What is the best way to instanciate/implement "Ord" for such an algebraic data type in Haskell?

Answer 1

The best way would be to just add deriving (Eq, Ord) to the type's definition.

Since you listed your constructors in ascending order, the derived Ord instance will give you exactly the order you want.

However, if changing the order in the definition is not an option for some reason you can still derive Eq, since for that the order does not matter. Given an instance of Eq, we can manually write an instance for Ord. The most succinct way to define compare would probably be to spell out all the combinations for which compare should return LT and then simply use compare xy | x == y = Eq; compare _ _ = GT for the remaining combinations.

Answer 2

As has been mention, you can derive Eq and Ord . Or you could derive Enum and then do

instance Eq Rating where
    x == y = fromEnum x == fromEnum y

Or just spell it all out

instance Eq Rating where
    OneStar == OneStar = True
    TwoStar == TwoStar = True
...
    _ == _ = False

Answer 3

For anyone wondering, here is the complete, explicit, boilerplate implementation:

Using roman numerals.
Using case for ease of reading.

data RN = I | II | III | IV | V

instance Eq RN where
    I == I     = True
    I == _     = False
    II == II   = True
    II == _    = False
    III == III = True
    III == _   = False
    IV == IV   = True
    IV == _    = False
    V == V     = True
    V == _     = False

instance Ord RN where
    compare I x = case x of
        I   -> EQ
        _   -> LT
    compare II x = case x of
        I   -> GT
        II  -> EQ
        _   -> LT
    compare III x = case x of
        I   -> GT
        II  -> GT
        III -> EQ
        _   -> LT
    compare IV x = case x of
        V   -> LT
        IV  -> EQ
        _   -> GT
    compare V x = case x of
        V   -> EQ
        _   -> GT