Ord – ordered types

The Ord class requires any type that wants to be an instance of it to first be an instance of the Eq class by using a class constraint, and additionally, to support the following methods:

class (Eq a) => Ord a where
  (<), (<=), (>), (>=) :: a -> a -> Bool
  min, max :: a -> a -> a

In other words, the Ord class extends the Eq class and supports additional methods (<), (<=), (>), (>=), min and max. The min and max methods are defined by default as:

min x y
 | x <= y = x
 | otherwise = y
 
max x y
 | x <= y = y
 | otherwise = x

And for a minimal definition of the class, we just need to define the (<=) method because the other ones also have default definitions:

class (Eq a) => Ord a where
  (<), (<=), (>), (>=) :: a -> a -> Bool
  min, max :: a -> a -> a

    -- Minimal complete definition:
    -- (<=)
    
  x < y = x <= y && x /= y
  x > y = y < x
  x >= y = y <= x
  
  min x y
    | x <= y = x
    | otherwise = y
  max x y
   | x <= y = y
   | otherwise = x

All the basic types of Haskell are also instances of the Ord class.