Eq – Equality Types

The Eq class supports the comparison methods (equality and inequality), so any two values of a type that is an instance of the Eq class can be compared using the functions:

(==) :: a -> a -> Bool
(/=) :: a -> a -> Bool

We have already used these functions many times, and we were able to because all the basic types (Char, Bool, Int....) are instances of the Eq class. Classes are defined using the class keyword followed by the class name, the type specification and the where keyword, followed by the default definitions of the class methods:

class Eq a where
  (==), (/=) :: a -> a-> Bool
  
    -- Minimal complete definition:
    -- (==) or (/=)
    
  x /= y = not (x == y)
  x == y = not (x /= y)

We see the two default methods above defined in terms of each other, which means we need to define one of them in a clear way to have a complete definition for an instance. For example, the Bool type can be made an instance of the Eq class with:

instance Eq Bool where
  False == True = False
  True == False = False
  _ == _ = True
  
-- or using the (/=) method
    
instance Eq Bool where
  False /= True = True
  True /= False = True
  _ /= _ = False

Keep in mind that the definitions of the required functions can be as simple or as complicated as you like, and default definitions can be overwritten when declaring instances.