Important Type Classes

Let’s continue by introducing a few more of the most important predefined Haskell type classes.

Comparing for equality with Eq

The type class Eq contains all types that can be compared for equality using ==. It is just as fundamental as Show and implemented by all basic Haskell data types except functions. Its definition is

data Eq a where
  (==), (/=) :: a -> a -> Bool
  x /= y = not (x == y)

While the class Eq contains two functions (the operators == and /=), only the == operator needs to be implemented for defining an instance of the class. This is because the /= operator contains a default implementation in the type class itself. Here it is defined as the negation of ==. This makes it sufficient to only implement equality. We say that defining only == is a minimal complete definition for an Eq instance.

Eq instances can also be derived. The derived implementation of == on custom data types first compares the constructors and then recursively compares the values inside them.

For example, let’s derive Eq for our Geometry data type. We can derive it together with Show at the same time.