Looking at our previous implementation, it would be nice if we didn't have to check whether an invoice has been discounted at runtime. Is there a way we could check whether an invoice has been discounted at compile time instead? With phantom types, we can.

Phantom types are types that have a type variable, but this type variable isn't used in its definition. To better understand, let's look again at the option type, as shown in the following code:

type option('a) =
  | None
  | Some('a);

The option type has a type variable, 'a, and the type variable is being used in its definition. As we've already learned, option is a polymorphic type because it has a type variable. On the other hand, a phantom type doesn't use the type variable in its definition. Let's see how this is useful with our invoice management example.

Let&apos...