EitherT[Option, A, B] === Option[Either[A,B]]

Question

If I understand correctly EitherT[Option,A,B ] should be identical to Option[Either[A,B]] , but the compiler doesn't agree. The following code fails to compile:

def f[A,B] = implicitly[EitherT[Option, A, B] === Option[Either[A,B]]] 

What am I missing?

Answer 1

They are isomorphic, but not the same value. EitherT[Option,A,B] wraps a value of type Option[Either[A,B]] in order to provide different behavior. Let's look at the definition:

final case class EitherT[F[_], A, B](run: F[A \/ B])

So EitherT here is wrapping an Option, and the value named run is a value which is of type Option[Either[A,B]]