iso.scala

trait Isomorphism[Arrow[_, _], A, B] {
  def to: Arrow[A, B]
  def from: Arrow[B, A]
}

isos.scala

trait Isomorphisms {
  type IsoSet[A, B] = Isomorphism[Function1, A, B]
  type <=>[A, B]    = IsoSet[A, B]

  implicit def eitherIsoSafe[A]: Either[List[Throwable], A] <=> Safe[A] =
    new (Either[List[Throwable], A] <=> Safe[A]) {
      override def to: Either[scala.List[scala.Throwable], A] => Safe[A] = {
        case Right(a)  => safe(a)
        case Left(exs) => Invalid(exs)
      }

      override def from: Safe[A] => Either[List[Throwable], A] = {
        case Valid(a)     => Right(a)
        case Invalid(exs) => Left(exs)
      }
    }

  trait IsoSetOps[A, B] {
    def iso: A <=> B
    def self: A
    def asT[C](implicit eq: B === C): C = eq.coerce(iso.to(self))
  }

  trait ToIsoSetOps {
    implicit def toIsoSetOps[A, B](target: A)(implicit tc: A <=> B): IsoSetOps[A, B] =
      new IsoSetOps[A, B] {
        val self: A      = target
        val iso: A <=> B = tc
      }
  }

  object iso extends ToIsoSetOps
}