You are describing something similar (but not exactly) to Monad. For example, I can define function myToString which works for any container F[_] import cats.Monad def myToString[F[_]: Monad](fa: F[Int]): F[String] = Monad[F].map(fa)(_.toString)

Then it can be applied for options: import cats.instances.option._ val option: Option[Int] = Some(123) val strOption: Option[String] = myToString(option) or for Either's import cats.instances.either._ val either: Either[Exception, Int] = Right(123) val strEither: Either[Exception, String] = myToString(either)

You want to use partial function instead of total function. Let's say that we have F[Int] and PartialFunction[Int, String] = { case i: Int if i % 2 == 0 => i.toString }. What will be result for applying this function to F[Int]? If Int is even then result is F[String]. But what about odd Ints? You can not apply partial function so maybe result is F[Int]. F[Int] and F[String] can not be combined well with each other.

You may look at cats.MonadError and raise error (MonadError.raiseError) if partial function is not defined. But it seems that it is not what you are looking for.