How to reduce Seq[Either[A,B]] to Either[A,Seq[B]]?

Question

Given a sequence of eithers Seq[Either[String,A]] with Left being an error message. I want to obtain an Either[String,Seq[A]] where I get a Right (which will be a Seq[A]), if all elements of the sequence are Right. If there is at least one Left (an error message), I'd like to obtain the first error message or a concatenation of all error messages.

Of course you can post scalaz code but I'm also interested in code not using it.

Edit

I've changed the title, which originally asked for an Either[Seq[A],Seq[B]] to reflect the body of the message.

Answer 1

Edit: I missed that the title of your question asked for Either[Seq[A],Seq[B]], but I did read "I'd like to obtain the first error message or a concatenation of all error messages", and this would give you the former:

def sequence[A, B](s: Seq[Either[A, B]]): Either[A, Seq[B]] =
  s.foldRight(Right(Nil): Either[A, List[B]]) {
    (e, acc) => for (xs <- acc.right; x <- e.right) yield x :: xs
  }

scala> sequence(List(Right(1), Right(2), Right(3)))
res2: Either[Nothing,Seq[Int]] = Right(List(1, 2, 3))

scala> sequence(List(Right(1), Left("error"), Right(3)))
res3: Either[java.lang.String,Seq[Int]] = Left(error)

---

Using Scalaz:

val xs: List[Either[String, Int]] = List(Right(1), Right(2), Right(3))

scala> xs.sequenceU
res0:  scala.util.Either[String,List[Int]] = Right(List(1, 2, 3))