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

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)

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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))

Given a starting sequence xs, here's my take:

xs collectFirst { case x@Left(_) => x } getOrElse
  Right(xs collect {case Right(x) => x})

This being in answer to the body of the question, obtaining only the first error as an Either[String,Seq[A]]. It's obviously not a valid answer to the question in the title

---

To return all errors:

val lefts = xs collect {case Left(x) => x }
def rights = xs collect {case Right(x) => x}
if(lefts.isEmpty) Right(rights) else Left(lefts)

Note that rights is defined as a method, so it'll only be evaluated on demand, if necessary

Here is the scalaz code:

_.sequence