scanEval.scala

def scanEval[F[_]: Sync, S, A](p: Stream[F, A])(start: F[S])(f: (S, A) => F[S]): Stream[F, S] = {
  def zipper(ref: Ref[F, S]): Stream[F, S] =
    p.zip(Stream.eval(ref.get).repeat).evalMap { case (a, s) =>
      for {
        ns <- f(s, a)
        _  <- ref.set(ns)
      } yield ns
    }

  for {
    st  <- Stream.eval(start)
    ref <- Stream.eval(Ref.of[F, S](st))
    rs  <- zipper(ref)
  } yield rs
}