Scala: recursive implicit type

Question

I have the following traits for parsing that give file positions for the beginning and end of the object:

case class FilePosn(lineNum :Int, tabs: Int, spaces: Int, fileName: String)
{/*code omitted*/}

trait PosnEnds
{
  def startPosn: FilePosn
  def endPosn: FilePosn
  def multiLine: Boolean = startPosn.lineNum != endPosn.lineNum
  def OneLine: Boolean = startPosn.lineNum == endPosn.lineNum
  def indent: Int = startPosn.tabs
  def startLine: Int = startPosn.lineNum
  def endLine: Int = endPosn.lineNum
}

object FilePosnVoid extends FilePosn(0, 0, 0, "There is no File position")
{ override def posnString(indentSize: Int): String = "No File Posn: " }

In the companion object I create an implicit, so sequences of PosnEnds are themselves implicitly PosnEnds:

object PosnEnds
{
  implicit class ImpPosnEndsSeq[A <: PosnEnds](thisSeq: Seq[A]) extends PosnEnds
  {
    override def startPosn: FilePosn = thisSeq.fHead(FilePosnVoid, (h, t) => h.startPosn)
    override def endPosn: FilePosn = thisSeq.fLast(FilePosnVoid, _.endPosn)     
  }
}

Is there anyway to use implicits recursively so a Seq[Seq[A]] and a Seq[Seq[Seq[A]]] etc will be implicitly converted to a PosnEnds trait? In practice I probably won't need huge levels of depth, but it would be nice to use an elegant solution that implicitly converted Seq of arbitrary depth.

Currently for depth 2 I'm using:

implicit class ImpPosnEndsSeqSeq[A <: PosnEnds](thisSeq: Seq[Seq[A]]) extends PosnEnds
{
  override def startPosn: FilePosn = thisSeq.fHead(FilePosnVoid, (h, t) => h.startPosn)
  override def endPosn: FilePosn = thisSeq.fLast(FilePosnVoid, _.endPosn)     
}

Answer 1

Yes. You could do it with typeclass mediator.

I allow myself to do some minor changes in your example to make it more reproducible. Inside object PosnEnds I have

val void = new FilePosn(0, 0, 0, "There is no File position") {
  override def posnString(indentSize: Int): String = "No File Posn: "
}

def empty = new PosnEnds {
  def startPosn: FilePosn = void
  def endPosn: FilePosn = void
}

Thing you need first is some simple typeclass like

trait MakePosnEnds[X] extends (X => PosnEnds)

Now you can introduce canonical elements for induction:

implicit object idMakePosnEnds extends MakePosnEnds[PosnEnds] {
  def apply(x: PosnEnds) = x
}

implicit def seqMakePosnEnds[X](implicit recur: MakePosnEnds[X]) = new MakePosnEnds[Seq[X]] {
  def apply(x: Seq[X]): PosnEnds = new PosnEnds {
    val thisSeq = x.map(recur)
    override def startPosn: FilePosn = thisSeq.headOption.fold(void)(_.startPosn)
    override def endPosn: FilePosn = thisSeq.lastOption.fold(void)(_.endPosn)
  }
}

Finally you can define your implicit conversion

implicit def toPosnEnds[X](x: X)(implicit make: MakePosnEnds[X]): PosnEnds = make(x)

From this point

Seq(Seq(Seq(empty))).startLine

compiles and runs succesfully

Major difference with your attempt: we dont wait implicit conversion to stack. Implicit resolution can be recursive, but implicit conversion can not.

So we are using some value-less type, i.e something that could be achieved using only implicit arguments which means could be constructed by the compiler. And only then projecting this logic to the concrete value.