Functional style early exit from depth-first recursion

Question

I have a question about writing recursive algorithms in a functional style. I will use Scala for my example here, but the question applies to any functional language.

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Answer 1

You can convert breadth into depth by passing along an index or taking the tail:

def suml(xs: List[Int], total: Int = 0) = xs match {
  case Nil => total
  case x :: rest => suml(rest, total+x)
}

def suma(xs: Array[Int], from: Int = 0, total: Int = 0) = {
  if (from >= xs.length) total
  else suma(xs, from+1, total + xs(from))
}

In the latter case, you already have something to limit your breadth if you want; in the former, just add a width or somesuch.