Mechanical steps to convert many algorithms written as a while loop to a tail-recursive function

imperative_to_recursive.scala

  def fibImperative(index: Int): Int = {


    var a = 0
    var b = 1
    var counter = 0

    while (counter < index) {
      val c = a + b
      a = b
      b = c
      counter = counter + 1
    }

    a
  }

  /*
    1. "Loop state" becomes function parameters
    2. while condition becomes decision when to return
    3. We loop by recursing
    4. Reassignments become arguments passed in recursion
    5. Resulting computation becomes what we return at the end
    6. Initializers become arguments to first (outer) invocation
   */

  def fibRecursive(index: Int): Int = {
    def loop(a: Int, b: Int, counter: Int): Int = {
      if (counter < index)
        loop(b, a + b, counter + 1)
      else
        a
    }

    loop(0, 1, 0)
  }