Problem Statement

Provide code that produces a list of numbers which is the   nth  order forward difference, given a non-negative integer (specifying the order) and a list of numbers.

The first-order forward difference of a list of numbers   A   is a new list   B,   where   Bn = An+1 - An. List   B   should have one fewer element as a result. The second-order forward difference of   A   will be: The same as the first-order forward difference of   B. That new list will have two fewer elements than   A   and one less than   B. The goal of this task is to repeat this process up to the desired order. For a more formal description, see the related   Mathworld article.

Let's start with the solution:

import "./fmt" for Fmt

var forwardDiff = Fn.new { |a, order|
    if (order < 0) Fiber.abort("Order must be a non-negative integer.")
    if (a.count == 0) return
    Fmt.print(" 0: $5d", a)
    if (a.count == 1) return
    if (order == 0) return
    for (o in 1..order) {
        var b = List.filled(a.count-1, 0)
        for (i in 0...b.count) b[i] = a[i+1] - a[i]
        Fmt.print("$2d: $5d", o, b)
        if (b.count == 1) return
        a = b
    }
}

forwardDiff.call([90, 47, 58, 29, 22, 32, 55, 5, 55, 73], 9)