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:

REAL :: n=10, list(n)

list = ( 90, 47, 58, 29, 22, 32, 55, 5, 55, 73 )
WRITE(Format='i1, (i6)') 0, list
    
DO i = 1, n-1
  ALIAS(list,1,  diff,n-i) ! rename list(1 ... n-i) with diff
  diff = list($+1) - diff  ! $ is the running left hand array index
  WRITE(Format='i1, (i6)') i, diff
ENDDO

END