Lists as inductive structures

A different way to perform an operation on all elements of a list is by exploiting the fact that lists are inductive structures:

• the empty list (i.e., the list with no nodes) is a list;
• if lis is a list and elem is an element, then we obtain a list by taking elem as first node and lis as rest;
• nothing else is a list.

Exploiting the inductive characterization of lists, we can realize all operations on list also through recursion. The typical structure of a recursive method that operates on a list is as follows:

if (the list is empty) {
  perform the operation for the empty list
} else {
  perform the operation on the first element of the list
  call the method recursively on the rest of the list
}