What makes a recursive function correct?

Recursion is a way to express a problem in terms of a smaller version of itself. The base case handles the smallest input directly. The recursive case assumes the smaller call is correct and combines its result. That assumption is the inductive step.

function factorial(n) {
  if (n <= 1) return 1;
  return n * factorial(n - 1);
}

function sum(values, index = 0) {
  if (index === values.length) return 0;
  return values[index] + sum(values, index + 1);
}

What to check

• Does every branch eventually reach a base case?
• Does the recursive argument strictly shrink?
• Does the base case cover empty and single-element inputs?
• Is the recursion depth safe for the expected input size?
• Are you recomputing the same subproblems? If so, memoize or use a loop

The call stack is finite. A recursion depth of tens of thousands can overflow in JavaScript. Tail calls are not reliably optimized, so a loop is often safer for deep linear recursion.