One-Layer Thinking

• Do not try to descend all layers. Instead:

      > (square 4) [Assume (square 3) does its job and gives
                    the right answer, 9.  Then add (8-1)]
      16

• Why can you make the assumption? Because you proved the correctness of foo!

• The Recursive Thinking Maxim: Don't try to think recursively about a recursive process.

• Instead, think inductively:
  1. Make sure there is a base case.

  2. Have "faith" that the smaller problem is solved.

  3. Reason from the smaller problem to the larger problem.