Recursive Thinking

• Rename foo as square:

      (define square
        (lambda (n)
          (if (= n 0)
  	    0
  	    (+ (square (- n 1))
  	       (- (+ n n) 1)))))

• When thinking about a problem recursively, it is tempting to go down through all the layers as in a trace:

      > (square 4)
  
      |(square 4)
      | (square 3)
      | |(square 2)
      | | (square 1)
      | | |(square 0)
      | | |0 [Resume previous call, add (2-1)]
      | | 1  [Resume previous call, add (4-1)]
      | |4   [Resume previous call, add (6-1)]
      | 9    [Resume previous call, add (8-1)]
      |16    [No previous call, so be done]
      16
      > 

• Can be confusing for all but the simplest procedures.