Recursing in a lambda function

Question

I have the following 2 functions that I wish to combine into one:

(defun fib (n)
  (if (= n 0) 0 (fib-r n 0 1)))

(defun fib-r (n a b)
  (if (= n 1) b (fib-r (-          


        

Answer 1

You can use Graham's alambda as an alternative to labels:

(defun fib (n)
  (funcall (alambda (n a b)
             (cond ((= n 0) 0)
                   ((= n 1) b)
                   (t (self (- n 1) b (+ a b))))) 
           n 0 1)) 

Or... you could look at the problem a bit differently: Use Norvig's defun-memo macro (automatic memoization), and a non-tail-recursive version of fib, to define a fib function that doesn't even need a helper function, more directly expresses the mathematical description of the fib sequence, and (I think) is at least as efficient as the tail recursive version, and after multiple calls, becomes even more efficient than the tail-recursive version.

(defun-memo fib (n)
  (cond ((= n 0) 0)
        ((= n 1) 1)
        (t (+ (fib (- n 1))
              (fib (- n 2))))))