fib.rkt

(define fib3 
  (letrec([memo null] ; list of pairs (arg . result)
          [f (lambda (x)
               (let ([ans (assoc x memo)])
                (if ans 
                  (cdr ans)
                  (let ([new-ans (if (or (= x 1) (= x 2))
                                   1
                                   (+ (f (- x 1))
                                      (f (- x 2))))])
                   (begin 
                     (set! memo (cons (cons x new-ans) memo))
                     new-ans)))))])
    f))