Scheme - fibonacci series with nested lambda

Question

Inspired this post .

I trying to implement a fibonacci series with nested lambda -

(( (lambda (x) (x x)) ;; evaluate x on x
    ((lambda (fibo-gen)) ;; fibo-gen get another func as arg
    (lambda (N it second first)
     (cond  ;; here the body of the above func ..
       ((= N 1) 1)
       ((= N 1) 1)
       ((= N it) (+ second first))
       (else (fibo-gen (+ it 1) (+ second first) (second)))
       )
     )
    )
   )
 5  1 1 1)

It's prompts r5rs:body: no expression in body in: (r5rs:body)

By my examination each function has a "body" here , so what I did wrong ?

Note that the implementation I trying to do here is iterative mode which avoid re-calculate previous series ..

Edit :

Another mode which also works -

(( (lambda (x) (x x)) ;; evaluate x on x
    (lambda (fibo-gen) ;; fibo-gen body use another lambda ..
    (lambda (N it second first)
     (cond  ;; here the body of the above func ..
       ((= N 1) 1)
       ((= N 2) 1)
       ((= N it) second)
       (else ((fibo-gen fibo-gen) N (+ it 1) (+ second first) second))
       )
     )
    )
   )
 5 1 1 1)
 => 8

Answer 1

Well, this is quite a contrived way to calculate fibonacci, but nevertheless possible:

(((lambda (x) (x x))
  (lambda (fib-gen)
    (lambda (it second first)
      (if (zero? it)
          first
          ((fib-gen fib-gen) (sub1 it) (+ first second) second)))))
 10 1 0) ; here n = 10

=> 55

If you're aiming for a general way for writing a recursive function without using define, first implement the Y-Combinator:

(define (Y X)
  ((lambda (proc) (proc proc))
   (lambda (proc)
     (X (lambda args
          (apply (proc proc) args))))))

With this, you can write anonymous recursive procedures with a variable number of arguments, for example:

((Y
  (lambda (fib-gen)
    (lambda (it second first)
      (if (zero? it)
          first
          (fib-gen (sub1 it) (+ first second) second)))))
 10 1 0)  ; here n = 10

=> 55