Composing More Procedures

fun_fun_function.scm

; 1.43

(define (repeated operation n)
  (define (operation-iter iterator composed-function)
    (if (= iterator 1)
        (lambda(x) (composed-function x))
        (operation-iter (- iterator 1) (compose operation composed-function))
   ))
   (operation-iter n operation)
  )

((repeated square 2) 5)   ;-----------> 625

; 1.44

(define (smooth f)
  (lambda (x dx) (/ (+ (f (- x dx)) (f x) (f (+ x dx))) 3))
)

((smooth square) 0 4)     ;-----------> 10 & 3/4
(repeated ((smooth square) 0 4) 5)