sicp exercise 1.43

;  Exercise 1.43.  If f is a numerical function and n is a positive integer, then we can form the nth
;  repeated application of f, which is defined to be the function whose value at x is f(f(...(f(x))...)).
;  For example, if f is the function x -> x + 1, then the nth repeated application of f is the function
;  x -> x + n. If f is the operation of squaring a number, then the nth repeated application of f is the
;  function that raises its argument to the 2^nth power. Write a procedure that takes as inputs a procedure
;  that computes f and a positive integer n and returns the procedure that computes the nth repeated
;  application of f. Your procedure should be able to be used as follows:

;  ((repeated square 2) 5)
;  625

;  Hint: You may find it convenient to use compose from exercise 1.42.

(define (square x) (* x x))

(define (compose f g)
  (lambda(x)
    (f (g x))))

(define (repeated f n)
    (define (iter i res)
      (if (>= i n)
          res
          (iter (+ i 1) (compose f res))))
  (iter 1 f))

(display ((repeated square 2) 5)) (newline)