sicp-ex-1.43

Define some primitives:

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

Define the procedure:

         (define (repeat f n) 
                 (lambda (x) 
                   (if (< n 1) x 
                         ((compose f (repeat f (- n 1)))x)))) 

Test with:

         ((repeat square 2) 5) 

Output:

         625 

Another solution using the linear iterative way.

  
 (define (repeat f n ) 
   (define (iter n result) 
     (cond ((= n 1) result) 
           (else (iter (- n 1) (compose f result))))) 
   (iter n f)) 

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