sicp每日一题[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^n-th 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.

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这道题稍微复杂一点，要用一个循环来实现重复调用目标函数 n 次。

; f 表示函数，参数只有一个且为数值；n 表示要嵌套执行多少次 f 函数
(define (repeated f n)
  (if (= n 1)
      (lambda (x) (f x))
      (compose f (repeated f (- n 1)))))

((repeated square 2) 5)
((repeated inc 10) 5)

; 执行结果
625
15