SICP Exercise 1.43 repeated

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 2nth 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.

SOLUTION

 The code and tests are here.

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