Exercise 1.46.  Several of the numerical methods described in this chapter are 
instances of an extremely general computational strategy known as iterative 
improvement. Iterative improvement says that, to compute something, we start 
with an initial guess for the answer, test if the guess is good enough, and 
otherwise improve the guess and continue the process using the improved guess 
as the new guess. Write a procedure iterative-improve that takes two procedures 
as arguments: a method for telling whether a guess is good enough and a method 
for improving a guess. Iterative-improve should return as its value a procedure 
that takes a guess as argument and keeps improving the guess until it is good 
enough. Rewrite the sqrt procedure of section 1.1.7 and the fixed-point 
procedure of section 1.3.3 in terms of iterative-improve.

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(define (iterative-improve good-enough? improve)
  (define (iter guess)
    (if (good-enough? guess)
        guess
        (iter (improve guess))))
  iter)

(define (sqrt x)
  ((iterative-improve (lambda (guess) (< (abs (- (square guess) x)) 0.001))
                      (lambda (guess) (average guess (/ x guess))))) 1.0)

(define (fixed-point f first-guess)
  (define (good-enough? guess)
    (< (abs (- (f guess) guess)) tolerance))
  ((iterative-improve good-enough? f) first-guess))

This fixed-point implementation is deeply unsatisfying as it calculates 
(f guess) twice as many times as necessary.  However, without mutable state 
or changing the interface of iterative-improve, I don't see a way around it.