(defn iterative-improve [good-enough? next]
  (fn [guess]
    (defn iter [prev current]
      (cond
        (good-enough? prev current) current 
        (iter current (next current))))
    (iter guess (next guess))))

(def tolerance 0.0001)
(defn good-enough? [prev current]
  (< (math/abs (- prev current))
     tolerance))

(defn improve-sqrt [x]
  (fn [y] (/ x y)))

(defn average-damp [f]
  (fn [x] (* 0.5 (+ x (f x)))))

(defn improve [x] (average-damp (improve-sqrt x)))

(defn sqrt [x] 
  (def run (iterative-improve good-enough? (improve x)))
  (run 1.0))

(defn fixed-point [f initial-guess]
  (def run (iterative-improve good-enough? f))
  (run initial-guess))

(defn fix-sqrt [x]
  (fixed-point (improve x) 1.0))

(print (sqrt 5.0))
(print (fix-sqrt 5.0))