1-06.scm

#lang sicp
(define (sqrt-iter guess x)
  (new-if (good-enough? guess x)
      guess
      (sqrt-iter (improve guess x) x)))
    
(define (improve guess x)
  (average guess (/ x guess)))

(define (average x y)
  (/ (+ x y) 2))

(define (good-enough? guess x)
  (< (abs (- (square guess) x)) 0.001))

(define (sqrt x)
  (sqrt-iter 1.0 x))

(define (square x)
  (* x x))

(define (new-if predicate then-clause else-clause)
  (cond (predicate then-clause)
        (else else-clause)))

(sqrt 11)

; new-if is a function. In Lisp this means that the args are evaluated before the function is applied.
; (Applicative-order evaluation). This causes an infinite loop in sqrt-iter because the else-clause
; recursively calls itself.