SICP exercise 1.6

sicp-exercise-1.6.scm

; SICP exercise 1.6

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

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

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

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

(define (sqrt-iter guess x)
  (new-if (good-enough? guess x)
	  guess
	  (sqrt-iter (improve guess x)
		     x)))

; What happends when Alyssa attemps to use this to compute square roots? Explain.
; When Alyssa attemps to use the new-if procedure the execution run into an infinite
; loop because the new-if procedure always evaluate the else-clause part that invoque
; the sqrt-iter procedure recursively. The result is that the good-enough? procedure
; is never called and the end condition is never reached. 

; Note: diferent behavior using natural or decimal numbers  

(sqrt-iter 1 10.0)
;(sqrt-iter 1 10)

(1)
(define (sqrt-iter 1 10)
  (new-if (good-enough? 1 10)
	  1
	  (sqrt-iter (improve 1 10)
		     10)))
(2)
(define (sqrt-iter 1 10)
  (new-if (good-enough? 1 10)
	  1
	  (sqrt-iter 5.5 
		     10)))

(3)
(define (sqrt-iter 1 10)
  (new-if (good-enough? 1 10)
	  1
	  (new-if (good-enough? 5.5 10)
		  5.5
		  (sqrt-iter (improve 5.5 10) 
			     10))))
(4)
(define (sqrt-iter 1 10)
  (new-if (good-enough? 1 10)
	  1
	  (new-if (good-enough? 5.5 10)
		  5.5
		  (sqrt-iter 3.659090909090909
			     10))))
(5)
(define (sqrt-iter 1 10)
  (new-if (good-enough? 1 10)
	  1
	  (new-if (good-enough? 5.5 10)
		  5.5
		  (new-if (good-enough? 3.659090909090909 10)
			  3.659090909090909
			  (sqrt-iter (improve 3.659090909090909 10)
				     10)))))
(6)
(define (sqrt-iter 1 10)
  (new-if (good-enough? 1 10)
	  1
	  (new-if (good-enough? 5.5 10)
		  5.5
		  (new-if (good-enough? 3.659090909090909 10)
			  3.659090909090909
			  (sqrt-iter 3.196005081874647)
				     10))))
(7)
(define (sqrt-iter 1 10)
  (new-if (good-enough? 1 10)
	  1
	  (new-if (good-enough? 5.5 10)
		  5.5
		  (new-if (good-enough? 3.659090909090909 10)
			  3.659090909090909
			  (new-if (good-enough? 3.196005081874647 10)
				  3.196005081874647
				  (sqrt-iter (improve 3.196005081874647 10)
					     10))))))
(8)
(define (sqrt-iter 1 10)
  (new-if (good-enough? 1 10)
	  1
	  (new-if (good-enough? 5.5 10)
		  5.5
		  (new-if (good-enough? 3.659090909090909 10)
			  3.659090909090909
			  (new-if (good-enough? 3.196005081874647 10)
				  3.196005081874647
				  (sqrt-iter 3.16245562280389)
					     10))))))
(9)
(define (sqrt-iter 1 10)
  (new-if (good-enough? 1 10)
	  1
	  (new-if (good-enough? 5.5 10)
		  5.5
		  (new-if (good-enough? 3.659090909090909 10)
			  3.659090909090909
			  (new-if (good-enough? 3.196005081874647 10)
				  3.196005081874647
				  (new-if (good-enough? 3.16245562280389 10)
					  3.16245562280389
					  (sqrt-iter (improve 3.16245562280389 10)
						     10)))))))
(10)
(define (sqrt-iter 1 10)
  (new-if (good-enough? 1 10)
	  1
	  (new-if (good-enough? 5.5 10)
		  5.5
		  (new-if (good-enough? 3.659090909090909 10)
			  3.659090909090909
			  (new-if (good-enough? 3.196005081874647 10)
				  3.196005081874647
				  (new-if (good-enough? 3.16245562280389 10)
					  3.16245562280389
					  (sqrt-iter 3.162277665175675
						     10)))))))
(11)
(define (sqrt-iter 1 10)
  (new-if (good-enough? 1 10)
	  1
	  (new-if (good-enough? 5.5 10)
		  5.5
		  (new-if (good-enough? 3.659090909090909 10)
			  3.659090909090909
			  (new-if (good-enough? 3.196005081874647 10)
				  3.196005081874647
				  (new-if (good-enough? 3.16245562280389 10)
					  3.16245562280389
					  (new-if (good-enough? 3.162277665175675 10)
						     10
						     (sqrt-iter (improve 3.162277665175675 10)
								10))))))))