Mohan Rajendran mohanrajendran

(define (a-plus-abs-b a b)
  ((if (> b 0) + -) a b))

When the if function is evaluated, based on the condition, the operator + or - is applied on the operands a and b. If b > 0, + operator is used, evaluating to a+b. Otherwise, - operator is issued which yields a-b. Ultimately, we evaluate a+|b|.

(define (p) (p))

(define (test x y)
  (if (= x 0)
      0
      y))

(test 0 (p))

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

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

The good-enough? function is not so effective when we use small numbers as arguments in the function.

For example, when we want to find the square root of 0.0001 which is 0.01,

(sqrt 0.0001)

;.03230844833048122

Expansion of (+ 4 5) using first definition

(define (+ a b)
  (if (= a 0)
      b
      (inc (+ (dec a) b))))

(+ 4 5)
(inc (+ (dec 4) 5))

The following are the results from defining and evaluating the Ackermann's function on various arguments.

(define (A x y)
  (cond ((= y 0) 0)
  	((= x 0) (* 2 y))
	((= y 1) 2)
	(else (A (- x 1)
	      	 (A x (- y 1))))))
; A

	10
	; 10

	(+ 5 3 4)
	; 12

	(- 9 1)
	; 8

	(/ 6 2)

	(define (sq x) (* x x))
	; sq

	(define (sumsq x y) (+ (sq x) (sq y)))
	; sumsq

	(define (largest2sq a b c)
	(cond ((and (<= a b) (<= a c)) (sumsq b c))
	((and (<= b a) (<= b c)) (sumsq a c))
	(else (sumsq a b))))

	(define (cbrt-iter guess prev-guess x)
	(if (good-enough? guess prev-guess)
	guess
	(sqrt-iter (improve guess x)
	guess
	x)))
	; cbrt-iter

	(define (improve guess x)
	(/ (+ (/ x (square guess)) (* 2 guess)) 3))

	(/ (+ 5 4 (- 2 (- 3 (+ 6 (/ 4 5)))))
	(* 3 (- 6 2) (- 2 7)))
	; -37/150