SICP Exercise 2.1-5

2.1

(define (make-rat-better n d) 
  (if (< n 0)
      ( if(< d 0)
          (cons (- 0 n) (- 0 d))
          (cons n d)
      )
      (if (< d 0)
           (cons (- 0 n) (- 0 d))
           (cons n d))
       )
 )

2.2

(define (make-segment n d) (make-rat n d))
(define (start-segment x) (car x))
(define (end-segment x) (cdr x))
(newline)
(start-segment (make-segment 1 3))
(end-segment (make-segment 1 3))

(define (make-point x y) (make-rat x y))
(define (x-point n) (car n))
(define (y-point n) (cdr n))

(define (midle-point a b) (make-rat (/ (+ (car a) (car b) ) 2 )
                                    (/ (+ (cdr a) (cdr b) ) 2 ) 
                                   )
  )
(midle-point (make-point 7 8) (make-point -1 -4)) 

2.3
(define (cons x y)
  (lambda (m) (m x y)))

(define (car z)
  (z (lambda (p q) p)))

(define (cdr z)
  (z (lambda (p q) q)))

(car (cons 1 2))
(cdr (cons 1 2))


2.4
(define (cons x y)
  (lambda (m) (m x y)))

(define (car z)
  (z (lambda (p q) p)))

(define (cdr z)
  (z (lambda (p q) q)))

(car (cons 1 2))
(cdr (cons 1 2))

2.5
(define (power x n) 
    (if (= n 0)
      1
      (* x (power x (- n 1)))
      )
  )
(power 2 4)

(define (cons a b) 
    (define (dispath m)
    (cond ((= m 0) (power 2 a))
          ((= m 1) (power 3 b))
          (else (* (power 2 a) (power 3 b)))
          )
    )
  dispath
  )

(cons 0 2)
(define (car x) (x 0))
(define (cdr x) (x 1))

(car (cons 2 2))
(cdr (cons 2 2))