SICP exercise 2.1

sicp_exercise_2_1.scm

(define (expect actual expectation expected)
  (display "• ")
  (display actual)
  (display " should equal ")
  (display expected)
  (display ": ")
  (expectation actual expected)
  (display "pass\n")
  )
  
(define (to-equal actual expected)
  (assert (= actual expected)))
  
(define (to-be-equal actual expected)
  (assert (equal? actual expected)))

(define (make-rat n d)
  (let ((g (gcd n d))
        (sign (if (< d 0) -1 1)))
    (cons
      (* (/ n g) sign)
      (* (/ d g) sign))))
  
(define one-half (make-rat 1 2))
(define one-third (make-rat 1 3))

(define (numer r) (car r))
(define (denom r) (cdr r))
(expect (numer one-half) to-equal 1)
(expect (denom one-half) to-equal 2)

(define (add-rat x y)
  (make-rat
    (+
      (* (numer x) (denom y))
      (* (numer y) (denom x)))
    (* (denom x) (denom y))))
    
(define (mul-rat x y)
  (make-rat
    (* (numer x) (numer y))
    (* (denom x) (denom y))))

(expect (add-rat one-half one-third) to-be-equal (make-rat 5 6))
(expect (mul-rat one-half one-third) to-be-equal (make-rat 1 6))
(expect (add-rat one-third one-third) to-be-equal (make-rat 2 3))

(expect (make-rat -1 3) to-be-equal (make-rat -1 3))
(expect (make-rat 1 -3) to-be-equal (make-rat -1 3))
(expect (make-rat -1 -3) to-be-equal (make-rat 1 3))