#lang racket

(define (add-interval x y)
  (make-interval (+ (lower-bound x) (lower-bound y))
                 (+ (upper-bound x) (upper-bound y))))

(define (mul-interval x y)
  (let ((p1 (* (lower-bound x) (lower-bound y)))
        (p2 (* (lower-bound x) (upper-bound y)))
        (p3 (* (upper-bound x) (lower-bound y)))
        (p4 (* (upper-bound x) (upper-bound y))))
    (make-interval (min p1 p2 p3 p4)
                   (max p1 p2 p3 p4))))

(define (div-interval x y)
  (mul-interval x
                (make-interval (/ 1.0 (upper-bound y))
                               (/ 1.0 (lower-bound y)))))

(define (make-interval a b) (cons a b))
(define (lower-bound x) (car x))
(define (upper-bound x) (cdr x))

(define (print-interval x)
  (newline)
  (display "interval{")
  (display (lower-bound x))
  (display ",")
  (display (upper-bound x))
  (display "}")
  (newline))

(define (print)
  (define test-interval (make-interval 1 2))
  (print-interval test-interval))

(print)