SICP_2.7-2.11

(define (make-interval x y)
  (cons x y))

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

;;;;;;;;;;;;;;;2.7
(define (upper-bound inter)
  (cdr inter))

(define (lower-bound inter)
  (car inter))
;;;;;;;;;;;;;;2.8
(define (sub-interval x y)
  (add-interval x
                (make-interval (- (upper-bound y))
                              (- (lower-bound y)))))

;;;;;;;;;;;;;;2.9
(define (width-interval x)
  (/ (- (upper-bound x) (lower-bound x)) 2))

;(width-interval (add-interval x y)) （1）
;(width-interval (sub-interval x y))  （2）
;(+ (width-interval x) (width-interval y)) （3）
;(- (width-interval x) (width-interval y)) （4）
;
;(1) (3)是等价的
;(width-interval (mul-interval x y)) (5)
;(* (width-interval x) (width-interval y)) (6)
;(5) (6) 不等价

;;;;;;;;;;;2.10
(define (div-interval x y)
  (if (< (* (upper-bound y) (lower-bound y)) 0)
      (error "division interval isn't right")
      (mul-interval x
                    (make-interval (/ 1.0 (upper-bound y))
                                   (/ 1.0 (lower-bound y))))))

;;;;;;;;;2.11
(define (mul-interval x y)
  (let ((xl (lower-bound x))
        (xu (upper-bound x))
        (yu (upper-bound y))
        (yl (lower-bound y)))
    (cond ((and (< xl 0) (< xu 0)) (cond ((and (< yl 0) (< yu 0))
                                          (make-interval
                                           (* xu yu) (* xl yl)))
                                          ((and (< yl 0) (> yu 0))
                                          (make-interval
                                           (* xl yu) (* xl yl)))
                                          ((and (> yl 0) (> yu 0))
                                          (make-interval
                                           (* xl yu) (* xu yl)))))
          ((and (< xl 0) (> xu 0)) (cond ((and (< yl 0) (< yu 0))
                                          (make-interval
                                           (* xu yl) (* xl yl)))
                                         ((and (< yl 0) (> yu 0))
                                          (make-interval
                                           (* xl yu) (* xu yu)))
                                         ((and (> yl 0) (> yu 0))
                                          (make-interval
                                           (* xl yu) (* xu yu)))))
          ((and (> xl 0) (> xu 0)) (cond ((and (< yl 0) (< yu 0))
                                          (make-interval
                                           (* xu yl) (* xl yu)))
                                         ((and (< yl 0) (> yu 0))
                                          (make-interval
                                           (* xu yl) (* xu yu)))
                                         ((and (> yl 0) (> yu 0))
                                          (make-interval
                                          (* xl yl) (* xu yu)))))))

;;;;;;;;;;;;;;;改成这种形式可能是因为当乘法代价比较高时
;;;;;;;;;;;;;;;可以提高效率