Exercise 2.7 of SICP

2009-07-23

sicp

Exercise 2.7: Alyssa’s program is incomplete because she has not specified the implementation of the interval abstraction. Here is a definition of the interval constructor:

(define (make-interval a b) (cons a b))

Define selectors upper-bound and lower-bound to complete the implementation.

(define (make-interval a b) (cons a b))

(define (lower-bound inter) (car inter))
(define (upper-bound inter) (cdr inter))

(define (add-interval x y)
  (make-interval (+ (lower-bound x) (lower-bound y))
				 (+ (upper-bound x) (upper-bound y))))
(define (add-interval x y)
  (make-interval (+ (lower-bound x) (lower-bound y))
				 (+ (upper-bound x) (upper-bound y))))
(define (div-interval x y)
  (mul-interval x 
				(make-interval (/ 1.0 (upper-bound y))
							   (/ 1.0 (lower-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 (print int)
  (newline)
  (display "[")
  (display (lower-bound int))
  (display ",")
  (display (upper-bound int))
  (display "]")
  (newline))

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