Exercise 2.7 of 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))

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