SICP Exercise 2.7: Representing Intervals

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.

A nice and straightforward exercise. We have two values held in a pair. The upper-bound will be the maximum of the two values; the lower-bound will be the minimum of the two. I've already noted that Scheme has a couple of predefined procedures, max and min that can make this determination for us, so the implementations are simply:

(define (upper-bound i) (max (car i) (cdr i)))
(define (lower-bound i) (min (car i) (cdr i)))

And a quick test:

> (define i1 (make-interval 5 10))
> (define i2 (make-interval 7 2))
> (lower-bound i1)
5
> (upper-bound i1)
10
> (lower-bound i2)
2
> (upper-bound i2)
7