SICP Exercise 2.10: Divide by Zero

Ben Bitdiddle, an expert systems programmer, looks over Alyssa's shoulder and comments that it is not clear what it means to divide by an interval that spans zero. Modify Alyssa's code to check for this condition and to signal an error if it occurs.

I must confess that, being the old AI graduate that I am, I read this and thought "expert systems? what on earth have they got to do with this exercise?" Nothing, of course - and this nicely illustrates why natural language understanding is difficult. Anyway...

How can we tell if an interval spans zero? Well, the lower bound of the number will be zero or less, while the upper bound of the number will be zero or more. Here's my modified procedure:

(define (div-interval x y)
  (if (and (<= (lower-bound y) 0) (>= (upper-bound y) 0))
      (error "Divisor spans zero")
      (mul-interval x
                    (make-interval (/ 1.0 (upper-bound y))
                                   (/ 1.0 (lower-bound y))))))

And here it is in action:

> (div-interval (make-interval 3 9) (make-interval 1 5))
'(0.6000000000000001 . 9.0)
> (div-interval (make-interval 3 9) (make-interval -4 -1))
'(-9.0 . -0.75)
> (div-interval (make-interval 3 9) (make-interval -4 0))
. . Divisor spans zero
> (div-interval (make-interval 3 9) (make-interval 0 5))
. . Divisor spans zero
> (div-interval (make-interval 3 9) (make-interval -4 5))
. . Divisor spans zero