sicp-ex-2.7



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jz

  
 ;; ex 2.7 
 (define (make-interval a b) (cons a b)) 
 (define (upper-bound interval) (max (car interval) (cdr interval))) 
 (define (lower-bound interval) (min (car interval) (cdr interval))) 
  
 ;; Usage 
 (define i (make-interval 2 7)) 
 (upper-bound i) 
 (lower-bound i) 
  
 (define j (make-interval 8 3)) 
 (upper-bound j) 
 (lower-bound j) 
  

We could create a function to get rid of the brief duplication in upper-bound and lower-bound, but it's not worth it.


mbsmith

The above is what I had as well; Though I think using min/max may not be necessary. If you look at the passage in the book regarding the add-interval procedure; The passage and the implementation indicate that lower-bound is positional rather than value dependent. At least as long as the make-interval procedure is unchanged.

Alyssa first writes a procedure for adding two intervals. She reasons that the minimum value the sum could be is the sum of the two lower bounds and the maximum value it could be is the sum of the two upper bounds:

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

So it looks like we could possibly define this as the following and still be within the constraints given by the book.

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