Question

In Concrete Abstractions, there is this example of recursion:

(define subtract-the-first (lambda (n)
                             (if (= n 0) 0
                                 (- (subtract-the-first (- n 1)) n))))

This I understand. For instance, if n = 3, this function evaluates to:
(- (+ (+ (+ 1) 2) 3)) -> -6

However, in one of the follow-up examples, one is supposed to explain why it’s not possible to switch the order of operations. For instance, let’s look at this:

(define subtract-the-first2 (lambda (n)
                             (if (= n 0) 0
                                 (- n (subtract-the-first2 (- n 1))))))

If I call (subtract-the-first2 4), the result is 2. However, I don’t quite understand the evaluation. Obviously, I am making a mistake here, because see this:
(- 4 (+ 3 (+ 2 (+ 1))) ), which is equal to (- 4 6) and thus evaluates to -2.

I appreciate any pointers as I’ve been banging me head against the wall for half an hour or so already…

Thank you!

Answer 1

You can check the evaluation of this function by adding some semiquotes and unquotes:

(define subtract-the-first2 (lambda (n)
                              (if (= n 0) 0
                                `(- ,n ,(subtract-the-first2 (- n 1))))))

Then evaluate:

> (subtract-the-first2 4)
(- 4 (- 3 (- 2 (- 1 0))))

This evaluates to 2. (I don’t see where you got the pluses…)