Student B goes to the student center to get some tutoring.

“I'm not doing so well in my intro to computer science course. I just took a quiz and didn't finish it. This may sound paranoid, but there's a blog that seems to be talking about the problems I'm having. They were discussing part of the program in the quiz.”

mquander wrote:
Where did student B get the idea that he was supposed to evaluate it?

Blaise Pascal wrote:
He didn't need to evaluate it to answer the quiz questions, and he wasn't asked to evaluate it.

Alexey wrote:
He was expected to ignore the evaluation path of the sanity check form.

“Anyway,”Student B continued, “I don't understand what they are talking about. What else would you do with a program but evaluate it? Isn't that what programs are for? They're telling what not to do, but not what I ought to be doing instead. Can you help me?“

---

How should the tutor approach this? What should he or she say?

Pop quiz fallout

At the end of the two hours, Student B was still furiously scribbling away. He had accumulated a suprising amount of paper around himself. The professor came over to talk to him.
“What seems to be the problem?”
‘I don't have enough time!’
“It isn't that hard a quiz, you know. Every other student has finished. What exactly are you doing?”
‘This part, right here.’
Student B pointed to this line in the quiz:

(= (- (fib 100) (fib 99)) (fib 98))

‘I decided to evaluate this from right to left because you said that order doesn't matter. I'm still working on the (fib 98) subexpression. I think that (fib 99) and (fib 100) are going to take even longer. I can't see how anyone could get past this. I'm getting discouraged. I don't even think a computer could solve this in two hours.’

This is a key question: What, if anything, is Student B doing wrong?

A pop quiz

Partway through the term the professor decides to give the students a pop quiz.

“The quiz is contained in the file quiz.scm which you can find in the usual location. For those of you that prefer hardcopy, I have a printout for you.

“I know that some of you” (and here the professor glared at Student A) “seem to have issues with the way I present code, so you should assume that this code is to be entered into an unmodified R5RS Scheme interpreter.

“You have two hours.

;; Question 1:
;; What does (fib 4) evaluate to?

;; Question 2:
;; What is domain and range of the EVEN? procedure?

;; Question 3:
;; How many top-level forms are in this file?

;; Question 4:
;; Make a list of the free variables in this file.

(define (even? x)
  (or (zero? x)
      (odd? (- x 1))))

(define (odd? x)
  (and (not (zero? x))
       (even? (- x 1))))

(define (fib n)
  (if (< n 2)
      n
      (+ (fib (- n 1)) 
         (fib (- n 2)))))

;; Sanity check
(= (- (fib 100) (fib 99)) (fib 98))

;; Question 5:
;; Are either of the following two forms an infinite loop?
;; Make an informal argument to support your answer.

(define (loop1 n)
  (if (positive? n)
      (loop1 (- n 1))
      (loop1 n)))

(define (loop2 n)
  (if (negative? n)
      (loop2 (+ n 1))
      n))

Meta-questions for readers of this blog:

1. Is this a reasonable quiz? If it is too difficult for first-year students, is there a year at which it would be appropriate or even too simple?
2. Is two hours enough time to answer the questions?
3. Are there any loopholes that will allow Student A to object?

Followup

Pascal Costanza wrote:

Student A's statement is self-contradictory. You can only meaningfully talk about making something incorrect when you have a correct meaning in mind in the first place. So for Student A, the program has a meaning, even if he/she denies that.

Student A might argue: “The professor is the one that is assuming there is a correct meaning. I'm simply pointing out that whatever meaning he might have in mind could be wrong.”

Student C's description of the program is circular. He/she states that FACTORIAL implements factorial, which doesn't say much at all - it's both times the same word, both times the same string of characters (only once in upper case and once in lower case).

Student C replies: “Oh, I meant that the program named FACTORIAL implements the mathematical function ‘factorial’.” (This is a beginner's course, so we shouldn't make him work too hard.)

Alexey wrote:

I would say to student A: That answer is useless. Of course someone could shadow * or IF; but what did the author of the program mean when they wrote it?

Student A replies: “How should I know? I can't read minds!”

What do we say to Student A?

I would say to student B: OK, that's what the program does, for a few trials with a few arguments, but what it does is beside the point. The question was: what does the program mean?

Student B asks: So what is the difference between what it “means” and what it “does”? Doesn't “(+ 2 3)” mean 5? Doesn't “(factorial 4)” mean 24?