Simple Assignments at Work

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Simple Assignments at Work

Consider the following definition and expression:

(define x 3)

(local ((define z (set! x (+ x 2)))) 
  x)

The definition says that x stands for 3. The local-expression introduces a definition for z. Its body is x so, in the past, the value of this local-expression would have been 3 (if anything). Now, with set! in the language, this is no longer true. To understand what happens, we must rewrite the program step by step until we have a final answer.

The first step in the evaluation lifts the local definition:

(define x 3)

(define z (set! x (+ x 2)))

x

Next we must determine the value of (set! x (+ x 2)). According to the general explanation of set!, this requires the evaluation of the right-hand side of the assignment:

(define x 3)

(define z (set! x 5))

x

That value is 5 because the current value of x is 3.

Finally, the general explanation says that the effect of the set! expression is to change the value that the left-hand side variable represents. In our example this means that from now on, x is no longer 3 but 5. The best way to express this change is to modify the definition of x for the next step:

(define x 5)

(define z (void))

x

The value of set! is (void), the invisible value. By replacing the set!-expression with the invisible value, we indicate that its evaluation is finished.

At this point, it is easy to see that the result is 5. The first definition says that x currently represents 5, and the last expression is x. Hence the value of the function evaluation is 5.

Exercises

Exercise 35.1.1

Consider the following:

```
(set! x 5)
```
```
(define x 3)
(set! (+ x 1) 5) 
```

(define x 3)
(define y 7) 
(define z false)

(set! (if z x y) 5)

Which ones are syntactically legal programs? Which ones are illegal? Solution

Exercise 35.1.2

Evaluate the following program:

(define x 1)
(define y 1)

(local ((define u (set! x (+ x 1))) 
        (define v (set! y (- y 1)))) 
  (* x y))

If set! were not a part of the language, what could we say about the result of the local-expression? That is, consider the skeleton

(define x 1)
(define y 1)

(local ((define u ...) 
        (define v ...)) 
  (* x y))

where the right-hand sides of the definitions have been removed. What would this expression have produced before the introduction of set!-expressions? Solution

Next: Sequencing Expression Evaluations Up: Assignment to Variables Previous: Assignment to Variables

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