SICP Exercise 3.8

Question

When we defined the evaluation model in 1.1.3, we said that the first step in evaluating an expression is to evaluate its sub-expressions. But we never specified the order in which the sub-expressions should be evaluated (e.g., left to right or right to left). When we introduce assignment, the order in which the arguments to a procedure are evaluated can make a difference to the result. Define a simple procedure f such that evaluating

copy(+ (f 0) (f 1))

will return 0 if the arguments to + are evaluated from left to right but will return 1 if the arguments are evaluated from right to left.

Answer

The following works:

copy(define f
  (let ((x 2))
    (λ (n)
      (set! x (- x 1))
      (* x n))))

If (+ (f 0) (f 1)) is evaluated from left to right, we get $(1\times 0)+(0\times 1)=0$. If it is evaluated from right to left, we get $(1\times 1)+(0\times 0)=1$.

Unfortunately, we can’t really test this without changing the Scheme interpreter itself. For what it’s worth, debugging through the program flow reveals that Scheme evaluates the two procedures from left to right, yielding a result of 0.