SICP Exercise 1.34

Question

Suppose we define the procedure

(define (f g)
  (g 2))

Then we have

(f square)

4

and

(f (λ (z) (* z (+ z 1))))

6

What happens if we (perversely) ask the interpreter to evaluate the combination (f f)? Explain.

Answer

The easiest way to explain this is to try running the function:

(define (f g)
  (g 2))

(f f)

We receive an error message:

application: not a procedure;
 expected a procedure that can be applied to arguments
 given: 2

Let us try to understand why this happens by stepping through (f f).

The function f could be translated into English as “apply the following function to 2”, or “call the following function with the parameter 2”. So if we call (f f), we are basically saying “call the function f with the parameter 2", which is the same thing as (f 2).

So, for the next step, we need to evaluate (f 2). (f 2) could be translated as “apply the function 2 to the value 2", or (2 2). The problem is that, of course, 2 is not a valid function. Therefore, we receive the above error message.