Exercise 1.34

This is the $34^{th}$ Exercise in Sicp, Here, we explain what happens when we we try to use a number as a procedure.

The Question

Exercise 1.34: Suppose we define the procedure

(define (f g)
  (g 2))

Then we have

(f square)
4

(f (lamda (z) (* z (+ z 1))))
6

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

The Answer

The function f, applies the parameter g as a function. It passes as the parameter 2.

Thus when we passed square as the parameter (square 2) is evaluated.

Let’s use the substitution model and find out what happens when we pass the f as the parameter to itself:

(f f)
(f 2)
(2 2)

As you can see, we finally try to use the integer 2 as a function. This will cause an error. In MIT Scheme at least, it returns the error “The object 2 is not applicable”.