2.3. Evaluating Scheme Expressions

Let's turn to a discussion of how Scheme evaluates the expressions you type. We have already established the rules for constant objects such as strings and numbers; the object itself is the value. You have probably also worked out in your mind a rule for evaluating procedure applications of the form (procedure arg₁ … arg_n). Here, procedure is an expression representing a Scheme procedure, and arg₁ … arg_n are expressions representing its arguments. One possibility is the following.

Find the value of procedure.
Find the value of arg₁.

⋮
Find the value of arg_n.
Apply the value of procedure to the values of arg₁ … arg_n.

For example, consider the simple procedure application (+ 3 4). The value of + is the addition procedure, the value of 3 is the number 3, and the value of 4 is the number 4. Applying the addition procedure to 3 and 4 yields 7, so our value is the object 7.

By applying this process at each level, we can find the value of the nested expression (* (+ 3 4) 2). The value of * is the multiplication procedure, the value of (+ 3 4) we can determine to be the number 7, and the value of 2 is the number 2. Multiplying 7 by 2 we get 14, so our answer is 14.

This rule works for procedure applications but not for quote expressions because the subexpressions of a procedure application are evaluated, whereas the subexpression of a quote expression is not. The evaluation of a quote expression is more similar to the evaluation of constant objects. The value of a quote expression of the form (quote object) is simply object.

Constant objects, procedure applications, and quote expressions are only three of the many syntactic forms provided by Scheme. Fortunately, only a few of the other syntactic forms need to be understood directly by a Scheme programmer; these are referred to as core syntactic forms. The remaining syntactic forms are syntactic extensions defined, ultimately, in terms of the core syntactic forms. We will discuss the remaining core syntactic forms and a few syntactic extensions in the remaining sections of this chapter. Section 3.1 summarizes the core syntactic forms and introduces the syntactic extension mechanism.

Before we go on to more syntactic forms and procedures, two points related to the evaluation of procedure applications are worthy of note. First, the process given above is overspecified, in that it requires the subexpressions to be evaluated from left to right. That is, procedure is evaluated before arg₁, arg₁ is evaluated before arg₂, and so on. This need not be the case. A Scheme evaluator is free to evaluate the expressions in any order|left to right, right to left, or any other sequential order. In fact, the subexpressions may be evaluated in different orders for different applications even in the same implementation.

The second point is that procedure is evaluated in the same manner as arg₁ … arg_n. While procedure is often a variable that names a particular procedure, this need not be the case. Exercise 2.2.3 had you determine the value of ((car (list + - * /)) 2 3). Here, procedure is (car (list + - * /)). The value of (car (list + - * /)) is the addition procedure, just as if procedure were simply the variable +.

Exercise 2.3.1.

Write down the steps necessary to evaluate the expression below.

 ((car (cdr (list + - * /))) 17 5)