Expressions

One easy way to get started at programming is to examine some typical
interactions with an interpreter for the Scheme dialect of Lisp.
Imagine that you are sitting at a computer terminal. You type an
*expression*, and the interpreter responds by displaying the result of
its *evaluating* that expression.

One kind of primitive expression you might type is a number. (More precisely, the expression that you type consists of the numerals that represent the number in base 10.) If you present Lisp with a number

486the interpreter will respond by printing

486

Expressions representing numbers may be combined with an
expression
representing a
primitive procedure (such as `+` or `*`) to form a
compound expression that represents the
application of the procedure to those numbers. For example:

(+ 137 349) 486 (- 1000 334) 666 (* 5 99) 495 (/ 10 5) 2 (+ 2.7 10) 12.7

Expressions such as these, formed by
delimiting a list of expressions
within parentheses in order to denote
procedure application,
are called *combinations*. The leftmost
element in the list is called the
*operator*, and the other
elements are called
*operands*. The
value of a combination is
obtained by applying the procedure specified by the operator to the
*arguments* that are the values of the operands.

The convention of placing the operator to the left of the operands is
known as
*prefix notation*, and it may be somewhat confusing at
first because it departs significantly from the customary mathematical
convention. Prefix notation has several advantages, however. One of
them is that it can accommodate
procedures that may take an arbitrary
number of arguments, as in the following examples:

(+ 21 35 12 7) 75No ambiguity can arise, because the operator is always the leftmost element and the entire combination is delimited by the parentheses.(* 25 4 12) 1200

A second advantage of prefix notation is that it extends in a
straightforward way to allow combinations to be *nested*, that is,
to have combinations whose elements are themselves
combinations:

(+ (* 3 5) (- 10 6)) 19

There is no limit (in principle) to the depth of such nesting and to the overall complexity of the expressions that the Lisp interpreter can evaluate. It is we humans who get confused by still relatively simple expressions such as

(+ (* 3 (+ (* 2 4) (+ 3 5))) (+ (- 10 7) 6))which the interpreter would readily evaluate to be 57. We can help ourselves by writing such an expression in the form

(+ (* 3 (+ (* 2 4) (+ 3 5))) (+ (- 10 7) 6))following a formatting convention known as

Even with complex expressions, the interpreter always operates in the
same basic cycle: It reads an expression from the terminal,
evaluates the expression, and prints the result.
This mode of operation is often expressed by saying that the
interpreter runs in a
*read-eval-print loop*.
Observe in particular that it is not necessary to explicitly
instruct the interpreter to print the value of the expression.
^{}