In this edition, the mouse click on Python statements with dark background is programmed in such a way that a Python interpreter is displayed, which can evaluate the statement and display the values it prints.

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 representing numbers may be combined with operators (such as + or *) to form a compound expression that represents the application of a corresponding primitive function to those numbers. For example, evaluate any of the following expression statements by clicking on it: print(137 + 349) 486 print(1000 - 334) 666 print(5 * 99) 495 print(10 / 4) 2.5 print(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.

Expressions such as 137 + 349, which contain other expressions as components, are called combinations. Combinations that are formed by an operator symbol in the middle, and operand expressions to the left and right of it, are called operator combinations. The value of an operator combination is obtained by applying the function 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) 75 (* 25 4 12) 1200 No ambiguity can arise, because the operator is always the leftmost element and the entire combination is delimited by the parentheses.

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

The convention of placing the operator between the operands is known as infix notation. It follows the mathematical notation that you are most likely familiar with from school and everyday life. As in mathematics, operator combinations can be nested, that is, they can have operands that themselves are operator combinations: print((3 * 5) + (10 - 6)) 19 As usual, parentheses are used to group operator combinations in order to avoid ambiguities. Python also follows the usual conventions when parentheses are omitted: multiplication and division bind more strongly than addition and subtraction. For example, 3 * 5 + 10 / 2 stands for (3 * 5) + (10 / 2) We say that * and / have higher precedence than + and -. Sequences of additions and subtractions are read from left to right, as are sequences of multiplications and divisions. Thus, 1 - 5 / 2 * 4 + 3 stands for (1 - ((5 / 2) * 4)) + 3 We say that the operators +, -, * and / are left-associative.

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 pretty-printing, in which each long combination is written so that the operands are aligned vertically. The resulting indentations display clearly the structure of the expression.[2]

There is no limit (in principle) to the depth of such nesting and to the overall complexity of the expressions that the Python interpreter can evaluate. It is we humans who might 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)) to visually separate the major components of the expression.[3]