2. Variables, expressions and statements

2.1. Values and types

A value is one of the basic things a program works with, like a letter or a number. The values we have seen so far are the numbers 1, and 2, and the phrase 'Hello, World!'.

These values belong to different types: 2 is an integer, and 'Hello, World!' is a string, so-called because it contains a “string”, or sequence, of letters. You (and the interpreter) can identify strings because they are enclosed in quotation marks. (Note that you can use both single and double quotes to enclose a Python string. More on strings soon.)

The print statement works as you might expect for integers.

>>> print 4

If you are not sure what type a value has, the interpreter can tell you.

>>> type('Hello, World!')
<type 'str'>
>>> type(17)
<type 'int'>

Not surprisingly, strings belong to the type str and integers belong to the type int. Less obviously, numbers with a decimal point belong to a type called float, because these numbers are represented in a format called floating-point.

>>> type(3.2)
<type 'float'>

What about values like '17' and '3.2'? They look like numbers, but they are in quotation marks like strings.

>>> type('17')
<type 'str'>
>>> type('3.2')
<type 'str'>

They’re strings.

When you type a large integer, you might be tempted to use commas between groups of three digits, as in 1,000,000. This is not a legal integer in Python, but it is still legal:

>>> print 1,000,000
1 0 0

Well, that’s not what we expected at all! Python interprets 1,000,000 as a comma-separated sequence of integers, which it prints with spaces between.

This is the first example we have seen of a semantic error: the code runs without producing an error message, but it doesn’t do the “right” thing.

2.2. Variables

One of the most powerful features of a programming language is the ability to manipulate variables. A variable is a name that refers to a value. Another way to think of a variable is as a named storage location in memory.

An assignment statement creates new variables and gives them values:

>>> message = 'And now for something completely different'
>>> n = 17
>>> pi = 3.1415926535897931

This example makes three assignments. The first assigns a string to a new variable named message; the second gives the integer 17 to n; the third assigns the (approximate) value of \pi to pi.

A common way to represent variables on paper is to write the name with an arrow pointing to the variable’s value. This kind of figure is called a state diagram because it shows what state each of the variables is in (think of it as the variable’s state of mind). This diagram shows the result of the previous example:

Variable assignment examples.

Variable assignment examples.

To display the value of a variable, you can use a print statement:

>>> print n
>>> print pi

The type of a variable is the type of the value it refers to.

>>> type(message)
<type 'str'>
>>> type(n)
<type 'int'>
>>> type(pi)
<type 'float'>


1. If you type an integer with a leading zero, you might get a
   confusing error:

               zipcode = 02492 ^ SyntaxError: invalid token

Other numbers seem to work, but the results are bizarre:


    >>> zipcode = 02132
    >>> print zipcode

Can you figure out what is going on? Hint: print the values ``01``,
``010``, ``0100`` and ``01000``.

2.3. Variable names and keywords

Programmers generally choose names for their variables that are meaningful — they document what the variable is used for.

Variable names can be arbitrarily long. They can contain both letters and numbers, but they have to begin with a letter. It is legal to use uppercase letters, but it is a good idea to begin variable names with a lowercase letter. (Beginning a variable name with an upper-case letter is often only done is certain situations, which we won’t see until a bit later.)

The underscore character (_) can appear in a name. It is often used in names with multiple words, such as my_name or airspeed_of_unladen_swallow.

If you give a variable an illegal name, you get a syntax error:

>>> 76trombones = 'big parade'
SyntaxError: invalid syntax
>>> more@ = 1000000
SyntaxError: invalid syntax
>>> class = 'Advanced Theoretical Zymurgy'
SyntaxError: invalid syntax

76trombones is illegal because it does not begin with a letter. more@ is illegal because it contains an illegal character, @. But what’s wrong with class?

It turns out that class is one of Python’s keywords. The interpreter uses keywords to recognize the structure of the program, and they cannot be used as variable names.

Python version 2 (which is what we’re using) has 31 keywords [1]:

and       del       from      not       while
as        elif      global    or        with
assert    else      if        pass      yield
break     except    import    print
class     exec      in        raise
continue  finally   is        return
def       for       lambda    try

You might want to keep this list handy. If the interpreter complains about one of your variable names and you don’t know why, see if it is on this list.

2.4. Statements

A statement is a unit of code that the Python interpreter can execute. We have seen two kinds of statements: print and assignment.

When you type a statement in interactive mode, the interpreter executes it and displays the result, if there is one.

A script usually contains an ordered sequence of statements. If there is more than one statement, the results appear one at a time as the statements execute, or run. In all the scripts we will see for now, statements execute one after another, top to bottom, just as you would normally read a page in English.

For example, the script

print 1
x = 2
print x
print 1,x

produces the output

1 2

The assignment statement produces no output. The last statement prints the literal integer 1 followed by a space, followed by the value referred to by the variable x. You can use commas to separate items to be printed in a print statement; Python will include spaces between each item (and the commas will not be shown in the output).

2.5. Operators and operands

Operators are special symbols that represent computations like addition and multiplication. The values the operator is applied to are called operands.

The operators +, -, *, / and ** perform addition, subtraction, multiplication, division and exponentiation, as in the following examples:


In some other languages, ^ is used for exponentiation, but in Python it is a bitwise operator called XOR. Bitwise operators will not be covered in this book, but you can read about them at http://wiki.python.org/moin/BitwiseOperators.

The division operator might not do what you expect:

>>> minute = 59
>>> minute/60

The value of minute is 59, and in conventional arithmetic 59 divided by 60 is 0.98333, not 0 . The reason for the discrepancy is that Python is performing floor division [2].

When both of the operands are integers, the result is also an integer; floor division chops off the fraction part, so in this example it rounds down to zero.

If either of the operands is a floating-point number, Python performs floating-point division, and the result is a float:

>>> minute/60.0

If you want floor division and you are working with floating point operands, you can use the // operator to perform integer division:

>>> minute // 60.0

The resulting type from // follows the same rule as with the “regular” division operator (/): if both operands are integers, the result is an integer, and if at least one operand is floating point, the result is floating point.

2.6. Expressions

An expression is a combination of values, variables, and operators. A value all by itself is considered an expression, and so is a variable, so the following are all legal expressions (assuming that the variable x has been assigned a value):

x + 17

If you type an expression in interactive mode, the interpreter evaluates it and displays the result:

>>> 1 + 1

But in a script, an expression all by itself doesn’t do anything! If you want to show output to the screen, you must use a print statement. This is a common source of confusion for beginners.


  1. Type the following statements in the Python interpreter to see what they do:

    x = 5
    x + 1
  2. Now put the same statements into a script and run it. What is the output? Modify the script by transforming each expression into a print statement and then run it again.

2.7. Order of operations

When more than one operator appears in an expression, the order of evaluation depends on the rules of precedence. For mathematical operators, Python follows mathematical convention. The acronym PEMDAS is a useful way to remember the rules:

  • Parentheses have the highest precedence and can be used to force an expression to evaluate in the order you want. Since expressions in parentheses are evaluated first, 2 * (3-1) is 4, and (1+1)**(5-2) is 8. You can also use parentheses to make an expression easier to read, as in (minute * 100) / 60, even if it doesn’t change the result.
  • Exponentiation has the next highest precedence, so 2**1+1 is 3, not 4, and 3*1**3 is 3, not 27.
  • Multiplication and Division have the same precedence, which is higher than Addition and Subtraction, which also have the same precedence. So 2*3-1 is 5, not 4, and 6+4/2 is 8, not 5.
  • Operators with the same precedence are evaluated from left to right. So in the expression degrees / 2 * pi, the division happens first and the result is multiplied by pi. To divide by 2 \pi, you can use parentheses or write degrees / 2 / pi.

2.8. String operations

As mentioned above, strings in Python can be enclosed in single or double quotes. The following two statements are equivalent:

mystring = 'green eggs and spam'
mystring = "green eggs and spam"

Sometimes you might need to create really long strings that span multiple lines. You can use yet another quoting method for that: triple quotes (three single quotes in a row). For example:

    mystring = '''

In general, you cannot perform mathematical operations on strings, even if the strings look like numbers, so the following are illegal:

'2'-'1'    'eggs'/'easy'    'third'*'a charm'

The + operator works with strings, but it might not do what you expect: it performs concatenation, which means joining the strings by glueing them end-to-end. For example:

first = 'throat'
second = 'warbler'
print first + second

The output of this program is throatwarbler.

The * operator also works on strings; it performs repetition. For example, 'Spam'*3 is 'SpamSpamSpam'. If one of the operands is a string, the other has to be an integer.

This use of + and * makes sense by analogy with addition and multiplication. Just as 4*3 is equivalent to 4+4+4, we expect 'Spam'*3 to be the same as 'Spam'+'Spam'+'Spam', and it is. On the other hand, there is a significant way in which string concatenation and repetition are different from integer addition and multiplication. Can you think of a property that addition has that string concatenation does not?

2.9. Reassignment

It is legal to make more than one assignment to the same variable. A new assignment makes an existing variable refer to a new value (and stop referring to the old value).

bruce = 5
print bruce,
bruce = 7
print bruce

The output of this program is 5 7, because the first time bruce is printed, its value is 5, and the second time, its value is 7. The comma at the end of the first print statement suppresses the newline, which is why both outputs appear on the same line.

Here is what reassignment looks like in a state diagram:

Reassignment state diagram.

Reassignment state diagram.

With reassignment it is especially important to distinguish between an assignment operation and a statement of equality. Because Python uses the equal sign (=) for assignment, it is tempting to interpret a statement like a = b as a statement of equality. It is not!

First, equality is a symmetric relation and assignment is not. For example, in mathematics, if a = 7 then 7 = a. But in Python, the statement a = 7 is legal and 7 = a is not.

Furthermore, in mathematics, a statement of equality is either true or false, for all time. If a = b now, then a will always equal b. In Python, an assignment statement can make two variables equal, but they don’t have to stay that way:

a = 5
b = a    # a and b are now equal
a = 3    # a and b are no longer equal

The third line changes the value of a but does not change the value of b, so they are no longer equal.

Although reassignment is frequently helpful, you should use it with care. If the values of variables change frequently, it can make the code difficult to read and debug.

You can also make multiple assignments on the same line:

a = b = c = 5
# a, b, and c each refer to the integer value 5

You can read such a statement from right to left: the value of 5 is assigned to c, which is also assigned to b, which is also assigned to a.

2.10. Updating variables

One of the most common forms of assignment is an update, where the new value of the variable depends on the old.

x = x+1

This means “get the current value of x, add one, and then update x with the new value.”

If you try to update a variable that doesn’t exist, you get an error, because Python evaluates the right side before it assigns a value to x:

>>> x = x+1
NameError: name 'x' is not defined

Before you can update a variable, you have to initialize it, usually with a simple assignment:

>>> x = 0
>>> x = x+1

Updating a variable by adding 1 is called an increment; subtracting 1 is called a decrement.

There are “convenience operators” built in to Python that make updating variables slightly simpler, syntactically. For example:

x += 2

does the same thing as

x = x + 2

with a couple fewer keystrokes. Similar to +=, there are -=, *=, and /= convenience operators. Many Pythonistas use these convenience operators, so if you look at code posted on, for example, Stack Overflow (http://stackoverflow.com/questions/tagged/python), you’ll often see these operators.


As programs get bigger and more complicated, they get more difficult to read. Formal languages are dense, and it is often difficult to look at a piece of code and figure out what it is doing, or why.

For this reason, it is a good idea to add notes to your programs to explain in natural language what the program is doing. These notes are called comments, and they start with the # symbol:

# compute the percentage of the hour that has elapsed
percentage = (minute * 100) / 60

In this case, the comment appears on a line by itself. You can also put comments at the end of a line:

percentage = (minute * 100) / 60 # percentage of an hour

Everything from the # to the end of the line is ignored—it has no effect on the program.

Comments are most useful when they document non-obvious features of the code. It is reasonable to assume that the reader can figure out what the code does; it is much more useful to explain why.

This comment is redundant with the code and useless:

v = 5     # assign 5 to v

This comment contains useful information that is not in the code:

v = 5     # velocity in meters/second.

Good variable names can reduce the need for comments, but long names can make complex expressions hard to read, so there is a tradeoff. It will be important in all the programs you create in this class (even short programs!) to carefully consider variable name choices and to include useful comments. Both of these items are considered part of the documentation of a program, and help humans (you and others) to better understand the purpose and intent of a program.

2.12. Debugging

At this point the syntax error you are most likely to make is an illegal variable name, like class and yield, which are keywords, or odd~job and US$, which contain illegal characters.

If you put a space in a variable name, Python thinks it is two operands without an operator:

>>> bad name = 5
SyntaxError: invalid syntax

For syntax errors, the error messages don’t help much. The most common messages are SyntaxError: invalid syntax and SyntaxError: invalid token, neither of which is very informative.

The runtime error you are most likely to make is a “use before def”; that is, trying to use a variable before you have assigned a value. This can happen if you spell a variable name wrong:

>>> principal = 327.68
>>> interest = principle * rate
NameError: name 'principle' is not defined

Variables names are case sensitive, so LaTeX is not the same as latex.

At this point the most likely cause of a semantic error is the order of operations. For example, to evaluate \frac{1}{2 \pi}, you might be tempted to write

>>> 1.0 / 2.0 * pi

But the division happens first, so you would get \pi / 2, which is not the same thing! There is no way for Python to know what you meant to write, so in this case you don’t get an error message; you just get the wrong answer.


  1. Rewrite the last expression (1.0 / 2.0 * pi) so that the correct answer is reached.

2.13. Glossary

One of the basic units of data, like a number or string, that a program manipulates.
A category of values. The types we have seen so far are integers (type int), floating-point numbers (type float), and strings (type str).
A type that represents whole numbers.
A type that represents numbers with fractional parts.
A type that represents sequences of characters.
A name that refers to a value.
A section of code that represents a command or action. So far, the statements we have seen are assignments and print statements.
A statement that assigns a value to a variable.
state diagram:
A graphical representation of a set of variables and the values they refer to.
A reserved word that is used by the compiler to parse a program; you cannot use keywords like if, def, and while as variable names.
A special symbol that represents a simple computation like addition, multiplication, or string concatenation.
One of the values on which an operator operates.
floor division:
The operation that divides two numbers and chops off the fraction part.
A combination of variables, operators, and values that represents a single result value.
To simplify an expression by performing the operations in order to yield a single value.
rules of precedence:
The set of rules governing the order in which expressions involving multiple operators and operands are evaluated.
To join two operands end-to-end.
Making more than one assignment to the same variable during the execution of a program.
An assignment where the new value of the variable depends on the old.
Information in a program that is meant for other programmers (or anyone reading the source code) and has no effect on the execution of the program.

2.14. Exercises

  1. Assume that we execute the following assignment statements:

    width = 17

    height = 12.0

    delimiter = '.'

    For each of the following expressions, write the value of the expression and the type (of the value of the expression).

    1. width/2
    2. width/2.0
    3. height/3
    4. 1 + 2 * 5
    5. delimiter * 5

    Use the Python interpreter to check your answers.

  2. Practice using the Python interpreter as a calculator:

    1. The volume of a sphere with radius r is \frac{4}{3} \pi r^3. What is the volume of a sphere with radius 5? Hint: 392.6 is wrong!
    2. Suppose the cover price of a book is $24.95, but bookstores get a 40% discount. Shipping costs $3 for the first copy and 75 cents for each additional copy. What is the total wholesale cost for 60 copies?
    3. If I leave my house at 6:52 am and run 1 mile at an easy pace (8:15 per mile), then 3 miles at tempo (7:12 per mile) and 1 mile at easy pace again, what time do I get home for breakfast?
  3. Consider the following two variable assignments:

    panicstring = "don't panic"
    answer = 42

    Write a Python statement to print the following: don't panic -- think 42

  4. Consider a modern computer processor that runs at 2 GHz, which simply means “2 billion cycles per second”. If the speed of light is 299, 792, 458 meters per second, how many centimeters does light travel in the time it takes a processor to execute one cycle? Write a one-line Python program to print the answer.

[1]In Python 3.0, exec is no longer a keyword, but nonlocal is.
[2]In Python 3.0, the result of this division is a float.