Variables and Statements

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from os.path import basename, exists

def download(url):
    filename = basename(url)
    if not exists(filename):
        from urllib.request import urlretrieve

        local, _ = urlretrieve(url, filename)
        print("Downloaded " + str(local))
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import working_in_python

2. Variables and Statements#

In the previous chapter, we used operators to write expressions that perform arithmetic computations.

In this chapter, you’ll learn about variables and statements, the import statement, and the print function. And I’ll introduce more of the vocabulary we use to talk about programs, including “argument” and “module”.

2.1. Variables#

A variable is a name that refers to a value. To create a variable, we can write a assignment statement like this.

n = 17

An assignment statement has three parts: the name of the variable on the left, the equals operator, =, and an expression on the right. In this example, the expression is an integer. In the following example, the expression is a floating-point number.

pi = 3.141592653589793

And in the following example, the expression is a string.

message = 'And now for something completely different'

When you run an assignment statement, there is no output. Python creates the variable and gives it a value, but the assignment statement has no visible effect. However, after creating a variable, you can use it as an expression. So we can display the value of message like this:

message

You can also use a variable as part of an expression with arithmetic operators.

n + 25

2 * pi

And you can use a variable when you call a function.

round(pi)

len(message)

2.2. State diagrams#

A common way to represent variables on paper is to write the name with an arrow pointing to its value.

import math

from diagram import make_binding, Frame

binding = make_binding("message", 'And now for something completely different')
binding2 = make_binding("n", 17)
binding3 = make_binding("pi", 3.141592653589793)

frame = Frame([binding2, binding3, binding])

from diagram import diagram, adjust


width, height, x, y = [3.62, 1.01, 0.6, 0.76]
ax = diagram(width, height)
bbox = frame.draw(ax, x, y, dy=-0.25)
# adjust(x, y, bbox)

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). We’ll use state diagrams throughout the book to represent a model of how Python stores variables and their values.

2.3. Variable names#

Variable names can be as long as you like. They can contain both letters and numbers, but they can’t begin with a number. It is legal to use uppercase letters, but it is conventional to use only lower case for variable names.

The only punctuation that can appear in a variable name is the underscore character, _. It is often used in names with multiple words, such as your_name or airspeed_of_unladen_swallow.

If you give a variable an illegal name, you get a syntax error. The name million! is illegal because it contains punctuation.

million! = 1000000

76trombones is illegal because it starts with a number.

76trombones = 'big parade'

class is also illegal, but it might not be obvious why.

class = 'Self-Defence Against Fresh Fruit'

It turns out that class is a keyword, which is a special word used to specify the structure of a program. Keywords can’t be used as variable names.

Here’s a complete list of Python’s keywords:

False      await      else       import     pass
None       break      except     in         raise
True       class      finally    is         return
and        continue   for        lambda     try
as         def        from       nonlocal   while
assert     del        global     not        with
async      elif       if         or         yield

from keyword import kwlist

len(kwlist)

You don’t have to memorize this list. In most development environments, keywords are displayed in a different color; if you try to use one as a variable name, you’ll know.

2.4. The import statement#

In order to use some Python features, you have to import them. For example, the following statement imports the math module.

import math

A module is a collection of variables and functions. The math module provides a variable called pi that contains the value of the mathematical constant denoted \(\pi\). We can display its value like this.

math.pi

To use a variable in a module, you have to use the dot operator (.) between the name of the module and the name of the variable.

The math module also contains functions. For example, sqrt computes square roots.

math.sqrt(25)

And pow raises one number to the power of a second number.

math.pow(5, 2)

At this point we’ve seen two ways to raise a number to a power: we can use the math.pow function or the exponentiation operator, **. Either one is fine, but the operator is used more often than the function.

2.5. Expressions and statements#

So far, we’ve seen a few kinds of expressions. An expression can be a single value, like an integer, floating-point number, or string. It can also be a collection of values and operators. And it can include variable names and function calls. Here’s an expression that includes several of these elements.

19 + n + round(math.pi) * 2

We have also seen a few kind of statements. A statement is a unit of code that has an effect, but no value. For example, an assignment statement creates a variable and gives it a value, but the statement itself has no value.

n = 17

Similarly, an import statement has an effect – it imports a module so we can use the variables and functions it contains – but it has no visible effect.

import math

Computing the value of an expression is called evaluation. Running a statement is called execution.

2.6. The print function#

When you evaluate an expression, the result is displayed.

n + 1

But if you evaluate more than one expression, only the value of the last one is displayed.

n + 2
n + 3

To display more than one value, you can use the print function.

print(n+2)
print(n+3)

It also works with floating-point numbers and strings.

print('The value of pi is approximately')
print(math.pi)

You can also use a sequence of expressions separated by commas.

print('The value of pi is approximately', math.pi)

Notice that the print function puts a space between the values.

2.7. Arguments#

When you call a function, the expression in parenthesis is called an argument. Normally I would explain why, but in this case the technical meaning of a term has almost nothing to do with the common meaning of the word, so I won’t even try.

Some of the functions we’ve seen so far take only one argument, like int.

int('101')

Some take two, like math.pow.

math.pow(5, 2)

Some can take additional arguments that are optional. For example, int can take a second argument that specifies the base of the number.

int('101', 2)

The sequence of digits 101 in base 2 represents the number 5 in base 10.

round also takes an optional second argument, which is the number of decimal places to round off to.

round(math.pi, 3)

Some functions can take any number of arguments, like print.

print('Any', 'number', 'of', 'arguments')

If you call a function and provide too many arguments, that’s a TypeError.

float('123.0', 2)

If you provide too few arguments, that’s also a TypeError.

math.pow(2)

And if you provide an argument with a type the function can’t handle, that’s a TypeError, too.

math.sqrt('123')

This kind of checking can be annoying when you are getting started, but it helps you detect and correct errors.

2.8. Comments#

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 and 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.

# number of seconds in 42:42
seconds = 42 * 60 + 42

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

miles = 10 / 1.61     # 10 kilometers in miles

Everything from the # to the end of the line is ignored—it has no effect on the execution of 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 more useful to explain why.

This comment is redundant with the code and useless:

v = 8     # assign 8 to v

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

v = 8     # velocity in miles per hour

Good variable names can reduce the need for comments, but long names can make complex expressions hard to read, so there is a tradeoff.

2.9. Debugging#

Three kinds of errors can occur in a program: syntax errors, runtime errors, and semantic errors. It is useful to distinguish between them in order to track them down more quickly.

  • Syntax error: “Syntax” refers to the structure of a program and the rules about that structure. If there is a syntax error anywhere in your program, Python does not run the program. It displays an error message immediately.

  • Runtime error: If there are no syntax errors in your program, it can start running. But if something goes wrong, Python displays an error message and stops. This type of error is called a runtime error. It is also called an exception because it indicates that something exceptional has happened.

  • Semantic error: The third type of error is “semantic”, which means related to meaning. If there is a semantic error in your program, it runs without generating error messages, but it does not do what you intended. Identifying semantic errors can be tricky because it requires you to work backward by looking at the output of the program and trying to figure out what it is doing.

As we’ve seen, an illegal variable name is a syntax error.

million! = 1000000

If you use an operator with a type it doesn’t support, that’s a runtime error.

'126' / 3

Finally, here’s an example of a semantic error. Suppose we want to compute the average of 1 and 3, but we forget about the order of operations and write this:

1 + 3 / 2

When this expression is evaluated, it does not produce an error message, so there is no syntax error or runtime error. But the result is not the average of 1 and 3, so the program is not correct. This is a semantic error because the program runs but it doesn’t do what’s intended.

2.10. Glossary#

variable: A name that refers to a value.

assignment statement: 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.

keyword: A special word used to specify the structure of a program.

import statement: A statement that reads a module file so we can use the variables and functions it contains.

module: A file that contains Python code, including function definitions and sometimes other statements.

dot operator: The operator, ., used to access a function in another module by specifying the module name followed by a dot and the function name.

evaluate: Perform the operations in an expression in order to compute a value.

statement: One or more lines of code that represent a command or action.

execute: Run a statement and do what it says.

argument: A value provided to a function when the function is called.

comment: Text included in a program that provides information about the program but has no effect on its execution.

runtime error: An error that causes a program to display an error message and exit.

exception: An error that is detected while the program is running.

semantic error: An error that causes a program to do the wrong thing, but not to display an error message.

See also: the full vocabulary glossary collects every term in this book, alphabetized, alongside the complete AP CSP exam vocabulary list.

2.11. Exercises#

# This cell tells Jupyter to provide detailed debugging information
# when a runtime error occurs. Run it before working on the exercises.

%xmode Verbose

2.11.1. Exercise#

Repeating my advice from the previous chapter, whenever you learn a new feature, you should make errors on purpose to see what goes wrong.

  • We’ve seen that n = 17 is legal. What about 17 = n?

  • How about x = y = 1?

  • In some languages every statement ends with a semi-colon (;). What happens if you put a semi-colon at the end of a Python statement?

  • What if you put a period at the end of a statement?

  • What happens if you spell the name of a module wrong and try to import maath?

2.11.2. Exercise#

Practice using the Python interpreter as a calculator:

Part 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? Start with a variable named radius and then assign the result to a variable named volume. Display the result. Add comments to indicate that radius is in centimeters and volume in cubic centimeters.

Part 2. A rule of trigonometry says that for any value of \(x\), \((\cos x)^2 + (\sin x)^2 = 1\). Let’s see if it’s true for a specific value of \(x\) like 42.

Create a variable named x with this value. Then use math.cos and math.sin to compute the sine and cosine of \(x\), and the sum of their squared.

The result should be close to 1. It might not be exactly 1 because floating-point arithmetic is not exact—it is only approximately correct.

Part 3. In addition to pi, the other variable defined in the math module is e, which represents the base of the natural logarithm, written in math notation as \(e\). Now let’s compute \(e^2\) three ways:

  • Use math.e and the exponentiation operator (**).

  • Use math.pow to raise math.e to the power 2.

  • Use math.exp, which takes as an argument a value, \(x\), and computes \(e^x\).

You might notice that the last result is slightly different from the other two. See if you can find out which is correct.

2.12. Homework#

These five exercises are your homework for this chapter, about 35 minutes total.

2.12.1. Exercise 1: trace the values#

Below is a short sequence of assignment statements. Before you run the cell, write down (in a comment above each line) what you think the value of each variable is after that line runs.

a = 5
b = a + 2
a = a + 1
b = a * 2

Then run the cell and check your predictions. If any were wrong, add a comment explaining what you missed.

2.12.2. Exercise 2: Python as a calculator, math-class edition#

Part a. A right triangle has legs of length 9 and 12. The Pythagorean theorem says the hypotenuse c satisfies c**2 = a**2 + b**2. Create variables a and b with these values, then compute c using math.sqrt and **. Display the result.

Part b. An isosceles triangle has two equal sides of length 10 and a base of length 12. The height from the top down to the base splits the triangle into two right triangles, each with a base of 6 – so it’s the same theorem again, with different numbers. Compute the height and store it in a variable named height. Display the result.

Part c. A ramp is 20 feet long and makes a 30-degree angle with the ground. The height it rises is length * sin(angle).

One catch: math.sin expects the angle in radians, not degrees, so convert first with math.radians. Compute the height the ramp rises, then compute how far it extends horizontally along the ground using math.cos the same way.

Note: the height won’t come out to a perfectly clean 10.0 – you’ll get something like 9.999999999999998. That’s the same floating-point-imprecision effect from the chapter’s own trig-identity exercise, not a mistake in your code.

2.12.3. Exercise 3: arguments and TypeError#

  1. Predict what round(3.14159, 2) displays, then run it.

  2. Now run round(3.14159, 2, 5). In a comment, explain what kind of TypeError this is – too many arguments, too few, or the wrong type?

  3. Now run round() with no arguments at all. In a comment, explain what kind of TypeError this one is, and how it’s different from part 2.

2.12.4. Exercise 4: bad comment, good comment#

Here’s a line of code:

temp = 98.6

Write two versions of this line below, each with a different comment: one that’s redundant with the code (like the chapter’s v = 8  # assign 8 to v example), and one that adds real information the code doesn’t already show.

2.12.5. Exercise 5: reflection#

Of the three error types from this chapter – syntax, runtime, and semantic – which do you think would be hardest to notice you’d made? Why?

2.12.6. Finished? Copy your work#

This isn’t part of Exercise 5 – it’s a tool. Run the cell below to copy this notebook (including anything you’ve run) so you can paste it into a document.

working_in_python.show_copy_notebook_button()

Working in Python — modified by Eric Brown for a high school Computer Science Principles class. Source and modifications: github.com/porttack/working-in-python

Think Python: 3rd Edition

Copyright 2024 Allen B. Downey

Code license: MIT License

Text license: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International

2.13. Standards alignment#

AP CSP: 3.1 Variables and Assignments, 3.14 Libraries (Big Idea 3, 30–35% of the exam). Also 1.4 Identifying and Correcting Errors (Big Idea 1, 10–13%), headers only. California 9-12: 9-12.AP.17 CSTA 2026: HS-PRO-PD-13, headers only — the libraries half of the standard; the rest is chapter 4’s territory. CA CTE (ICT): C4.6, C4.9, C4.11 (Pathway C). Also C5.6, headers only.

Assignment statements here are the exam’s 3.1: a name bound to a value. The import statement is this book’s first real use of a library, matching the exam’s 3.14 and California’s AP.17, which frames modular design as building with pieces someone else already wrote. This chapter’s variables and comments are also ICT’s C4.9 and C4.11 in different words.

Vocabulary: this book writes assignment as =. The exam’s pseudocode uses ←.