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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
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<html xmlns="http://www.w3.org/1999/xhtml">
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<title>Preface — Pense Python 2e documentation</title>
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<p>[chapter]</p>
<div class="line-block">
<div class="line">3 Think Python</div>
<div class="line">How to Think Like a Computer Scientist</div>
</div>
<p>2nd Edition, Version 2.2.14</p>
<div class="line-block">
<div class="line">3 Think Python</div>
<div class="line">How to Think Like a Computer Scientist</div>
</div>
<p>2nd Edition, Version 2.2.14</p>
<p>Allen Downey</p>
<p>Green Tea Press</p>
<p>Needham, Massachusetts</p>
<p>Copyright © 2015 Allen Downey.</p>
<div class="line-block">
<div class="line">Green Tea Press</div>
<div class="line">9 Washburn Ave</div>
<div class="line">Needham MA 02492</div>
</div>
<p>Permission is granted to copy, distribute, and/or modify this document
under the terms of the Creative Commons Attribution-NonCommercial 3.0
Unported License, which is available at
<a class="reference external" href="http://creativecommons.org/licenses/by-nc/3.0/">http://creativecommons.org/licenses/by-nc/3.0/</a>.</p>
<p>The original form of this book is LaTeX source code. Compiling this
LaTeX source has the effect of generating a device-independent
representation of a textbook, which can be converted to other formats
and printed.</p>
<p>The LaTeX source for this book is available from
<a class="reference external" href="http://www.thinkpython2.com">http://www.thinkpython2.com</a></p>
<p>Think Python: How to Think Like a Computer Scientist</p>
<p>Allen B. Downey</p>
<p>2nd Edition, Version 2.2.14</p>
<div class="section" id="preface">
<h1>Preface<a class="headerlink" href="#preface" title="Permalink to this headline">¶</a></h1>
<div class="section" id="the-strange-history-of-this-book">
<h2>The strange history of this book<a class="headerlink" href="#the-strange-history-of-this-book" title="Permalink to this headline">¶</a></h2>
<p>In January 1999 I was preparing to teach an introductory programming
class in Java. I had taught it three times and I was getting frustrated.
The failure rate in the class was too high and, even for students who
succeeded, the overall level of achievement was too low.</p>
<p>One of the problems I saw was the books. They were too big, with too
much unnecessary detail about Java, and not enough high-level guidance
about how to program. And they all suffered from the trap door effect:
they would start out easy, proceed gradually, and then somewhere around
Chapter 5 the bottom would fall out. The students would get too much new
material, too fast, and I would spend the rest of the semester picking
up the pieces.</p>
<p>Two weeks before the first day of classes, I decided to write my own
book. My goals were:</p>
<ul class="simple">
<li>Keep it short. It is better for students to read 10 pages than not
read 50 pages.</li>
<li>Be careful with vocabulary. I tried to minimize jargon and define
each term at first use.</li>
<li>Build gradually. To avoid trap doors, I took the most difficult
topics and split them into a series of small steps.</li>
<li>Focus on programming, not the programming language. I included the
minimum useful subset of Java and left out the rest.</li>
</ul>
<p>I needed a title, so on a whim I chose <em>How to Think Like a Computer
Scientist</em>.</p>
<p>My first version was rough, but it worked. Students did the reading, and
they understood enough that I could spend class time on the hard topics,
the interesting topics and (most important) letting the students
practice.</p>
<p>I released the book under the GNU Free Documentation License, which
allows users to copy, modify, and distribute the book.</p>
<p>What happened next is the cool part. Jeff Elkner, a high school teacher
in Virginia, adopted my book and translated it into Python. He sent me a
copy of his translation, and I had the unusual experience of learning
Python by reading my own book. As Green Tea Press, I published the first
Python version in 2001.</p>
<p>In 2003 I started teaching at Olin College and I got to teach Python for
the first time. The contrast with Java was striking. Students struggled
less, learned more, worked on more interesting projects, and generally
had a lot more fun.</p>
<p>Since then I’ve continued to develop the book, correcting errors,
improving some of the examples and adding material, especially
exercises.</p>
<p>The result is this book, now with the less grandiose title <em>Think
Python</em>. Some of the changes are:</p>
<ul class="simple">
<li>I added a section about debugging at the end of each chapter. These
sections present general techniques for finding and avoiding bugs,
and warnings about Python pitfalls.</li>
<li>I added more exercises, ranging from short tests of understanding to
a few substantial projects. Most exercises include a link to my
solution.</li>
<li>I added a series of case studies—longer examples with exercises,
solutions, and discussion.</li>
<li>I expanded the discussion of program development plans and basic
design patterns.</li>
<li>I added appendices about debugging and analysis of algorithms.</li>
</ul>
<p>The second edition of <em>Think Python</em> has these new features:</p>
<ul class="simple">
<li>The book and all supporting code have been updated to Python 3.</li>
<li>I added a few sections, and more details on the web, to help
beginners get started running Python in a browser, so you don’t have
to deal with installing Python until you want to.</li>
<li>For Chapter [turtle] I switched from my own turtle graphics package,
called Swampy, to a more standard Python module, turtle, which is
easier to install and more powerful.</li>
<li>I added a new chapter called “The Goodies”, which introduces some
additional Python features that are not strictly necessary, but
sometimes handy.</li>
</ul>
<p>I hope you enjoy working with this book, and that it helps you learn to
program and think like a computer scientist, at least a little bit.</p>
<div class="line-block">
<div class="line">Allen B. Downey</div>
<div class="line">Olin College</div>
</div>
</div>
<div class="section" id="acknowledgments">
<h2>Acknowledgments<a class="headerlink" href="#acknowledgments" title="Permalink to this headline">¶</a></h2>
<p>Many thanks to Jeff Elkner, who translated my Java book into Python,
which got this project started and introduced me to what has turned out
to be my favorite language.</p>
<p>Thanks also to Chris Meyers, who contributed several sections to <em>How to
Think Like a Computer Scientist</em>.</p>
<p>Thanks to the Free Software Foundation for developing the GNU Free
Documentation License, which helped make my collaboration with Jeff and
Chris possible, and Creative Commons for the license I am using now.</p>
<p>Thanks to the editors at Lulu who worked on <em>How to Think Like a
Computer Scientist</em>.</p>
<p>Thanks to the editors at O’Reilly Media who worked on <em>Think Python</em>.</p>
<p>Thanks to all the students who worked with earlier versions of this book
and all the contributors (listed below) who sent in corrections and
suggestions.</p>
</div>
<div class="section" id="contributor-list">
<h2>Contributor List<a class="headerlink" href="#contributor-list" title="Permalink to this headline">¶</a></h2>
<p>More than 100 sharp-eyed and thoughtful readers have sent in suggestions
and corrections over the past few years. Their contributions, and
enthusiasm for this project, have been a huge help.</p>
<p>If you have a suggestion or correction, please send email to
<a class="reference external" href="mailto:feedback%40thinkpython.com">feedback<span>@</span>thinkpython<span>.</span>com</a>. If I make a change based on your feedback, I
will add you to the contributor list (unless you ask to be omitted).</p>
<p>If you include at least part of the sentence the error appears in, that
makes it easy for me to search. Page and section numbers are fine, too,
but not quite as easy to work with. Thanks!</p>
<ul class="simple">
<li>Lloyd Hugh Allen sent in a correction to Section 8.4.</li>
<li>Yvon Boulianne sent in a correction of a semantic error in Chapter 5.</li>
<li>Fred Bremmer submitted a correction in Section 2.1.</li>
<li>Jonah Cohen wrote the Perl scripts to convert the LaTeX source for
this book into beautiful HTML.</li>
<li>Michael Conlon sent in a grammar correction in Chapter 2 and an
improvement in style in Chapter 1, and he initiated discussion on the
technical aspects of interpreters.</li>
<li>Benoit Girard sent in a correction to a humorous mistake in Section
5.6.</li>
<li>Courtney Gleason and Katherine Smith wrote horsebet.py, which was
used as a case study in an earlier version of the book. Their program
can now be found on the website.</li>
<li>Lee Harr submitted more corrections than we have room to list here,
and indeed he should be listed as one of the principal editors of the
text.</li>
<li>James Kaylin is a student using the text. He has submitted numerous
corrections.</li>
<li>David Kershaw fixed the broken catTwice function in Section 3.10.</li>
<li>Eddie Lam has sent in numerous corrections to Chapters 1, 2, and 3.
He also fixed the Makefile so that it creates an index the first time
it is run and helped us set up a versioning scheme.</li>
<li>Man-Yong Lee sent in a correction to the example code in Section 2.4.</li>
<li>David Mayo pointed out that the word ``unconsciously“ in Chapter 1
needed to be changed to ``subconsciously”.</li>
<li>Chris McAloon sent in several corrections to Sections 3.9 and 3.10.</li>
<li>Matthew J. Moelter has been a long-time contributor who sent in
numerous corrections and suggestions to the book.</li>
<li>Simon Dicon Montford reported a missing function definition and
several typos in Chapter 3. He also found errors in the increment
function in Chapter 13.</li>
<li>John Ouzts corrected the definition of ``return value” in Chapter
3.</li>
<li>Kevin Parks sent in valuable comments and suggestions as to how to
improve the distribution of the book.</li>
<li>David Pool sent in a typo in the glossary of Chapter 1, as well as
kind words of encouragement.</li>
<li>Michael Schmitt sent in a correction to the chapter on files and
exceptions.</li>
<li>Robin Shaw pointed out an error in Section 13.1, where the printTime
function was used in an example without being defined.</li>
<li>Paul Sleigh found an error in Chapter 7 and a bug in Jonah Cohen’s
Perl script that generates HTML from LaTeX.</li>
<li>Craig T. Snydal is testing the text in a course at Drew University.
He has contributed several valuable suggestions and corrections.</li>
<li>Ian Thomas and his students are using the text in a programming
course. They are the first ones to test the chapters in the latter
half of the book, and they have made numerous corrections and
suggestions.</li>
<li>Keith Verheyden sent in a correction in Chapter 3.</li>
<li>Peter Winstanley let us know about a longstanding error in our Latin
in Chapter 3.</li>
<li>Chris Wrobel made corrections to the code in the chapter on file I/O
and exceptions.</li>
<li>Moshe Zadka has made invaluable contributions to this project. In
addition to writing the first draft of the chapter on Dictionaries,
he provided continual guidance in the early stages of the book.</li>
<li>Christoph Zwerschke sent several corrections and pedagogic
suggestions, and explained the difference between <em>gleich</em> and
<em>selbe</em>.</li>
<li>James Mayer sent us a whole slew of spelling and typographical
errors, including two in the contributor list.</li>
<li>Hayden McAfee caught a potentially confusing inconsistency between
two examples.</li>
<li>Angel Arnal is part of an international team of translators working
on the Spanish version of the text. He has also found several errors
in the English version.</li>
<li>Tauhidul Hoque and Lex Berezhny created the illustrations in Chapter
1 and improved many of the other illustrations.</li>
<li>Dr. Michele Alzetta caught an error in Chapter 8 and sent some
interesting pedagogic comments and suggestions about Fibonacci and
Old Maid.</li>
<li>Andy Mitchell caught a typo in Chapter 1 and a broken example in
Chapter 2.</li>
<li>Kalin Harvey suggested a clarification in Chapter 7 and caught some
typos.</li>
<li>Christopher P. Smith caught several typos and helped us update the
book for Python 2.2.</li>
<li>David Hutchins caught a typo in the Foreword.</li>
<li>Gregor Lingl is teaching Python at a high school in Vienna, Austria.
He is working on a German translation of the book, and he caught a
couple of bad errors in Chapter 5.</li>
<li>Julie Peters caught a typo in the Preface.</li>
<li>Florin Oprina sent in an improvement in makeTime, a correction in
printTime, and a nice typo.</li>
<li>D. J. Webre suggested a clarification in Chapter 3.</li>
<li>Ken found a fistful of errors in Chapters 8, 9 and 11.</li>
<li>Ivo Wever caught a typo in Chapter 5 and suggested a clarification in
Chapter 3.</li>
<li>Curtis Yanko suggested a clarification in Chapter 2.</li>
<li>Ben Logan sent in a number of typos and problems with translating the
book into HTML.</li>
<li>Jason Armstrong saw the missing word in Chapter 2.</li>
<li>Louis Cordier noticed a spot in Chapter 16 where the code didn’t
match the text.</li>
<li>Brian Cain suggested several clarifications in Chapters 2 and 3.</li>
<li>Rob Black sent in a passel of corrections, including some changes for
Python 2.2.</li>
<li>Jean-Philippe Rey at Ecole Centrale Paris sent a number of patches,
including some updates for Python 2.2 and other thoughtful
improvements.</li>
<li>Jason Mader at George Washington University made a number of useful
suggestions and corrections.</li>
<li>Jan Gundtofte-Bruun reminded us that “a error” is an error.</li>
<li>Abel David and Alexis Dinno reminded us that the plural of “matrix”
is “matrices”, not “matrixes”. This error was in the book for years,
but two readers with the same initials reported it on the same day.
Weird.</li>
<li>Charles Thayer encouraged us to get rid of the semi-colons we had put
at the ends of some statements and to clean up our use of “argument”
and “parameter”.</li>
<li>Roger Sperberg pointed out a twisted piece of logic in Chapter 3.</li>
<li>Sam Bull pointed out a confusing paragraph in Chapter 2.</li>
<li>Andrew Cheung pointed out two instances of “use before def”.</li>
<li>C. Corey Capel spotted the missing word in the Third Theorem of
Debugging and a typo in Chapter 4.</li>
<li>Alessandra helped clear up some Turtle confusion.</li>
<li>Wim Champagne found a brain-o in a dictionary example.</li>
<li>Douglas Wright pointed out a problem with floor division in arc.</li>
<li>Jared Spindor found some jetsam at the end of a sentence.</li>
<li>Lin Peiheng sent a number of very helpful suggestions.</li>
<li>Ray Hagtvedt sent in two errors and a not-quite-error.</li>
<li>Torsten Hübsch pointed out an inconsistency in Swampy.</li>
<li>Inga Petuhhov corrected an example in Chapter 14.</li>
<li>Arne Babenhauserheide sent several helpful corrections.</li>
<li>Mark E. Casida is is good at spotting repeated words.</li>
<li>Scott Tyler filled in a that was missing. And then sent in a heap of
corrections.</li>
<li>Gordon Shephard sent in several corrections, all in separate emails.</li>
<li>Andrew Turner spotted an error in Chapter 8.</li>
<li>Adam Hobart fixed a problem with floor division in arc.</li>
<li>Daryl Hammond and Sarah Zimmerman pointed out that I served up
math.pi too early. And Zim spotted a typo.</li>
<li>George Sass found a bug in a Debugging section.</li>
<li>Brian Bingham suggested Exercise [exrotatepairs].</li>
<li>Leah Engelbert-Fenton pointed out that I used tuple as a variable
name, contrary to my own advice. And then found a bunch of typos and
a “use before def”.</li>
<li>Joe Funke spotted a typo.</li>
<li>Chao-chao Chen found an inconsistency in the Fibonacci example.</li>
<li>Jeff Paine knows the difference between space and spam.</li>
<li>Lubos Pintes sent in a typo.</li>
<li>Gregg Lind and Abigail Heithoff suggested Exercise [checksum].</li>
<li>Max Hailperin has sent in a number of corrections and suggestions.
Max is one of the authors of the extraordinary <em>Concrete
Abstractions</em>, which you might want to read when you are done with
this book.</li>
<li>Chotipat Pornavalai found an error in an error message.</li>
<li>Stanislaw Antol sent a list of very helpful suggestions.</li>
<li>Eric Pashman sent a number of corrections for Chapters 4–11.</li>
<li>Miguel Azevedo found some typos.</li>
<li>Jianhua Liu sent in a long list of corrections.</li>
<li>Nick King found a missing word.</li>
<li>Martin Zuther sent a long list of suggestions.</li>
<li>Adam Zimmerman found an inconsistency in my instance of an “instance”
and several other errors.</li>
<li>Ratnakar Tiwari suggested a footnote explaining degenerate triangles.</li>
<li>Anurag Goel suggested another solution for <code class="docutils literal"><span class="pre">is_abecedarian</span></code> and
sent some additional corrections. And he knows how to spell Jane
Austen.</li>
<li>Kelli Kratzer spotted one of the typos.</li>
<li>Mark Griffiths pointed out a confusing example in Chapter 3.</li>
<li>Roydan Ongie found an error in my Newton’s method.</li>
<li>Patryk Wolowiec helped me with a problem in the HTML version.</li>
<li>Mark Chonofsky told me about a new keyword in Python 3.</li>
<li>Russell Coleman helped me with my geometry.</li>
<li>Wei Huang spotted several typographical errors.</li>
<li>Karen Barber spotted the the oldest typo in the book.</li>
<li>Nam Nguyen found a typo and pointed out that I used the Decorator
pattern but didn’t mention it by name.</li>
<li>Stéphane Morin sent in several corrections and suggestions.</li>
<li>Paul Stoop corrected a typo in <code class="docutils literal"><span class="pre">uses_only</span></code>.</li>
<li>Eric Bronner pointed out a confusion in the discussion of the order
of operations.</li>
<li>Alexandros Gezerlis set a new standard for the number and quality of
suggestions he submitted. We are deeply grateful!</li>
<li>Gray Thomas knows his right from his left.</li>
<li>Giovanni Escobar Sosa sent a long list of corrections and
suggestions.</li>
<li>Alix Etienne fixed one of the URLs.</li>
<li>Kuang He found a typo.</li>
<li>Daniel Neilson corrected an error about the order of operations.</li>
<li>Will McGinnis pointed out that polyline was defined differently in
two places.</li>
<li>Swarup Sahoo spotted a missing semi-colon.</li>
<li>Frank Hecker pointed out an exercise that was under-specified, and
some broken links.</li>
<li>Animesh B helped me clean up a confusing example.</li>
<li>Martin Caspersen found two round-off errors.</li>
<li>Gregor Ulm sent several corrections and suggestions.</li>
<li>Dimitrios Tsirigkas suggested I clarify an exercise.</li>
<li>Carlos Tafur sent a page of corrections and suggestions.</li>
<li>Martin Nordsletten found a bug in an exercise solution.</li>
<li>Lars O.D. Christensen found a broken reference.</li>
<li>Victor Simeone found a typo.</li>
<li>Sven Hoexter pointed out that a variable named input shadows a
build-in function.</li>
<li>Viet Le found a typo.</li>
<li>Stephen Gregory pointed out the problem with cmp in Python 3.</li>
<li>Matthew Shultz let me know about a broken link.</li>
<li>Lokesh Kumar Makani let me know about some broken links and some
changes in error messages.</li>
<li>Ishwar Bhat corrected my statement of Fermat’s last theorem.</li>
<li>Brian McGhie suggested a clarification.</li>
<li>Andrea Zanella translated the book into Italian, and sent a number of
corrections along the way.</li>
<li>Many, many thanks to Melissa Lewis and Luciano Ramalho for excellent
comments and suggestions on the second edition.</li>
<li>Thanks to Harry Percival from PythonAnywhere for his help getting
people started running Python in a browser.</li>
<li>Xavier Van Aubel made several useful corrections in the second
edition.</li>
</ul>
</div>
</div>
<div class="section" id="the-way-of-the-program">
<h1>The way of the program<a class="headerlink" href="#the-way-of-the-program" title="Permalink to this headline">¶</a></h1>
<p>The goal of this book is to teach you to think like a computer
scientist. This way of thinking combines some of the best features of
mathematics, engineering, and natural science. Like mathematicians,
computer scientists use formal languages to denote ideas (specifically
computations). Like engineers, they design things, assembling components
into systems and evaluating tradeoffs among alternatives. Like
scientists, they observe the behavior of complex systems, form
hypotheses, and test predictions.</p>
<p>The single most important skill for a computer scientist is <strong>problem
solving</strong>. Problem solving means the ability to formulate problems,
think creatively about solutions, and express a solution clearly and
accurately. As it turns out, the process of learning to program is an
excellent opportunity to practice problem-solving skills. That’s why
this chapter is called, “The way of the program”.</p>
<p>On one level, you will be learning to program, a useful skill by itself.
On another level, you will use programming as a means to an end. As we
go along, that end will become clearer.</p>
<div class="section" id="what-is-a-program">
<h2>What is a program?<a class="headerlink" href="#what-is-a-program" title="Permalink to this headline">¶</a></h2>
<p>A <strong>program</strong> is a sequence of instructions that specifies how to
perform a computation. The computation might be something mathematical,
such as solving a system of equations or finding the roots of a
polynomial, but it can also be a symbolic computation, such as searching
and replacing text in a document or something graphical, like processing
an image or playing a video.</p>
<p>The details look different in different languages, but a few basic
instructions appear in just about every language:</p>
<dl class="docutils">
<dt>input:</dt>
<dd>Get data from the keyboard, a file, the network, or some other
device.</dd>
<dt>output:</dt>
<dd>Display data on the screen, save it in a file, send it over the
network, etc.</dd>
<dt>math:</dt>
<dd>Perform basic mathematical operations like addition and
multiplication.</dd>
<dt>conditional execution:</dt>
<dd>Check for certain conditions and run the appropriate code.</dd>
<dt>repetition:</dt>
<dd>Perform some action repeatedly, usually with some variation.</dd>
</dl>
<p>Believe it or not, that’s pretty much all there is to it. Every program
you’ve ever used, no matter how complicated, is made up of instructions
that look pretty much like these. So you can think of programming as the
process of breaking a large, complex task into smaller and smaller
subtasks until the subtasks are simple enough to be performed with one
of these basic instructions.</p>
</div>
<div class="section" id="running-python">
<h2>Running Python<a class="headerlink" href="#running-python" title="Permalink to this headline">¶</a></h2>
<p>One of the challenges of getting started with Python is that you might
have to install Python and related software on your computer. If you are
familiar with your operating system, and especially if you are
comfortable with the command-line interface, you will have no trouble
installing Python. But for beginners, it can be painful to learn about
system administration and programming at the same time.</p>
<p>To avoid that problem, I recommend that you start out running Python in
a browser. Later, when you are comfortable with Python, I’ll make
suggestions for installing Python on your computer.</p>
<p>There are a number of web pages you can use to run Python. If you
already have a favorite, go ahead and use it. Otherwise I recommend
PythonAnywhere. I provide detailed instructions for getting started at
<a class="reference external" href="http://tinyurl.com/thinkpython2e">http://tinyurl.com/thinkpython2e</a>.</p>
<p>There are two versions of Python, called Python 2 and Python 3. They are
very similar, so if you learn one, it is easy to switch to the other. In
fact, there are only a few differences you will encounter as a beginner.
This book is written for Python 3, but I include some notes about Python
2.</p>
<p>The Python <strong>interpreter</strong> is a program that reads and executes Python
code. Depending on your environment, you might start the interpreter by
clicking on an icon, or by typing python on a command line. When it
starts, you should see output like this:</p>
<div class="highlight-python"><div class="highlight"><pre>Python 3.4.0 (default, Jun 19 2015, 14:20:21)
[GCC 4.8.2] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>>
</pre></div>
</div>
<p>The first three lines contain information about the interpreter and the
operating system it’s running on, so it might be different for you. But
you should check that the version number, which is 3.4.0 in this
example, begins with 3, which indicates that you are running Python 3.
If it begins with 2, you are running (you guessed it) Python 2.</p>
<p>The last line is a <strong>prompt</strong> that indicates that the interpreter is
ready for you to enter code. If you type a line of code and hit Enter,
the interpreter displays the result:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="mi">1</span> <span class="o">+</span> <span class="mi">1</span>
<span class="go">2</span>
</pre></div>
</div>
<p>Now you’re ready to get started. From here on, I assume that you know
how to start the Python interpreter and run code.</p>
</div>
<div class="section" id="the-first-program">
<h2>The first program<a class="headerlink" href="#the-first-program" title="Permalink to this headline">¶</a></h2>
<p>Traditionally, the first program you write in a new language is called
“Hello, World!” because all it does is display the words “Hello,
World!”. In Python, it looks like this:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span><span class="p">(</span><span class="s">'Hello, World!'</span><span class="p">)</span>
</pre></div>
</div>
<p>This is an example of a <strong>print statement</strong>, although it doesn’t
actually print anything on paper. It displays a result on the screen. In
this case, the result is the words</p>
<div class="highlight-python"><div class="highlight"><pre>Hello, World!
</pre></div>
</div>
<p>The quotation marks in the program mark the beginning and end of the
text to be displayed; they don’t appear in the result.</p>
<p>The parentheses indicate that print is a function. We’ll get to
functions in Chapter [funcchap].</p>
<p>In Python 2, the print statement is slightly different; it is not a
function, so it doesn’t use parentheses.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">print</span> <span class="s">'Hello, World!'</span>
</pre></div>
</div>
<p>This distinction will make more sense soon, but that’s enough to get
started.</p>
</div>
<div class="section" id="arithmetic-operators">
<h2>Arithmetic operators<a class="headerlink" href="#arithmetic-operators" title="Permalink to this headline">¶</a></h2>
<p>After “Hello, World”, the next step is arithmetic. Python provides
<strong>operators</strong>, which are special symbols that represent computations
like addition and multiplication.</p>
<p>The operators +, -, and perform addition, subtraction, and
multiplication, as in the following examples:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="mi">40</span> <span class="o">+</span> <span class="mi">2</span>
<span class="go">42</span>
<span class="gp">>>> </span><span class="mi">43</span> <span class="o">-</span> <span class="mi">1</span>
<span class="go">42</span>
<span class="gp">>>> </span><span class="mi">6</span> <span class="o">*</span> <span class="mi">7</span>
<span class="go">42</span>
</pre></div>
</div>
<p>The operator / performs division:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="mi">84</span> <span class="o">/</span> <span class="mi">2</span>
<span class="go">42.0</span>
</pre></div>
</div>
<p>You might wonder why the result is 42.0 instead of 42. I’ll explain in
the next section.</p>
<p>Finally, the operator * performs exponentiation; that is, it raises a
number to a power:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="mi">6</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">6</span>
<span class="go">42</span>
</pre></div>
</div>
<p>In some other languages, <code class="docutils literal"><span class="pre">^</span></code> is used for exponentiation, but in Python
it is a bitwise operator called XOR. If you are not familiar with
bitwise operators, the result will surprise you:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="mi">6</span> <span class="o">^</span> <span class="mi">2</span>
<span class="go">4</span>
</pre></div>
</div>
<p>I won’t cover bitwise operators in this book, but you can read about
them at <a class="reference external" href="http://wiki.python.org/moin/BitwiseOperators">http://wiki.python.org/moin/BitwiseOperators</a>.</p>
</div>
<div class="section" id="values-and-types">
<h2>Values and types<a class="headerlink" href="#values-and-types" title="Permalink to this headline">¶</a></h2>
<p>A <strong>value</strong> is one of the basic things a program works with, like a
letter or a number. Some values we have seen so far are 2, 42.0, and
<code class="docutils literal"><span class="pre">'Hello,</span> <span class="pre">World!'</span></code>.</p>
<p>These values belong to different <strong>types</strong>: 2 is an <strong>integer</strong>, 42.0 is
a <strong>floating-point number</strong>, and <code class="docutils literal"><span class="pre">'Hello,</span> <span class="pre">World!'</span></code> is a <strong>string</strong>,
so-called because the letters it contains are strung together.</p>
<p>If you are not sure what type a value has, the interpreter can tell you:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="nb">type</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="go"><class 'int'></span>
<span class="gp">>>> </span><span class="nb">type</span><span class="p">(</span><span class="mf">42.0</span><span class="p">)</span>
<span class="go"><class 'float'></span>
<span class="gp">>>> </span><span class="nb">type</span><span class="p">(</span><span class="s">'Hello, World!'</span><span class="p">)</span>
<span class="go"><class 'str'></span>
</pre></div>
</div>
<p>In these results, the word “class” is used in the sense of a category; a
type is a category of values.</p>
<p>Not surprisingly, integers belong to the type int, strings belong to str
and floating-point numbers belong to float.</p>
<p>What about values like <code class="docutils literal"><span class="pre">'2'</span></code> and <code class="docutils literal"><span class="pre">'42.0'</span></code>? They look like numbers,
but they are in quotation marks like strings.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="nb">type</span><span class="p">(</span><span class="s">'2'</span><span class="p">)</span>
<span class="go"><class 'str'></span>
<span class="gp">>>> </span><span class="nb">type</span><span class="p">(</span><span class="s">'42.0'</span><span class="p">)</span>
<span class="go"><class 'str'></span>
</pre></div>
</div>
<p>They’re strings.</p>
<p>When you type a large integer, you might be tempted to use commas
between groups of digits, as in 1,000,000. This is not a legal <em>integer</em>
in Python, but it is legal:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="mi">1</span><span class="p">,</span><span class="mo">000</span><span class="p">,</span><span class="mo">000</span>
<span class="go">(1, 0, 0)</span>
</pre></div>
</div>
<p>That’s not what we expected at all! Python interprets 1,000,000 as a
comma-separated sequence of integers. We’ll learn more about this kind
of sequence later.</p>
</div>
<div class="section" id="formal-and-natural-languages">
<h2>Formal and natural languages<a class="headerlink" href="#formal-and-natural-languages" title="Permalink to this headline">¶</a></h2>
<p><strong>Natural languages</strong> are the languages people speak, such as English,
Spanish, and French. They were not designed by people (although people
try to impose some order on them); they evolved naturally.</p>
<p><strong>Formal languages</strong> are languages that are designed by people for
specific applications. For example, the notation that mathematicians use
is a formal language that is particularly good at denoting relationships
among numbers and symbols. Chemists use a formal language to represent
the chemical structure of molecules. And most importantly:</p>
<blockquote>
<div><strong>Programming languages are formal languages that have been designed
to express computations.</strong></div></blockquote>
<p>Formal languages tend to have strict <strong>syntax</strong> rules that govern the
structure of statements. For example, in mathematics the statement
<span class="math">3 + 3 = 6</span> has correct syntax, but <span class="math">3 + = 3 \$ 6</span> does not.
In chemistry <span class="math">H_2O</span> is a syntactically correct formula, but
<span class="math">_2Zz</span> is not.</p>
<p>Syntax rules come in two flavors, pertaining to <strong>tokens</strong> and
structure. Tokens are the basic elements of the language, such as words,
numbers, and chemical elements. One of the problems with
<span class="math">3 += 3 \$ 6</span> is that :math:` $ ` is not a legal token in
mathematics (at least as far as I know). Similarly, <span class="math">_2Zz</span> is not
legal because there is no element with the abbreviation <span class="math">Zz</span>.</p>
<p>The second type of syntax rule pertains to the way tokens are combined.
The equation <span class="math">3 += 3</span> is illegal because even though <span class="math">+</span> and
<span class="math">=</span> are legal tokens, you can’t have one right after the other.
Similarly, in a chemical formula the subscript comes after the element
name, not before.</p>
<p>This is @ well-structured Engli$h sentence with invalid t*kens in it.
This sentence all valid tokens has, but invalid structure with.</p>
<p>When you read a sentence in English or a statement in a formal language,
you have to figure out the structure (although in a natural language you
do this subconsciously). This process is called <strong>parsing</strong>.</p>
<p>Although formal and natural languages have many features in
common—tokens, structure, and syntax—there are some differences:</p>
<dl class="docutils">
<dt>ambiguity:</dt>
<dd>Natural languages are full of ambiguity, which people deal with by
using contextual clues and other information. Formal languages are
designed to be nearly or completely unambiguous, which means that
any statement has exactly one meaning, regardless of context.</dd>
<dt>redundancy:</dt>
<dd>In order to make up for ambiguity and reduce misunderstandings,
natural languages employ lots of redundancy. As a result, they are
often verbose. Formal languages are less redundant and more concise.</dd>
<dt>literalness:</dt>
<dd>Natural languages are full of idiom and metaphor. If I say, “The
penny dropped”, there is probably no penny and nothing dropping
(this idiom means that someone understood something after a period
of confusion). Formal languages mean exactly what they say.</dd>
</dl>
<p>Because we all grow up speaking natural languages, it is sometimes hard
to adjust to formal languages. The difference between formal and natural
language is like the difference between poetry and prose, but more so:</p>
<dl class="docutils">
<dt>Poetry:</dt>
<dd>Words are used for their sounds as well as for their meaning, and
the whole poem together creates an effect or emotional response.
Ambiguity is not only common but often deliberate.</dd>
<dt>Prose:</dt>
<dd>The literal meaning of words is more important, and the structure
contributes more meaning. Prose is more amenable to analysis than
poetry but still often ambiguous.</dd>
<dt>Programs:</dt>
<dd>The meaning of a computer program is unambiguous and literal, and
can be understood entirely by analysis of the tokens and structure.</dd>
</dl>
<p>Formal languages are more dense than natural languages, so it takes
longer to read them. Also, the structure is important, so it is not
always best to read from top to bottom, left to right. Instead, learn to
parse the program in your head, identifying the tokens and interpreting
the structure. Finally, the details matter. Small errors in spelling and
punctuation, which you can get away with in natural languages, can make
a big difference in a formal language.</p>
</div>
<div class="section" id="debugging">
<h2>Debugging<a class="headerlink" href="#debugging" title="Permalink to this headline">¶</a></h2>
<p>Programmers make mistakes. For whimsical reasons, programming errors are
called <strong>bugs</strong> and the process of tracking them down is called
<strong>debugging</strong>.</p>
<p>Programming, and especially debugging, sometimes brings out strong
emotions. If you are struggling with a difficult bug, you might feel
angry, despondent, or embarrassed.</p>
<p>There is evidence that people naturally respond to computers as if they
were people. When they work well, we think of them as teammates, and
when they are obstinate or rude, we respond to them the same way we
respond to rude, obstinate people (Reeves and Nass, <em>The Media Equation:
How People Treat Computers, Television, and New Media Like Real People
and Places</em>).</p>
<p>Preparing for these reactions might help you deal with them. One
approach is to think of the computer as an employee with certain
strengths, like speed and precision, and particular weaknesses, like
lack of empathy and inability to grasp the big picture.</p>
<p>Your job is to be a good manager: find ways to take advantage of the
strengths and mitigate the weaknesses. And find ways to use your
emotions to engage with the problem, without letting your reactions
interfere with your ability to work effectively.</p>
<p>Learning to debug can be frustrating, but it is a valuable skill that is
useful for many activities beyond programming. At the end of each
chapter there is a section, like this one, with my suggestions for
debugging. I hope they help!</p>
</div>
<div class="section" id="glossary">
<h2>Glossary<a class="headerlink" href="#glossary" title="Permalink to this headline">¶</a></h2>
<dl class="docutils">
<dt>problem solving:</dt>
<dd>The process of formulating a problem, finding a solution, and
expressing it.</dd>
<dt>high-level language:</dt>
<dd>A programming language like Python that is designed to be easy for
humans to read and write.</dd>
<dt>low-level language:</dt>
<dd>A programming language that is designed to be easy for a computer to
run; also called “machine language” or “assembly language”.</dd>
<dt>portability:</dt>
<dd>A property of a program that can run on more than one kind of
computer.</dd>
<dt>interpreter:</dt>
<dd>A program that reads another program and executes it</dd>
<dt>prompt:</dt>
<dd>Characters displayed by the interpreter to indicate that it is ready
to take input from the user.</dd>
<dt>program:</dt>
<dd>A set of instructions that specifies a computation.</dd>
<dt>print statement:</dt>
<dd>An instruction that causes the Python interpreter to display a value
on the screen.</dd>
<dt>operator:</dt>
<dd>A special symbol that represents a simple computation like addition,
multiplication, or string concatenation.</dd>
<dt>value:</dt>
<dd>One of the basic units of data, like a number or string, that a
program manipulates.</dd>
<dt>type:</dt>
<dd>A category of values. The types we have seen so far are integers
(type int), floating-point numbers (type float), and strings (type
str).</dd>
<dt>integer:</dt>
<dd>A type that represents whole numbers.</dd>
<dt>floating-point:</dt>
<dd>A type that represents numbers with fractional parts.</dd>
<dt>string:</dt>
<dd>A type that represents sequences of characters.</dd>
<dt>natural language:</dt>
<dd>Any one of the languages that people speak that evolved naturally.</dd>
<dt>formal language:</dt>
<dd>Any one of the languages that people have designed for specific
purposes, such as representing mathematical ideas or computer
programs; all programming languages are formal languages.</dd>
<dt>token:</dt>
<dd>One of the basic elements of the syntactic structure of a program,
analogous to a word in a natural language.</dd>
<dt>syntax:</dt>
<dd>The rules that govern the structure of a program.</dd>
<dt>parse:</dt>
<dd>To examine a program and analyze the syntactic structure.</dd>
<dt>bug:</dt>
<dd>An error in a program.</dd>
<dt>debugging:</dt>
<dd>The process of finding and correcting bugs.</dd>
</dl>
</div>
<div class="section" id="exercises">
<h2>Exercises<a class="headerlink" href="#exercises" title="Permalink to this headline">¶</a></h2>
<p>It is a good idea to read this book in front of a computer so you can
try out the examples as you go.</p>
<p>Whenever you are experimenting with a new feature, you should try to
make mistakes. For example, in the “Hello, world!” program, what happens
if you leave out one of the quotation marks? What if you leave out both?
What if you spell print wrong?</p>
<p>This kind of experiment helps you remember what you read; it also helps
when you are programming, because you get to know what the error
messages mean. It is better to make mistakes now and on purpose than
later and accidentally.</p>
<ol class="arabic simple">
<li>In a print statement, what happens if you leave out one of the
parentheses, or both?</li>
<li>If you are trying to print a string, what happens if you leave out
one of the quotation marks, or both?</li>
<li>You can use a minus sign to make a negative number like -2. What
happens if you put a plus sign before a number? What about 2++2?</li>
<li>In math notation, leading zeros are ok, as in 02. What happens if you
try this in Python?</li>
<li>What happens if you have two values with no operator between them?</li>
</ol>
<p>Start the Python interpreter and use it as a calculator.</p>
<ol class="arabic simple">
<li>How many seconds are there in 42 minutes 42 seconds?</li>
<li>How many miles are there in 10 kilometers? Hint: there are 1.61
kilometers in a mile.</li>
<li>If you run a 10 kilometer race in 42 minutes 42 seconds, what is your
average pace (time per mile in minutes and seconds)? What is your
average speed in miles per hour?</li>
</ol>
</div>
</div>
<div class="section" id="variables-expressions-and-statements">
<h1>Variables, expressions and statements<a class="headerlink" href="#variables-expressions-and-statements" title="Permalink to this headline">¶</a></h1>
<p>One of the most powerful features of a programming language is the
ability to manipulate <strong>variables</strong>. A variable is a name that refers to
a value.</p>
<div class="section" id="assignment-statements">
<h2>Assignment statements<a class="headerlink" href="#assignment-statements" title="Permalink to this headline">¶</a></h2>
<p>An <strong>assignment statement</strong> creates a new variable and gives it a value:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">message</span> <span class="o">=</span> <span class="s">'And now for something completely different'</span>
<span class="gp">>>> </span><span class="n">n</span> <span class="o">=</span> <span class="mi">17</span>
<span class="gp">>>> </span><span class="n">pi</span> <span class="o">=</span> <span class="mf">3.141592653589793</span>
</pre></div>
</div>
<p>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 <span class="math">\pi</span> to pi.</p>
<p>A common way to represent variables on paper is to write the name with
an arrow pointing to its value. This kind of figure is called a <strong>state
diagram</strong> because it shows what state each of the variables is in (think
of it as the variable’s state of mind). Figure [fig.state2] shows the
result of the previous example.</p>
<div class="figure" id="id66">
<img alt="State diagram." src="_images/state2.pdf" />
<p class="caption"><span class="caption-text">State diagram.</span></p>
</div>
</div>
<div class="section" id="variable-names">
<h2>Variable names<a class="headerlink" href="#variable-names" title="Permalink to this headline">¶</a></h2>
<p>Programmers generally choose names for their variables that are
meaningful—they document what the variable is used for.</p>
<p>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
variables names.</p>
<p>The underscore character, <code class="docutils literal"><span class="pre">_</span></code>, can appear in a name. It is often used
in names with multiple words, such as <code class="docutils literal"><span class="pre">your_name</span></code> or
<code class="docutils literal"><span class="pre">airspeed_of_unladen_swallow</span></code>.</p>
<p>If you give a variable an illegal name, you get a syntax error:</p>
<div class="highlight-python"><div class="highlight"><pre>>>> 76trombones = 'big parade'
SyntaxError: invalid syntax
>>> more@ = 1000000
SyntaxError: invalid syntax
>>> class = 'Advanced Theoretical Zymurgy'
SyntaxError: invalid syntax
</pre></div>
</div>
<p>76trombones is illegal because it begins with a number. more@ is illegal
because it contains an illegal character, @. But what’s wrong with
class?</p>
<p>It turns out that class is one of Python’s <strong>keywords</strong>. The interpreter
uses keywords to recognize the structure of the program, and they cannot
be used as variable names.</p>
<p>Python 3 has these keywords:</p>
<div class="highlight-python"><div class="highlight"><pre>False class finally is return
None continue for lambda try
True def from nonlocal while
and del global not with
as elif if or yield
assert else import pass
break except in raise
</pre></div>
</div>
<p>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.</p>
</div>
<div class="section" id="expressions-and-statements">
<h2>Expressions and statements<a class="headerlink" href="#expressions-and-statements" title="Permalink to this headline">¶</a></h2>
<p>An <strong>expression</strong> 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:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="mi">42</span>
<span class="go">42</span>
<span class="gp">>>> </span><span class="n">n</span>
<span class="go">17</span>
<span class="gp">>>> </span><span class="n">n</span> <span class="o">+</span> <span class="mi">25</span>
<span class="go">42</span>
</pre></div>
</div>
<p>When you type an expression at the prompt, the interpreter <strong>evaluates</strong>
it, which means that it finds the value of the expression. In this
example, n has the value 17 and n + 25 has the value 42.</p>
<p>A <strong>statement</strong> is a unit of code that has an effect, like creating a
variable or displaying a value.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">n</span> <span class="o">=</span> <span class="mi">17</span>
<span class="gp">>>> </span><span class="k">print</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
</pre></div>
</div>
<p>The first line is an assignment statement that gives a value to n. The
second line is a print statement that displays the value of n.</p>
<p>When you type a statement, the interpreter <strong>executes</strong> it, which means
that it does whatever the statement says. In general, statements don’t
have values.</p>
</div>
<div class="section" id="script-mode">
<h2>Script mode<a class="headerlink" href="#script-mode" title="Permalink to this headline">¶</a></h2>
<p>So far we have run Python in <strong>interactive mode</strong>, which means that you
interact directly with the interpreter. Interactive mode is a good way
to get started, but if you are working with more than a few lines of
code, it can be clumsy.</p>
<p>The alternative is to save code in a file called a <strong>script</strong> and then
run the interpreter in <strong>script mode</strong> to execute the script. By
convention, Python scripts have names that end with .py.</p>
<p>If you know how to create and run a script on your computer, you are
ready to go. Otherwise I recommend using PythonAnywhere again. I have
posted instructions for running in script mode at
<a class="reference external" href="http://tinyurl.com/thinkpython2e">http://tinyurl.com/thinkpython2e</a>.</p>
<p>Because Python provides both modes, you can test bits of code in
interactive mode before you put them in a script. But there are
differences between interactive mode and script mode that can be
confusing.</p>
<p>For example, if you are using Python as a calculator, you might type</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">miles</span> <span class="o">=</span> <span class="mf">26.2</span>
<span class="gp">>>> </span><span class="n">miles</span> <span class="o">*</span> <span class="mf">1.61</span>
<span class="go">42.182</span>
</pre></div>
</div>
<p>The first line assigns a value to miles, but it has no visible effect.
The second line is an expression, so the interpreter evaluates it and
displays the result. It turns out that a marathon is about 42
kilometers.</p>
<p>But if you type the same code into a script and run it, you get no
output at all. In script mode an expression, all by itself, has no
visible effect. Python actually evaluates the expression, but it doesn’t
display the value unless you tell it to:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">miles</span> <span class="o">=</span> <span class="mf">26.2</span>
<span class="k">print</span><span class="p">(</span><span class="n">miles</span> <span class="o">*</span> <span class="mf">1.61</span><span class="p">)</span>
</pre></div>
</div>
<p>This behavior can be confusing at first.</p>
<p>A script usually contains a sequence of statements. If there is more
than one statement, the results appear one at a time as the statements
execute.</p>
<p>For example, the script</p>
<div class="highlight-python"><div class="highlight"><pre><span class="k">print</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="n">x</span> <span class="o">=</span> <span class="mi">2</span>
<span class="k">print</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
</pre></div>
</div>
<p>produces the output</p>
<div class="highlight-python"><div class="highlight"><pre><span class="mi">1</span>
<span class="mi">2</span>
</pre></div>
</div>
<p>The assignment statement produces no output.</p>
<p>To check your understanding, type the following statements in the Python
interpreter and see what they do:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="mi">5</span>
<span class="n">x</span> <span class="o">=</span> <span class="mi">5</span>
<span class="n">x</span> <span class="o">+</span> <span class="mi">1</span>
</pre></div>
</div>
<p>Now put the same statements in 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.</p>
</div>
<div class="section" id="order-of-operations">
<h2>Order of operations<a class="headerlink" href="#order-of-operations" title="Permalink to this headline">¶</a></h2>
<p>When an expression contains more than one operator, the order of
evaluation depends on the <strong>order of operations</strong>. For mathematical
operators, Python follows mathematical convention. The acronym
<strong>PEMDAS</strong> is a useful way to remember the rules:</p>
<ul class="simple">
<li><strong>P</strong>arentheses 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.</li>
<li><strong>E</strong>xponentiation has the next highest precedence, so 1 + 2**3
is 9, not 27, and 2 * 3**2 is 18, not 36.</li>
<li><strong>M</strong>ultiplication and <strong>D</strong>ivision have higher precedence than
<strong>A</strong>ddition and <strong>S</strong>ubtraction. So 2*3-1 is 5, not 4, and
6+4/2 is 8, not 5.</li>
<li>Operators with the same precedence are evaluated from left to right
(except exponentiation). So in the expression degrees / 2 * pi, the
division happens first and the result is multiplied by pi. To divide
by <span class="math">2 \pi</span>, you can use parentheses or write degrees / 2 / pi.</li>
</ul>
<p>I don’t work very hard to remember the precedence of operators. If I
can’t tell by looking at the expression, I use parentheses to make it
obvious.</p>
</div>
<div class="section" id="string-operations">
<h2>String operations<a class="headerlink" href="#string-operations" title="Permalink to this headline">¶</a></h2>
<p>In general, you can’t perform mathematical operations on strings, even
if the strings look like numbers, so the following are illegal:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="s">'2'</span><span class="o">-</span><span class="s">'1'</span> <span class="s">'eggs'</span><span class="o">/</span><span class="s">'easy'</span> <span class="s">'third'</span><span class="o">*</span><span class="s">'a charm'</span>
</pre></div>
</div>
<p>But there are two exceptions, + and .</p>
<p>The + operator performs <strong>string concatenation</strong>, which means it joins
the strings by linking them end-to-end. For example:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">first</span> <span class="o">=</span> <span class="s">'throat'</span>
<span class="gp">>>> </span><span class="n">second</span> <span class="o">=</span> <span class="s">'warbler'</span>
<span class="gp">>>> </span><span class="n">first</span> <span class="o">+</span> <span class="n">second</span>
<span class="go">throatwarbler</span>
</pre></div>
</div>
<p>The operator also works on strings; it performs repetition. For example,
<code class="docutils literal"><span class="pre">'Spam'*3</span></code> is <code class="docutils literal"><span class="pre">'SpamSpamSpam'</span></code>. If one of the values is a string,
the other has to be an integer.</p>
<p>This use of + and makes sense by analogy with addition and
multiplication. Just as 4*3 is equivalent to 4+4+4, we expect
<code class="docutils literal"><span class="pre">'Spam'*3</span></code> to be the same as <code class="docutils literal"><span class="pre">'Spam'+'Spam'+'Spam'</span></code>, and it is. On