ERT: Emacs Lisp Regression Testing
Copyright © 2008, 2010–2021 Free Software Foundation, Inc.
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ERT is a tool for automated testing in Emacs Lisp. Its main features are facilities for defining tests, running them and reporting the results, and for debugging test failures interactively.
ERT is similar to tools for other environments such as JUnit, but has unique features that take advantage of the dynamic and interactive nature of Emacs. Despite its name, it works well both for test-driven development (see https://en.wikipedia.org/wiki/Test-driven_development) and for traditional software development methods.
|Introduction||A simple example of an ERT test.|
|How to Run Tests||Run tests in Emacs or from the command line.|
|How to Write Tests||How to add tests to your Emacs Lisp code.|
|How to Debug Tests||What to do if a test fails.|
|Extending ERT||ERT is extensible in several ways.|
|Other Testing Concepts||Features not in ERT.|
|Index||Concept, Function and Variable Index|
|GNU Free Documentation License||The license for this documentation.|
Detailed Node Listing
|How to Run Tests|
|Running Tests Interactively||Run tests in your current Emacs.|
|Running Tests in Batch Mode||Run tests in emacs -Q.|
|Test Selectors||Choose which tests to run.|
|How to Write Tests|
||A powerful way to express assertions.|
|Expected Failures||Tests for known bugs.|
|Tests and Their Environment||Don’t depend on customizations; no side effects.|
|Useful Techniques||Some examples.|
|How to Debug Tests|
|Understanding Explanations||How ERT gives details on why an assertion failed.|
|Interactive Debugging||Tools available in the ERT results buffer.|
|Defining Explanation Functions||Teach ERT about more predicates.|
|Low-Level Functions for Working with Tests||Use ERT’s data for your purposes.|
|Other Testing Concepts|
|Mocks and Stubs||Stubbing out code that is irrelevant to the test.|
|Fixtures and Test Suites||How ERT differs from tools for other languages.|
|Index||Concept, Function and Variable Index|
|GNU Free Documentation License||The license for this documentation.|
ERT allows you to define tests in addition to functions, macros, variables, and the other usual Lisp constructs. Tests are simply Lisp code: code that invokes other code and checks whether it behaves as expected.
ERT keeps track of the tests that are defined and provides convenient commands to run them to verify whether the definitions that are currently loaded in Emacs pass the tests.
Some Lisp files have comments like the following (adapted from the
;; (pp-to-string '(quote quote)) ; expected: "'quote" ;; (pp-to-string '((quote a) (quote b))) ; expected: "('a 'b)\n" ;; (pp-to-string '('a 'b)) ; same as above
The code contained in these comments can be evaluated from time to time to compare the output with the expected output. ERT formalizes this and introduces a common convention, which simplifies Emacs development, since programmers no longer have to manually find and evaluate such comments.
An ERT test definition equivalent to the above comments is this:
(ert-deftest pp-test-quote () "Tests the rendering of `quote' symbols in `pp-to-string'." (should (equal (pp-to-string '(quote quote)) "'quote")) (should (equal (pp-to-string '((quote a) (quote b))) "('a 'b)\n")) (should (equal (pp-to-string '('a 'b)) "('a 'b)\n")))
If you know
defun, the syntax of
ert-deftest should look
familiar: This example defines a test named
will pass if the three calls to
equal all return non-
should is a macro with the same meaning as
better error reporting. See The
Each test should have a name that describes what functionality it tests. Test names can be chosen arbitrarily—they are in a namespace separate from functions and variables—but should follow the usual Emacs Lisp convention of having a prefix that indicates which package they belong to. Test names are displayed by ERT when reporting failures and can be used when selecting which tests to run.
The empty parentheses
() in the first line don’t currently have
any meaning and are reserved for future extension. They also make
the syntax of
ert-deftest more similar to that of
The docstring describes what feature this test tests. When running tests interactively, the first line of the docstring is displayed for tests that fail, so it is good if the first line makes sense on its own.
The body of a test can be arbitrary Lisp code. It should have as few side effects as possible; each test should be written to clean up after itself, leaving Emacs in the same state as it was before the test. Tests should clean up even if they fail. See Tests and Their Environment.
2 How to Run Tests
You can run tests either in the Emacs you are working in, or on the command line in a separate Emacs process in batch mode (i.e., with no user interface). The former mode is convenient during interactive development, the latter is useful to make sure that tests pass independently of your customizations; and it allows you to invoke tests from makefiles, and to write scripts that run tests in several different Emacs versions.
|• Running Tests Interactively||Run tests in your current Emacs.|
|• Running Tests in Batch Mode||Run tests in emacs -Q.|
|• Test Selectors||Choose which tests to run.|
2.1 Running Tests Interactively
You can run the tests that are currently defined in your Emacs with
the command M-x ert RET t RET. (For an
explanation of the
t argument, see Test Selectors.) ERT will pop
up a new buffer, the ERT results buffer, showing the results of the
tests run. It looks like this:
Selector: t Passed: 31 Skipped: 0 Failed: 2 (2 unexpected) Total: 33/33 Started at: 2008-09-11 08:39:25-0700 Finished. Finished at: 2008-09-11 08:39:27-0700 FF............................... F addition-test (ert-test-failed ((should (= (+ 1 2) 4)) :form (= 3 4) :value nil)) F list-test (ert-test-failed ((should (equal (list 'a 'b 'c) '(a b d))) :form (equal (a b c) (a b d)) :value nil :explanation (list-elt 2 (different-atoms c d))))
At the top, there is a summary of the results: we ran all tests defined
in the current Emacs (
Selector: t), 31 of them passed, and 2
failed unexpectedly. See Expected Failures, for an explanation of
the term unexpected in this context.
The line of dots and
Fs is a progress bar where each character
represents one test; it fills while the tests are running. A dot
means that the test passed, an
F means that it failed. Below
the progress bar, ERT shows details about each test that had an
unexpected result. In the example above, there are two failures, both
due to failed
should forms. See Understanding Explanations,
for more details.
In the ERT results buffer, TAB and S-TAB cycle between buttons. Each name of a function or macro in this buffer is a button; moving point to it and typing RET jumps to its definition.
Pressing r re-runs the test near point on its own. Pressing d re-runs it with the debugger enabled. . jumps to the definition of the test near point (RET has the same effect if point is on the name of the test). On a failed test, b shows the backtrace of the failure. See Backtraces in GNU Emacs Lisp Reference Manual, for more information about backtraces.
l shows the list of
should forms executed in the test.
If any messages were generated (with the Lisp function
in a test or any of the code that it invoked, m will show them.
By default, long expressions in the failure details are abbreviated
print-level. Pressing L
while point is on a test failure will increase the limits to show more
of the expression.
2.2 Running Tests in Batch Mode
ERT supports automated invocations from the command line or from
scripts or makefiles. There are two functions for this purpose,
They can be used like this:
emacs -batch -l ert -l my-tests.el -f ert-run-tests-batch-and-exit
This command will start up Emacs in batch mode, load ERT, load
my-tests.el, and run all tests defined in it. It will exit
with a zero exit status if all tests passed, or nonzero if any tests
failed or if anything else went wrong. It will also print progress
messages and error diagnostics to standard output.
You can also redirect the above output to a log file, say
output.log, and use the
ert-summarize-tests-batch-and-exit function to produce a neat
summary as shown below:
emacs -batch -l ert -f ert-summarize-tests-batch-and-exit output.log
By default, ERT in batch mode is quite verbose, printing a line with
result after each test. This gives you progress information: how many
tests have been executed and how many there are. However, in some
cases this much output may be undesirable. In this case, set
ert-quiet variable to a non-nil value:
emacs -batch -l ert -l my-tests.el \ --eval "(let ((ert-quiet t)) (ert-run-tests-batch-and-exit))"
In quiet mode ERT prints only unexpected results and summary.
You can specify selectors to only run a subset of your tests (see Test Selectors). For example, the following would run all tests where the name of the test matches the regular expression “to-match”.
emacs -batch -l ert -l my-tests.el \ -eval '(ert-run-tests-batch-and-exit "to-match")'
2.3 Test Selectors
ert accept a test selector, a Lisp
expression specifying a set of tests. Test selector syntax is similar
to Common Lisp’s type specifier syntax:
nilselects no tests.
tselects all tests.
:newselects all tests that have not been run yet.
:passedselect tests according to their most recent result.
:unexpectedselect tests according to their most recent result.
- A string is a regular expression that selects all tests with matching names.
- A test (i.e., an object of
ert-testdata type) selects that test.
- A symbol selects the test that the symbol names.
(member tests...)selects the elements of tests, a list of tests or symbols naming tests.
(eql test)selects test, a test or a symbol naming a test.
(and selectors…)selects the tests that match all selectors.
(or selectors…)selects the tests that match any of the selectors.
(not selector)selects all tests that do not match selector.
(tag tag)selects all tests that have tag on their tags list. (Tags are optional labels you can apply to tests when you define them.)
(satisfies predicate)selects all tests that satisfy predicate, a function that takes a test as argument and returns non-
nilif it is selected.
Selectors that are frequently useful when selecting tests to run
t to run all tests that are currently defined in Emacs,
"^foo-" to run all tests in package
foo (this assumes
foo uses the prefix
foo- for its test names),
result-based selectors such as
(or :new :unexpected) to
run all tests that have either not run yet or that had an unexpected
result in the last run, and tag-based selectors such as
(tag :causes-redisplay)) to run all tests that are not tagged
3 How to Write Tests
ERT lets you define tests in the same way you define functions. You
ert-deftest forms in a buffer and evaluate them there
compile-defun, or you can save the
file and load it, optionally byte-compiling it first.
find-function is only able to find where a function
was defined if the function was loaded from a file, ERT is only able
to find where a test was defined if the test was loaded from a file.
|• The ||A powerful way to express assertions.|
|• Expected Failures||Tests for known bugs.|
|• Tests and Their Environment||Don’t depend on customizations; no side effects.|
|• Useful Techniques||Some examples.|
Test bodies can include arbitrary code; but to be useful, they need to
check whether the code being tested (or code under test)
does what it is supposed to do. The macro
should is similar to
cl-assert from the cl package
(see Assertions in Common Lisp Extensions),
but analyzes its argument form and records information that ERT can
display to help debugging.
This test definition
(ert-deftest addition-test () (should (= (+ 1 2) 4)))
will produce this output when run via M-x ert:
F addition-test (ert-test-failed ((should (= (+ 1 2) 4)) :form (= 3 4) :value nil))
In this example,
should recorded the fact that (= (+ 1 2) 4)
reduced to (= 3 4) before it reduced to
nil. When debugging why the
test failed, it helps to know that the function
+ returned 3
here. ERT records the return value for any predicate called directly
In addition to
should, ERT provides
checks that the predicate returns
checks that the form called within it signals an error. An example
(ert-deftest test-divide-by-zero () (should-error (/ 1 0) :type 'arith-error))
This checks that dividing one by zero signals an error of type
:type argument to
is optional; if absent, any type of error is accepted.
should-error returns an error description of the error that was
signaled, to allow additional checks to be made. The error
description has the format
(ERROR-SYMBOL . DATA).
There is no
should-not-error macro since tests that signal an
error fail anyway, so
should-not-error is effectively the
See Understanding Explanations, for more details on what
3.2 Expected Failures
Some bugs are complicated to fix, or not very important, and are left as
known bugs. If there is a test case that triggers the bug and
fails, ERT will alert you of this failure every time you run all
tests. For known bugs, this alert is a distraction. The way to
suppress it is to add
:expected-result :failed to the test
(ert-deftest future-bug () "Test `time-forward' with negative arguments. Since this functionality isn't implemented, the test is known to fail." :expected-result :failed (time-forward -1))
ERT will still display a small
f in the progress bar as a
reminder that there is a known bug, and will count the test as failed,
but it will be quiet about it otherwise.
An alternative to marking the test as a known failure this way is to delete the test. This is a good idea if there is no intent to fix it, i.e., if the behavior that was formerly considered a bug has become an accepted feature.
In general, however, it can be useful to keep tests that are known to fail. If someone wants to fix the bug, they will have a very good starting point: an automated test case that reproduces the bug. This makes it much easier to fix the bug, demonstrate that it is fixed, and prevent future regressions.
ERT displays the same kind of alerts for tests that pass unexpectedly
as it displays for unexpected failures. This way, if you make code
changes that happen to fix a bug that you weren’t aware of, you will
know to remove the
:expected-result clause of that test and
close the corresponding bug report, if any.
:expected-result evaluates its argument when the test is
loaded, tests can be marked as known failures only on certain Emacs
versions, specific architectures, etc.:
(ert-deftest foo () "A test that is expected to fail on Emacs 23 but succeed elsewhere." :expected-result (if (string-match "GNU Emacs 23[.]" (emacs-version)) :failed :passed) ...)
3.3 Tests and Their Environment
Sometimes, it doesn’t make sense to run a test due to missing
preconditions. A required Emacs feature might not be compiled in, the
function to be tested could call an external binary which might not be
available on the test machine, you name it. In this case, the macro
skip-unless could be used to skip the test:
(ert-deftest test-dbus () "A test that checks D-BUS functionality." (skip-unless (featurep 'dbusbind)) ...)
The outcome of running a test should not depend on the current state of the environment, and each test should leave its environment in the same state it found it in. In particular, a test should not depend on any Emacs customization variables or hooks, and if it has to make any changes to Emacs’s state or state external to Emacs (such as the file system), it should undo these changes before it returns, regardless of whether it passed or failed.
Tests should not depend on the environment because any such
dependencies can make the test brittle or lead to failures that occur
only under certain circumstances and are hard to reproduce. Of
course, the code under test may have settings that affect its
behavior. In that case, it is best to make the test
all such setting variables to set up a specific configuration for the
duration of the test. The test can also set up a number of different
configurations and run the code under test with each.
Tests that have side effects on their environment should restore it to
its original state because any side effects that persist after the
test can disrupt the workflow of the programmer running the tests. If
the code under test has side effects on Emacs’s current state, such as
on the current buffer or window configuration, the test should create
a temporary buffer for the code to manipulate (using
with-temp-buffer), or save and restore the window configuration
save-window-excursion), respectively. For aspects of
the state that can not be preserved with such macros, cleanup should
be performed with
unwind-protect, to ensure that the cleanup
occurs even if the test fails.
An exception to this are messages that the code under test prints with
message and similar logging; tests should not bother restoring
the *Message* buffer to its original state.
The above guidelines imply that tests should avoid calling highly
customizable commands such as
find-file, except, of course, if
such commands are what they want to test. The exact behavior of
find-file depends on many settings such as
auto-mode-alist. It is difficult to write a meaningful test if
its behavior can be affected by so many external factors. Also,
find-file has side effects that are hard to predict and thus
hard to undo: It may create a new buffer or reuse an existing
buffer if one is already visiting the requested file; and it runs
find-file-hook, which can have arbitrary side effects.
Instead, it is better to use lower-level mechanisms with simple and
predictable semantics like
insert-file-contents-literally, and to activate any desired mode
by calling the corresponding function directly, after binding the
hook variables to
nil. This avoids the above problems.
3.4 Useful Techniques when Writing Tests
Testing simple functions that have no side effects and no dependencies on their environment is easy. Such tests often look like this:
(ert-deftest ert-test-mismatch () (should (eql (cl-mismatch "" "") nil)) (should (eql (cl-mismatch "" "a") 0)) (should (eql (cl-mismatch "a" "a") nil)) (should (eql (cl-mismatch "ab" "a") 1)) (should (eql (cl-mismatch "Aa" "aA") 0)) (should (eql (cl-mismatch '(a b c) '(a b d)) 2)))
This test calls the function
cl-mismatch several times with
various combinations of arguments and compares the return value to the
expected return value. (Some programmers prefer
EXPECTED ACTUAL)) over the
(should (eql ACTUAL EXPECTED))
shown here. ERT works either way.)
Here’s a more complicated test:
(ert-deftest ert-test-record-backtrace () (let ((test (make-ert-test :body (lambda () (ert-fail "foo"))))) (let ((result (ert-run-test test))) (should (ert-test-failed-p result)) (with-temp-buffer (ert--print-backtrace (ert-test-failed-backtrace result)) (goto-char (point-min)) (end-of-line) (let ((first-line (buffer-substring-no-properties (point-min) (point)))) (should (equal first-line " signal(ert-test-failed (\"foo\"))")))))))
This test creates a test object using
make-ert-test whose body
will immediately signal failure. It then runs that test and asserts
that it fails. Then, it creates a temporary buffer and invokes
ert--print-backtrace to print the backtrace of the failed test
to the current buffer. Finally, it extracts the first line from the
buffer and asserts that it matches what we expect. It uses
equal to ignore text
properties; for a test that takes properties into account,
could be used instead.
The reason why this test only checks the first line of the backtrace
is that the remainder of the backtrace is dependent on ERT’s internals
as well as whether the code is running interpreted or compiled. By
looking only at the first line, the test checks a useful property—that
the backtrace correctly captures the call to
results from the call to
ert-fail—without being brittle.
This example also shows that writing tests is much easier if the code under test was structured with testing in mind.
For example, if
ert-run-test accepted only symbols that name
tests rather than test objects, the test would need a name for the
failing test, which would have to be a temporary symbol generated with
make-symbol, to avoid side effects on Emacs’s state. Choosing
the right interface for
ert-run-tests allows the test to be
ert--print-backtrace printed the backtrace to a
buffer with a fixed name rather than the current buffer, it would be
much harder for the test to undo the side effect. Of course, some
code somewhere needs to pick the buffer name. But that logic is
independent of the logic that prints backtraces, and keeping them in
separate functions allows us to test them independently.
A lot of code that you will encounter in Emacs was not written with testing in mind. Sometimes, the easiest way to write tests for such code is to restructure the code slightly to provide better interfaces for testing. Usually, this makes the interfaces easier to use as well.
4 How to Debug Tests
This section describes how to use ERT’s features to understand why a test failed.
|• Understanding Explanations||How ERT gives details on why an assertion failed.|
|• Interactive Debugging||Tools available in the ERT results buffer.|
4.1 Understanding Explanations
should forms are reported like this:
F addition-test (ert-test-failed ((should (= (+ 1 2) 4)) :form (= 3 4) :value nil))
ERT shows what the
should expression looked like and what
values its subexpressions had: The source code of the assertion was
(should (= (+ 1 2) 4)), which applied the function
4, resulting in the value
nil. In this case, the test is wrong; it should expect 3
rather than 4.
If a predicate like
equal is used with
provides a so-called explanation:
F list-test (ert-test-failed ((should (equal (list 'a 'b 'c) '(a b d))) :form (equal (a b c) (a b d)) :value nil :explanation (list-elt 2 (different-atoms c d))))
In this case, the function
equal was applied to the arguments
(a b c) and
(a b d). ERT’s explanation shows that
the item at index 2 differs between the two lists; in one list, it is
the atom c, in the other, it is the atom d.
In simple examples like the above, the explanation is unnecessary. But in cases where the difference is not immediately apparent, it can save time:
F test1 (ert-test-failed ((should (equal x y)) :form (equal a a) :value nil :explanation (different-symbols-with-the-same-name a a)))
ERT only provides explanations for predicates that have an explanation function registered. See Defining Explanation Functions.
4.2 Interactive Debugging
Debugging failed tests essentially works the same way as debugging any other problems with Lisp code. Here are a few tricks specific to tests:
- Re-run the failed test a few times to see if it fails in the same way each time. It’s good to find out whether the behavior is deterministic before spending any time looking for a cause. In the ERT results buffer, r re-runs the selected test.
- Use . to jump to the source code of the test to find out exactly what it does. Perhaps the test is broken rather than the code under test.
- If the test contains a series of
shouldforms and you can’t tell which one failed, use l, which shows you the list of all
shouldforms executed during the test before it failed.
- Use b to view the backtrace. You can also use d to re-run the test with debugging enabled, this will enter the debugger and show the backtrace as well; but the top few frames shown there will not be relevant to you since they are ERT’s own debugger hook. b strips them out, so it is more convenient.
- If the test or the code under testing prints messages using
message, use m to see what messages it printed before it failed. This can be useful to figure out how far it got.
You can instrument tests for debugging the same way you instrument
defuns for debugging: go to the source code of the test and type C-u C-M-x. Then, go back to the ERT buffer and re-run the test with r or d.
- If you have been editing and rearranging tests, it is possible that ERT remembers an old test that you have since renamed or removed: renamings or removals of definitions in the source code leave around a stray definition under the old name in the running process (this is a common problem in Lisp). In such a situation, hit D to let ERT forget about the obsolete test.
5 Extending ERT
There are several ways to add functionality to ERT.
|• Defining Explanation Functions||Teach ERT about more predicates.|
|• Low-Level Functions for Working with Tests||Use ERT’s data for your purposes.|
5.1 Defining Explanation Functions
The explanation function for a predicate is a function that takes the
same arguments as the predicate and returns an explanation.
The explanation should explain why the predicate, when invoked with
the arguments given to the explanation function, returns the value
that it returns. The explanation can be any object but should have a
comprehensible printed representation. If the return value of the
predicate needs no explanation for a given list of arguments, the
explanation function should return
To associate an explanation function with a predicate, add the
ert-explainer to the symbol that names the predicate.
The value of the property should be the symbol that names the
5.2 Low-Level Functions for Working with Tests
are implemented on top of the lower-level test handling code in the
sections of ert.el labeled “Facilities for running a single test”,
“Test selectors”, and “Facilities for running a whole set of tests”.
If you want to write code that works with ERT tests, you should take a
look at this lower-level code. Symbols that start with
are internal to ERT, whereas those that start with
meant to be usable by other code. But there is no mature API yet.
Contributions to ERT are welcome.
6 Other Testing Concepts
For information on mocks, stubs, fixtures, or test suites, see below.
|• Mocks and Stubs||Stubbing out code that is irrelevant to the test.|
|• Fixtures and Test Suites||How ERT differs from tools for other languages.|
6.1 Other Tools for Emacs Lisp
Stubbing out functions or using so-called mocks can make it easier to write tests. See https://en.wikipedia.org/wiki/Mock_object for an explanation of the corresponding concepts in object-oriented languages.
ERT does not have built-in support for mocks or stubs. The package
el-mock (see https://www.emacswiki.org/emacs/el-mock.el)
offers mocks for Emacs Lisp and can be used in conjunction with ERT.
6.2 Fixtures and Test Suites
In many ways, ERT is similar to frameworks for other languages like SUnit or JUnit. However, two features commonly found in such frameworks are notably absent from ERT: fixtures and test suites.
Fixtures are mainly used (e.g., in SUnit or JUnit) to provide an environment for a set of tests, and consist of set-up and tear-down functions.
While fixtures are a useful syntactic simplification in other
languages, this does not apply to Lisp, where higher-order functions
unwind-protect are available. One way to implement and use a
fixture in ERT is
(defun my-fixture (body) (unwind-protect (progn [set up] (funcall body)) [tear down])) (ert-deftest my-test () (my-fixture (lambda () [test code])))
(Another way would be a
with-my-fixture macro.) This solves
the set-up and tear-down part, and additionally allows any test
to use any combination of fixtures, so it is more flexible than what
other tools typically allow.
If the test needs access to the environment the fixture sets up, the fixture can be modified to pass arguments to the body.
These are well-known Lisp techniques. Special syntax for them could be added but would provide only a minor simplification.
(If you are interested in such syntax, note that splitting set-up and
tear-down into separate functions, like *Unit tools usually do, makes
it impossible to establish dynamic
let bindings as part of the
fixture. So, blindly imitating the way fixtures are implemented in
other languages would be counter-productive in Lisp.)
The purpose of test suites is to group related tests together.
The most common use of this is to run just the tests for one
particular module. Since symbol prefixes are the usual way of
separating module namespaces in Emacs Lisp, test selectors already
solve this by allowing regexp matching on test names; e.g., the
"^ert-" selects ERT’s self-tests.
Other uses include grouping tests by their expected execution time,
e.g., to run quick tests during interactive development and slow tests less
often. This can be achieved with the
:tag argument to
tag test selectors.
B D E F H I J K L M P R S T U
B D E F H I J K L M P R S T U
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- APPLICABILITY AND DEFINITIONS
This License applies to any manual or other work, in any medium, that contains a notice placed by the copyright holder saying it can be distributed under the terms of this License. Such a notice grants a world-wide, royalty-free license, unlimited in duration, to use that work under the conditions stated herein. The “Document”, below, refers to any such manual or work. Any member of the public is a licensee, and is addressed as “you”. You accept the license if you copy, modify or distribute the work in a way requiring permission under copyright law.
A “Modified Version” of the Document means any work containing the Document or a portion of it, either copied verbatim, or with modifications and/or translated into another language.
A “Secondary Section” is a named appendix or a front-matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Document’s overall subject (or to related matters) and contains nothing that could fall directly within that overall subject. (Thus, if the Document is in part a textbook of mathematics, a Secondary Section may not explain any mathematics.) The relationship could be a matter of historical connection with the subject or with related matters, or of legal, commercial, philosophical, ethical or political position regarding them.
The “Invariant Sections” are certain Secondary Sections whose titles are designated, as being those of Invariant Sections, in the notice that says that the Document is released under this License. If a section does not fit the above definition of Secondary then it is not allowed to be designated as Invariant. The Document may contain zero Invariant Sections. If the Document does not identify any Invariant Sections then there are none.
The “Cover Texts” are certain short passages of text that are listed, as Front-Cover Texts or Back-Cover Texts, in the notice that says that the Document is released under this License. A Front-Cover Text may be at most 5 words, and a Back-Cover Text may be at most 25 words.
A “Transparent” copy of the Document means a machine-readable copy, represented in a format whose specification is available to the general public, that is suitable for revising the document straightforwardly with generic text editors or (for images composed of pixels) generic paint programs or (for drawings) some widely available drawing editor, and that is suitable for input to text formatters or for automatic translation to a variety of formats suitable for input to text formatters. A copy made in an otherwise Transparent file format whose markup, or absence of markup, has been arranged to thwart or discourage subsequent modification by readers is not Transparent. An image format is not Transparent if used for any substantial amount of text. A copy that is not “Transparent” is called “Opaque”.
Examples of suitable formats for Transparent copies include plain ASCII without markup, Texinfo input format, LaTeX input format, SGML or XML using a publicly available DTD, and standard-conforming simple HTML, PostScript or PDF designed for human modification. Examples of transparent image formats include PNG, XCF and JPG. Opaque formats include proprietary formats that can be read and edited only by proprietary word processors, SGML or XML for which the DTD and/or processing tools are not generally available, and the machine-generated HTML, PostScript or PDF produced by some word processors for output purposes only.
The “Title Page” means, for a printed book, the title page itself, plus such following pages as are needed to hold, legibly, the material this License requires to appear in the title page. For works in formats which do not have any title page as such, “Title Page” means the text near the most prominent appearance of the work’s title, preceding the beginning of the body of the text.
The “publisher” means any person or entity that distributes copies of the Document to the public.
A section “Entitled XYZ” means a named subunit of the Document whose title either is precisely XYZ or contains XYZ in parentheses following text that translates XYZ in another language. (Here XYZ stands for a specific section name mentioned below, such as “Acknowledgements”, “Dedications”, “Endorsements”, or “History”.) To “Preserve the Title” of such a section when you modify the Document means that it remains a section “Entitled XYZ” according to this definition.
The Document may include Warranty Disclaimers next to the notice which states that this License applies to the Document. These Warranty Disclaimers are considered to be included by reference in this License, but only as regards disclaiming warranties: any other implication that these Warranty Disclaimers may have is void and has no effect on the meaning of this License.
- VERBATIM COPYING
You may copy and distribute the Document in any medium, either commercially or noncommercially, provided that this License, the copyright notices, and the license notice saying this License applies to the Document are reproduced in all copies, and that you add no other conditions whatsoever to those of this License. You may not use technical measures to obstruct or control the reading or further copying of the copies you make or distribute. However, you may accept compensation in exchange for copies. If you distribute a large enough number of copies you must also follow the conditions in section 3.
You may also lend copies, under the same conditions stated above, and you may publicly display copies.
- COPYING IN QUANTITY
If you publish printed copies (or copies in media that commonly have printed covers) of the Document, numbering more than 100, and the Document’s license notice requires Cover Texts, you must enclose the copies in covers that carry, clearly and legibly, all these Cover Texts: Front-Cover Texts on the front cover, and Back-Cover Texts on the back cover. Both covers must also clearly and legibly identify you as the publisher of these copies. The front cover must present the full title with all words of the title equally prominent and visible. You may add other material on the covers in addition. Copying with changes limited to the covers, as long as they preserve the title of the Document and satisfy these conditions, can be treated as verbatim copying in other respects.
If the required texts for either cover are too voluminous to fit legibly, you should put the first ones listed (as many as fit reasonably) on the actual cover, and continue the rest onto adjacent pages.
If you publish or distribute Opaque copies of the Document numbering more than 100, you must either include a machine-readable Transparent copy along with each Opaque copy, or state in or with each Opaque copy a computer-network location from which the general network-using public has access to download using public-standard network protocols a complete Transparent copy of the Document, free of added material. If you use the latter option, you must take reasonably prudent steps, when you begin distribution of Opaque copies in quantity, to ensure that this Transparent copy will remain thus accessible at the stated location until at least one year after the last time you distribute an Opaque copy (directly or through your agents or retailers) of that edition to the public.
It is requested, but not required, that you contact the authors of the Document well before redistributing any large number of copies, to give them a chance to provide you with an updated version of the Document.
You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above, provided that you release the Modified Version under precisely this License, with the Modified Version filling the role of the Document, thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it. In addition, you must do these things in the Modified Version:
- Use in the Title Page (and on the covers, if any) a title distinct from that of the Document, and from those of previous versions (which should, if there were any, be listed in the History section of the Document). You may use the same title as a previous version if the original publisher of that version gives permission.
- List on the Title Page, as authors, one or more persons or entities responsible for authorship of the modifications in the Modified Version, together with at least five of the principal authors of the Document (all of its principal authors, if it has fewer than five), unless they release you from this requirement.
- State on the Title page the name of the publisher of the Modified Version, as the publisher.
- Preserve all the copyright notices of the Document.
- Add an appropriate copyright notice for your modifications adjacent to the other copyright notices.
- Include, immediately after the copyright notices, a license notice giving the public permission to use the Modified Version under the terms of this License, in the form shown in the Addendum below.
- Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document’s license notice.
- Include an unaltered copy of this License.
- Preserve the section Entitled “History”, Preserve its Title, and add to it an item stating at least the title, year, new authors, and publisher of the Modified Version as given on the Title Page. If there is no section Entitled “History” in the Document, create one stating the title, year, authors, and publisher of the Document as given on its Title Page, then add an item describing the Modified Version as stated in the previous sentence.
- Preserve the network location, if any, given in the Document for public access to a Transparent copy of the Document, and likewise the network locations given in the Document for previous versions it was based on. These may be placed in the “History” section. You may omit a network location for a work that was published at least four years before the Document itself, or if the original publisher of the version it refers to gives permission.
- For any section Entitled “Acknowledgements” or “Dedications”, Preserve the Title of the section, and preserve in the section all the substance and tone of each of the contributor acknowledgements and/or dedications given therein.
- Preserve all the Invariant Sections of the Document, unaltered in their text and in their titles. Section numbers or the equivalent are not considered part of the section titles.
- Delete any section Entitled “Endorsements”. Such a section may not be included in the Modified Version.
- Do not retitle any existing section to be Entitled “Endorsements” or to conflict in title with any Invariant Section.
- Preserve any Warranty Disclaimers.
If the Modified Version includes new front-matter sections or appendices that qualify as Secondary Sections and contain no material copied from the Document, you may at your option designate some or all of these sections as invariant. To do this, add their titles to the list of Invariant Sections in the Modified Version’s license notice. These titles must be distinct from any other section titles.
You may add a section Entitled “Endorsements”, provided it contains nothing but endorsements of your Modified Version by various parties—for example, statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard.
You may add a passage of up to five words as a Front-Cover Text, and a passage of up to 25 words as a Back-Cover Text, to the end of the list of Cover Texts in the Modified Version. Only one passage of Front-Cover Text and one of Back-Cover Text may be added by (or through arrangements made by) any one entity. If the Document already includes a cover text for the same cover, previously added by you or by arrangement made by the same entity you are acting on behalf of, you may not add another; but you may replace the old one, on explicit permission from the previous publisher that added the old one.
The author(s) and publisher(s) of the Document do not by this License give permission to use their names for publicity for or to assert or imply endorsement of any Modified Version.
- COMBINING DOCUMENTS
You may combine the Document with other documents released under this License, under the terms defined in section 4 above for modified versions, provided that you include in the combination all of the Invariant Sections of all of the original documents, unmodified, and list them all as Invariant Sections of your combined work in its license notice, and that you preserve all their Warranty Disclaimers.
The combined work need only contain one copy of this License, and multiple identical Invariant Sections may be replaced with a single copy. If there are multiple Invariant Sections with the same name but different contents, make the title of each such section unique by adding at the end of it, in parentheses, the name of the original author or publisher of that section if known, or else a unique number. Make the same adjustment to the section titles in the list of Invariant Sections in the license notice of the combined work.
In the combination, you must combine any sections Entitled “History” in the various original documents, forming one section Entitled “History”; likewise combine any sections Entitled “Acknowledgements”, and any sections Entitled “Dedications”. You must delete all sections Entitled “Endorsements.”
- COLLECTIONS OF DOCUMENTS
You may make a collection consisting of the Document and other documents released under this License, and replace the individual copies of this License in the various documents with a single copy that is included in the collection, provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects.
You may extract a single document from such a collection, and distribute it individually under this License, provided you insert a copy of this License into the extracted document, and follow this License in all other respects regarding verbatim copying of that document.
- AGGREGATION WITH INDEPENDENT WORKS
A compilation of the Document or its derivatives with other separate and independent documents or works, in or on a volume of a storage or distribution medium, is called an “aggregate” if the copyright resulting from the compilation is not used to limit the legal rights of the compilation’s users beyond what the individual works permit. When the Document is included in an aggregate, this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document.
If the Cover Text requirement of section 3 is applicable to these copies of the Document, then if the Document is less than one half of the entire aggregate, the Document’s Cover Texts may be placed on covers that bracket the Document within the aggregate, or the electronic equivalent of covers if the Document is in electronic form. Otherwise they must appear on printed covers that bracket the whole aggregate.
Translation is considered a kind of modification, so you may distribute translations of the Document under the terms of section 4. Replacing Invariant Sections with translations requires special permission from their copyright holders, but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections. You may include a translation of this License, and all the license notices in the Document, and any Warranty Disclaimers, provided that you also include the original English version of this License and the original versions of those notices and disclaimers. In case of a disagreement between the translation and the original version of this License or a notice or disclaimer, the original version will prevail.
If a section in the Document is Entitled “Acknowledgements”, “Dedications”, or “History”, the requirement (section 4) to Preserve its Title (section 1) will typically require changing the actual title.
You may not copy, modify, sublicense, or distribute the Document except as expressly provided under this License. Any attempt otherwise to copy, modify, sublicense, or distribute it is void, and will automatically terminate your rights under this License.
However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation.
Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice.
Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License. If your rights have been terminated and not permanently reinstated, receipt of a copy of some or all of the same material does not give you any rights to use it.
- FUTURE REVISIONS OF THIS LICENSE
The Free Software Foundation may publish new, revised versions of the GNU Free Documentation License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. See https://www.gnu.org/licenses/.
Each version of the License is given a distinguishing version number. If the Document specifies that a particular numbered version of this License “or any later version” applies to it, you have the option of following the terms and conditions either of that specified version or of any later version that has been published (not as a draft) by the Free Software Foundation. If the Document does not specify a version number of this License, you may choose any version ever published (not as a draft) by the Free Software Foundation. If the Document specifies that a proxy can decide which future versions of this License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Document.
“Massive Multiauthor Collaboration Site” (or “MMC Site”) means any World Wide Web server that publishes copyrightable works and also provides prominent facilities for anybody to edit those works. A public wiki that anybody can edit is an example of such a server. A “Massive Multiauthor Collaboration” (or “MMC”) contained in the site means any set of copyrightable works thus published on the MMC site.
“CC-BY-SA” means the Creative Commons Attribution-Share Alike 3.0 license published by Creative Commons Corporation, a not-for-profit corporation with a principal place of business in San Francisco, California, as well as future copyleft versions of that license published by that same organization.
“Incorporate” means to publish or republish a Document, in whole or in part, as part of another Document.
An MMC is “eligible for relicensing” if it is licensed under this License, and if all works that were first published under this License somewhere other than this MMC, and subsequently incorporated in whole or in part into the MMC, (1) had no cover texts or invariant sections, and (2) were thus incorporated prior to November 1, 2008.
The operator of an MMC Site may republish an MMC contained in the site under CC-BY-SA on the same site at any time before August 1, 2009, provided the MMC is eligible for relicensing.
ADDENDUM: How to use this License for your documents
To use this License in a document you have written, include a copy of the License in the document and put the following copyright and license notices just after the title page:
Copyright (C) year your name. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled ``GNU Free Documentation License''.
If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the “with…Texts.” line with this:
with the Invariant Sections being list their titles, with the Front-Cover Texts being list, and with the Back-Cover Texts being list.
If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation.
If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software.