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reSTify PEP 285 (#366)

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Huang Huang 2017-09-13 07:27:12 +08:00 committed by Guido van Rossum
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@ -5,437 +5,453 @@ Last-Modified: $Date$
Author: guido@python.org (Guido van Rossum)
Status: Final
Type: Standards Track
Content-Type: text/x-rst
Created: 8-Mar-2002
Python-Version: 2.3
Post-History: 8-Mar-2002, 30-Mar-2002, 3-Apr-2002
Abstract
========
This PEP proposes the introduction of a new built-in type, bool,
with two constants, False and True. The bool type would be a
straightforward subtype (in C) of the int type, and the values
False and True would behave like 0 and 1 in most respects (for
example, False==0 and True==1 would be true) except repr() and
str(). All built-in operations that conceptually return a Boolean
result will be changed to return False or True instead of 0 or 1;
for example, comparisons, the "not" operator, and predicates like
isinstance().
This PEP proposes the introduction of a new built-in type, bool,
with two constants, ``False`` and ``True``. The bool type would be a
straightforward subtype (in C) of the int type, and the values
``False`` and ``True`` would behave like 0 and 1 in most respects (for
example, ``False==0`` and ``True==1`` would be true) except ``repr()`` and
``str()``. All built-in operations that conceptually return a Boolean
result will be changed to return ``False`` or ``True`` instead of 0 or 1;
for example, comparisons, the "not" operator, and predicates like
``isinstance()``.
Review
======
I've collected enough feedback to last me a lifetime, so I declare
the review period officially OVER. I had Chinese food today; my
fortune cookie said "Strong and bitter words indicate a weak
cause." It reminded me of some of the posts against this
PEP... :-)
I've collected enough feedback to last me a lifetime, so I declare
the review period officially OVER. I had Chinese food today; my
fortune cookie said "Strong and bitter words indicate a weak
cause." It reminded me of some of the posts against this
PEP... :-)
Anyway, here are my BDFL pronouncements. (Executive summary: I'm
not changing a thing; all variants are rejected.)
Anyway, here are my BDFL pronouncements. (Executive summary: I'm
not changing a thing; all variants are rejected.)
1) Should this PEP be accepted?
1) Should this PEP be accepted?
=> Yes.
=> Yes.
There have been many arguments against the PEP. Many of them
were based on misunderstandings. I've tried to clarify some of
the most common misunderstandings below in the main text of the
PEP. The only issue that weighs at all for me is the tendency
of newbies to write "if x == True" where "if x" would suffice.
More about that below too. I think this is not a sufficient
reason to reject the PEP.
There have been many arguments against the PEP. Many of them
were based on misunderstandings. I've tried to clarify some of
the most common misunderstandings below in the main text of the
PEP. The only issue that weighs at all for me is the tendency
of newbies to write "if x == True" where "if x" would suffice.
More about that below too. I think this is not a sufficient
reason to reject the PEP.
2) Should str(True) return "True" or "1"? "1" might reduce
backwards compatibility problems, but looks strange.
(repr(True) would always return "True".)
2) Should ``str(True)`` return "True" or "1"? "1" might reduce
backwards compatibility problems, but looks strange.
(``repr(True)`` would always return "True".)
=> "True".
=> "True".
Almost all reviewers agree with this.
Almost all reviewers agree with this.
3) Should the constants be called 'True' and 'False' (similar to
None) or 'true' and 'false' (as in C++, Java and C99)?
3) Should the constants be called 'True' and 'False' (similar to
None) or 'true' and 'false' (as in C++, Java and C99)?
=> True and False.
=> True and False.
Most reviewers agree that consistency within Python is more
important than consistency with other languages.
Most reviewers agree that consistency within Python is more
important than consistency with other languages.
4) Should we strive to eliminate non-Boolean operations on bools
in the future, through suitable warnings, so that for example
True+1 would eventually (in Python 3000) be illegal?
4) Should we strive to eliminate non-Boolean operations on bools
in the future, through suitable warnings, so that for example
True+1 would eventually (in Python 3000) be illegal?
=> No.
=> No.
There's a small but vocal minority that would prefer to see
"textbook" bools that don't support arithmetic operations at
all, but most reviewers agree with me that bools should always
allow arithmetic operations.
There's a small but vocal minority that would prefer to see
"textbook" bools that don't support arithmetic operations at
all, but most reviewers agree with me that bools should always
allow arithmetic operations.
5) Should operator.truth(x) return an int or a bool?
5) Should ``operator.truth(x)`` return an int or a bool?
=> bool.
=> bool.
Tim Peters believes it should return an int, but almost all
other reviewers agree that it should return a bool. My
rationale: operator.truth() exists to force a Boolean context
on its argument (it calls the C API PyObject_IsTrue()).
Whether the outcome is reported as int or bool is secondary; if
bool exists there's no reason not to use it. (Under the PEP,
operator.truth() now becomes an alias for bool(); that's fine.)
Tim Peters believes it should return an int, but almost all
other reviewers agree that it should return a bool. My
rationale: ``operator.truth()`` exists to force a Boolean context
on its argument (it calls the C API ``PyObject_IsTrue())``.
Whether the outcome is reported as int or bool is secondary; if
bool exists there's no reason not to use it. (Under the PEP,
``operator.truth()`` now becomes an alias for ``bool()``; that's fine.)
6) Should bool inherit from int?
6) Should bool inherit from int?
=> Yes.
=> Yes.
In an ideal world, bool might be better implemented as a
separate integer type that knows how to perform mixed-mode
arithmetic. However, inheriting bool from int eases the
implementation enormously (in part since all C code that calls
PyInt_Check() will continue to work -- this returns true for
subclasses of int). Also, I believe this is right in terms of
substitutability: code that requires an int can be fed a bool
and it will behave the same as 0 or 1. Code that requires a
bool may not work when it is given an int; for example, 3 & 4
is 0, but both 3 and 4 are true when considered as truth
values.
In an ideal world, bool might be better implemented as a
separate integer type that knows how to perform mixed-mode
arithmetic. However, inheriting bool from int eases the
implementation enormously (in part since all C code that calls
``PyInt_Check()`` will continue to work -- this returns true for
subclasses of int). Also, I believe this is right in terms of
substitutability: code that requires an int can be fed a bool
and it will behave the same as 0 or 1. Code that requires a
bool may not work when it is given an int; for example, 3 & 4
is 0, but both 3 and 4 are true when considered as truth
values.
7) Should the name 'bool' be changed?
7) Should the name 'bool' be changed?
=> No.
=> No.
Some reviewers have argued for boolean instead of bool, because
this would be easier to understand (novices may have heard of
Boolean algebra but may not make the connection with bool) or
because they hate abbreviations. My take: Python uses
abbreviations judiciously (like 'def', 'int', 'dict') and I
don't think these are a burden to understanding. To a newbie,
it doesn't matter whether it's called a waffle or a bool; it's
a new word, and they learn quickly what it means.
Some reviewers have argued for boolean instead of bool, because
this would be easier to understand (novices may have heard of
Boolean algebra but may not make the connection with bool) or
because they hate abbreviations. My take: Python uses
abbreviations judiciously (like 'def', 'int', 'dict') and I
don't think these are a burden to understanding. To a newbie,
it doesn't matter whether it's called a waffle or a bool; it's
a new word, and they learn quickly what it means.
One reviewer has argued to make the name 'truth'. I find this
an unattractive name, and would actually prefer to reserve this
term (in documentation) for the more abstract concept of truth
values that already exists in Python. For example: "when a
container is interpreted as a truth value, an empty container
is considered false and a non-empty one is considered true."
One reviewer has argued to make the name 'truth'. I find this
an unattractive name, and would actually prefer to reserve this
term (in documentation) for the more abstract concept of truth
values that already exists in Python. For example: "when a
container is interpreted as a truth value, an empty container
is considered false and a non-empty one is considered true."
8) Should we strive to require that Boolean operations (like "if",
"and", "not") have a bool as an argument in the future, so that
for example "if []:" would become illegal and would have to be
written as "if bool([]):" ???
8) Should we strive to require that Boolean operations (like "if",
"and", "not") have a bool as an argument in the future, so that
for example "if []:" would become illegal and would have to be
written as "if bool([]):" ???
=> No!!!
=> No!!!
Some people believe that this is how a language with a textbook
Boolean type should behave. Because it was brought up, others
have worried that I might agree with this position. Let me
make my position on this quite clear. This is not part of the
PEP's motivation and I don't intend to make this change. (See
also the section "Clarification" below.)
Some people believe that this is how a language with a textbook
Boolean type should behave. Because it was brought up, others
have worried that I might agree with this position. Let me
make my position on this quite clear. This is not part of the
PEP's motivation and I don't intend to make this change. (See
also the section "Clarification" below.)
Rationale
=========
Most languages eventually grow a Boolean type; even C99 (the new
and improved C standard, not yet widely adopted) has one.
Most languages eventually grow a Boolean type; even C99 (the new
and improved C standard, not yet widely adopted) has one.
Many programmers apparently feel the need for a Boolean type; most
Python documentation contains a bit of an apology for the absence
of a Boolean type. I've seen lots of modules that defined
constants "False=0" and "True=1" (or similar) at the top and used
those. The problem with this is that everybody does it
differently. For example, should you use "FALSE", "false",
"False", "F" or even "f"? And should false be the value zero or
None, or perhaps a truth value of a different type that will print
as "true" or "false"? Adding a standard bool type to the language
resolves those issues.
Many programmers apparently feel the need for a Boolean type; most
Python documentation contains a bit of an apology for the absence
of a Boolean type. I've seen lots of modules that defined
constants "False=0" and "True=1" (or similar) at the top and used
those. The problem with this is that everybody does it
differently. For example, should you use "FALSE", "false",
"False", "F" or even "f"? And should false be the value zero or
None, or perhaps a truth value of a different type that will print
as "true" or "false"? Adding a standard bool type to the language
resolves those issues.
Some external libraries (like databases and RPC packages) need to
be able to distinguish between Boolean and integral values, and
while it's usually possible to craft a solution, it would be
easier if the language offered a standard Boolean type. This also
applies to Jython: some Java classes have separately overloaded
methods or constructors for int and boolean arguments. The bool
type can be used to select the boolean variant. (The same is
apparently the case for some COM interfaces.)
Some external libraries (like databases and RPC packages) need to
be able to distinguish between Boolean and integral values, and
while it's usually possible to craft a solution, it would be
easier if the language offered a standard Boolean type. This also
applies to Jython: some Java classes have separately overloaded
methods or constructors for int and boolean arguments. The bool
type can be used to select the boolean variant. (The same is
apparently the case for some COM interfaces.)
The standard bool type can also serve as a way to force a value to
be interpreted as a Boolean, which can be used to normalize
Boolean values. When a Boolean value needs to be normalized to
one of two values, bool(x) is much clearer than "not not x" and
much more concise than
The standard bool type can also serve as a way to force a value to
be interpreted as a Boolean, which can be used to normalize
Boolean values. When a Boolean value needs to be normalized to
one of two values, ``bool(x)`` is much clearer than "not not x" and
much more concise than
if x:
return 1
else:
return 0
::
Here are some arguments derived from teaching Python. When
showing people comparison operators etc. in the interactive shell,
I think this is a bit ugly:
if x:
return 1
else:
return 0
>>> a = 13
>>> b = 12
>>> a > b
1
>>>
Here are some arguments derived from teaching Python. When
showing people comparison operators etc. in the interactive shell,
I think this is a bit ugly::
If this was:
>>> a = 13
>>> b = 12
>>> a > b
1
>>>
>>> a > b
True
>>>
If this was::
it would require a millisecond less thinking each time a 0 or 1
was printed.
>>> a > b
True
>>>
There's also the issue (which I've seen baffling even experienced
Pythonistas who had been away from the language for a while) that
if you see:
it would require a millisecond less thinking each time a 0 or 1
was printed.
>>> cmp(a, b)
1
>>> cmp(a, a)
0
>>>
There's also the issue (which I've seen baffling even experienced
Pythonistas who had been away from the language for a while) that
if you see::
you might be tempted to believe that cmp() also returned a truth
value, whereas in reality it can return three different values
(-1, 0, 1). If ints were not (normally) used to represent
Booleans results, this would stand out much more clearly as
something completely different.
>>> cmp(a, b)
1
>>> cmp(a, a)
0
>>>
you might be tempted to believe that ``cmp()`` also returned a truth
value, whereas in reality it can return three different values
``(-1, 0, 1)``. If ints were not (normally) used to represent
Booleans results, this would stand out much more clearly as
something completely different.
Specification
=============
The following Python code specifies most of the properties of the
new type:
The following Python code specifies most of the properties of the
new type::
class bool(int):
class bool(int):
def __new__(cls, val=0):
# This constructor always returns an existing instance
if val:
return True
else:
return False
def __new__(cls, val=0):
# This constructor always returns an existing instance
if val:
return True
else:
return False
def __repr__(self):
if self:
return "True"
else:
return "False"
def __repr__(self):
if self:
return "True"
else:
return "False"
__str__ = __repr__
__str__ = __repr__
def __and__(self, other):
if isinstance(other, bool):
return bool(int(self) & int(other))
else:
return int.__and__(self, other)
def __and__(self, other):
if isinstance(other, bool):
return bool(int(self) & int(other))
else:
return int.__and__(self, other)
__rand__ = __and__
__rand__ = __and__
def __or__(self, other):
if isinstance(other, bool):
return bool(int(self) | int(other))
else:
return int.__or__(self, other)
def __or__(self, other):
if isinstance(other, bool):
return bool(int(self) | int(other))
else:
return int.__or__(self, other)
__ror__ = __or__
__ror__ = __or__
def __xor__(self, other):
if isinstance(other, bool):
return bool(int(self) ^ int(other))
else:
return int.__xor__(self, other)
def __xor__(self, other):
if isinstance(other, bool):
return bool(int(self) ^ int(other))
else:
return int.__xor__(self, other)
__rxor__ = __xor__
__rxor__ = __xor__
# Bootstrap truth values through sheer willpower
False = int.__new__(bool, 0)
True = int.__new__(bool, 1)
# Bootstrap truth values through sheer willpower
False = int.__new__(bool, 0)
True = int.__new__(bool, 1)
The values False and True will be singletons, like None. Because
the type has two values, perhaps these should be called
"doubletons"? The real implementation will not allow other
instances of bool to be created.
The values ``False`` and ``True`` will be singletons, like None. Because
the type has two values, perhaps these should be called
"doubletons"? The real implementation will not allow other
instances of bool to be created.
True and False will properly round-trip through pickling and
marshalling; for example pickle.loads(pickle.dumps(True)) will
return True, and so will marshal.loads(marshal.dumps(True)).
``True`` and ``False`` will properly round-trip through pickling and
marshalling; for example ``pickle.loads(pickle.dumps(True))`` will
return ``True``, and so will ``marshal.loads(marshal.dumps(True))``.
All built-in operations that are defined to return a Boolean
result will be changed to return False or True instead of 0 or 1.
In particular, this affects comparisons (<, <=, ==, !=, >, >=, is,
is not, in, not in), the unary operator 'not', the built-in
functions callable(), hasattr(), isinstance() and issubclass(),
the dict method has_key(), the string and unicode methods
endswith(), isalnum(), isalpha(), isdigit(), islower(), isspace(),
istitle(), isupper(), and startswith(), the unicode methods
isdecimal() and isnumeric(), and the 'closed' attribute of file
objects. The predicates in the operator module are also changed
to return a bool, including operator.truth().
All built-in operations that are defined to return a Boolean
result will be changed to return ``False`` or ``True`` instead of 0 or 1.
In particular, this affects comparisons (``<``, ``<=``, ``==``, ``!=``,
``>``, ``>=``, is, is not, in, not in), the unary operator 'not', the built-in
functions ``callable()``, ``hasattr()``, ``isinstance()`` and ``issubclass()``,
the dict method ``has_key()``, the string and unicode methods
``endswith()``, ``isalnum()``, ``isalpha()``, ``isdigit()``, ``islower()``, ``isspace()``,
``istitle()``, ``isupper()``, and ``startswith()``, the unicode methods
``isdecimal()`` and ``isnumeric()``, and the 'closed' attribute of file
objects. The predicates in the operator module are also changed
to return a bool, including ``operator.truth()``.
Because bool inherits from int, True+1 is valid and equals 2, and
so on. This is important for backwards compatibility: because
comparisons and so on currently return integer values, there's no
way of telling what uses existing applications make of these
values.
Because bool inherits from int, True+1 is valid and equals 2, and
so on. This is important for backwards compatibility: because
comparisons and so on currently return integer values, there's no
way of telling what uses existing applications make of these
values.
It is expected that over time, the standard library will be
updated to use False and True when appropriate (but not to require
a bool argument type where previous an int was allowed). This
change should not pose additional problems and is not specified in
detail by this PEP.
It is expected that over time, the standard library will be
updated to use ``False`` and ``True`` when appropriate (but not to require
a bool argument type where previous an int was allowed). This
change should not pose additional problems and is not specified in
detail by this PEP.
C API
=====
The header file "boolobject.h" defines the C API for the bool
type. It is included by "Python.h" so there is no need to include
it directly.
The header file "boolobject.h" defines the C API for the bool
type. It is included by "Python.h" so there is no need to include
it directly.
The existing names Py_False and Py_True reference the unique bool
objects False and True (previously these referenced static int
objects with values 0 and 1, which were not unique amongst int
values).
The existing names ``Py_False`` and ``Py_True`` reference the unique bool
objects ``False`` and ``True`` (previously these referenced static int
objects with values 0 and 1, which were not unique amongst int
values).
A new API, PyObject *PyBool_FromLong(long), takes a C long int
argument and returns a new reference to either Py_False (when the
argument is zero) or Py_True (when it is nonzero).
A new API, ``PyObject *PyBool_FromLong(long)``, takes a C long int
argument and returns a new reference to either ``Py_False`` (when the
argument is zero) or ``Py_True`` (when it is nonzero).
To check whether an object is a bool, the macro PyBool_Check() can
be used.
To check whether an object is a bool, the macro ``PyBool_Check()`` can
be used.
The type of bool instances is PyBoolObject *.
The type of bool instances is ``PyBoolObject *``.
The bool type object is available as PyBool_Type.
The bool type object is available as PyBool_Type.
Clarification
=============
This PEP does *not* change the fact that almost all object types
can be used as truth values. For example, when used in an if
statement, an empty list is false and a non-empty one is true;
this does not change and there is no plan to ever change this.
This PEP does **not** change the fact that almost all object types
can be used as truth values. For example, when used in an if
statement, an empty list is false and a non-empty one is true;
this does not change and there is no plan to ever change this.
The only thing that changes is the preferred values to represent
truth values when returned or assigned explicitly. Previously,
these preferred truth values were 0 and 1; the PEP changes the
preferred values to False and True, and changes built-in
operations to return these preferred values.
The only thing that changes is the preferred values to represent
truth values when returned or assigned explicitly. Previously,
these preferred truth values were 0 and 1; the PEP changes the
preferred values to ``False`` and ``True``, and changes built-in
operations to return these preferred values.
Compatibility
=============
Because of backwards compatibility, the bool type lacks many
properties that some would like to see. For example, arithmetic
operations with one or two bool arguments is allowed, treating
False as 0 and True as 1. Also, a bool may be used as a sequence
index.
Because of backwards compatibility, the bool type lacks many
properties that some would like to see. For example, arithmetic
operations with one or two bool arguments is allowed, treating
``False`` as 0 and ``True`` as 1. Also, a bool may be used as a sequence
index.
I don't see this as a problem, and I don't want evolve the
language in this direction either. I don't believe that a
stricter interpretation of "Booleanness" makes the language any
clearer.
I don't see this as a problem, and I don't want evolve the
language in this direction either. I don't believe that a
stricter interpretation of "Booleanness" makes the language any
clearer.
Another consequence of the compatibility requirement is that the
expression "True and 6" has the value 6, and similarly the
expression "False or None" has the value None. The "and" and "or"
operators are usefully defined to return the first argument that
determines the outcome, and this won't change; in particular, they
don't force the outcome to be a bool. Of course, if both
arguments are bools, the outcome is always a bool. It can also
easily be coerced into being a bool by writing for example "bool(x
and y)".
Another consequence of the compatibility requirement is that the
expression "True and 6" has the value 6, and similarly the
expression "False or None" has the value None. The "and" and "or"
operators are usefully defined to return the first argument that
determines the outcome, and this won't change; in particular, they
don't force the outcome to be a bool. Of course, if both
arguments are bools, the outcome is always a bool. It can also
easily be coerced into being a bool by writing for example "bool(x
and y)".
Resolved Issues
===============
(See also the Review section above.)
(See also the Review section above.)
- Because the repr() or str() of a bool value is different from an
int value, some code (for example doctest-based unit tests, and
possibly database code that relies on things like "%s" % truth)
may fail. It is easy to work around this (without explicitly
referencing the bool type), and it is expected that this only
affects a very small amount of code that can easily be fixed.
- Because the ``repr()`` or ``str()`` of a bool value is different from an
int value, some code (for example doctest-based unit tests, and
possibly database code that relies on things like "%s" % truth)
may fail. It is easy to work around this (without explicitly
referencing the bool type), and it is expected that this only
affects a very small amount of code that can easily be fixed.
- Other languages (C99, C++, Java) name the constants "false" and
"true", in all lowercase. For Python, I prefer to stick with
the example set by the existing built-in constants, which all
use CapitalizedWords: None, Ellipsis, NotImplemented (as well as
all built-in exceptions). Python's built-in namespace uses all
lowercase for functions and types only.
- Other languages (C99, C++, Java) name the constants "false" and
"true", in all lowercase. For Python, I prefer to stick with
the example set by the existing built-in constants, which all
use CapitalizedWords: ``None``, ``Ellipsis``, ``NotImplemented`` (as well as
all built-in exceptions). Python's built-in namespace uses all
lowercase for functions and types only.
- It has been suggested that, in order to satisfy user
expectations, for every x that is considered true in a Boolean
context, the expression x == True should be true, and likewise
if x is considered false, x == False should be true. In
particular newbies who have only just learned about Boolean
variables are likely to write
- It has been suggested that, in order to satisfy user
expectations, for every x that is considered true in a Boolean
context, the expression ``x == True`` should be true, and likewise
if x is considered false, ``x == False`` should be true. In
particular newbies who have only just learned about Boolean
variables are likely to write
::
if x == True: ...
if x == True: ...
instead of the correct form,
instead of the correct form,
::
if x: ...
if x: ...
There seem to be strong psychological and linguistic reasons why
many people are at first uncomfortable with the latter form, but
I believe that the solution should be in education rather than
in crippling the language. After all, == is general seen as a
transitive operator, meaning that from a==b and b==c we can
deduce a==c. But if any comparison to True were to report
equality when the other operand was a true value of any type,
atrocities like 6==True==7 would hold true, from which one could
infer the falsehood 6==7. That's unacceptable. (In addition,
it would break backwards compatibility. But even if it didn't,
I'd still be against this, for the stated reasons.)
There seem to be strong psychological and linguistic reasons why
many people are at first uncomfortable with the latter form, but
I believe that the solution should be in education rather than
in crippling the language. After all, == is general seen as a
transitive operator, meaning that from ``a==b`` and ``b==c`` we can
deduce ``a==c``. But if any comparison to ``True`` were to report
equality when the other operand was a true value of any type,
atrocities like ``6==True==7`` would hold true, from which one could
infer the falsehood ``6==7``. That's unacceptable. (In addition,
it would break backwards compatibility. But even if it didn't,
I'd still be against this, for the stated reasons.)
Newbies should also be reminded that there's never a reason to
write
Newbies should also be reminded that there's never a reason to
write
::
if bool(x): ...
if bool(x): ...
since the bool is implicit in the "if". Explicit is *not*
better than implicit here, since the added verbiage impairs
redability and there's no other interpretation possible. There
is, however, sometimes a reason to write
since the bool is implicit in the "if". Explicit is **not**
better than implicit here, since the added verbiage impairs
redability and there's no other interpretation possible. There
is, however, sometimes a reason to write
::
b = bool(x)
b = bool(x)
This is useful when it is unattractive to keep a reference to an
arbitrary object x, or when normalization is required for some
other reason. It is also sometimes appropriate to write
This is useful when it is unattractive to keep a reference to an
arbitrary object x, or when normalization is required for some
other reason. It is also sometimes appropriate to write
::
i = int(bool(x))
i = int(bool(x))
which converts the bool to an int with the value 0 or 1. This
conveys the intention to henceforth use the value as an int.
which converts the bool to an int with the value 0 or 1. This
conveys the intention to henceforth use the value as an int.
Implementation
==============
A complete implementation in C has been uploaded to the
SourceForge patch manager:
A complete implementation in C has been uploaded to the
SourceForge patch manager: http://python.org/sf/528022
http://python.org/sf/528022
This will soon be checked into CVS for python 2.3a0.
This will soon be checked into CVS for python 2.3a0.
Copyright
=========
This document has been placed in the public domain.
This document has been placed in the public domain.
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