In Python, the built-in functions all and any return True and False respectively for empty iterables. I realise that if it were the other way around, this question could still be asked. But I'd like to know why that specific behaviour was chosen. Was it arbitrary, ie. could it just as easily have been the other way, or is there an underlying reason?
(The reason I ask is simply because I never remember which is which, and if I knew the rationale behind it then I might. Also, curiosity.)
How about some analogies...
You have a sock drawer, but it is currently empty. Does it contain any black sock? No - you don't have any socks at all so you certainly don't have a black one. Clearly any([]) must return false - if it returned true this would be counter-intuitive.
The case for all([]) is slightly more difficult. See the Wikipedia article on vacuous truth. Another analogy: If there are no people in a room then everyone in that room can speak French.
Mathematically all([]) can be written:
where the set A is empty.
There is considerable debate about whether vacuous statements should be considered true or not, but from a logical viewpoint it makes the most sense:
The main argument that all vacuously true statements are true is as follows: As explained in the article on logical conditionals, the axioms of propositional logic entail that if P is false, then P => Q is true. That is, if we accept those axioms, we must accept that vacuously true statements are indeed true.
Also from the article:
There seems to be no direct reason to pick true; it’s just that things blow up in our face if we don’t.
Defining a "vacuously true" statement to return false in Python would violate the principle of least astonishment.
One property of any is its recursive definition
any([x,y,z,...]) == (x or any([y,z,...]))
That means
x == any([x]) == (x or any([]))
The equality is correct for any x if and only if any([]) is defined to be False. Similar for all.
I believe all([])==True is generally harder to grasp, so here are a collection of examples where I think that behaviour is obviously correct:
A movie is suitable for the hard of hearing if all the dialog in the film is captioned. A movie without dialog is still suitable for the hard of hearing.
A windowless room is dark when all the lights inside are turned off. When there are no lights inside, it is dark.
You can pass through airport security when all your liquids are contained in 100ml bottles. If you have no liquids you can still pass through security.
You can fit a soft bag through a narrow slot if all the items in the bag are narrower than the slot. If the bag is empty, it still fits through the slot.
A task is ready to start when all its prerequisites have been met. If a task has no prerequisites, it's ready to start.
I think of them as being implemented this way
def all(seq):
for item in seq:
if not item:
return False
return True
def any(seq):
for item in seq:
if item:
return True
return False
not sure they are implemented that way though
Perl 6 also takes the position that all() and any() on empty lists should serve as sane base-cases for their respective reduction operators, and therefore all() is true and any() is false.
That is to say, all(a, b, c) is equivalent to [&] a, b, c, which is equivalent to a & b & c (reduction on the "junctive and" operator, but you can ignore junctions and consider it a logical and for this post), and any(a, b, c) is equivalent to [|] a, b, c, which is equivalent to a | b | c (reduction on the "junctive or" operator -- again, you can pretend it's the same as logical or without missing anything).
Any operator which can have reduction applied to it needs to have a defined behavior when reducing 0 terms, and usually this is done by having a natural identity element -- for instance, [+]() (reduction of addition across zero terms) is 0 because 0 is the additive identity; adding zero to any expression leaves it unchanged. [*]() is likewise 1 because 1 is the multiplicative identity. We've already said that all is equivalent to [&] and any is equivalent to [|] -- well, truth is the and-identity, and falsity is the or-identity -- x and True is x, and x or False is x. This makes it inevitable that all() should be true and any() should be false.
To put it in an entirely different (but practical) perspective, any is a latch that starts off false and becomes true whenever it sees something true; all is a latch that starts off true and becomes false whenever it sees something false. Giving them no arguments means giving them no chance to change state, so you're simply asking them what their "default" state is. :)
any and all have the same meaning in python as everywhere else:
any is true if at least one is true
all is not true if at least one is not true
For general interest, here's the blog post in which GvR proposes any/all with a sample implementation like gnibbler's and references quanifiers in ABC.
This is really more of a comment, but code in comments doesn't work very well.
In addition to the other logical bases for why any() and all() work as they do, they have to have opposite "base" cases so that this relationship holds true:
all(x for x in iterable) == not any(not x for x in iterable)
If iterable is zero-length, the above still should hold true. Therefore
all(x for x in []) == not any(not x for x in [])
which is equivalent to
all([]) == not any([])
And it would be very surprising if any([]) were the one that is true.
The official reason is unclear, but from the docs (confirming #John La Rooy's post):
all(iterable)
Return True if all elements of the iterable are true (or if the iterable is empty).
Equivalent to:
def all(iterable):
for element in iterable:
if not element:
return False
return True
any(iterable)
Return True if any element of the iterable is true. If the iterable is empty, return False. Equivalent to:
def any(iterable):
for element in iterable:
if element:
return True
return False
See also the CPython-implementation and comments.
Related
I'm learning Python and I just started learning conditionals with booleans
I am very confused though as to the specific topic of "If Not". Could someone please explain to me the difference between :
x = False
if not x:
print("hello")
if x == False:
print("hello")
When testing this code on a Python compiler, I receive "hello" twice. I can assume this means that they both mean the same thing to the computer.
Could someone please explain to me why one would use one method over the other method?
It depends™. Python doesn't know what any of its operators should do. It calls magic methods on objects and lets them decide. We can see this with a simple test
class Foo:
"""Demonstrates the difference between a boolean and equality test
by overriding the operations that implement them."""
def __bool__(self):
print("bool")
return True
def __eq__(self, other):
print("eq", repr(other))
return True
x = Foo()
print("This is a boolean operation without an additional parameter")
if not x:
print("one")
print("This is an equality operation with a parameter")
if x == False:
print("two")
Produces
This is a boolean operation without an additional parameter
bool
This is an equality operation with a parameter
eq False
two
In the first case, python did a boolean test by calling __bool__, and in the second, an equality test by calling __eq__. What this means depends on the class. Its usually obvious but things like pandas may decide to get tricky.
Usually not x is faster than x == False because the __eq__ operator will typically do a second boolean comparison before it knows for sure. In your case, when x = False you are dealing with a builtin class written in C and its two operations will be similar. But still, the x == False comparison needs to do a type check against the other side, so it will be a bit slower.
There are already several good answers here, but none discuss the general concept of "truthy" and "falsy" expressions in Python.
In Python, truthy expressions are expression that return True when converted to bool, and falsy expressions are expressions that return False when converted to bool. (Ref: Trey Hunner's regular expression tutorial; I'm not affiliated with Hunner, I just love his tutorials.)
Truthy stuff:
What's important here is that 0, 0.0, [], None and False are all falsy.
When used in an if statement, they will fail the test, and they will pass the test in an if not statement.
Falsy stuff:
Non-zero numbers, non-empty lists, many objects (but read #tdelaney's answer for more details here), and True are all truthy, so they pass if and fail if not tests.
Equality tests
When you use equality tests, you're not asking about the truthiness of an expression, you're asking whether it is equal to the other thing you provide, which is much more restrictive than general truthiness or falsiness.
EDIT: Additional references
Here are more references on "Truthy" and "Falsy" values in Python:
Truth value testing in the Python manual
The exhaustive list of Falsy values
Truthy and Falsy tutorial from freeCodeCamp
In one case you are checking for equality with the value "False", on the other you are performing a boolean test on a variable. In Python, several variables pass the "if not x" test but only x = False passes "if x == False".
See example code:
x = [] # an empty list
if not x: print("Here!")
# x passes this test
if x == False: print("There!")
# x doesn't pass this test
Try it with x = None: not x would be True then and x == False would be False. Unlike with x = False when both of these are True. not statement also accounts for an empty value.
In Python, the built-in functions all and any return True and False respectively for empty iterables. I realise that if it were the other way around, this question could still be asked. But I'd like to know why that specific behaviour was chosen. Was it arbitrary, ie. could it just as easily have been the other way, or is there an underlying reason?
(The reason I ask is simply because I never remember which is which, and if I knew the rationale behind it then I might. Also, curiosity.)
How about some analogies...
You have a sock drawer, but it is currently empty. Does it contain any black sock? No - you don't have any socks at all so you certainly don't have a black one. Clearly any([]) must return false - if it returned true this would be counter-intuitive.
The case for all([]) is slightly more difficult. See the Wikipedia article on vacuous truth. Another analogy: If there are no people in a room then everyone in that room can speak French.
Mathematically all([]) can be written:
where the set A is empty.
There is considerable debate about whether vacuous statements should be considered true or not, but from a logical viewpoint it makes the most sense:
The main argument that all vacuously true statements are true is as follows: As explained in the article on logical conditionals, the axioms of propositional logic entail that if P is false, then P => Q is true. That is, if we accept those axioms, we must accept that vacuously true statements are indeed true.
Also from the article:
There seems to be no direct reason to pick true; it’s just that things blow up in our face if we don’t.
Defining a "vacuously true" statement to return false in Python would violate the principle of least astonishment.
One property of any is its recursive definition
any([x,y,z,...]) == (x or any([y,z,...]))
That means
x == any([x]) == (x or any([]))
The equality is correct for any x if and only if any([]) is defined to be False. Similar for all.
I believe all([])==True is generally harder to grasp, so here are a collection of examples where I think that behaviour is obviously correct:
A movie is suitable for the hard of hearing if all the dialog in the film is captioned. A movie without dialog is still suitable for the hard of hearing.
A windowless room is dark when all the lights inside are turned off. When there are no lights inside, it is dark.
You can pass through airport security when all your liquids are contained in 100ml bottles. If you have no liquids you can still pass through security.
You can fit a soft bag through a narrow slot if all the items in the bag are narrower than the slot. If the bag is empty, it still fits through the slot.
A task is ready to start when all its prerequisites have been met. If a task has no prerequisites, it's ready to start.
I think of them as being implemented this way
def all(seq):
for item in seq:
if not item:
return False
return True
def any(seq):
for item in seq:
if item:
return True
return False
not sure they are implemented that way though
Perl 6 also takes the position that all() and any() on empty lists should serve as sane base-cases for their respective reduction operators, and therefore all() is true and any() is false.
That is to say, all(a, b, c) is equivalent to [&] a, b, c, which is equivalent to a & b & c (reduction on the "junctive and" operator, but you can ignore junctions and consider it a logical and for this post), and any(a, b, c) is equivalent to [|] a, b, c, which is equivalent to a | b | c (reduction on the "junctive or" operator -- again, you can pretend it's the same as logical or without missing anything).
Any operator which can have reduction applied to it needs to have a defined behavior when reducing 0 terms, and usually this is done by having a natural identity element -- for instance, [+]() (reduction of addition across zero terms) is 0 because 0 is the additive identity; adding zero to any expression leaves it unchanged. [*]() is likewise 1 because 1 is the multiplicative identity. We've already said that all is equivalent to [&] and any is equivalent to [|] -- well, truth is the and-identity, and falsity is the or-identity -- x and True is x, and x or False is x. This makes it inevitable that all() should be true and any() should be false.
To put it in an entirely different (but practical) perspective, any is a latch that starts off false and becomes true whenever it sees something true; all is a latch that starts off true and becomes false whenever it sees something false. Giving them no arguments means giving them no chance to change state, so you're simply asking them what their "default" state is. :)
any and all have the same meaning in python as everywhere else:
any is true if at least one is true
all is not true if at least one is not true
For general interest, here's the blog post in which GvR proposes any/all with a sample implementation like gnibbler's and references quanifiers in ABC.
This is really more of a comment, but code in comments doesn't work very well.
In addition to the other logical bases for why any() and all() work as they do, they have to have opposite "base" cases so that this relationship holds true:
all(x for x in iterable) == not any(not x for x in iterable)
If iterable is zero-length, the above still should hold true. Therefore
all(x for x in []) == not any(not x for x in [])
which is equivalent to
all([]) == not any([])
And it would be very surprising if any([]) were the one that is true.
The official reason is unclear, but from the docs (confirming #John La Rooy's post):
all(iterable)
Return True if all elements of the iterable are true (or if the iterable is empty).
Equivalent to:
def all(iterable):
for element in iterable:
if not element:
return False
return True
any(iterable)
Return True if any element of the iterable is true. If the iterable is empty, return False. Equivalent to:
def any(iterable):
for element in iterable:
if element:
return True
return False
See also the CPython-implementation and comments.
False is equivalent to 0 and True is equivalent 1 so it's possible to do something like this:
def bool_to_str(value):
"""value should be a bool"""
return ['No', 'Yes'][value]
bool_to_str(True)
Notice how value is bool but is used as an int.
Is this this kind of use Pythonic or should it be avoided?
I'll be the odd voice out (since all answers are decrying the use of the fact that False == 0 and True == 1, as the language guarantees) as I claim that the use of this fact to simplify your code is perfectly fine.
Historically, logical true/false operations tended to simply use 0 for false and 1 for true; in the course of Python 2.2's life-cycle, Guido noticed that too many modules started with assignments such as false = 0; true = 1 and this produced boilerplate and useless variation (the latter because the capitalization of true and false was all over the place -- some used all-caps, some all-lowercase, some cap-initial) and so introduced the bool subclass of int and its True and False constants.
There was quite some pushback at the time since many of us feared that the new type and constants would be used by Python newbies to restrict the language's abilities, but Guido was adamant that we were just being pessimistic: nobody would ever understand Python so badly, for example, as to avoid the perfectly natural use of False and True as list indices, or in a summation, or other such perfectly clear and useful idioms.
The answers to this thread prove we were right: as we feared, a total misunderstanding of the roles of this type and constants has emerged, and people are avoiding, and, worse!, urging others to avoid, perfectly natural Python constructs in favor of useless gyrations.
Fighting against the tide of such misunderstanding, I urge everybody to use Python as Python, not trying to force it into the mold of other languages whose functionality and preferred style are quite different. In Python, True and False are 99.9% like 1 and 0, differing exclusively in their str(...) (and thereby repr(...)) form -- for every other operation except stringification, just feel free to use them without contortions. That goes for indexing, arithmetic, bit operations, etc, etc, etc.
I'm with Alex. False==0 and True==1, and there's nothing wrong with that.
Still, in Python 2.5 and later I'd write the answer to this particular question using Python's conditional expression:
def bool_to_str(value):
return 'Yes' if value else 'No'
That way there's no requirement that the argument is actually a bool -- just as if x: ... accepts any type for x, the bool_to_str() function should do the right thing when it is passed None, a string, a list, or 3.14.
surely:
def bool_to_str(value):
"value should be a bool"
return 'Yes' if value else 'No'
is more readable.
Your code seems inaccurate in some cases:
>>> def bool_to_str(value):
... """value should be a bool"""
... return ['No', 'Yes'][value]
...
>>> bool_to_str(-2)
'No'
And I recommend you to use just the conditional operator for readability:
def bool_to_str(value):
"""value should be a bool"""
return "Yes" if value else "No"
It is actually a feature of the language that False == 0 and True == 1 (it does not depend on the implementation): Is False == 0 and True == 1 in Python an implementation detail or is it guaranteed by the language?
However, I do agree with most of the other answers: there are more readable ways of obtaining the same result as ['No', 'Yes'][value], through the use of the … if value else … or of a dictionary, which have the respective advantages of hinting and stating that value is a boolean.
Plus, the … if value else … follows the usual convention that non-0 is True: it also works even when value == -2 (value is True), as hinted by dahlia. The list and dict approaches are not as robust, in this case, so I would not recommend them.
Using a bool as an int is quite OK because bool is s subclass of int.
>>> isinstance(True, int)
True
>>> isinstance(False, int)
True
About your code: Putting it in a one-line function like that is over the top. Readers need to find your function source or docs and read it (the name of the function doesn't tell you much). This interrupts the flow. Just put it inline and don't use a list (built at run time), use a tuple (built at compile time if the values are constants). Example:
print foo, bar, num_things, ("OK", "Too many!)[num_things > max_things]
Personally I think it depends on how do you want to use this fact, here are two examples
Just simply use boolean as conditional statement is fine. People do this all the time.
a = 0
if a:
do something
However say you want to count how many items has succeed, the code maybe not very friendly for other people to read.
def succeed(val):
if do_something(val):
return True
else:
return False
count = 0
values = [some values to process]
for val in values:
count += succeed(val)
But I do see the production code look like this.
all_successful = all([succeed(val) for val in values])
at_least_one_successful = any([succeed(val) for val in values])
total_number_of_successful = sum([succeed(val) for val in values])
In answer to a question about Python and/or logic, Spacetoast wrote:
x and y returns true if both x and y are true.
x or y returns if either one is true.
I manage to confuse myself by using "or" when it should have been "and". Without having to drawing up truth tables, is there an mnemonic to help remember the correct usage of and/or?
Not a true Mnemonic, but NOAH has helped my students in the past.
How many inputs must be true?
None => Nor
One => Or
All => And
Honestly => Heed the truth tables
To be honest the skill of being able to use a truth table is worth persevering with. (Note there is not a NOR operator in python, its a Not-or).
The confusion from the pointed answer to that question come from the fact that he says the OR contains AND which is true in your case. There's is nothing to remember here, if you use or operator and at least one of the two expressions is True then it returns True if none of the two expressions are True it returns False
This means that if both x and y are True the or will be True too because as soon as the first expression x is True there's no need for evaluating the second one.
On the other hand, if you're using and and the first expression doesn't evaluate to True, there's no need to evaluate the second one, since it's impossible for both of them to be True anymore.
there is no need of mnemonic for this
remember this by a simple concept:
or -> any one true
and -> all true
true or false = True
true and false = False
>What's wrong with this..
Code-1
def first_last6(nums):
if nums[0]==6 or nums[len(nums)-1] == 6:
return True
else:
return False
Code-2
def first_last6(nums):
return (nums[0]==6 or nums[-1]== 6)
How come both True?
There seem to be two questions inside, so I’ll answer both.
First of all, why are nums[len(nums)-1] and nums[-1] the same? When specifying an index, Python allows you to use negative numbers that are interpreted like this: if i in nums[i] is negative, then the index len(nums)+i is returned. So, basically, [-1] will get the last element, [-2] the second to last etc.
The second question is why the two formats are identical:
if expression:
return True
else
return False
and
return expression
expression in this case is an expression that returns a boolean type, so either True or False. The if statements checks exactly that; if the expression equals to true, it will return true, otherwise (if the expression equals to false) it will return false.
So you can (and should, to make it cleaner) just return the expression itself, as it is already true or false.
In the case expression itself is not a boolean expression, the if statement will still check to what boolean type it would evaluate (for example a non-empty string would be true, or a number other than 0 would be true too). To keep the short syntax, you can then explicitely convert the expression to a boolean value, using bool(expression), as larsmans mentioned in the comments.
nums[-k] is a shorthand for nums[len(nums)-k]. To get the k-th last element you use the notation nums[-k]. Usually it is clear what the notation stands for and the compiler knows how to turn that python code into machine code, which is why certain language contructs are possible and others are not. Other short hands include nums[:k] to get the first k elements, nums[:-k] to get all elements up to the k-th last element etc. Via google, python docs, you will find much more on this. List operations are a great strength of the python.
http://www.diveintopython.net/native_data_types/lists.html
uh, because both are exactly the same and they both evaluate to True.