Python map function, passing by reference/value? - python

I have a question about the map function in Python.
From what I understand, the function does not mutate the list it's operating on, but rather create a new one and return it. Is this correct ?
Additionally, I have the following piece of code
def reflect(p,dir):
if(dir == 'X'):
func = lambda (a,b) : (a * -1, b)
else:
func = lambda (a,b) : (a, b * -1)
p = map(func,p)
print 'got', p
points is an array of tuples such as: [(1, 1), (-1, 1), (-1, -1), (1, -1)]
If I call the above function in such a manner:
print points
reflect(points,'X')
print points
the list points does not change. Inside the function though, the print function properly prints what I want.
Could someone maybe point me in some direction where I could learn how all this passing by value / reference etc works in python, and how I could fix the above ? Or maybe I'm trying too hard to emulate Haskell in python...
Thanks
edit:
Say instead of p = map(func,p) I do
for i in range(len(p)):
p[i] = func(p[i])
The value of the list is updated outside of the function, as if working by reference. Ugh, hope this is clear :S

You misunderstand how references work in Python. Here, all names are references, there are no "values". Names are bound to objects. But = doesn't modify the object that's pointed to by the name — it rebinds the name to a different object:
x = 42
y = x
# now:
# 'is' is a identity operator — it checks whether two names point to the
# exact same object
print x is y # => True
print x, y # 42 42
y = 69
# now y has been rebound, but that does not change the '42' object, nor rebinds x
print x is y # => False
print x, y # 42 69
To modify the object itself, it needs to be mutable — i.e. expose members that mutate it or have a modifiable dict. The same thing as above happens when you rebind p — it doesn't touch points at all, it simply modifies the meaning of local p name.
If you want to simulate C++-like references, you need to encapsulate the object into a mutable container, e.g. a list.
reflect([points], 'X')
# inside reflect:
p[0] = ...
But you shouldn't, at least in this case — you should just return the new object instead.
points = reflect(points, 'X')
# inside reflect, instead of p = ...
return map(func, p)
Well, now that I think about it, you can also do
p[:] = map(func, p)
But again, returning new object is usually better.

The data model of Python is based on a trilogy:
identifier - reference - object
.
The identifier is a string written in the code.
The reference is a variable stricto sensu, that is to say "a chunk of
memory whose content can change". The value of a reference is the adress of the object.
The object has an
implementation based on the structures of the langage C that is the
foundations of Python.
Other words are also used to designate the 'identifier' :
1) name
2) variable ; because this word is used by metonymy in mathematics to designate the symbols that represent the real mathematical variables, and the variables in a computer have conceptually the same functioning as the mathematical variables (their values can change).
This use in Python is a very bad habit in my opinion : it creates ambiguities and confusion with what is called 'variable' in computer science: "chunk of memory whose content can change".
The best is to use the word : identifier
.
An identifier and an object are binded in a certain namespace. Namespaces are displayed under the form of Python's dictionaries, but they ARE NOT dictionaries.
The binding of the identifier and the object is indirect, via the reference.
The binding of the identifier and the reference is direct, and realized in the SYMBOL TABLE (or symbol-table).
In computer science, a symbol table is a data structure used by a
language translator such as a compiler or interpreter, where each
identifier in a program's source code is associated with information
relating to its declaration or appearance in the source, such as its
type, scope level and sometimes its location.
http://en.wikipedia.org/wiki/Symbol_table
They say: identifiers. Precisely.
I rarely see allusions to symbol table, though it's the crucial thing that sheds light on the functioning of the Python's data model IMO.
In my opinion, the word
binding
doesn't designate a precise and unique mechanism but globally the set of all the mechanisms concerning the trilogy identifier - reference - object
.
I dont' pretend that I perfectly understood all the matters concerning the data and execution models of Python, and that the above considerations are the more exact and precisely expressed that can be done.
However, they allow me to have an operational understanding of what happens during executions of code.
I would be very happy to be corrected on some points if I am wrong (for exemple, I am very satisfied to have learnt from Michael Foord that the nature of namespaces is not being dictionary, which is only the way they are represented)
.
That said, I don't know what is called value and reference when the subject of passing something as argument in Python is discussed, and I have the impression that a lot of the persons that have expressed on the subject in numerous esoteric discussions don't know more than me.
I think that there is no best and lucid opinion on the subject that this one of Alex Martelli:
"Trying to reuse terminology that is more generally applied to
languages where "variables are boxes" to a language where "variables
are post-it tags" is, IMHO, more likely to confuse than to help."
Alex Martelli
http://bytes.com/topic/python/answers/37219-value-reference

I want to bump this. The answers don't really answer the question - they disregard the fact that the OP was able to achieve the desired result by iterating. The question comes down to the behavior of map. Here is a more direct example:
f=(lambda pair: pair[0].append(pair[1]))
a = ([],1)
f(a)
print(a) #prints ([1],1)
a=([],1)
map(f,[a])
print(a) #prints ([0],1)
So map isn't mutating objects in the way the OP is expecting. I have the same confusion.
Can anyone comment on exactly what is going on here? I think that'd be a good answer to the OP's question.
Note that we have different behavior if we assign the output of map as follows (as per Cat Plus Plus' answer)
f=(lambda pair: pair[0].append(pair[1]))
a = ([],1)
x = [a]
x[:] = map(f,x)
print(x) #prints None
print(a) # prints [1]
Please note that in the first example, we simply called f(a), not a=f(a). Why do we need assignment when using map and not when working outside of map?

Related

assignment operator for a function return

Clearly, it may not make that much sense to make an assignment to a function return, yet I've just encountered a strange situation and could not find a proper rule for that.
The code below does not run:
def foo():
a = [1,2,3,4,5]
return a
foo()= 10
however,
def foo():
a = [1,2,3,4,5]
return a
foo()[2] = 10
works perfectly. It is not clear to me what is going on here. It looks to me that there is an inconsistency here...
Thanks a lot.
It is not clear to me what is going on here.
It's fairly simple, really; the left-hand-side of an assignment statement is not allowed to just be any kind of expression, but some "kinds" of expression are valid assignment targets, and for those kinds of expression it doesn't matter what kinds of sub-expressions they may have. In your example, the left-hand-side is a subscription, which is a valid assignment target, so it's a syntactically valid assignment statement.
In particular, a subscription has two sub-expressions but it doesn't matter what lexical form those sub-expressions have. For example, the below may look perfectly normal to you, where the first sub-expression foo.bar is an attributeref and the second sub-expression index + 5 is an a_expr:
foo.bar[index + 5] = value
This example probably also looks perfectly normal: the first sub-expression baz[get_x()] is another subscription, and the second sub-expression get_y() is a call.
baz[get_x()][get_y()] = value
As for why it's allowed, the simple reason is that it would be a bit silly and arbitrary for the Python developers to decide on a list of restrictions on the sub-expressions. The meaning of the assignment statement is well-defined so long as the left-hand-side is one of the required lexical forms, so the only reason to impose further restrictions on the sub-expressions of those lexical forms would be to try to prevent mistakes by the programmer.
On the other hand, code like func_call()[index] = value is not necessarily a mistake anyway, because the list that func_call() returns might well be referenced elsewhere, so the mutation will be visible through other references to that list.
In python, not every value can be used of the left side of the assignment (so called lvalue). Basically, only 3 things can be lvalues:
a name, like abc
an attribute any_expression.name
a subscript any_expression[slice]
Other values, like literals, arithmetic expressions, function calls etc cannot be used on the left side:
123 = 123 # no
a + b = 123 # no
func() = 123 # no
See assignment in the grammar spec: https://docs.python.org/3/reference/grammar.html

what does it mean by 'passed by assignment'?

As follow is my understanding of types & parameters passing in java and python:
In java, there are primitive types and non-primitive types. Former are not object, latter are objects.
In python, they are all objects.
In java, arguments are passed by value because:
primitive types are copied and then passed, so they are passed by value for sure. non-primitive types are passed by reference but reference(pointer) is also value, so they are also passed by value.
In python, the only difference is that 'primitive types'(for example, numbers) are not copied, but simply taken as objects.
Based on official doc, arguments are passed by assignment. What does it mean by 'passed by assignment'? Is objects in java work the same way as python? What result in the difference (passed by value in java and passed by argument in python)?
And is there any wrong understanding above?
tl;dr: You're right that Python's semantics are essentially Java's semantics, without any primitive types.
"Passed by assignment" is actually making a different distinction than the one you're asking about.1 The idea is that argument passing to functions (and other callables) works exactly the same way assignment works.
Consider:
def f(x):
pass
a = 3
b = a
f(a)
b = a means that the target b, in this case a name in the global namespace, becomes a reference to whatever value a references.
f(a) means that the target x, in this case a name in the local namespace of the frame built to execute f, becomes a reference to whatever value a references.
The semantics are identical. Whenever a value gets assigned to a target (which isn't always a simple name—e.g., think lst[0] = a or spam.eggs = a), it follows the same set of assignment rules—whether it's an assignment statement, a function call, an as clause, or a loop iteration variable, there's just one set of rules.
But overall, your intuitive idea that Python is like Java but with only reference types is accurate: You always "pass a reference by value".
Arguing over whether that counts as "pass by reference" or "pass by value" is pointless. Trying to come up with a new unambiguous name for it that nobody will argue about is even more pointless. Liskov invented the term "call by object" three decades ago, and if that never caught on, anything someone comes up with today isn't likely to do any better.
You understand the actual semantics, and that's what matters.
And yes, this means there is no copying. In Java, only primitive values are copied, and Python doesn't have primitive values, so nothing is copied.
the only difference is that 'primitive types'(for example, numbers) are not copied, but simply taken as objects
It's much better to see this as "the only difference is that there are no 'primitive types' (not even simple numbers)", just as you said at the start.
It's also worth asking why Python has no primitive types—or why Java does.2
Making everything "boxed" can be very slow. Adding 2 + 3 in Python means dereferencing the 2 and 3 objects, getting the native values out of them, adding them together, and wrapping the result up in a new 5 object (or looking it up in a table because you already have an existing 5 object). That's a lot more work than just adding two ints.3
While a good JIT like Hotspot—or like PyPy for Python—can often automatically do those optimizations, sometimes "often" isn't good enough. That's why Java has native types: to let you manually optimize things in those cases.
Python, instead, relies on third-party libraries like Numpy, which let you pay the boxing costs just once for a whole array, instead of once per element. Which keeps the language simpler, but at the cost of needing Numpy.4
1. As far as I know, "passed by assignment" appears a couple times in the FAQs, but is not actually used in the reference docs or glossary. The reference docs already lean toward intuitive over rigorous, but the FAQ, like the tutorial, goes much further in that direction. So, asking what a term in the FAQ means, beyond the intuitive idea it's trying to get across, may not be a meaningful question in the first place.
2. I'm going to ignore the issue of Java's lack of operator overloading here. There's no reason they couldn't include special language rules for a handful of core classes, even if they didn't let you do the same thing with your own classes—e.g., Go does exactly that for things like range, and people rarely complain.
3. … or even than looping over two arrays of 30-bit digits, which is what Python actually does. The cost of working on unlimited-size "bigints" is tiny compared to the cost of boxing, so Python just always pays that extra, barely-noticeable cost. Python 2 did, like Java, have separate fixed and bigint types, but a couple decades of experience showed that it wasn't getting any performance benefits out of the extra complexity.
4. The implementation of Numpy is of course far from simple. But using it is pretty simple, and a lot more people need to use Numpy than need to write Numpy, so that turns out to be a pretty decent tradeoff.
Similar to passing reference types by value in C#.
Docs: https://learn.microsoft.com/en-us/dotnet/csharp/programming-guide/classes-and-structs/passing-reference-type-parameters#passing-reference-types-by-value
Code demo:
# mutable object
l = [9, 8, 7]
def createNewList(l1: list):
# l1+[0] will create a new list object, the reference address of the local variable l1 is changed without affecting the variable l
l1 = l1+[0]
def changeList(l1: list):
# Add an element to the end of the list, because l1 and l refer to the same object, so l will also change
l1.append(0)
print(l)
createNewList(l)
print(l)
changeList(l)
print(l)
# immutable object
num = 9
def changeValue(val: int):
# int is an immutable type, and changing the val makes the val point to the new object 8,
# it's not change the num value
value = 8
print(num)
changeValue(num)
print(num)

What is an object reference in Python?

A introductory Python textbook defined 'object reference' as follows, but I didn't understand:
An object reference is nothing more than a concrete representation of the object’s identity (the memory address where the object is stored).
The textbook tried illustrating this by using an arrow to show an object reference as some sort of relation going from a variable a to an object 1234 in the assignment statement a = 1234.
From what I gathered off of Wikipedia, the (object) reference of a = 1234 would be an association between a and 1234 were a was "pointing" to 1234 (feel free to clarify "reference vs. pointer"), but it has been a bit difficult to verify as (1) I'm teaching myself Python, (2) many search results talk about references for Java, and (3) not many search results are about object references.
So, what is an object reference in Python? Thanks for the help!
Whatever is associated with a variable name has to be stored in the program's memory somewhere. An easy way to think of this, is that every byte of memory has an index-number. For simplicity's sake, lets imagine a simple computer, these index-numbers go from 0 (the first byte), upwards to however many bytes there are.
Say we have a sequence of 37 bytes, that a human might interpret as some words:
"The Owl and the Pussy-cat went to sea"
The computer is storing them in a contiguous block, starting at some index-position in memory. This index-position is most often called an "address". Obviously this address is absolutely just a number, the byte-number of the memory these letters are residing in.
#12000 The Owl and the Pussy-cat went to sea
So at address 12000 is a T, at 12001 an h, 12002 an e ... up to the last a at 12037.
I am labouring the point here because it's fundamental to every programming language. That 12000 is the "address" of this string. It's also a "reference" to it's location. For most intents and purposes an address is a pointer is a reference. Different languages have differing syntactic handling of these, but essentially they're the same thing - dealing with a block of data at a given number.
Python and Java try to hide this addressing as much as possible, where languages like C are quite happy to expose pointers for exactly what they are.
The take-away from this, is that an object reference is the number of where the data is stored in memory. (As is a pointer.)
Now, most programming languages distinguish between simple types: characters and numbers, and complex types: strings, lists and other compound-types. This is where the reference to an object makes a difference.
So when performing operations on simple types, they are independent, they each have their own memory for storage. Imagine the following sequence in python:
>>> a = 3
>>> b = a
>>> b
3
>>> b = 4
>>> b
4
>>> a
3 # <-- original has not changed
The variables a and b do not share the memory where their values are stored. But with a complex type:
>>> s = [ 1, 2, 3 ]
>>> t = s
>>> t
[1, 2, 3]
>>> t[1] = 8
>>> t
[1, 8, 3]
>>> s
[1, 8, 3] # <-- original HAS changed
We assigned t to be s, but obviously in this case t is s - they share the same memory. Wait, what! Here we have found out that both s and t are a reference to the same object - they simply share (point to) the same address in memory.
One place Python differs from other languages is that it considers strings as a simple type, and these are independent, so they behave like numbers:
>>> j = 'Pussycat'
>>> k = j
>>> k
'Pussycat'
>>> k = 'Owl'
>>> j
'Pussycat' # <-- Original has not changed
Whereas in C strings are definitely handled as complex types, and would behave like the Python list example.
The upshot of all this, is that when objects that are handled by reference are modified, all references-to this object "see" the change. So if the object is passed to a function that modifies it (i.e.: the content of memory holding the data is changed), the change is reflected outside that function too.
But if a simple type is changed, or passed to a function, it is copied to the function, so the changes are not seen in the original.
For example:
def fnA( my_list ):
my_list.append( 'A' )
a_list = [ 'B' ]
fnA( a_list )
print( str( a_list ) )
['B', 'A'] # <-- a_list was changed inside the function
But:
def fnB( number ):
number += 1
x = 3
fnB( x )
print( x )
3 # <-- x was NOT changed inside the function
So keeping in mind that the memory of "objects" that are used by reference is shared by all copies, and memory of simple types is not, it's fairly obvious that the two types operate differently.
Objects are things. Generally, they're what you see on the right hand side of an equation.
Variable names (often just called "names") are references to the actual object. When a name is on the right hand side of an equation1, the object that it references is automatically looked up and used in the equation. The result of the expression on the right hand side is an object. The name on the left hand side of the equation becomes a reference to this (possibly new) object.
Note, you can have object references that aren't explicit names if you are working with container objects (like lists or dictionaries):
a = [] # the name a is a reference to a list.
a.append(12345) # the container list holds a reference to an integer object
In a similar way, multiple names can refer to the same object:
a = []
b = a
We can demonstrate that they are the same object by looking at the id of a and b and noting that they are the same. Or, we can look at the "side-effects" of mutating the object referenced by a or b (if we mutate one, we mutate both because they reference the same object).
a.append(1)
print a, b # look mom, both are [1]!
1More accurately, when a name is used in an expression
In python, strictly speaking, the language has only naming references to the objects, that behave as labels. The assignment operator only binds to the name. The objects will stay in the memory until they are garbage collected
Ok, first things first.
Remember, there are two types of objects in python.
Mutable : Whose values can be changed. Eg: dictionaries, lists and user defined objects(unless defined immutable)
Immutable : Whose values can't be changed. Eg: tuples, numbers, booleans and strings.
Now, when python says PASS BY OBJECT REFERENECE, just remember that
If the underlying object is mutable, then any modifications done will persist.
and,
If the underlying object is immutable, then any modifications done will not persist.
If you still want examples for clarity, scroll down or click here .

How to make a variable (truly) local to a procedure or function

ie we have the global declaration, but no local.
"Normally" arguments are local, I think, or they certainly behave that way.
However if an argument is, say, a list and a method is applied which modifies the list, some surprising (to me) results can ensue.
I have 2 questions: what is the proper way to ensure that a variable is truly local?
I wound up using the following, which works, but it can hardly be the proper way of doing it:
def AexclB(a,b):
z = a+[] # yuk
for k in range(0, len(b)):
try: z.remove(b[k])
except: continue
return z
Absent the +[], "a" in the calling scope gets modified, which is not desired.
(The issue here is using a list method,
The supplementary question is, why is there no "local" declaration?
Finally, in trying to pin this down, I made various mickey mouse functions which all behaved as expected except the last one:
def fun4(a):
z = a
z = z.append(["!!"])
return z
a = ["hello"]
print "a=",a
print "fun4(a)=",fun4(a)
print "a=",a
which produced the following on the console:
a= ['hello']
fun4(a)= None
a= ['hello', ['!!']]
...
>>>
The 'None' result was not expected (by me).
Python 2.7 btw in case that matters.
PS: I've tried searching here and elsewhere but not succeeded in finding anything corresponding exactly - there's lots about making variables global, sadly.
It's not that z isn't a local variable in your function. Rather when you have the line z = a, you are making z refer to the same list in memory that a already points to. If you want z to be a copy of a, then you should write z = a[:] or z = list(a).
See this link for some illustrations and a bit more explanation http://henry.precheur.org/python/copy_list
Python will not copy objects unless you explicitly ask it to. Integers and strings are not modifiable, so every operation on them returns a new instance of the type. Lists, dictionaries, and basically every other object in Python are mutable, so operations like list.append happen in-place (and therefore return None).
If you want the variable to be a copy, you must explicitly copy it. In the case of lists, you slice them:
z = a[:]
There is a great answer than will cover most of your question in here which explains mutable and immutable types and how they are kept in memory and how they are referenced. First section of the answer is for you. (Before How do we get around this? header)
In the following line
z = z.append(["!!"])
Lists are mutable objects, so when you call append, it will update referenced object, it will not create a new one and return it. If a method or function do not retun anything, it means it returns None.
Above link also gives an immutable examle so you can see the real difference.
You can not make a mutable object act like it is immutable. But you can create a new one instead of passing the reference when you create a new object from an existing mutable one.
a = [1,2,3]
b = a[:]
For more options you can check here
What you're missing is that all variable assignment in python is by reference (or by pointer, if you like). Passing arguments to a function literally assigns values from the caller to the arguments of the function, by reference. If you dig into the reference, and change something inside it, the caller will see that change.
If you want to ensure that callers will not have their values changed, you can either try to use immutable values more often (tuple, frozenset, str, int, bool, NoneType), or be certain to take copies of your data before mutating it in place.
In summary, scoping isn't involved in your problem here. Mutability is.
Is that clear now?
Still not sure whats the 'correct' way to force the copy, there are
various suggestions here.
It differs by data type, but generally <type>(obj) will do the trick. For example list([1, 2]) and dict({1:2}) both return (shallow!) copies of their argument.
If, however, you have a tree of mutable objects and also you don't know a-priori which level of the tree you might modify, you need the copy module. That said, I've only needed this a handful of times (in 8 years of full-time python), and most of those ended up causing bugs. If you need this, it's a code smell, in my opinion.
The complexity of maintaining copies of mutable objects is the reason why there is a growing trend of using immutable objects by default. In the clojure language, all data types are immutable by default and mutability is treated as a special cases to be minimized.
If you need to work on a list or other object in a truly local context you need to explicitly make a copy or a deep copy of it.
from copy import copy
def fn(x):
y = copy(x)

Why should I refer to "names" and "binding" in Python instead of "variables" and "assignment"?

Why should I refer to "names" and "binding" in Python instead of "variables" and "assignment"?
I know this question is a bit general but I really would like to know :)
In C and C++, a variable is a named memory location. The value of the variable is the value stored in that location. Assign to the variable and you modify that value. So the variable is the memory location, not the name for it.
In Python, a variable is a name used to refer to an object. The value of the variable is that object. So far sounds like the same thing. But assign to the variable and you don't modify the object itself, rather you alter which object the variable refers to. So the variable is the name, not the object.
For this reason, if you're considering the properties of Python in the abstract, or if you're talking about multiple languages at once, then it's useful to use different names for these two different things. To keep things straight you might avoid talking about variables in Python, and refer to what the assignment operator does as "binding" rather than "assignment".
Note that The Python grammar talks about "assignments" as a kind of statement, not "bindings". At least some of the Python documentation calls names variables. So in the context of Python alone, it's not incorrect to do the same. Different definitions for jargon words apply in different contexts.
In, for example, C, a variable is a location in memory identified by a specific name. For example, int i; means that there is a 4-byte (usually) variable identified by i. This memory location is allocated regardless of whether a value is assigned to it yet. When C runs i = 1000, it is changing the value stored in the memory location i to 1000.
In python, the memory location and size is irrelevant to the interpreter. The closest python comes to a "variable" in the C sense is a value (e.g. 1000) which exists as an object somewhere in memory, with or without a name attached. Binding it to a name happens by i = 1000. This tells python to create an integer object with a value of 1000, if it does not already exist, and bind to to the name 'i'. An object can be bound to multiple names quite easily, e.g:
>>> a = [] # Create a new list object and bind it to the name 'a'
>>> b = a # Get the object bound to the name 'a' and bind it to the name 'b'
>>> a is b # Are the names 'a' and 'b' bound to the same object?
True
This explains the difference between the terms, but as long as you understand the difference it doesn't really matter which you use. Unless you're pedantic.
I'm not sure the name/binding description is the easiest to understand, for example I've always been confused by it even if I've a somewhat accurate understanding of how Python (and cpython in particular) works.
The simplest way to describe how Python works if you're coming from a C background is to understand that all variables in Python are indeed pointers to objects and for example that a list object is indeed an array of pointers to values. After a = b both a and b are pointing to the same object.
There are a couple of tricky parts where this simple model of Python semantic seems to fail, for example with list augmented operator += but for that it's important to note that a += b in Python is not the same as a = a + b but it's a special increment operation (that can also be defined for user types with the __iadd__ method; a += b is indeed a = a.__iadd__(b)).
Another important thing to understand is that while in Python all variables are indeed pointers still there is no pointer concept. In other words you cannot pass a "pointer to a variable" to a function so that the function can change the variable: what in C++ is defined by
void increment(int &x) {
x += 1;
}
or in C by
void increment(int *x) {
*x += 1;
}
in Python cannot be defined because there's no way to pass "a variable", you can only pass "values". The only way to pass a generic writable place in Python is to use a callback closure.
who said you should? Unless you are discussing issues that are directly related to name binding operations; it is perfectly fine to talk about variables and assignments in Python as in any other language. Naturally the precise meaning is different in different programming languages.
If you are debugging an issue connected with "Naming and binding" then use this terminology because Python language reference uses it: to be as specific and precise as possible, to help resolve the problem by avoiding unnecessary ambiguity.
On the other hand, if you want to know what is the difference between variables in C and Python then these pictures might help.
I would say that the distinction is significant because of several of the differences between C and Python:
Duck typing: a C variable is always an instance of a given type - in Python it isn't the type that a name refers to can change.
Shallow copies - Try the following:
>>> a = [4, 5, 6]
>>> b = a
>>> b[1] = 0
>>> a
[4, 0, 6]
>>> b = 3
>>> a
[4, 0, 6]
This makes sense as a and b are both names that spend some of the time bound to a list instance rather than being separate variables.

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