The `is` operator behaves unexpectedly with non-cached integers

tl;dr:

As the reference manual states:

A block is a piece of Python program text that is executed as a unit.
The following are blocks: a module, a function body, and a class definition.
Each command typed interactively is a block.

This is why, in the case of a function, you have a single code block which contains a single object for the numeric literal
1000, so id(a) == id(b) will yield True.

In the second case, you have two distinct code objects each with their own different object for the literal 1000 so id(a) != id(b).

Take note that this behavior doesn’t manifest with int literals only, you’ll get similar results with, for example, float literals (see here).

Of course, comparing objects (except for explicit is None tests ) should always be done with the equality operator == and not is.

_{Everything stated here applies to the most popular implementation of Python, CPython. Other implementations might differ so no assumptions should be made when using them.}

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Longer Answer:

To get a little clearer view and additionally verify this seemingly odd behaviour we can look directly in the code objects for each of these cases using the dis module.

For the function func:

Along with all other attributes, function objects also have a __code__ attribute that allows you to peek into the compiled bytecode for that function. Using dis.code_info we can get a nice pretty view of all stored attributes in a code object for a given function:

>>> print(dis.code_info(func))
Name:              func
Filename:          <stdin>
Argument count:    0
Kw-only arguments: 0
Number of locals:  2
Stack size:        2
Flags:             OPTIMIZED, NEWLOCALS, NOFREE
Constants:
   0: None
   1: 1000
Variable names:
   0: a
   1: b

We’re only interested in the Constants entry for function func. In it, we can see that we have two values, None (always present) and 1000. We only have a single int instance that represents the constant 1000. This is the value that a and b are going to be assigned to when the function is invoked.

Accessing this value is easy via func.__code__.co_consts[1] and so, another way to view our a is b evaluation in the function would be like so:

>>> id(func.__code__.co_consts[1]) == id(func.__code__.co_consts[1]) 

Which, of course, will evaluate to True because we’re referring to the same object.

For each interactive command:

As noted previously, each interactive command is interpreted as a single code block: parsed, compiled and evaluated independently.

We can get the code objects for each command via the compile built-in:

>>> com1 = compile("a=1000", filename="", mode="single")
>>> com2 = compile("b=1000", filename="", mode="single")

For each assignment statement, we will get a similar looking code object which looks like the following:

>>> print(dis.code_info(com1))
Name:              <module>
Filename:          
Argument count:    0
Kw-only arguments: 0
Number of locals:  0
Stack size:        1
Flags:             NOFREE
Constants:
   0: 1000
   1: None
Names:
   0: a

The same command for com2 looks the same but has a fundamental difference: each of the code objects com1 and com2 have different int instances representing the literal 1000. This is why, in this case, when we do a is b via the co_consts argument, we actually get:

>>> id(com1.co_consts[0]) == id(com2.co_consts[0])
False

Which agrees with what we actually got.

Different code objects, different contents.

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Note: I was somewhat curious as to how exactly this happens in the source code and after digging through it I believe I finally found it.

During compilations phase the co_consts attribute is represented by a dictionary object. In compile.c we can actually see the initialization:

/* snippet for brevity */

u->u_lineno = 0;
u->u_col_offset = 0;
u->u_lineno_set = 0;
u->u_consts = PyDict_New();  

/* snippet for brevity */

During compilation this is checked for already existing constants. See @Raymond Hettinger’s answer below for a bit more on this.

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Caveats:

• Chained statements will evaluate to an identity check of True

  It should be more clear now why exactly the following evaluates to True:

   >>> a = 1000; b = 1000;
   >>> a is b
  

  In this case, by chaining the two assignment commands together we tell the interpreter to compile these together. As in the case for the function object, only one object for the literal 1000 will be created resulting in a True value when evaluated.

• Execution on a module level yields True again:

  As previously mentioned, the reference manual states that:

  … The following are blocks: a module …

  So the same premise applies: we will have a single code object (for the module) and so, as a result, single values stored for each different literal.

• The same doesn’t apply for mutable objects:

Meaning that unless we explicitly initialize to the same mutable object (for example with a = b = []), the identity of the objects will never be equal, for example:

    a = []; b = []
    a is b  # always evaluates to False

Again, in the documentation, this is specified:

after a = 1; b = 1, a and b may or may not refer to the same object with the value one, depending on the implementation, but after c = []; d = [], c and d are guaranteed to refer to two different, unique, newly created empty lists.