Introduction

In most programming languages you learn early on to separate values from
variables: a variable is a labelled box, and you drop a value inside it. Python
quietly breaks that mental model. In Python, everything is an object — integers,
strings, lists, functions, even classes themselves — and a variable is never the box.
It is a name that points at an object living somewhere in memory.

That single idea explains a surprising number of "wait, what?" moments: why changing
one list seems to change another, why a is b is sometimes True and sometimes
False for equal values, and why a function can modify your list but not your integer.
Let's unpack it.

id and type

Every object in Python carries two things we can always ask about: what it is and
where it is.

  • type(obj) tells you the object's type (its class).
  • id(obj) returns a unique identifier for the object. In CPython (the reference implementation) this identifier is the object's memory address. 
>>> a = 89
>>> type(a)
<class 'int'>
>>> id(a)
140234981234567
>>> type("Best School")
<class 'str'>
>>> type([1, 2, 3])
<class 'list'>

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Two names refer to the same object if and only if they share the same id. That
is exactly what the is operator checks, while == only checks whether the values
are equal:

>>> a = [1, 2, 3]
>>> b = [1, 2, 3]
>>> a == b      # same value?
True
>>> a is b      # same object?
False
>>> id(a) == id(b)
False

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Mutable objects

A mutable object can be changed in place after it is created — its id stays
the same while its contents change.

The mutable built-in types are:

  • list
  • dict
  • set
  • bytearray 
>>> my_list = [1, 2, 3]
>>> id(my_list)
140234981000000
>>> my_list.append(4)
>>> my_list
[1, 2, 3, 4]
>>> id(my_list)
140234981000000   # SAME id — we mutated the very same object

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Immutable objects

An immutable object can never be changed after creation. Any operation that looks
like a change actually builds a brand-new object.

The immutable built-in types are:

  • Numbers: int, float, complex
  • str (string)
  • tuple
  • frozenset
  • bytes 
>>> n = 10
>>> id(n)
140234980000100
>>> n += 5          # looks like a mutation...
>>> n
15
>>> id(n)
140234980000260   # ...but it's a DIFFERENT object

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The name n was simply re-pointed at a new integer object 15. The original 10
was never touched.

Assignment vs. referencing

This is the distinction that trips everyone up.

  • Referencing (aliasing): b = a does not copy anything. It makes b a second name for the same object a points to.
  • Assignment to a name: a = something re-binds the name a to a new object. It never changes the object a previously referred to. 
>>> a = [1, 2, 3]
>>> b = a          # b is an ALIAS of a — same object
>>> b is a
True
>>> a = a + [4]    # re-binds the NAME a to a new list
>>> a
[1, 2, 3, 4]
>>> b
[1, 2, 3]          # b still points at the original object
>>> a is b
False

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How an immutable object is stored in memory

Because immutable objects can never change, CPython is free to reuse them. When
you write the literal 89 in two places, the interpreter can safely hand back the
same object both times — there is no risk that someone mutates it and surprises
everyone else. This is why identity results can look strange for immutables.

Memory schemas (the pictures)

Schema 1 — aliasing a mutable object 

a = [1, 2, 3]
b = a
b.append(4)

   Names            Objects in memory
   -----            -----------------
   a ---------\
               >---> [ 1, 2, 3, 4 ]   (id: 0x1000)
   b ---------/

Both names point to ONE list. Mutating through b is visible through a.
print(a)  ->  [1, 2, 3, 4]

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Schema 2 — rebinding vs. mutating 

l1 = [1, 2, 3]
l2 = l1
l1 = l1 + [4]        # rebinding: builds a NEW list

   Names            Objects in memory
   -----            -----------------
   l2 --------> [ 1, 2, 3 ]        (id: 0x2000)
   l1 --------> [ 1, 2, 3, 4 ]     (id: 0x2500)  <- new object

print(l2)  ->  [1, 2, 3]     (unchanged)


Compare with in-place mutation:
l1 = [1, 2, 3]
l2 = l1
l1 += [4]            # in-place extend: SAME object

   l1 -------\
              >---> [ 1, 2, 3, 4 ]   (id: 0x2000, unchanged id)
   l2 -------/

print(l2)  ->  [1, 2, 3, 4]

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That + vs += difference is real and worth internalizing:

>>> a = [1, 2, 3, 4]
>>> before = id(a)
>>> a = a + [5]        # new object
>>> id(a) == before
False
>>> a = [1, 2, 3]
>>> before = id(a)
>>> a += [4]           # in-place, same object
>>> id(a) == before
True

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Why it matters: how Python treats mutable and immutable objects differently

  • Immutable objects are safe to share. Since nobody can change them, CPython reuses and caches them freely. Equality and identity often coincide for small, common immutables.
  • Mutable objects are dangerous to share accidentally. Two names pointing at the same list means a change through one name is seen through the other. This is a feature when you want it and a bug when you don't — which is why you copy lists (new = old[:] or list(old)) when you need independence.

How arguments are passed to functions

Python passes arguments by assignment (often called "pass by object reference").
The parameter name inside the function becomes a new name bound to the same object
the caller passed in. What happens next depends entirely on whether that object is
mutable and on what you do with it.

Immutable argument — the caller is unaffected:

def increment(n):
    n += 1          # rebinds the LOCAL name to a new int
                    # the caller's object is untouched

a = 1
increment(a)
print(a)            # 1

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Mutable argument, mutated in place — the caller sees the change:

def increment(n):
    n.append(4)     # mutates the SAME list object

l = [1, 2, 3]
increment(l)
print(l)            # [1, 2, 3, 4]

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Mutable argument, but rebinding inside — the caller is unaffected:

def assign_value(n, v):
    n = v           # rebinds the LOCAL name only

l1 = [1, 2, 3]
l2 = [4, 5, 6]
assign_value(l1, l2)
print(l1)           # [1, 2, 3]   (unchanged — we only moved a local name)

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The rule of thumb: mutating an object (calling a method like .append, or index
assignment) affects everyone who shares it; rebinding a name (n = ...) affects
only that name.

Integer pre-allocation and the small-integer cache

Here is where identity gets genuinely surprising:

>>> a = 89
>>> b = 89
>>> a is b
True                # same object!

>>> a = 1000
>>> b = 1000
>>> a is b
False               # different objects

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When CPython starts up, it pre-allocates a pool of small integer objects and keeps
them around for the entire lifetime of the program. Any time you use one of these
values, you get the same cached object instead of a freshly created one. That's why
89 is 89 is True but 1000 is 1000 is not.

NSMALLPOSINTS and NSMALLNEGINTS

The size of that cache is defined in CPython's source (Objects/longobject.c) by two
constants:

  • NSMALLPOSINTS = 257 → the positive integers 0 through 256
  • NSMALLNEGINTS = 5 → the negative integers -5 through -1

Together they cache the integers in the range -5 to 256, which is
5 + 257 = 262 pre-allocated integer objects.

>>> a = 256
>>> b = 256
>>> a is b
True                # 256 is cached

>>> a = 257
>>> b = 257
>>> a is b
False               # 257 is outside the cache

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Why those particular values?

The range -5 to 256 was chosen because these are the most frequently used
integers in real programs: loop counters, small indices, byte values (0–255),
flags, and the like. Caching them avoids constantly allocating and freeing the same
tiny objects, which is a real performance and memory win. Values outside that range
are rare enough that caching them wouldn't pay off.

⚠️ Never rely on this in your code. The small-integer cache is an implementation
detail of CPython. Use == to compare values and reserve is for identity checks
like x is None.

The special case of tuples and frozensets

Tuples and frozensets are immutable containers — you cannot add, remove, or replace
their elements. But there's a subtle catch: immutability of the container does not
make its contents immutable. A tuple can hold a mutable object, and that object can
still change:

>>> t = (1, 2, [3, 4])
>>> t[2].append(5)
>>> t
(1, 2, [3, 4, 5])       # the tuple's list element changed!
>>> t[2] = [9]          # but you can't rebind a slot
Traceback (most recent call last):
  ...
TypeError: 'tuple' object does not support item assignment

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So the tuple itself never changed which objects it references — that binding is
frozen — but a mutable object it references can still be mutated internally. This is
also why a tuple containing a list is not hashable (and therefore can't be a dict
key or set member), while a tuple of only immutables is.

Also note the empty-tuple singleton and single-element quirks:

>>> a = ()
>>> b = ()
>>> a is b
True                # CPython uses a single shared empty tuple

>>> a = (1)         # NOT a tuple — just the int 1 in parentheses
>>> type(a)
<class 'int'>
>>> a = (1,)        # the trailing comma makes it a tuple
>>> type(a)
<class 'tuple'>

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Conclusion

Once you internalize that variables are names, not boxes, and that every value is
an object with an identity (id), a type (type), and a mutability, Python's behavior
stops being mysterious:

  • Assignment binds a name; it never copies an object.
  • Aliasing lets two names share one object — harmless for immutables, powerful (and occasionally dangerous) for mutables.
  • Functions receive references by assignment, so mutation leaks out but rebinding doesn't.
  • CPython caches small integers (-5 to 256) and the empty tuple for performance.
  • Immutable containers freeze their bindings, not necessarily their contents.

Keep == for values, is for identity, and you'll write code that behaves exactly
the way you expect.

Thanks for reading! If this helped clarify Python's object model, drop a ❤️ and a
comment — and connect with me on LinkedIn.