Python Variables and Memory Model

Memory

Computer memory is a very long series of on/off switches, called bits (short for binary digit). Eight consecutive bits form a byte; 4 or 8 bytes form a word (depending on machine architecture).

We put something in memory by toggling the bits into some meaningful configuration — in Python, the “somethings” we put in memory are called objects.

Interpreting memory: the integer type

A word of memory can be interpreted as an arithmetic expression in binary — e.g. \(1 \cdot 2^{32} + 1 \cdot 2^{31} + 1 \cdot 2^{30} + 0 \cdot 2^{29} + \cdots + 1 \cdot 2^0 = 3{,}931{,}377{,}233\).

When Python executes x = 3931377233 it toggles the bits at x’s memory location to this value and remembers to interpret that region as an (unsigned 32-bit) integer — its type. A value’s type ultimately dictates which functions are compatible with it.

Addresses and id

Memory is divided into addressed words. We can determine any object’s address with id:

>>> 42
42
>>> id(42)
4384160760

Variables

A variable is a nickname we give to an address in memory.

Assigning

>>> x = 3931377233
>>>

Assignment toggles the bits at the memory location nicknamed x. Nothing is printed, because the imperative here is to perform an action (a state change to memory), not to evaluate an expression.

Retrieving

Once x has been assigned a value, we retrieve it by evaluating it in the REPL — a variable evaluates to the value it was assigned, and can stand in for that value inside larger expressions:

>>> x
3931377233
>>> x // 100
39313772

Evaluating a name that has never been assigned raises a NameError:

>>> bear
NameError: name 'bear' is not defined

Meaningful names

Variable names should convey meaning. x = 2; y = 3; z = x*y is not meaningful, but width = 2; height = 3; area = width*height is — and area keeps working even after width/height change, which is another reason we use variables that can vary.

Naming rules

Variable names must start with a letter (a-z, A-Z) or underscore (_). Starting a name with a digit is a SyntaxError; digits are otherwise allowed.

>>> 1 = "one"
SyntaxError: cannot assign to literal
>>> x1 = 1
>>>

Reassignment

= in Python means assignment (“gets”), not mathematical equality:

>>> x = 1        # x "gets" 1
>>> x = x + 1    # x "gets" x+1
>>> x
2

In mathematics, \(x = x + 1 \implies 0 = 1\), a contradiction — so this would be an “illegal” statement. In Python it’s perfectly valid, because = is a one-time action performed left-to-right, not a persistent equality claim.