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The ^= operator is the augmented assignment operator for bitwise Exclusive OR (XOR) and set symmetric difference. It evaluates the operation between the left and right operands, updating the left operand with the computed result in a single statement. Depending on the mutability and type of the left operand, this operation either mutates the object in-place or rebinds the variable name to a newly created object.

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Syntax

x ^= y
This operation is functionally equivalent to the standard assignment combined with the bitwise XOR/symmetric difference operator, though it prioritizes in-place modification if supported by the object: 
x = x ^ y

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Behavior with Integers and Booleans (Bitwise XOR)

When applied to integers, the operator performs a bit-by-bit comparison of the binary representations of the two operands. For each bit position, it applies the following logic:
  • Returns 1 if the bits are different (one is 0 and the other is 1).
  • Returns 0 if the bits are identical (both 0 or both 1).
Because integers in Python are immutable, this operation does not mutate the object in memory. Instead, it computes the new integer and rebinds the variable reference on the left side to point to this new value. 
x = 10      # Binary: 1010
y = 6       # Binary: 0110

x ^= y      # Binary result: 1100 (Decimal: 12)
Because Python’s bool type is a subclass of int (where True is 1 and False is 0), the ^= operator can also be applied to boolean variables. It evaluates to True only if the operands have different boolean values. 
flag = True
flag ^= True   # True ^ True -> False
flag ^= False  # False ^ False -> False

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Behavior with Sets (Symmetric Difference)

When applied to Python set objects, the ^= operator performs an in-place symmetric difference. It updates the left set to retain only the elements found in either the left set or the right set, but not in both. Because sets are mutable, this operation modifies the original object in memory rather than creating a new set. 
s1 = {1, 2, 3}
s2 = {3, 4, 5}

s1 ^= s2    # Modifies s1 in-place

print(s1)   # Output: {1, 2, 4, 5}

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Object Model Implementation

Under the hood, the ^= operator triggers the __ixor__(self, other) special method. According to the Python Data Model, special methods are always resolved on the class of the object, bypassing the instance dictionary. 

# Conceptual representation of the initial method resolution for x ^= y
x = type(x).__ixor__(x, y)
If the left operand’s class implements __ixor__() (as is the case with set), the method mutates the object in-place and returns self, which is then reassigned to the variable x. If the left operand’s class does not implement __ixor__() or the method returns the NotImplemented singleton (which is the case for immutable built-in types like int and bool), Python automatically falls back to evaluating the standard ^ operator (x = x ^ y). This fallback mechanism follows a strict resolution order:
  1. Python attempts to call the left operand’s class-level __xor__(self, other) method.
  2. If __xor__() is missing or returns NotImplemented, Python attempts to call the right operand’s class-level reverse method, __rxor__(self, other).
  3. If both methods return NotImplemented (or are missing), Python raises a TypeError.
  4. If a valid result is computed, the variable x is rebound to that result.

# Conceptual fallback execution chain if __ixor__ is missing or returns NotImplemented
result = type(x).__xor__(x, y)

if result is NotImplemented:
    result = type(y).__rxor__(y, x)

if result is NotImplemented:
    raise TypeError(f"unsupported operand type(s) for ^=: '{type(x).__name__}' and '{type(y).__name__}'")

x = result
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