Python Basics — Frozenset

Frozenset

A frozenset is an immutable version of a set. Once created, you cannot add, remove, or modify its elements.

Creating Frozensets

fs = frozenset([1, 2, 3, 2, 1])
print(fs)       # frozenset({1, 2, 3})
print(type(fs)) # <class 'frozenset'>

# From a set
s = {4, 5, 6}
fs = frozenset(s)
print(fs)  # frozenset({4, 5, 6})

# Empty frozenset
empty = frozenset()
print(empty)  # frozenset()

Immutability

fs = frozenset([1, 2, 3])

# ❌ All mutation methods are unavailable
# fs.add(4)       # AttributeError
# fs.remove(1)    # AttributeError
# fs.discard(2)   # AttributeError
# fs.pop()        # AttributeError
# fs.clear()      # AttributeError

Frozenset as Dictionary Key

Since frozensets are hashable (immutable), they can be used as dictionary keys:

# Group permissions
permissions = {
    frozenset({"read"}): "viewer",
    frozenset({"read", "write"}): "editor",
    frozenset({"read", "write", "admin"}): "admin",
}

user_perms = frozenset({"read", "write"})
print(permissions[user_perms])  # editor

Frozenset as Set Element

A frozenset can be an element of another set:

# Set of sets (using frozensets)
groups = {
    frozenset({1, 2}),
    frozenset({3, 4}),
    frozenset({1, 2}),  # duplicate — removed
}
print(groups)
# {frozenset({3, 4}), frozenset({1, 2})}

You cannot put a regular set inside another set because sets are mutable (unhashable).

Frozenset Operations

All non-mutating set operations work:

a = frozenset({1, 2, 3})
b = frozenset({3, 4, 5})

print(a | b)   # frozenset({1, 2, 3, 4, 5})
print(a & b)   # frozenset({3})
print(a - b)   # frozenset({1, 2})
print(a ^ b)   # frozenset({1, 2, 4, 5})

print(a.issubset(b))    # False
print(a.isdisjoint(b))  # False

Operations between set and frozenset return the type of the left operand:

s = {1, 2, 3}
fs = frozenset({3, 4, 5})

result1 = s | fs
print(type(result1))  # <class 'set'>

result2 = fs | s
print(type(result2))  # <class 'frozenset'>

When to Use Frozenset vs Set

Use Frozenset When…	Use Set When…
Need hashable set (dict key)	Need to add/remove elements
Need set as element of another set	Data will change over time
Want to ensure immutability	Working with dynamic collections
Representing constants	Normal set operations with mutations

Summary

• frozenset() creates an immutable set
• Cannot add, remove, or modify elements
• Hashable — can be dict keys or set elements
• Supports all read-only set operations (union, intersection, etc.)
• In-place operations (update, add, remove) are not available
• Operations between set and frozenset return the left operand’s type

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