Immutable vs Mutable types

I'm confused on what an immutable type is. I know the float object is considered to be immutable, with this type of example from my book:

class RoundFloat(float):
    def __new__(cls, val):
        return float.__new__(cls, round(val, 2))

Is this considered to be immutable because of the class structure / hierarchy?, meaning float is at the top of the class and is its own method call. Similar to this type of example (even though my book says dict is mutable):

class SortedKeyDict(dict):
    def __new__(cls, val):
        return dict.__new__(cls, val.clear())

Whereas something mutable has methods inside the class, with this type of example:

class SortedKeyDict_a(dict):
    def example(self):
        return self.keys()

Also, for the last class(SortedKeyDict_a), if I pass this type of set to it:

d = (('zheng-cai', 67), ('hui-jun', 68),('xin-yi', 2))

without calling the example method, it returns a dictionary. The SortedKeyDict with __new__ flags it as an error. I tried passing integers to the RoundFloat class with __new__ and it flagged no errors.

What? Floats are immutable? But can't I do

x = 5.0
x += 7.0
print x # 12.0

Doesn't that "mut" x?

Well you agree strings are immutable right? But you can do the same thing.

s = 'foo'
s += 'bar'
print s # foobar

The value of the variable changes, but it changes by changing what the variable refers to. A mutable type can change that way, and it can also change "in place".

Here is the difference.

x = something # immutable type
print x
func(x)
print x # prints the same thing

x = something # mutable type
print x
func(x)
print x # might print something different

x = something # immutable type
y = x
print x
# some statement that operates on y
print x # prints the same thing

x = something # mutable type
y = x
print x
# some statement that operates on y
print x # might print something different

Concrete examples

x = 'foo'
y = x
print x # foo
y += 'bar'
print x # foo

x = [1, 2, 3]
y = x
print x # [1, 2, 3]
y += [3, 2, 1]
print x # [1, 2, 3, 3, 2, 1]

def func(val):
    val += 'bar'

x = 'foo'
print x # foo
func(x)
print x # foo

def func(val):
    val += [3, 2, 1]

x = [1, 2, 3]
print x # [1, 2, 3]
func(x)
print x # [1, 2, 3, 3, 2, 1]

You have to understand that Python represents all its data as objects. Some of these objects like lists and dictionaries are mutable, meaning you can change their content without changing their identity. Other objects like integers, floats, strings and tuples are objects that can not be changed. An easy way to understand that is if you have a look at an objects ID.

Below you see a string that is immutable. You can not change its content. It will raise a TypeError if you try to change it. Also, if we assign new content, a new object is created instead of the contents being modified.

>>> s = "abc"
>>> id(s)
4702124
>>> s[0] 
'a'
>>> s[0] = "o"
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: 'str' object does not support item assignment
>>> s = "xyz"
>>> id(s)
4800100
>>> s += "uvw"
>>> id(s)
4800500

You can do that with a list and it will not change the objects identity

>>> i = [1,2,3]
>>> id(i)
2146718700
>>> i[0] 
1
>>> i[0] = 7
>>> id(i)
2146718700

To read more about Python's data model you could have a look at the Python language reference:

Python 2 datamodel
Python 3 datamodel

Immutable vs Mutable types

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