Chapter 1. The Python Data Model

Guido’s sense of the aesthetics of language design is amazing. I’ve met many fine language designers who could build theoretically beautiful languages that no one would ever use, but Guido is one of those rare people who can build a language that is just slightly less theoretically beautiful but thereby is a joy to write programs in.1

Jim Hugunin, Creator of Jython, cocreator of AspectJ, architect of the .Net DLR

One of the best qualities of Python is its consistency. After working with Python for a while, you are able to start making informed, correct guesses about features that are new to you.

However, if you learned another object-oriented language before Python, you may have found it strange to use len(collection) instead of collection.len(). This apparent oddity is the tip of an iceberg that, when properly understood, is the key to everything we call Pythonic. The iceberg is called the Python data model, and it describes the API that you can use to make your own objects play well with the most idiomatic language features.

You can think of the data model as a description of Python as a framework. It formalizes the interfaces of the building blocks of the language itself, such as sequences, iterators, functions, classes, context managers, and so on.

While coding with any framework, you spend a lot of time implementing methods that are called by the framework. The same happens when you leverage the Python data model. The Python interpreter invokes special methods to perform basic object operations, often triggered by special syntax. The special method names are always written with leading and trailing double underscores (i.e., __getitem__). For example, the syntax obj[key] is supported by the __getitem__ special method. In order to evaluate my_collection[key], the interpreter calls my_collection.__getitem__(key).

The special method names allow your objects to implement, support, and interact with basic language constructs such as:

  • Iteration

  • Collections

  • Attribute access

  • Operator overloading

  • Function and method invocation

  • Object creation and destruction

  • String representation and formatting

  • Managed contexts (i.e., with blocks)

Magic and Dunder

The term magic method is slang for special method, but when talking about a specific method like __getitem__, some Python developers take the shortcut of saying “under-under-getitem” which is ambiguous, because the syntax __x has another special meaning.2 Being precise and pronouncing “under-under-getitem-under-under” is tiresome, so I follow the lead of author and teacher Steve Holden and say “dunder-getitem.” All experienced Pythonistas understand that shortcut. As a result, the special methods are also known as dunder methods.3

A Pythonic Card Deck

The following is a very simple example, but it demonstrates the power of implementing just two special methods, __getitem__ and __len__.

Example 1-1 is a class to represent a deck of playing cards.

Example 1-1. A deck as a sequence of cards
import collections

Card = collections.namedtuple('Card', ['rank', 'suit'])

class FrenchDeck:
    ranks = [str(n) for n in range(2, 11)] + list('JQKA')
    suits = 'spades diamonds clubs hearts'.split()

    def __init__(self):
        self._cards = [Card(rank, suit) for suit in self.suits
                                        for rank in self.ranks]

    def __len__(self):
        return len(self._cards)

    def __getitem__(self, position):
        return self._cards[position]

The first thing to note is the use of collections.namedtuple to construct a simple class to represent individual cards. Since Python 2.6, namedtuple can be used to build classes of objects that are just bundles of attributes with no custom methods, like a database record. In the example, we use it to provide a nice representation for the cards in the deck, as shown in the console session:

>>> beer_card = Card('7', 'diamonds')
>>> beer_card
Card(rank='7', suit='diamonds')

But the point of this example is the FrenchDeck class. It’s short, but it packs a punch. First, like any standard Python collection, a deck responds to the len() function by returning the number of cards in it:

>>> deck = FrenchDeck()
>>> len(deck)

Reading specific cards from the deck—say, the first or the last—should be as easy as deck[0] or deck[-1], and this is what the __getitem__ method provides:

>>> deck[0]
Card(rank='2', suit='spades')
>>> deck[-1]
Card(rank='A', suit='hearts')

Should we create a method to pick a random card? No need. Python already has a function to get a random item from a sequence: random.choice. We can just use it on a deck instance:

>>> from random import choice
>>> choice(deck)
Card(rank='3', suit='hearts')
>>> choice(deck)
Card(rank='K', suit='spades')
>>> choice(deck)
Card(rank='2', suit='clubs')

We’ve just seen two advantages of using special methods to leverage the Python data model:

  • The users of your classes don’t have to memorize arbitrary method names for standard operations (“How to get the number of items? Is it .size(), .length(), or what?”).

  • It’s easier to benefit from the rich Python standard library and avoid reinventing the wheel, like the random.choice function.

But it gets better.

Because our __getitem__ delegates to the [] operator of self._cards, our deck automatically supports slicing. Here’s how we look at the top three cards from a brand new deck, and then pick just the aces by starting on index 12 and skipping 13 cards at a time:

>>> deck[:3]
[Card(rank='2', suit='spades'), Card(rank='3', suit='spades'),
Card(rank='4', suit='spades')]
>>> deck[12::13]
[Card(rank='A', suit='spades'), Card(rank='A', suit='diamonds'),
Card(rank='A', suit='clubs'), Card(rank='A', suit='hearts')]

Just by implementing the __getitem__ special method, our deck is also iterable:

>>> for card in deck:  # doctest: +ELLIPSIS
...   print(card)
Card(rank='2', suit='spades')
Card(rank='3', suit='spades')
Card(rank='4', suit='spades')

The deck can also be iterated in reverse:

>>> for card in reversed(deck):  # doctest: +ELLIPSIS
...   print(card)
Card(rank='A', suit='hearts')
Card(rank='K', suit='hearts')
Card(rank='Q', suit='hearts')

Ellipsis in doctests

Whenever possible, the Python console listings in this book were extracted from doctests to ensure accuracy. When the output was too long, the elided part is marked by an ellipsis (...) like in the last line in the preceding code. In such cases, we used the # doctest: +ELLIPSIS directive to make the doctest pass. If you are trying these examples in the interactive console, you may omit the doctest directives altogether.

Iteration is often implicit. If a collection has no __contains__ method, the in operator does a sequential scan. Case in point: in works with our FrenchDeck class because it is iterable. Check it out:

>>> Card('Q', 'hearts') in deck
>>> Card('7', 'beasts') in deck

How about sorting? A common system of ranking cards is by rank (with aces being highest), then by suit in the order of spades (highest), then hearts, diamonds, and clubs (lowest). Here is a function that ranks cards by that rule, returning 0 for the 2 of clubs and 51 for the ace of spades:

suit_values = dict(spades=3, hearts=2, diamonds=1, clubs=0)

def spades_high(card):
    rank_value = FrenchDeck.ranks.index(card.rank)
    return rank_value * len(suit_values) + suit_values[card.suit]

Given spades_high, we can now list our deck in order of increasing rank:

>>> for card in sorted(deck, key=spades_high):  # doctest: +ELLIPSIS
...      print(card)
Card(rank='2', suit='clubs')
Card(rank='2', suit='diamonds')
Card(rank='2', suit='hearts')
... (46 cards ommitted)
Card(rank='A', suit='diamonds')
Card(rank='A', suit='hearts')
Card(rank='A', suit='spades')

Although FrenchDeck implicitly inherits from object,4 its functionality is not inherited, but comes from leveraging the data model and composition. By implementing the special methods __len__ and __getitem__, our FrenchDeck behaves like a standard Python sequence, allowing it to benefit from core language features (e.g., iteration and slicing) and from the standard library, as shown by the examples using random.choice, reversed, and sorted. Thanks to composition, the __len__ and __getitem__ implementations can hand off all the work to a list object, self._cards.

How About Shuffling?

As implemented so far, a FrenchDeck cannot be shuffled, because it is immutable: the cards and their positions cannot be changed, except by violating encapsulation and handling the _cards attribute directly. In Chapter 11, that will be fixed by adding a one-line __setitem__ method.

How Special Methods Are Used

The first thing to know about special methods is that they are meant to be called by the Python interpreter, and not by you. You don’t write my_object.__len__(). You write len(my_object) and, if my_object is an instance of a user-defined class, then Python calls the __len__ instance method you implemented.

But for built-in types like list, str, bytearray, and so on, the interpreter takes a shortcut: the CPython implementation of len() actually returns the value of the ob_size field in the PyVarObject C struct that represents any variable-sized built-in object in memory. This is much faster than calling a method.

More often than not, the special method call is implicit. For example, the statement for i in x: actually causes the invocation of iter(x), which in turn may call x.__iter__() if that is available.

Normally, your code should not have many direct calls to special methods. Unless you are doing a lot of metaprogramming, you should be implementing special methods more often than invoking them explicitly. The only special method that is frequently called by user code directly is __init__, to invoke the initializer of the superclass in your own __init__ implementation.

If you need to invoke a special method, it is usually better to call the related built-in function (e.g., len, iter, str, etc). These built-ins call the corresponding special method, but often provide other services and—for built-in types—are faster than method calls. See, for example, “A Closer Look at the iter Function” in Chapter 14.

Avoid creating arbitrary, custom attributes with the __foo__ syntax because such names may acquire special meanings in the future, even if they are unused today.

Emulating Numeric Types

Several special methods allow user objects to respond to operators such as +. We will cover that in more detail in Chapter 13, but here our goal is to further illustrate the use of special methods through another simple example.

We will implement a class to represent two-dimensional vectors—that is Euclidean vectors like those used in math and physics (see Figure 1-1).

2D vectors
Figure 1-1. Example of two-dimensional vector addition; Vector(2, 4) + Vector(2, 1) results in Vector(4, 5).

The built-in complex type can be used to represent two-dimensional vectors, but our class can be extended to represent n-dimensional vectors. We will do that in Chapter 14.

We will start by designing the API for such a class by writing a simulated console session that we can use later as a doctest. The following snippet tests the vector addition pictured in Figure 1-1:

>>> v1 = Vector(2, 4)
>>> v2 = Vector(2, 1)
>>> v1 + v2
Vector(4, 5)

Note how the + operator produces a Vector result, which is displayed in a friendly manner in the console.

The abs built-in function returns the absolute value of integers and floats, and the magnitude of complex numbers, so to be consistent, our API also uses abs to calculate the magnitude of a vector:

>>> v = Vector(3, 4)
>>> abs(v)

We can also implement the * operator to perform scalar multiplication (i.e., multiplying a vector by a number to produce a new vector with the same direction and a multiplied magnitude):

>>> v * 3
Vector(9, 12)
>>> abs(v * 3)

Example 1-2 is a Vector class implementing the operations just described, through the use of the special methods __repr__, __abs__, __add__ and __mul__.

Example 1-2. A simple two-dimensional vector class
from math import hypot

class Vector:

    def __init__(self, x=0, y=0):
        self.x = x
        self.y = y

    def __repr__(self):
        return 'Vector(%r, %r)' % (self.x, self.y)

    def __abs__(self):
        return hypot(self.x, self.y)

    def __bool__(self):
        return bool(abs(self))

    def __add__(self, other):
        x = self.x + other.x
        y = self.y + other.y
        return Vector(x, y)

    def __mul__(self, scalar):
        return Vector(self.x * scalar, self.y * scalar)

Note that although we implemented four special methods (apart from __init__), none of them is directly called within the class or in the typical usage of the class illustrated by the console listings. As mentioned before, the Python interpreter is the only frequent caller of most special methods. In the following sections, we discuss the code for each special method.

String Representation

The __repr__ special method is called by the repr built-in to get the string representation of the object for inspection. If we did not implement __repr__, vector instances would be shown in the console like <Vector object at 0x10e100070>.

The interactive console and debugger call repr on the results of the expressions evaluated, as does the %r placeholder in classic formatting with the % operator, and the !r conversion field in the new Format String Syntax used in the str.format method.


Speaking of the % operator and the str.format method, you will notice I use both in this book, as does the Python community at large. I am increasingly favoring the more powerful str.format, but I am aware many Pythonistas prefer the simpler %, so we’ll probably see both in Python source code for the foreseeable future.

Note that in our __repr__ implementation, we used %r to obtain the standard representation of the attributes to be displayed. This is good practice, because it shows the crucial difference between Vector(1, 2) and Vector('1', '2')—the latter would not work in the context of this example, because the constructor’s arguments must be numbers, not str.

The string returned by __repr__ should be unambiguous and, if possible, match the source code necessary to re-create the object being represented. That is why our chosen representation looks like calling the constructor of the class (e.g., Vector(3, 4)).

Contrast __repr__ with __str__, which is called by the str() constructor and implicitly used by the print function. __str__ should return a string suitable for display to end users.

If you only implement one of these special methods, choose __repr__, because when no custom __str__ is available, Python will call __repr__ as a fallback.


“Difference between __str__ and __repr__ in Python” is a Stack Overflow question with excellent contributions from Pythonistas Alex Martelli and Martijn Pieters.

Arithmetic Operators

Example 1-2 implements two operators: + and *, to show basic usage of __add__ and __mul__. Note that in both cases, the methods create and return a new instance of Vector, and do not modify either operand—self or other are merely read. This is the expected behavior of infix operators: to create new objects and not touch their operands. I will have a lot more to say about that in Chapter 13.


As implemented, Example 1-2 allows multiplying a Vector by a number, but not a number by a Vector, which violates the commutative property of multiplication. We will fix that with the special method __rmul__ in Chapter 13.

Boolean Value of a Custom Type

Although Python has a bool type, it accepts any object in a boolean context, such as the expression controlling an if or while statement, or as operands to and, or, and not. To determine whether a value x is truthy or falsy, Python applies bool(x), which always returns True or False.

By default, instances of user-defined classes are considered truthy, unless either __bool__ or __len__ is implemented. Basically, bool(x) calls x.__bool__() and uses the result. If __bool__ is not implemented, Python tries to invoke x.__len__(), and if that returns zero, bool returns False. Otherwise bool returns True.

Our implementation of __bool__ is conceptually simple: it returns False if the magnitude of the vector is zero, True otherwise. We convert the magnitude to a Boolean using bool(abs(self)) because __bool__ is expected to return a boolean.

Note how the special method __bool__ allows your objects to be consistent with the truth value testing rules defined in the “Built-in Types” chapter of The Python Standard Library documentation.


A faster implementation of Vector.__bool__ is this:

    def __bool__(self):
        return bool(self.x or self.y)

This is harder to read, but avoids the trip through abs, __abs__, the squares, and square root. The explicit conversion to bool is needed because __bool__ must return a boolean and or returns either operand as is: x or y evaluates to x if that is truthy, otherwise the result is y, whatever that is.

Overview of Special Methods

The “Data Model” chapter of The Python Language Reference lists 83 special method names, 47 of which are used to implement arithmetic, bitwise, and comparison operators.

As an overview of what is available, see Tables 1-1 and 1-2.


The grouping shown in the following tables is not exactly the same as in the official documentation.

Table 1-1. Special method names (operators excluded)
Category Method names

String/bytes representation

__repr__, __str__, __format__, __bytes__

Conversion to number

__abs__, __bool__, __complex__, __int__, __float__, __hash__, __index__

Emulating collections

__len__, __getitem__, __setitem__, __delitem__, __contains__


__iter__, __reversed__, __next__

Emulating callables


Context management

__enter__, __exit__

Instance creation and destruction

__new__, __init__, __del__

Attribute management

__getattr__, __getattribute__, __setattr__, __delattr__, __dir__

Attribute descriptors

__get__, __set__, __delete__

Class services

__prepare__, __instancecheck__, __subclasscheck__

Table 1-2. Special method names for operators
Category Method names and related operators

Unary numeric operators

__neg__ -, __pos__ +, __abs__ abs()

Rich comparison operators

__lt__ <, __le__ <=, __eq__ ==, __ne__ !=, __gt__ >, __ge__ >=

Arithmetic operators

__add__ +, __sub__ -, __mul__ *, __truediv__ /, __floordiv__ //, __mod__ %, __divmod__ divmod() , __pow__ ** or pow(), __round__ round()

Reversed arithmetic operators

__radd__, __rsub__, __rmul__, __rtruediv__, __rfloordiv__, __rmod__, __rdivmod__, __rpow__

Augmented assignment arithmetic operators

__iadd__, __isub__, __imul__, __itruediv__, __ifloordiv__, __imod__, __ipow__

Bitwise operators

__invert__ ~, __lshift__ <<, __rshift__ >>, __and__ &, __or__ |, __xor__ ^

Reversed bitwise operators

__rlshift__, __rrshift__, __rand__, __rxor__, __ror__

Augmented assignment bitwise operators

__ilshift__, __irshift__, __iand__, __ixor__, __ior__


The reversed operators are fallbacks used when operands are swapped (b * a instead of a * b), while augmented assignments are shortcuts combining an infix operator with variable assignment (a = a * b becomes a *= b). Chapter 13 explains both reversed operators and augmented assignment in detail.

Why len Is Not a Method

I asked this question to core developer Raymond Hettinger in 2013 and the key to his answer was a quote from The Zen of Python: “practicality beats purity.” In “How Special Methods Are Used”, I described how len(x) runs very fast when x is an instance of a built-in type. No method is called for the built-in objects of CPython: the length is simply read from a field in a C struct. Getting the number of items in a collection is a common operation and must work efficiently for such basic and diverse types as str, list, memoryview, and so on.

In other words, len is not called as a method because it gets special treatment as part of the Python data model, just like abs. But thanks to the special method __len__, you can also make len work with your own custom objects. This is a fair compromise between the need for efficient built-in objects and the consistency of the language. Also from The Zen of Python: “Special cases aren’t special enough to break the rules.”


If you think of abs and len as unary operators, you may be more inclined to forgive their functional look-and-feel, as opposed to the method call syntax one might expect in an OO language. In fact, the ABC language—a direct ancestor of Python that pioneered many of its features—had an # operator that was the equivalent of len (you’d write #s). When used as an infix operator, written x#s, it counted the occurrences of x in s, which in Python you get as s.count(x), for any sequence s.

Chapter Summary

By implementing special methods, your objects can behave like the built-in types, enabling the expressive coding style the community considers Pythonic.

A basic requirement for a Python object is to provide usable string representations of itself, one used for debugging and logging, another for presentation to end users. That is why the special methods __repr__ and __str__ exist in the data model.

Emulating sequences, as shown with the FrenchDeck example, is one of the most widely used applications of the special methods. Making the most of sequence types is the subject of Chapter 2, and implementing your own sequence will be covered in Chapter 10 when we create a multidimensional extension of the Vector class.

Thanks to operator overloading, Python offers a rich selection of numeric types, from the built-ins to decimal.Decimal and fractions.Fraction, all supporting infix arithmetic operators. Implementing operators, including reversed operators and augmented assignment, will be shown in Chapter 13 via enhancements of the Vector example.

The use and implementation of the majority of the remaining special methods of the Python data model are covered throughout this book.

Further Reading

The “Data Model” chapter of The Python Language Reference is the canonical source for the subject of this chapter and much of this book.

Python in a Nutshell, 2nd Edition (O’Reilly) by Alex Martelli has excellent coverage of the data model. As I write this, the most recent edition of the Nutshell book is from 2006 and focuses on Python 2.5, but there have been very few changes in the data model since then, and Martelli’s description of the mechanics of attribute access is the most authoritative I’ve seen apart from the actual C source code of CPython. Martelli is also a prolific contributor to Stack Overflow, with more than 5,000 answers posted. See his user profile at Stack Overflow.

David Beazley has two books covering the data model in detail in the context of Python 3: Python Essential Reference, 4th Edition (Addison-Wesley Professional), and Python Cookbook, 3rd Edition (O’Reilly), coauthored with Brian K. Jones.

The Art of the Metaobject Protocol (AMOP, MIT Press) by Gregor Kiczales, Jim des Rivieres, and Daniel G. Bobrow explains the concept of a metaobject protocol (MOP), of which the Python data model is one example.

1 Story of Jython, written as a Foreword to Jython Essentials (O’Reilly, 2002), by Samuele Pedroni and Noel Rappin.

2 See “Private and “Protected” Attributes in Python”.

3 I personally first heard “dunder” from Steve Holden. Wikipedia credits Mark Johnson and Tim Hochberg for the first written records of “dunder” in responses to the question “How do you pronounce __ (double underscore)?” in the python-list on September 26, 2002: Johnson’s message; Hochberg’s (11 minutes later).

4 In Python 2, you’d have to be explicit and write FrenchDeck(object), but that’s the default in Python 3.

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