operator_overloading.md

Operator overloading

This practical assumes you are familiar with the basics of object-oriented programming in Python.

Operator overloading, in an object-oriented programming language, is the process of customising the behaviour of operators (e.g. +, *, / and -) on user-defined types. This practical aims to show you that operator overloading is very easy to do in Python.

Overview

In Python, when you add two numbers together:

a = 5
b = 10
r = a + b
print(r)

What actually goes on behind the scenes is this:

r = a.__add__(b)
print(r)

In other words, whenever you use the + operator on two variables (the operands to the + operator), the Python interpreter calls the __add__ method of the first operand (a), and passes the second operand (b) as an argument.

So it is very easy to use the + operator with our own classes - all we have to do is implement a method called __add__.

Arithmetic operators

Let's play with an example - a class which represents a 2D vector:

class Vector(object):
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __str__(self):
        return 'Vector({}, {})'.format(self.x, self.y)

Note that we have implemented the special __str__ method, which allows our Vector instances to be converted into strings.

If we try to use the + operator on this class, we are bound to get an error:

v1 = Vector(2, 3)
v2 = Vector(4, 5)
print(v1 + v2)

But all we need to do to support the + operator is to implement a method called __add__:

class Vector(object):
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __str__(self):
        return 'Vector({}, {})'.format(self.x, self.y)

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

And now we can use + on Vector objects - it's that easy:

v1 = Vector(2, 3)
v2 = Vector(4, 5)
print('{} + {} = {}'.format(v1, v2, v1 + v2))

Our __add__ method creates and returns a new Vector which contains the sum of the x and y components of the Vector on which it is called, and the Vector which is passed in. We could also make the __add__ method work with scalars, by extending its definition a bit:

class Vector(object):
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __add__(self, other):
        if isinstance(other, Vector):
            return Vector(self.x + other.x,
                          self.y + other.y)
        else:
            return Vector(self.x + other, self.y + other)

    def __str__(self):
        return 'Vector({}, {})'.format(self.x, self.y)

So now we can add both Vectors and scalars numbers together:

v1 = Vector(2, 3)
v2 = Vector(4, 5)
n  = 6

print('{} + {} = {}'.format(v1, v2, v1 + v2))
print('{} + {} = {}'.format(v1, n,  v1 + n))

Other nuemric and logical operators can be supported by implementing the appropriate method, for example:

• Multiplication (*): __mul__
• Division (/): __div__
• Negation (-): __neg__
• In-place addition (+=): __iadd__
• Exclusive or (^): __xor__

Take a look at the official documentation for a full list of the arithmetic and logical operators that your classes can support.

Equality and comparison operators

Adding support for equality (==, !=) and comparison (e.g. >=) operators is just as easy. Imagine that we have a class called Label, which represents a label in a lookup table. Our Label has an integer label, a name, and an RGB colour:

class Label(object):
    def __init__(self, label, name, colour):
        self.label  = label
        self.name   = name
        self.colour = colour

In order to ensure that a list of Label objects is ordered by their label values, we can implement a set of functions, so that Label classes can be compared using the standard comparison operators:

import functools

@functools.total_ordering
class Label(object):
    def __init__(self, label, name, colour):
        self.label  = label
        self.name   = name
        self.colour = colour

    def __str__(self):
        rgb = ''.join(['{:02x}'.format(c) for c in self.colour])
        return 'Label({}, {}, #{})'.format(self.label, self.name, rgb)

    def __repr__(self):
        return str(self)

    def __eq__(self, other):
        return self.label == other.label

    def __lt__(self, other):
        return self.label < other.label

We also added __str__ and __repr__ methods to the Label class so that Label instances will be printed nicely.

Now we can compare and sort our Label instances:

l1 = Label(1, 'Parietal',  (255,   0,   0))
l2 = Label(2, 'Occipital', (  0, 255,   0))
l3 = Label(3, 'Temporal',  (  0,   0, 255))

print('{} >  {}: {}'.format(l1, l2, l1  > l2))
print('{} <  {}: {}'.format(l1, l3, l1  < l3))
print('{} != {}: {}'.format(l2, l3, l2 != l3))
print(sorted((l3, l1, l2)))

The @functools.total_ordering is a convenience decorator which, given a class that implements equality and a single comparison function (__lt__ in the above code), will "fill in" the remainder of the comparison operators. If you need very specific or complicated behaviour, then you can provide methods for all of the comparison operators, e.g. __gt__ for >, __ge__ for >=, etc.).

But if you just want the operators to work in the conventional manner, you can just use the @functools.total_ordering decorator, and provide __eq__, and just one of __lt__, __le__, __gt__ or __ge__.

Refer to the official documentation for all of the details on supporting comparison operators.

You may see the __cmp__ method in older code bases - this provides a C-style comparison function which returns <0, 0, or >0 based on comparing two items. This has been superseded by the rich comparison operators and is no longer used in Python 3.

The indexing operator []

The indexing operator ([]) is generally used by "container" types, such as the built-in list and dict classes.

At its essence, there are only three types of behaviours that are possible with the [] operator. All that is needed to support them are to implement three special methods in your class, regardless of whether your class will be indexed by sequential integers (like a list) or by hashable values (like a dict):

• Retrieval is performed by the __getitem__ method
• Assignment is performed by the __setitem__ method
• Deletion is performed by the __delitem__ method

Note that, if you implement these methods in your own class, there is no requirement for them to actually provide any form. However if you don't, you will probably confuse users of your code - make sure you explain it all in your comprehensive documentation!

The following contrived example demonstrates all three behaviours:

class TwoTimes(object):

    def __init__(self):
        self.__deleted  = set()
        self.__assigned = {}

    def __getitem__(self, key):
        if key in self.__deleted:
            raise KeyError('{} has been deleted!')
        elif key in self.__assigned:
            return self.__assigned[key]
        else:
            return key * 2

    def __setitem__(self, key, value):
        self.__assigned[key] = value

    def __delitem__(self, key):
        self.__deleted.add(key)

Guess what happens whenever we index a TwoTimes object:

tt = TwoTimes()
print('TwoTimes[{}] = {}'.format(2,     tt[2]))
print('TwoTimes[{}] = {}'.format(6,     tt[6]))
print('TwoTimes[{}] = {}'.format('abc', tt['abc']))

For some unknown reason, the TwoTimes class allows us to override the value for a specific key:

print(tt[4])
tt[4] = 'this is not 4 * 4'
print(tt[4])

And we can also "delete" keys:

print(tt['12345'])
del tt['12345']

# this is going to raise an error
print(tt['12345'])

If you wish to support the Python start:stop:step slice notation, you simply need to write your __getitem__ and __setitem__ methods so that they can detect slice objects:

class TwoTimes(object):

    def __init__(self, max):
        self.__max = max

    def __getitem__(self, key):
        if isinstance(key, slice):
            start = key.start or 0
            stop  = key.stop  or self.__max
            step  = key.step  or 1
        else:
            start = key
            stop  = key + 1
            step  = 1

        return [i * 2 for i in range(start, stop, step)]

tt = TwoTimes(10)

print(tt[5])
print(tt[3:7])
print(tt[::2])

It is possible to sub-class the built-in list and dict classes if you wish to extend their functionality in some way. However, if you are writing a class that should mimic the one of the list or dict classes, but work in a different way internally (e.g. a dict-like object which uses a different hashing algorithm), the Sequence and MutableMapping classes are a better choice - you can find them in the collections.abc module.

The call operator ()

Remember how everything in Python is an object, even functions? When you call a function, a method called __call__ is called on the function object. We can implement the __call__ method on our own class, which will allow us to "call" objects as if they are functions.

For example, the TimedFunction class allows us to calculate the execution time of any function:

The dot operator .

Python allows us to override the . (dot) operator which is used to access the attributes and methods of an object. attributes and methods of an object. This is a fairly niche feature, and you need to be careful that you don't unintentionally introduce recursive attribute lookups into your code.

class Vector(object):
    def __init__(self, xyz):
        self.__xyz = list(xyz)

    def __str__(self):
        return 'Vector({})'.format(', '.join(self.__xyz))

    def __getattr__(self, key):
        key = ['xyz'.index(c) for c in key]
        return [self.__xyz[c] for c in key]

    def __setattr__(self, key, value):
        pass        # key = ['xyz'.index(c) for c in key]

v = Vector((4, 5, 6))

print('xyz: ', v.xyz)
print('yz:  ', v.yz)
print('zxy: ', v.xzy)
print('y:   ', v.y)

Other special methods