Polymorphism and Operator Overloading
Polymorphism means literally “having many forms.” In computer science, it is when the same interface can be used for different types. In most cases the interface is a function name. Many of the built-in Python functions are polymorphic; the len function can be applied to lists, dictionaries, and strings. Polymorphic functions are often said to be overloaded. The function’s signature is the unique description of the number and type of the arguments, and if relevant, the class to which it belongs. The signature is the means by which the interpreter determines which version of the function to apply. This is called overload resolution.
Method Overriding
A particular type of polymorphism is subtype polymorphism. We can define a function in a subclass that has the same name as in the base class, but which applies to instances of the subclass. This is overriding the method.
Example
class Animal:
def __init__(self, name, species):
self.name=name
self.species=species
def speak(self):
raise NotImplementedError("Subclasses must implement this")
class Feline(Animal):
def speak(self):
return "Roar"
class Canine(Animal):
def speak(self):
return "Howl"
class Bird(Animal):
def speak(self):
return "Squawk"
zoo=[]
zoo.append(Feline("Raja","lion"))
zoo.append(Canine("Sasha","wolf"))
zoo.append(Bird("Polly","parrot"))
for critter in zoo:
print(critter.name+" says "+critter.speak())
Notice that in this code the base class throws a NotImplementedError if it is invoked with an instance of Animal. In our code, the Animal class is not intended to be used to create instances, and we do not have a base implementation of speak, so we make sure to warn the user of our class.
Since Python is mostly dynamically typed, the correct polymorphic instance is determined at runtime. Python uses “duck typing” (if it walks like a duck and quacks like a duck…); the type is determined dynamically from context. If your usage does not agree with what the interpreter thinks it should be, it will throw a type exception.
These built-in functions specify whether a given object is an instance of a particular class, or is a subclass of another specified class. All return Booleans.
In Jupyter or Spyder, enter the classes shown above, then in the interpreter window or cell type these lines. (Recall that >>> is the interpreter prompt; you may see something different.)
>>>print(issubclass(Animal, Canine))
>>>print(issubclass(Canine, Animal))
>>>print(issubclass(Animal, Feline))
>>>print(issubclass(Feline, Canine))
>>>print(issubclass(Feline, Feline))
>>>print(isinstance(zoo[0], Animal))
>>>print(isinstance(zoo[0], Canine))
>>>print(isinstance(zoo[0], Feline))
Operator Overloading
Operators are themselves functions and can be overloaded. In Python the arithmetic operators are already overloaded, since floats and integers are different within the computer. The addition operator + is also overloaded for other purposes, such as to concatenate strings or lists.
print(1+2)
print(1.+2.)
print("1"+"2")
We can overload operators in our classes so that we can, say, add two instances of our class. Of course “adding” the instances should make sense. Python defines a number of special methods which are distinguised by having a double underscore before and after the name; for this reason they are sometimes called “dunders” or they may be called “magic methods.” We have already encountered the __init__ dunder but there are many others.
Example We would like to create a Point class to define points in a three-dimensional Euclidean space. Points are added by adding corresponding components; i.e. $$ p1=(1,2,3),\ p2=(7,8,9),\ p1+p2=(8,10,12) $$
To implement addition we will use the __add__ dunder. This dunder will take self as its first argument, another instance of Point as its second, and it must return another instance of the class Point, so we invoke the constructor in the dunder.
class Point:
def __init__(self,x,y,z):
self.x=x
self.y=y
self.z=z
def __add__(self,p2):
return Point(self.x+p2.x,self.y+p2.y,self.z+p2.z)
p1=Point(1,2,3)
p2=Point(7,8,9)
p3=p1+p2
print(p3.x,p3.y,p3.z)
We could similarly define subtraction with __sub__.
Exercise
Implement subtraction for points using the rule $x_1-x_2$, $y_1-y_2$, $z_1-z_2).
Example solution
class Point:
def __init__(self,x,y,z):
self.x=x
self.y=y
self.z=z
def __add__(self,p2):
return Point(self.x+p2.x,self.y+p2.y,self.z+p2.z)
def __sub__(self,p2):
return Point(self.x-p2.x,self.y-p2.y,self.z-p2.z)
p1=Point(1,2,3)
p2=Point(7,8,9)
p3=p1+p2
print(p3.x,p3.y,p3.z)
p4=p1-p2
print(p4.x,p4.y,p4.z)
We’d like to be able to print a Point object in the standard mathematical format $(x,y,z)$. To allow print to handle our class we overload the __str__ dunder. The __str__ dunder is used by str, print, and format.
class Point:
def __init__(self,x,y,z):
self.x=x
self.y=y
self.z=z
def __add__(self,p2):
return Point(self.x+p2.x,self.y+p2.y,self.z+p2.z)
def __str__(self):
return "("+str(self.x)+","+str(self.y)+","+str(self.z)+")"
p1=Point(1,2,3)
p2=Point(7,8,9)
p3=p1+p2
print(p3)
There are many other dunders we can use in our classes. Multiplication and division don’t make sense for points, but they can be defined with __mul__ and __truediv__ respectively.
If we define the comparison dunders then we can invoke sort on our class instances.
A list of the most widely used magic methods is here.
Resources
A longer discussion of OOP in Python is available here.