Week 7


This is the first of three lectures on inheritance. This lecture discusses the general principles involved in defining classes in an inheritance hierarchy and using the hierarchy to find attributes of objects. It focuses on the rules needed to understand single inheritance, showing an example using counters. The second lecture discusses multiple inheritance and generalizes these rules; it actually includes code that illustrates how classes reference each other and how attributes are found by Python in complicated inheritance hierarchies. The third lecture discusses various concrete uses of inheritance and how we can use inheritance to simplify real programming.

Just an inheritance (of money) makes the life of descendants easier, inheritance (of attributes) makes derived classes easier to write.

Class Inheritance

At present we know about defining classes and constructing objects that are instances of classes. We have explored various relationships between an object and the class from which it was constructed (including adding attributes to objects after they are constructed and adding attributes to classes after they are defined).

We have studed the Fundamental Equation of Object-Oriented Programming (FEOOP) to determine how Python locates attributes for objects, mostly meaning how methods are called on objects: by first trying to locate the attribute in the object itself, and if that fails, locating the attribute in the class from which the object was constructed. Objects mostly store their own state attributes (data), while the classes they are constructed from mostly store their behavior attributes (methods). So objects keep their own state but share the methods that operate on them; sometimes, though, objects can store special methods that apply only to them and class object store state that is shared by objects as well.

To get to full object-oriented programming, we must also learn how to define derived classes from base classes (aka create subclasses from superclasses) and learn how objects constructed from these derived/sub classes behave in regards to inherited state and behavior: specifically, we will learn that all classes are defined in an inheritance hierarchy and learn how attibutes of instance objects can found by searching the objects themselves first, and if needed search the inheritance hierarchy.

Fundamentally, what inheritance is about is writing small derived classes that reuse attributes from base classes in a natural way. The attribute location process is captured by augmenting the meaning of The Fundamental Equation of Object-Oriented Programming for class inheritance hierarchies (below we discuss a simple extension for single-inheritance, which is the most common kind of inheritance; in the next lecture we discuss the more complicated but complete extension for multiple inheritance).

We can define a trivial class with no state/behavior (not even an __init__ method) in Python by just writing

class C: pass
Note the lack of parentheses after the class name C (just a colon). This means that the class C is implicitly a class derived from the "object" class (yes, there is a class named "object" in Python: try x = object() and print(x)); the object class acts as the root of Python's inheritance hierarchy. The object class itself is defined in the builtins module and serves as the base class by default of any classes defined with no explicit base class. In fact, this class defines very many methods (e.g., __repr__, __setattr__, etc.). We can call the repr function (which calls the __repr__ method) on objects constructed from classes that don't define __repr___ and Python will still find a __repr__ method too call. Because, if we do not define such methods in our classes, they are inherited; when we do define a method like __repr__ in a derived class, it overrides (see this term defined and explained below) the __repr__ method inherited from the "object" class. If we want to specify one or more different base classes when definining a class, we must put their names between the parentheses, separated by commas. So, the meaning of class C: -with no parentheses- is the same as
class C(object): pass
In both cases we illustrate the base/derived inheritance relationship with the simple hierarchy: the derived class refers upward to its direct base class.
object ^ | C
There actually is a reference in the derived class C to the base class "object" which we will use in the next lecture: the arrow's direction is meaningful. Note that many other classe that we know inherit only from the object class (list, set, and dict), and we shall soon see that defaultdict inherits from dict). Here is how we show the inheritance hierarchy of these classes.
object ^ ^ ^ / | \ list set dict ^ | defaultdict
If we use only single-inheritance the resulting inheritance hierarchy is an N-ary tree with object at its root. Derived classes are children of their base classes. Note that the derived classes can themselves be base classes of other derived classes (e.g., dict). Eventually (tracing from any class towards the root of the inheritance hierarchy) -following arrows from a derived class to its base class- will lead upward in the inheritance tree until the root (the object class) is reached. The situation gets a bit more complicated when multiple-inheritance is allowed (more details in the next lecture). So in this lecture we will being seeing class definitions like
class Derived_Class(Base_Class): # single-inheritance
and in the next lecture like
class Derived_Class(Base_Class1, Base_Class2, ...): # multiple-inheritance
Many languages support just single-inheritance (a derived class can have only one direct base class: Java and Smalltalk are examples of such languages) but Python (like C++) supports multiple inheritance: a derived class can have many direct base classes. Once we understand the general principal of locating attributes in a single-inheritance hierarchy, we can generalize the look up rules for multiple-inheritance hierarchies (where our knowledge of pre-order traversal, from the lectures on trees, will be important to our understanding; forgot what that was? go back and read about it). Finally, note an asymmetry: a derived class specifically states the name of (and refers to) its base classes, but a base class says nothing about (and doesn't refer to or know anything about) its derived classes. There is no way for a base class to know what derived classes will inherit from it: so derived classes can access attributes in their base classes, but base classes cannot access attributes in their derived classes.

The Fundamental Equation of Object-Oriented Programming (generalizing for single-Inheritance)

At present we know that instance objects refer to the class objects they are constructed from, and we can use the type function on any instance to return a reference to the class object that it was constructed from. When we look up an attibute of an instance, Python first looks for the attribute in the namespace of the instance object itself, but it if doesn't find the attribute there, it looks for the attribute in the class the object was constructed from. We captured this rule in the Fundamental Equation of Object-Oriented Programming (shown again below) in its current form, but soon expanded for inheritance. So, if m is a method, we have seen that

o.m(...) -> type(o).m(o,...) for method attributes o.a -> type(o).a for data attributes
When locating a method attribute for instance o, if it is not found in o itself (it typically isn't) Python uses the attribute in the type(o) class: the class o was constructed from, calling that method with o as the first argument (which is why methods defined in classes all have the first parameter named self). By this mechanism, an object doesn't need to store in its own namespace all the methods that operate on it. The methods are mostly stored (and shared) in the class object for the instance object, and located there as needed. This mechanism works for non-method attributes too: if any data attribute is not found in the instance object's namespace (although state is typically found there), Python will try to locate it by using the namespace of the class the instance object was constructed from. So, it is possible for objects to share data in its class's namespaces, just as methods are shared. A useful example of data sharing might occur in a Person class. Suppose that we need to store how many fingers every person (object constructed from that class) has. We could store this information by adding an attribute to every person object (e.g., person1.fingers = 10). But the vast majority of people have 10 fingers, so we could store Person.fingers = 10 (an attribute in the Person class). Now if we don't store the fingers attribute in the person1 object, it will be found in the Person class object, with value 10. If person1 has fewer than 10 fingers, we can store person1.fingers = 9; now, for person1, the fingers attribute will be found in the object itself, not in its class. Using this approach, we can save space by storing the fingers attribute only for people not having 10 fingers (likely to be a small percentage of all the people objects). We now generalize this look up mechanism for single-inheritance hierarchies: Python first tries to find the attribute in the instance object; if Python fails, it next tries to find the attribute in the class object from which the instance was constructed; if Python fails, it tries to find the attribute in the base class of the class from which the instance was constructed; ... If Python does not find an attribute in a class, it next tries to find it in the base class of that class, and continues until it reaches the object class: if Python fails to find the attribute in the object class, it raises an AttributeError exception. Pictorally, where Python looks for an o.attribute
object <-- looks here last (root of hierarchy) ^ | ... ^ | class <-- looks here 3rd ^ | Look here 1st --> o --> class <-- looks here 2nd (instance) (constructed from) ^ | class <-- doesn't look here ^ | class <-- doesn't look here

Simple Inheritance Example

Examine the following two simple classes (which are in the counts.py module that you can download with this lecture). We can examine and use the Counter class by itself (it is a fully working class), but Counter also acts as the base class of the derived Modular_Counter class. Together, most interesting issues concerning inheritance are illustrated simply in these two classes, in which Counter is the base class and Modular_Counter is the derived class.

class Counter: #implicitly use object as its base class hierarchy_depth = 1 # object is depth 0, Counter is 1 beneath it counter_base = 0 # how many times Counter.__init__ called def __init__(self,init_value=0): assert init_value >= 0,\ 'Counter.__init__ init_value('+str(init_value)+') < 0' self._value = init_value Counter.counter_base += 1 def __str__(self): return str(self._value) def reset(self): self._value = 0 def inc(self): self._value += 1 def value_of(self): return self._value
class Modular_Counter(Counter): # explicitly use Counter as its base class hierarchy_depth = Counter.hierarchy_depth + 1 # 1 more than Counter's depth counter_derived = 0 # how many times Modular_Counter.__init__ called def __init__(self,init_value,modulus): assert modulus >= 1,\ 'Modular_Counter.__init__ modulus('+str(init_value)+') < 1' assert 0 <= init_value < modulus,\ 'Modular_Counter.__init__ init_value('+str(init_value)+') not in [0,'+str(modulus)+')' Counter.__init__(self,init_value) self._modulus = modulus Modular_Counter.counter_derived += 1 def __str__(self): return Counter.__str__(self)+' mod '+str(self._modulus) # Note, calling self.value_of() and self.reset is equivalent to (and # preferred to) calling Counter.value_of(self) and Counter.reset(self) # But it is critical that Counter.inc(self) is called that way, because # calling self.inc() would be an infinitely recursive call to inc. def inc(self): if self.value_of() == self._modulus - 1: self.reset() else: Counter.inc(self) def modulus_of(self): return self._modulus
The main script at the bottom of the module creates Counter and Modular_Counter objects and then allows the user to type in commands using the names c and mc (including defining new/more names). You can put more code down there using c and mc, or enter commands that are executed by calling the exec function.
if __name__ == '__main__': import prompt c = Counter(0) mc = Modular_Counter(0,3) while True: try: exec(prompt.for_string('Command')) except Exception as report: import traceback traceback.print_exc()
---------- The Counter base class First we will discuss the Counter class, and then discuss the Modular_Counter class, which is derived from the base class Counter. The Counter class defines two class state names (hierarchy_depth, which doesn't change and counter_base which is incremented in __init__) and the class method names __init__, __str__, reset, inc, and value_of.
(1) hierarchy_depth is an int representing the depth of the Counter class in the N-ary inheritance tree: it is 1, because it is below the root of the tree, the object class (which has depth 0). (2) counter_base is an int that counts how many times __init__ in the Counter class is called (it is called when we construct Counter objects, but also when we construct Modular_Counter objects: which calls __init__ directly: it is common for __init__ in the derived class to call __init__ in its base class (base classes for multiple inheritance). (3) __init__ initalizes each Counter object to have one piece of state: an int that is always (so it must start) >= 0 representing the counter's value. It verifies this property of init_value first, and then increments counter_base.
So, understand the following difference: the Counter class object stores the attributes hierarchy_depth and counter_base attribute (as well as all the other method attributes). Each object constructed from the Counter class stores its own _value attribute (and shares the attributes in the Counter class using the Fundamental Equation of Object-Oriented Programming).
(4) __str__ is a query that returns a string representing the Counter object's _value attribute. (5) reset is a command that resets the Counter object's _value attribute to 0 (6) inc is a command that increases the Counter object's _value attribute by 1 (7) value_of is a query that returns the _value attribute of the Counter object The difference between (4) and (7) is that (4) returns a str while (7) returns an int.
Using the code in main, we can construct and experiment with objects from the Counter class: looking up state/calling methods on c (an object already constructed in the code) or constructing more Counter objects and doing the same on them. For example, try
c = Counter(0) # OK print(c.hiearchy_depth) # prints 1 print(c.counter_base) # prints 1 (because c = ...) c.inc() # OK c.inc() # OK c.inc() # OK print(c) # prints 3 print(c.value_of()) # prints 3
---------- The Modular_Counter derived class Now we will move on to discussing the Modular_Counter class. We will classify every attribute usable in this class as
(a)a new attribute defined in the class (not an inherited attribute) (b)an inherited attribute (not defined/overridden) (c)an inherited attribute (re)defined in the class (overriding an inherited one)
These last two options rely on an understanding of what it means for a derived class to override an inherited attribute. A derived class overrides an inherited attribute if it defines an attribute (using the same name) as an attribute it inherits: one defined in its base class, the base class of its base class, etc. all the way back to the object class at the root of the inheritance hierarchy. When we describe the Modular_Counter class below, we will discuss alld its defined attributes in these terms. Generally a modular counter is a special kind of counter. In fact, derived classes are often specializations of base classes: but for inheritance to be natural, all operations on the base class must make sense on the derived class, although the derived class may change the meaning of (override) the inherited attributes and define new attributes). Modular counters can store values between 0 up to but not including the modulus (so the biggest a value can get is modulus-1): think of a counter for strikes in baseball as a modulus 3 counter. A batter goes from 0 strikes to 1 strikes to 2 strikes to being out, with the next batter starting again back at 0 strikes. The Modular_Counter class defines two class names storing state: hierarchy_depth is (c), which doesn't change and counter_derived is (a) which is incremented in __init__) and the class method names __init__ is (c), __str__ is (c), inc is (c), and modulus_of is (a). It also inherits and does not override (all are b) the attributes counter_base, reset, and value_of.
(1) hierarchy_depth is an int representing the depth of the Modular_Counter class in the N-ary inheritance tree: it is 2, because it is derived from the Counter class, whose depth is 1. (2) counter_derived is an int that counts how many times __init__ in the Modular_Counter class is called (in this two-class hirerarchy, it is called only when we construct Modular_Counter objects). (3) __init__ initalizes each Modular_Counter object to have two pieces of state: first, an int that remains unchanged and must be >= 1 representing the counter's modulus; second, an int that is always (so it must start) >= 0 and < the modulus, representing the counter's value. It verifies these properties of modulus and init_value first, and increments counter_derived. Note that the _value attribute is not directly defined in this __init__ methdod, but instead is defined in the instance object when __init__ calls Counter.__init__ on this object (which adds to its attributes). The self passed to Counter's __init__ is updated. (4) __str__ is a query that returns a string representing the Modular_Counter object's _value attribute, by calling Counter.__str__(self) concatenated with the word ' mod ' and the modulus attribute. (5) inc is a command that resets the Modular_Counter object's _value attribute to 0 if the current value is one less than the modulus, otherwise it increments the Modular_Counter's _value attribute by 1, by calling Counter.inc(self). (6) value_of is a query that returns the value attribute of the Modular_Counter object.
Generally in programming, the methods in a class should refer to a state attribute (by a.o) ONLY IF IT IS DEFINED IN THAT SAME CLASS. That is why in Modular_Counter's __init__, _value is not defined directly, but is instead defined/initialized by calling Counter's __init__; it is also why Modular_Counter's inc method calls the inherited methods reset, inc, and value_of, instead of directly manipulating its _value attribute. In this approach, we consider state names to be private and should be used only within the class that is responsible for defining and manipulating that attribute. It is that class that ensures the integrity/invariant of that attribute. In contrast, generally method names are considered public and usable with any object (unless they start with _ or __). Because we can refer to all the state and behavior attributes in Python, Python programmers don't always follow this rule (although we have seen how to use __setattr__ to disallow changing an attribute in an object). Java and C++ programmers must define each attribute as public (usable anywhere) or private (usable only within the class in which it is defined) and the computer ensures and enforces that private attributes are examined/changed only in the class that defines them (there are other, more subtle options in these languages). ---------- Constructing an Object from a Derived Class When we call Modular_Counter(0,3) -or just Modular_Counter(modulus=3)- Python constructs an instance object whose class/type is Modular_Counter; this instance object starts with an empty namespace (dictionary). It checks the 2 assertions about the arguments: both are True, so Python calls Counter.__init__(init_value). Counter.__init__ checks its assertion: it is True, so it adds the binding _value to the namespace of the constructed Modular_Counter object passed to self and binds it to an int_value (here 0); it also increments Counter.counter_base: the attribute counter_base defined in the Counter class object Then, returning to Modular_Counter.__init__ Python adds the binding _modulus to the namespace of the constructed Modular_Counter object (so this object now has two attributes in its dictionary: _value and _modulus) and binds it to the modulus (here 3); it also increments Modular_Counter.counter_derived: the attribute counter_derived defined in the Modular_Counter class object. So, at this point the newly constructed Modular_Counter object has two attributes (_value (storing 0) and _modulus (storing 3)), the Counter class object has two attributes (hierarchy_depth (storing 1) and counter_base (storing 1), along with all its methods), and the Modular_Counter class object has two attributes (hierarchy_depth (storing 2) and counter_derived (storing 1), along iwth all its methods).
Note that executing x = Modular_Counter(0,3) means type(x) is Modular_Counter; while executing x = Counter(0) means type(x) is Counter. The type function returns the class object from which any instance object is constructed.
---------- Avoiding Infinite Recursion in Methods called defined in Derived Classes Note carefully the __str__ method defined in the Modular_Counter class overrides the __str__ method this class inherits from the Counter class.
def __str__(self): return Counter.__str__(self)+' mod '+str(self._modulus)
Suppose we define x = Modular_Counter(0,3). Then the Fundamental Equation of Object-Oriented Programming tells us str(x) is executed as x.str() which is executed as type(x).__str__(x) or Modular_Counter.__str__(x). Which executes Counter.__str__(x)+... which returns '0'+.... Now, what would happen if we instead defined
def __str__(self): return str(self)+' mod '+str(self._modulus)
Now, str(x) is still executed as x.__str__() which is still executed as type(x).__str__(x) or Modular_Counter.__str__(x). But now the body of this function calls str(x) which is executed again as type(x).__str__(x) or Modular_Counter.__str__(x) so we have created infinite recursion with this change. So generally, in a method that overrides an inherited method, if we want to call the inherited method, we must preface it with the class in which the inherited method is to be called. This was also done in the call to inc in the Modular_Counter's inc method. Notice that it was not done for the call to reset, which appears as just self.reset(); the reason is that the reset method inherited from the Counter class is not overridden in Modular_Counter, so when making a call to reset on a Modular_Counter object, if finds the reset attribute note in the Modular_Counter class, but in the Counter class, so it calls that method. This is all by the augmented Fundamental Equation of Object-Oriented Programming rule. Let us predict (and verify) what is printed (and why) in the following code.
c = Counter(0) # OK m = Modular_Counter(0,3) # OK print(c.hiearchy_depth) # 1 print(c.counter_base) # 2 (from both c = ... and m = ...) print(c.counter_derived) # AttributeError exception print(m.hiearchy_depth) # 2 print(m.counter_base) # 2 (same as c.counter_base) print(m.counter_derived) # 1 (from only m = ...) c.inc() # OK c.inc() # OK c.inc() # OK print(c.value_of()) # 3 print(c.modulus_of()) # AttributeError exception m.inc() # OK m.inc() # OK m.inc() # OK print(m.value_of()) # 0 print(m.modulus_of()) # 3

Inheritance Design Rules

In languages like Java/C++, if a class adds an attribute (state) to an object (mostly in __init__) then only THAT class is allowed to access that state directly as an attribute. That is, if x = C() and C's __init__ contains self.a = ... then if another class contains any attempt to refer to x.a or rebind x.a (e.g., x.a = ....) it will raise an exception. Python does NOT have this restriction, but it is still considered bad design form to write such accesses/rebinding.

To solve this problem, each class should define methods to access/set all the attributes it defines. That is why in there are reset/inc/value_of methods in the Counter class: so the ModularCounter class can examine/update the _value attribute defined in Counter. So,

1) If a class adds an attribute to an object (e.g., in __init__) then methods defined in only that class should access the attribute directly. 2) If other classes (including derived/subclasses) need to access/update the information stored in that attribute, then the defining class should define methods that do the job, which the other class should call.
Some languages use the terms accessors/getters for methods that return the value of such attributres, and mutators/setters for methods that rebind an attribute to refer to a different value.


1) Decribes what happen using the following defintions and code

class B: def __init__(self): self.a = 1 class D: def __init__(self): self.a = 2 b = B() d = D() print(b.a) print(d.a)
2) Suppose that we define the __str__ method in the Counter class to return a string representing value as a roman numeral; what will the statments print(Modular_Counter(2,3)) print? 3) Suppose that we define the print_it method in the Counter class as follows:
def print_it(self): print(self.__str__())
What is the result of defining c = Counter(0) and c.print_it(); same for mc = Modular__Counter(0,3) and mc.print_it()? Does defining print_it as follows change the result printed? Explain how each determines what value to print and what value it prints.
def print_it(self): print(str(self))
4) Define __repr__ functions in Count and Modular_Counter classes. 5) Suppose that we defined
l = [counter(0), Modular_Counter(0,3), Modular_Counter(0,3), Counter(0)]
What would be printed if we executed the code
for i in range(3): for c in l: c.inc() print(l)