1. EECE 310: Software Engineering
Type Hierarchies and the Substitution Principle

2. Objectives
Apply the Liskov Substitution Principle (LSP) to the design of type hierarchies
Use abstract base classes to solve LSP problem
Decide when to favor composition over inheritance and vice versa

3. NonEmptySet Type
Consider a subtype of IntSet called non-empty set, with the stipulation that it must *never* be empty. i.e., it has at least 1 element always
Constructor takes the element as an argument and adds it to the els vector (the rep)
insert, size, isIn work as before (no change)
remove must make sure it never leaves the set empty, otherwise it throws an EmptySetException

4. NonEmptySet: Remove
public class NonEmptySet extends IntSet { … public void remove(int x) throws EmptySetException { // EFFECTS: If set has at least two elements, // then remove x from the set // Otherwise, throw the EmptySetException …. }

5. RemoveAny procedure
public static boolean removeAny(IntSet s) { // EFFECTS: Remove an arbitrary element from // the IntSet if the set is not empty, return true // Otherwise do nothing and return false if (s.size() == 0) return false; int x = s.choose(); s.remove(x); return true; }

6. Usage of removeAny
IntSet s = new IntSet(); … // Add elements to s while ( removeAny(s) ) { } // s is empty at this point

7. What about this one ?
IntSet s = new NonEmptySet(3); … // Add elements to s while ( removeAny(s) ) { } // control never reaches here !
Can potentially
throw an EmptySet exception !

8. Liskov Substitution principle
Intuition
Users can use and reason about subtypes just using the supertype specification.
Definition
Subtype specification must support reasoning based on the super-type specification according to following rules:
signature rule
methods rule
properties rule
1. The code should behave the same way a supertype would have even when subtype is used

9. Signature Rule
Every call that is type-correct with the super-type objects must also be type-correct with the sub-type objects
Sub-type objects must have all the methods of the super-type
Signatures of the subtype’s implementations must be compatible with the signatures of the corresponding super-type methods

10. Signature Rule in Java
Subtype’s method can have fewer exceptions but NOT throw more exceptions
Arguments and return type should be identical: (stricter than necessary)
Foo clone();
Foo x = y.clone();
Object clone();
Foo x = (Foo) y.clone();
Enforced by the compiler at compile-time
Subtypes can have fewer exceptions
Enforced by the compiler

11. NonEmptySet: Remove
public class NonEmptySet extends IntSet { … public void remove(int x) throws EmptySetException { // EFFECTS: If set has at least two elements, // then remove x // Otherwise, throw the EmptySetException …. }
Violates signature rule – will not compile

12. Will this solve the problem ?
public class NonEmptySet extends IntSet { … public void remove(int x) { // EFFECTS: If set has at least two elements, // then remove x // Otherwise, do nothing …. }

13. What will happen in this case ?
IntSet s = new NonEmptySet(3); … // Add elements to s while ( removeAny(s) ) { } // control never reaches here !
Will loop forever because the set never becomes empty (why ?)

14. What’s the problem here ?
The remove method of NonEmptyIntSet has a different behavior than the remove method of the IntSet ADT (it’s parent type)
In the IntSet ADT, after you call remove(x), you are assured that x is no longer part of the set (provided the set was non-empty prior to the call)
In the NonEmptyIntSet ADT, after you call remove(x), you do not have this assurance anymore which violates the substitution principle

15. Methods rule
A sub-type method can weaken the pre-condition (REQUIRES) of the parent method and strengthen its post-condition (EFFECTS)
Pre-condition rule: presuper=> presub
Post-condition rule: presuper && postsub => postsuper
Both conditions must be satisfied to achieve compatibility between the sub-type and super-type methods

16. Remember … Weakening of pre-condition: REQUIRES less
Example: Parent-type requires a non-empty collection, but the sub-type does not
Example: Parent-type requires a value > 0, sub-type can take a value >=0 in its required clause
Strengthening of post-condition: DOES more
Example: Sub-type returns the elements of the set in sorted order while parent-type returns them in any arbitrary order (sorted => arbitrary)

17. Example of methods rule
Consider a sub-type of IntSet LogIntSet which keeps track of all elements that were ever in the set even after they are removed
public void insert(int x)
// MODIFIES: this
// EFFECTS: Adds x to the set and to the log
Does this satisfy the methods rule ?

18. Is the methods rule satisfied here ?
Consider another sub-type PositiveIntSet which only adds positive Integers to the set
public void insert(int x)
// MODIFIED: this
// EFFECTS: if x >= 0 adds it to this
// else does nothing

19. Back to the NonEmptySet Type
public class NonEmptySet { // Not derived from IntSet // A Non-empty IntSet is a mutable set of integers // whose size is at least 1 always public void removeNonEmpty(int x) { // EFFECTS: If set has at least two elements, // then remove x // Otherwise, do nothing …. }

20. Regular IntSet
public class IntSet extends NonEmptySet { // Overview: A regular IntSet as before public void remove(int x) { // MODIFIES: this // EFFECTS: Removes x from this … }

21. What happens in this code ?
public static void findMax (NonEmptySet s) { int max = s.choose(); iterator g = s.elements(); while (g.hasNext() ) { … }
Can throw an exception if IntSet is passed in as argument

22. What’s the problem here ?
The IntSet type has an operation remove which causes it to violate the invariant property of its parent type NonEmptySet
Calling code may be able to make the set empty by calling remove and then pass it to findMax
Not enough if the derived methods preserve the parent-type’s invariant, the new methods in sub-type must do so as well

23. Properties Rule
Subtype must preserve each property of the super-type in each of its methods
Invariant properties (always true)
Evolution properties (evolve over time)
Examples
Invariant property: The set never becomes empty
Evolution property: The set size never decreases

24. Putting it together: Substitution Principle
Signature rule: If program is type-correct based on super-type specification, it is also type-correct with respect to the sub-type specification.
Methods rule: Ensures that reasoning about calls of super-type methods is valid even if the call goes to code that implements a subtype.
Properties rule: Reasoning about properties of objects based on super-type specification is still valid even when objects belong to the sub-type.

25. Summary of LSP
Liskov Substitution Principle (LSP) is a unifying way of reasoning about the use of sub-types
Signature rule: Syntactic constraint and can be enforced by compiler
Methods rule and properties rule: Pertain to semantics (behavior) and must be enforced by programmer
LSP is essential for locality and modifiability of programs using types and sub-types

26. Group Activity
In the handout

27. Objectives
Apply the Liskov Substitution Principle (LSP) to the design of type hierarchies
Use abstract base classes to solve LSP problem
Decide when to favor composition over inheritance and vice versa

28. Why do we use sub-types ? Define relationships among a group of types
SortedList and UnsortedList are sub-types of List
Specification reuse (common interface)
Using code simply says “give me a list”
Implementation reuse (code sharing)
SortedList need not re-implement all of List’s methods
Modifiability of parent type
Client need not change if parent class implementation changes (if done through public interface)

29. Why not to use sub-types ?
Sub-types are not appropriate in many cases
Sub-type must satisfy Liskov Substitution Principle. In other words, it must not cause existing code to break.
Subtype’s implementation must not depend on the implementation details of the parent type
Common rule of thumb: “Sub-types must model is a special kind of relationship”
Not always as simple or true as we will soon see

30. Example: Rectangle
// A vanilla Rectangle class. public class Rectangle { private double width; private double height; public Rectangle(double w, double h) { width = w; height = h; } public double getWidth() {return width;} public double getHeight() {return height;} public void setWidth(double w) {width = w;} public void setHeight(double h) {height = h;}

31. Example: Square Sub-type ?
Should we model a square as a sub-type of rectangle (isn’t square a “type of” rectangle ?)
We won’t need two instance variables, height and width, but this is a minor irritant
Need to override setHeight and setWidth operations so that width and height cannot be changed independently
Remember, you cannot change the Rectangle class

32. Example: Square
public class Square extends Rectangle { private double width; private double height; public Square(double s) { super(s, s); } public void setWidth(double w) { super.setWidth(w); super.setHeight(w); public void setHeight(double h) { super.setWidth(h); super.setHeight(h);

33. What is the problem here ?
void testRectangle(Rectangle r) { r.setWidth(4); r.setHeight(5); assert( r.getHeight() * r.getWidth() == 20 ); } testRectangle( new Square(3) );

34. Problem
Although Square is a type of rectangle in the real world, a square object is NOT a sub-type of a rectangle object because it is more constrained than the rectangle object
Which rule of LSP does it break ?
We should NOT model square as a sub-type of rectangle because behaviorally, a square object cannot be substituted for a rectangle object.

35. So how do you fix this ?
Square and rectangle should not be in an inheritance relationship with one-another
They are really doing two different things, just so happens they share some (minimal) features
Do not satisfy the LSP (behavioral substitution)
But, how to share code between two ADTs which are not in inherited from each other ?

36. One “Solution”: Abstract base class
public abstract class Quadrilateral { // Represents a generic square or rectangle protected Quad(); // do we need this ? public int getHeight(); public int getWidth(); public abstract void setWidth(); public abstract void setHeight(); }

37. Abstract Base Class
Abstract classes are used for providing partial implementations of data types
Declared using the keyword abstract in Java
May or may not have instance variables
Needs to have constructors if it has instance vars
Has one or more methods partially implemented, other methods are declared as abstract
Sub-classes implement the abstract methods
Can call the base class’s (non-abstract) methods
Need not implement all abstract methods

38. Abstract Classes Vs. Interfaces

39. Class Exercise
Distributed as a handout in class

40. Objectives
Apply the Liskov Substitution Principle (LSP) to the design of type hierarchies
Use abstract base classes to solve LSP problem
Decide when to favor composition over inheritance and vice versa

41. Fragile Base Class Problem
LSP is not the only problem with inheritance. Even if LSP is satisfied, there are other issues
Assume that you add a new method to IntSet
public void addAll(Collection<int> c) {
// EFFECTS: Adds all elements of c to IntSet
Iterator<int> ci = c.elements();
while (ci.hasNext()){
this.add( c.next() ); }

42. InstrumentedIntSet
Consider an example InstrumentedIntSet which keeps track of the number of elements ever added to the IntSet ADT (different from its size). Assume this type inherits from IntSet
Must add a new field to keep track of count
Override the add method to increment count
Override the addAll method to increment count

43. InstrumentedIntSet: Inheritance
public class InstrumentedIntSet extends IntSet {
private int addCount; // The number of attempted element insertions
public InstrumentedIntSet() { super(); addCount = 0; }
public boolean add(Object o) {
addCount++;
return super.add(o); }
public boolean addAll(Collection<int> c) {
addCount += c.size();
return super.addAll(c);
public int getAddCount() {
return addCount;

44. What’s the problem here ?
Consider the following code:
IntSet s = new InstrumentedIntSet();
Vector v = new Vector<int>();
// Assume that vector v has 3 int elements
s.addAll( v );
int i = s.getAddCount( ); // What does it return ?
How will you fix this problem ?
1. Modify addAll to not do the increment, but what if base class does not call the add method?
2. Write your own version of addAll in the derived class to do the iteration (no reuse)

45. Solution: Use Composition
Instead of making InstrumentedIntSet a sub-type of IntSet, make it contain an IntSet
In Java, it holds a reference to an IntSet rather than a copy, so be careful to not expose it
Do not have to worry about substitution principle (though that is not a problem in this example)
Make both classes implement a common Set interface if you want them to be inter-changeable

46. InstrumentedIntSet: Composition-1
public class InstrumentedIntSet implements Set { private IntSet s; private int addCount; public InstrumentedIntSet( ) { addCount = 0; s = new IntSet(); }

47. InstrumentedIntSet: Composition-2
public class InstrumentedIntSet implements Set { public void add(int element) { addCount = addCount + 1; s.add(element); } public void addAll(Collection c) { addCount = addCount + c.size(); s.addAll( c );

48. Should B be a subtype of A ?
Do we need to use B in place of A ?
Start NO
YES
Does B satisfy the LSP ?
Do B and A need to share any code ? NO NO
YES
YES
Make B and A independent types (common interface if necessary)
Make B a sub-type of A, but try to use the public interface of A in B if possible and efficient
Make B contain an object of type A (common interface if necessary)

49. Class Exercise
Consider the NonEmptySet type that we saw earlier. Can you rewrite it to use an IntSet rather than be derived from an IntSet ?
How will you make them inherit from a common base class ?

50. Summary of Sub-typing
Inheritance is often over-used without regard for its consequences (e.g., Java class library)
Not always straightforward to ensure behavioral substitutability of parent-type with sub-type
Subtle dependencies of sub-type on parent type’s implementation details can cause fragility
Use composition instead of inheritance whenever possible (with interfaces if necessary)