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1. EECE 210: Software Design
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 use composition over
inheritance

3. 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

4. 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

5. 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

6. 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

7. Usage of removeAny
IntSet s = new IntSet();
…
// Add elements to s
while ( removeAny(s) ) {
…
}
// s is empty at this point
7

8. 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

9. 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:
1. signature rule
2. methods rule
3. properties rule
9

10. Signature Rule
• Every call that is type-correct with the supertype 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

11. Signature Rule in Java
1. Subtype’s method can have fewer exceptions
but NOT throw more exceptions
2. Arguments and return type should be identical:
(stricter than necessary)
Foo clone();
Foo x = y.clone();
Object clone();
Foo x = (Foo) y.clone();
1. Enforced by the compiler at compile-time
11

12. NonEmptySet: Remove
public class NonEmptySet extends IntSet {
Violates signature rule
…
– will not compile
public void remove(int x) throws
EmptySetException {
// EFFECTS: If set has at least two elements,
// then remove x
// Otherwise, throw the EmptySetException
….
}
}
12

13. 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

14. 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

15. 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

16. Methods rule
• A sub-type method can weaken the precondition (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

17. 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, subtype 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

18. 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

19. 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

20. 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

21. 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

22. What happens in this code ?
public static void findMax (NonEmptySet s) {
int max = s.choose();
Can throw an
iterator g = s.elements();
exception if IntSet is
passed in as argument
while (g.hasNext() ) {
…
}
}
22

23. 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

24. 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

25. 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

26. 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

27. Group Activity
• In the handout

28. 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

29. 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)

30. 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

31. 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;}
}

32. 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

33. 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);
}
}

34. 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) );

35. 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.

36. 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 ?

37. 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();

38. 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

39. Abstract Classes Vs. Interfaces

40. Class Exercise
• Distributed as a handout in class

41. 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

42. 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() );
}
}

43. 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

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

45. 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)

46. Solution: Use Composition
• Instead of making InstrumentedIntSet a subtype 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

47. InstrumentedIntSet: Composition1
public class InstrumentedIntSet implements Set
{
private IntSet s;
private int addCount;
public InstrumentedIntSet( ) {
addCount = 0;
s = new IntSet();
}

48. InstrumentedIntSet: Composition2
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 );
}

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

50. 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 ?

51. 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