1. Type Abstraction
SWE Spring 2013

2. Substitution Principle
“In any client code, if supertype object is substituted by subtype object, the client will not notice any difference in behavior”
Object o = getNewObject();
Case 1: public Object getNewObject();
Case 2: public String getNewObject();

3. Why do we subtype? Extended Behavior Multiple implementations
Standard “Is-A” Relationships
Multiple implementations
SparsePoly, DensePoly
Different implementations
Same specifications
All supertype behavior must be supported
No extra stuff!

4. Extended behavior Extended Behavior
Specialize the behavior of supertype
Classic ‘IS A’ relationship
Usually has additional rep.
Vehicle
Car
Bike
CAR
Vehicle
Constraint View: for contracts
Object View: for rep

5. Conflict in two goals? Poly Poly SparsePoly DensePoly LogPoly
LogPoly: Extends the behavior of Poly
by keeping track of how many times it was accessed by the calling code. It has additional rep (a log of accesses)
LogPoly

6. Dispatching Object[] x = new Object[2]; X[0] = new String(“abc”);
X[1] = new Integer(1);
for(int i=0; i<x.length;i++)
System.out.println(x[i].toString());
Compiler does not complain (apparent type is fine!)
Which toString method is called? Object.toString(), String.toString() or Integer.toString()?
At run time, “best fit” code is called.

7. MaxIntSet Example (Fig 7.5)
public class MaxIntSet extends IntSet {
private int biggest; // biggest element of set if not empty
public MaxIntSet {super (); } //Why call super() ???
public void insert (int x) {
if (size() == 0 || x > biggest) biggest = x;
super.insert(x); }
public int max () throws EmptyException {
if (size() == 0) throw new EmptyException (“MaxIS.max”);
return biggest; }

8. MaxIntSet.remove() public void remove (int x) { super.remove(x);
if (size()==0 || x <biggest) return;
Iterator g = elements();
biggest = ((Integer) g.next()).intValue();
while (g.hasNext() {
int z = ((Integer) g.next()).intValue();
if (z>biggest) biggest = z; }
Need to call supertype’s remove functionality. (private rep!)
Must maintain subtype’s rep invariant

9. MaxIntSet.repOk() public boolean repOk() {
if (!super.repOk()) return false;
if (size() == 0) return true;
boolean found = false;
Iterator g = elements();
while(g.hasNext()) {
int z = ((Integer)g.next()).intValue();
if (z>biggest) return false;
if (z==biggest) found = true;
return found; }

10. MaxIntSet Abstract State
// Overview: MaxIntSet is a subtype of IntSet with an additional
// method, max, to determine the maximum element of the set
Two possible abstract states:
{x1, x2, ... xN} - same as IntSet
<biggest, {x1, x2, ... xN}> - visible abstract state
Which one to choose?
Design decision - either is possible
Second may seem more natural, but there are significant advantages to the first.
We will revisit this via Bloch later in the semester.

11. repOk() and Dynamic Dispatching
public class IntSet {
public void insert(int x) {...; repOk();}
public void remove(int x) {...; repOk();} // where to?
public boolean repOk() {...} }
public class MaxIntSet extends IntSet {
public void insert(int x) {...; super.insert(x); repOk();}
public void remove(int x) {super.remove(x); ...; repOk();
public boolean repOk() {super.repOk(); ...;}
MaxIntSet s = {3, 5}; s.remove(5); // repOk()????

12. Mechanisms: Abstract class
Defines a type + partial implementation
Contains both abstract methods and concrete methods
May have instance variables + constructor
Users can’t call constructor
Subtype extends the supertype
Can call constructors to initialize supertype rep.
Template pattern

13. Mechanisms: Interface
Defines a type (no implementation)
Only non static public method
All methods are abstract
Implementation is provided by a class that implements the interface
public class foo implements someInterface { … }

14. Meaning of subtypes
Subtypes behavior must support supertype behavior – (SP)
In particular following three properties:
Signature Rule
Methods Rule
Properties Rule

15. Signature Rule Subtypes must have all methods of supertype
Signatures of methods must be compatible with supertype signature
Return types must be same
Guaranteed by Java compiler
Caution: Overriding vs. overloading
public boolean equals(Foo foo) {...}
public boolean equals(Object foo) {...}
Exceptions
Signature Rule allows Subtype to throw fewer
But methods rule must be satisfied

16. Methods Rule When object belongs to subtype, subtype method is called
We must still be able to reason about these methods using supertype specs
Suppose SortedIntSet extends IntSet
IntSet x = new IntSet();
IntSet y = new SortedIntSet();
x.insert(3); //What is this_post?
y.insert(3); //What is this_post?

17. Methods Rule Cannot take away methods! Must maintain the contract!
Subtype API should atleast be equal or greater than supertype API
Must maintain the contract!
Precondition rule: What can a subclass do with preconditions in supertype spec?
Post condition rule: What can a subclass do with postconditions in supertype spec?

18. Precondition rule Subtype is allowed to weaken the precondition!
Formally:
pre_super |- pre_sub
Super //Requires: x > 5
Case 1: Sub //Requires x > 6
Case 2: Sub // Requires x > 4
x>5  x>4? Which is weaker?
x>5  x>6?
Not checked by compiler

19. Post condition rule
Subtype is allowed to strengthen the post condition
Formally:
pre_super && post_sub |- post_super
Super: // Effects: returns y < 5
Sub: //Effects: returns y < 4
Sub: //Effects: returns y < 6
Which one is a stronger condition?

20. Same Diagram as Method Verification
Supertype State (Pre-Super)
Supertype State (Post-Super)
SuperType Method
Contract ?
AF()
AF()
Subtype State (Post-Sub)
Subtype State (Pre-Sub)
Subtype Method
Contract

21. Other examples Sub Super public void addZero() public void addZero()
//E: add zero to this
public void addZero() throws EE
//R: true
//E: if this is empty, throw EE else add zero to this
Super
public void addZero()
//R: this is not empty
//E: add zero to this
public void addZero() throws EE

22. More examples Sub Super public void addZero() throws EE
//E: add zero to this
public void addZero()
//R: true
Super
public void addZero()
//R: this is not empty
//E: add zero to this
public void addZero() throws EE
//E: if this is empty, throws EE
// else add zero to this

23. Client code private void foo { … try{ o.addZero(); } (catch EE){
//do something: Client expects to get here! }

24. Methods rule vs. Properties rule
Methods rule is for single method invocation
Properties rule about abstract objects.
Invariants: E.g. IntSets do not contain duplicates
s.isIn(x) following s.remove(x) always false
Evolution properties: E.g. MonotoneSets only grow (no remove method allowed).

25. Liskov 7.8, 7.9, 7.10 public class Counter{ // Liskov 7.8
public Counter() //EFF: Makes this contain 0
public int get() //EFF: Returns the value of this
public void incr() //MOD: this //EFF: Increments value of this }
public class Counter2 extends Counter { // Liskov 7.9
public Counter2() //EFF: Makes this contain 0
public void incr() // MOD: this //EFF: double this
public class Counter3 extends Counter { // Liskov 7.10
public Counter3(int n) //EFF: Makes this contain n
public void incr(int n) // MOD: this //EFF: if n>0 add n to this

26. Anaylsis Signature rule: Careful with over- load vs. ride
Counter2 ok?
Counter3 ok?
Methods rule:
Precondition rule:
Counter 2 ok?
Counter 3 ok?
Postcondition rule:

27. Liskov 7.11 Is IntBag a legitimate subtype of IntSet? Analysis:
public void insert(int x);
// Effects: ???
public void remove(int x);