Type Abstraction

1. Type Abstraction Liskov, Chapter 7

2. Liskov Substitution Principle In any client code, if the supertype object is substituted by a subtype object, the client’s expectations will still be satisfied. Everyone learns this in intro OO courses, but this is a lot harder than it looks.

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

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

5. Conflict in two goals? Poly Poly SparsePoly DensePoly LogPoly SparsePoly DensePoly 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 • 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 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.

10. 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; }

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

13. Signature Rule • Subtypes must have all methods of supertype • Signatures of methods must be compatible with supertype signature • Return types identical; Covariant after Java 1.5 • 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

14. 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?

15. Methods Rule • Cannot take away methods! • 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?

16. 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

17. Post condition rule • Informally, 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?

18. 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

19. Super public void addZero() //pre: this is not empty //post: add zero to this public void addZero() throws ISE //pre: this is not empty //post: add zero to this Sub public void addZero() //post: add zero to this public void addZero() throws ISE //post: if this is empty, throw ISE else add zero to this Examples Satisfies Signature and Method rules Satisfies Signature and Method rules

20. Super public void addZero() //pre: this is not empty //post: add zero to this public void addZero() throws ISE //post: if this is empty, throws ISE // else add zero to this Sub public void addZero() throws ISE //post: add zero to this public void addZero() //post: add zero to this More examples Does not satisfy Signature rule Does not satisfy Postcondition part of methods rule

21. A Java Example • What may subtypes of Iterator do?

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

23. 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).

24. 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 }

25. 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: • Counter 2 ok? • Counter 3 ok?

26. More About Properties Rule Collection <String> c = ...; c.add (“cat”); c.add (“cat”); c.remove(“cat”); // consider the following observer call: // What is behavior if c is a Set? // What is behavior if c is a Bag? if (c.contains(“cat”) { ... } // Such “algebraic” relations are extremely useful for testing