1. Type Abstraction SWE 619 - Spring 2006

2. October 05Kaushik, Ammann 20052 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. October 05Kaushik, Ammann 20053 Why do we subtype? Multiple implementations Extended Behavior Multiple implementations SparsePoly, DensePoly Different implementations Same specifications All supertype behavior must be supported No extra stuff!

4. October 05Kaushik, Ammann 20054 Extended behavior Extended Behavior Specialize the behavior of supertype Classic ‘IS A’ relationship Usually has additional rep. Vehicle Car Bike Constraint View: for contracts CAR Object View: for rep Vehicle

5. October 05Kaushik, Ammann 20055 Conflict in two goals? Poly SparsePolyLogPolyDensePoly Poly SparsePoly LogPoly 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)

6. October 05Kaushik, Ammann 20056 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. October 05Kaushik, Ammann 20057 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. October 05Kaushik, Ammann 20058 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. October 05Kaushik, Ammann 20059 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. October 05Kaushik, Ammann 200510 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 - 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 cover this via Bloch later in the semester.)

11. October 05Kaushik, Ammann 200511 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. October 05Kaushik, Ammann 200512 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. October 05Kaushik, Ammann 200513 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. October 05Kaushik, Ammann 200514 Meaning of subtypes Subtypes behavior must support supertype behavior – (SP) In particular following three properties: 1. Signature Rule 2. Methods Rule 3. Properties Rule

15. October 05Kaushik, Ammann 200515 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: Can subtype throw more? Fewer Methods rule must be satisfied

16. October 05Kaushik, Ammann 200516 Methods Rule When object belongs to subtype, subtype method is called Can we still 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. October 05Kaushik, Ammann 200517 Methods Rule 1. Cannot take away methods! 1. Subtype API should atleast be equal or greater than supertype API 2. Must maintain the contract! 1. Precondition rule: What can a subclass do with preconditions in supertype spec? 2. Post condition rule: What can a subclass do with postconditions in supertype spec?

18. October 05Kaushik, Ammann 200518 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. October 05Kaushik, Ammann 200519 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. October 05Kaushik, Ammann 200520 Other examples Super public void addZero() //R: this is not empty //E: add zero to this public void addZero() throws EE //R: this is not empty //E: add zero to this Sub 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

21. October 05Kaushik, Ammann 200521 More examples 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 Sub public void addZero() throws EE //E: add zero to this public void addZero() //R: true //E: add zero to this

22. October 05Kaushik, Ammann 200522 Client code private void foo { … try{ o.addZero(); } (catch EE){ //do something: Client expects to get here! }

23. October 05Kaushik, Ammann 200523 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. October 05Kaushik, Ammann 200524 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. October 05Kaushik, Ammann 200525 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. What is a bag? Set – each element may occur only once Bag – elements may be present more than once Sequence – is a bag in which the elements are ordered OrderedSet – is a set in which the elements are ordered October 05Kaushik, Ammann 200526

27. October 05Kaushik, Ammann 200527 Liskov 7.11 Is IntBag a legitimate subtype of IntSet? Analysis: public void insert(int x); // Effects: ??? public void remove(int x); // Effects: ???