Type Abstraction SWE 619 - Spring 2009

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();

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!

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

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

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.

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; }

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

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; }

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.

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()????

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

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 { … }

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

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

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?

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?

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

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?

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

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

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

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

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).

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

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:

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