Type Abstraction

SWE 619 - Spring 2013

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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();

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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!

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Extended behavior

Extended Behavior Specialize the behavior of supertype Classic ‘IS A’ relationship Usually has additional rep.

VehicleCar Bike

Constraint View: for contracts

CAR

Object View: for rep

Vehicle

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Conflict in two goals?

Poly

SparsePoly LogPolyDensePoly

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)

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DispatchingObject[] 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.

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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; }

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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

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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;}

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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.

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repOk() and Dynamic Dispatchingpublic 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()????

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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

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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 {…}

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Meaning of subtypes

Subtypes behavior must support supertype behavior – (SP)

In particular following three properties:

1. Signature Rule2. Methods Rule3. Properties Rule

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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

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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 IntSetIntSet x = new IntSet();IntSet y = new SortedIntSet();x.insert(3); //What is this_post?y.insert(3); //What is this_post?

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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?

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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

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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?

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Same Diagram as Method Verification

SuperType Method

Contract

Subtype Method

Contract

AF() AF()

Supertype State (Post-Super)

Supertype State (Pre-Super)

Subtype State (Post-Sub)

Subtype State (Pre-Sub)

?

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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

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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

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Client code

private void foo {…try{

o.addZero();} (catch EE){

//do something: Client expects to get here!}

}

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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).

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Liskov 7.8, 7.9, 7.10public class Counter{ // Liskov 7.8

public Counter() //EFF: Makes this contain 0public int get() //EFF: Returns the value of thispublic void incr() //MOD: this //EFF: Increments value of this

}public class Counter2 extends Counter { // Liskov 7.9

public Counter2() //EFF: Makes this contain 0public void incr() // MOD: this //EFF: double this

}public class Counter3 extends Counter { // Liskov 7.10

public Counter3(int n) //EFF: Makes this contain npublic void incr(int n) // MOD: this //EFF: if n>0 add n to this

}

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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?

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Liskov 7.11 Is IntBag a legitimate subtype of IntSet? Analysis:

public void insert(int x); // Effects: ???

public void remove(int x); // Effects: ???