Type Abstraction

Liskov, Chapter 7

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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.

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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 Polyby 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 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 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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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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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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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 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

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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 specsSuppose 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 Rule1. 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 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?

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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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Examples Superpublic 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

Subpublic void addZero()//post: add zero to this

public void addZero() throws ISE

//post: if this is empty, throw ISE else add zero to this

Satisfies Signatureand Method rules

Satisfies Signatureand Method rules

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More examples 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

Subpublic void addZero() throws

ISE//post: add zero to this

public void addZero()//post: add zero to this

Does not satisfy Signature rule

Does not satisfy Postconditionpart of methods rule

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A Java Example What may subtypes of Iterator do?

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Client codeprivate 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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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