Data Abstraction

SWE 619Software Construction

Last Modified, Spring 2009Paul Ammann

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Data Abstraction

Abstract State (Client State) Representation State (Internal

State) Methods

Constructors (create objects) Producers (return immutable object) Mutators (change state) Observers (report about state)

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Motivation

Why data abstraction? Why hide implementation? Client code breaks Malicious or clueless clients don’t

depend on/mess up the state Maintain properties like rep invariant Hence, encapsulation

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IntSet and Poly

IntSet{4,6} {}, {3,5,9},{x1, …, xn}

MutableStudents find this

easy to implement

Poly5+3x+8x3, 4x+6x2

c0+c1x+…

ImmutableStudents find this

harder to implement

but a better approach

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Specification of IntSetpublic class IntSet {

//Overview: IntSets are mutable, unbounded sets of integers// A typical IntSet is {x1, …, xn}

//constructorspublic IntSet() //Effects: Initializes this to be empty//methodspublic void Insert (int x) // Modifies: this // Effects: Adds x to this, i.e., this_post = this + {x}

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Specification of IntSet (2)public void remove (int x) //Modifies: this //Effects: Removes x from this, i.e., this_post=this –{x}public boolean isIn (int x) //Effects: If x is in this, returns true, else returns falsepublic int size () //Effects: Returns the cardinality of thispublic int choose () throws EmptyException // Effects: If this is empty, throws EmptyException else // returns an arbitrary element of this

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Remember! Don’t mention internal state in

constructor or method specifications

Always override toString() (don’t show the rep)

Client should not see in-between state, all operations atomic

this_post after execution of procedure

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Set Notation – figure 5.3

A set is denoted {x1, … xn}Set union: t = s1 + s2Set difference: t = s1 – s2Set intersection: t = s1 & s2Cardinality |s| denotes the size of set sSet membership: x in true if x element of

set sSet former: t = { x | p(x)} is the set of all

x such that p(x) is trueThese few notions are extremely powerful!

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Specification of Polypublic class Poly {

// Overview: Polys are immutable polynomials with integer co-// -efficients. A typical Poly is c0+c1x+ …

//constructorspublic Poly() // Effects: Initializes this to be the zero polynomial

public Poly (int c, int n) throws NegativeExponentException // Effects: If n<0 throws NegativeExponentException

// else initializes this to be the Poly cxn

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Specification of Poly (2)//methodspublic int degree () //Effects: Returns the degree of this (the largest exponent // with non zero coeff. Returns 0 if this is the zero Poly

public int coeff (int d) //Effects: Returns the coeff of the term of this with exp. d

(what if d > degree? what if d < 0?)public Poly add (Poly q) throws NullPointerException //Effects: If q is null throws NPE else // returns the Poly this + qpublic Poly mul (Poly q) throws NPE //Effects: if q is null throws NPE, else returns this * q

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Poly in detail 5+3x+8x3 can’t build with the

constructor Only zero or monomial NegativeExponentException No modifies clause: Immutable No mutators

How does it support add, remove, multiply etc.?

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Collections – A Slight Diversion

Ordering

SetInjective-

List

BagVector,

ListY

N

YN

DUPLICATESOne collection is often implemented with another.

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Implementation (IntSet)

Rep: Vector Abstract state: Set Design decision (els never null) Use of special value in getIndex,

justified? Design decision, duplicates in insert Why is remove as shown?

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Implementation of IntSet (2)

private Vector els; // the reppublic void insert (int x) { //Modifies: this (NOT els!)

//Effects: Adds x to the elements of this (NOT els!) Integer y = new Integer(x); if (getIndex(y) < 0) els.add(y); }

private int getIndex(Integer x) { // Effects: If x is in this return index where x appears // else return -1 for (int i=0; i < els.size(); i++) if (x.equals(els.get(i))) return i; return -1; }

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Implementation of IntSet (3)

public void remove (int x) { //Modifies: this

//Effects: Remove x from this int i = getIndex(new Integer(x)); if (i < 0) return; els.set(i, els.lastElement()); els.remove(els.size() - 1); }

public int choose() { // Effects: If this empty throw EE else return arbitrary

element of this if (els.size() == 0) throw new EE(“IntSet.choose”); return ((Integer) els.lastElement()).intValue(); }

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Implementation of Poly (1)private int[] trms;private int deg; public Poly() { //Effects: Initializes this to be the zero polynomial trms = new int[1]; trms[0] = 0; deg = 0; }

public Poly (int c, int n) throws IAE { //Effects if n < 0 throw IAE else initializes this to cx^n if (n < 0) throw new IAE(“Poly.constructor”); if (c ==0) { trms = new int[1]; trms[0] = 0; deg = 0; return} trms = new int[n+1]; deg = n; for (int i = 0; i < n; i++) trms[i] = 0; trms[n] = c; }

private Poly (int n) { trms = new int[n+1] deg = n;}

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Implementation of Poly (2)public int degree() { //Effects: Return degree of this, ie the largest exponent // with a nonzero coefficient. Returns 0 if this is the zero Poly return deg;}

public coef (int d) { // Effects: Returns the coefficient of the term of this whose exp

is d if (d < 0 || d > deg) return 0; else return trms[d];}

// implementations of add, sub, minus, mul

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Abstraction Function Abstract state {x1, …, xn} Representation state?

Vector els = [y0, y1, …, yn] Representation state is designer’s choice. Clients don’t see rep (representation

state), only see abstract state Clients don’t care for rep, as long as it

satisfies properties of abstract state Implementer can change rep at any time!

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Abstraction Function (IntSet)

Abstraction function is a mapping from representation state to abstract state

Abstraction function for IntSet: AF(c) = c.els[i] | 0 i < c.els.size() } If duplicates allowed, what should

AF(c) be? What if null is mapped to {}?

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AF() for IntSet

Abstract State (IntSet s)

Representation State (Vector els)

AF()

els = []els = null

els = [1, 2]

els = [2, 1]els = [“cat”, “hat”] els = [7, 1, 7]

s = {}

s = {1}s = {1, 2}

s = {1, 7}

els = [null, 5]

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Rep Invariant Rep Invariant is the expression of

combined restrictions on representation1. c.els != null2. No duplicates in c.els3. All entries in c.els are Integers4. No null entries English descriptions are fine! These are DESIGN DECISIONS.

For example, we COULD allow duplicates...

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Additional Methods1. clone() wrong in Liskov; we will use Bloch2. toString() Implementation of abstraction function3. equals() non standard wrt Java - understand why

In terms of mutability– different for mutable and immutable types

Bias towards correctness Three different things are required:1. == // This checks if same object2. equals() // for immutable only (same abstract state)3. similar() // Mutable (same current abstract state)

// Not implemented in Java

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equals() Involves three important criteria: reflexivity,

symmetry, transitivity Often difficult to implement For abstract extensions of instantiable

superclasses, impossible to implement! Details later...

toString Should match with “typical object”

Trick: Do it backwards - implement toString() first and then write the abstraction function.

SWE 619 24

Mutable/Immutable Transform Stack example in Bloch

Mutable Transform to an immutable version

We should be fine with immutable stacks:Immutable Stack s = new Stack();

s = s.push(“cat”);s =s.push(“dog”);

How to tranform:

SWE 619 25

Mutator ProducerConsider a mutator method in class C: public void m(T t) or

public S m(T t) What do the corresponding immutable methods

look like?public C m(T t) orpublic ??? m(T t)

Second needs to be split into two methods:Example: pop() vs. pop(), top() in Stack