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Formal Specification of

Object-Oriented Design

Amnon H. EdenDepartment of Computer Science, University of Essex

Research seminar given at the Department of Computer Science, University of

Essex

25 October, 2003

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Context

AbstractionsDesign Vs. Architecture

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Levels of Abstraction

Architecture

Design

Implementation

while (true) doc := c - 1;d := d + 1;if c < 0 goto continue;

continue: ...

while (true) doc := c - 1;d := d + 1;if c < 0 goto continue;

continue: ...

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Software ArchitectureAn emerging discipline

Origins: Perry & Wolf [92]

“Architectural Styles”: Shaw & Garlan [96]

Underlying formalisms Statecharts finite automata CSP

Architecture Description Languages (ADLs) ACME Rapide UniCon Wright, …

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Implementations Programming languages Denotational/operational semantics Computational models

Turing machine, RAM machine, Abstract State Machines

Formal Languages Lambda calculus, sigma calculus, …

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(Object-Oriented) Design Design Methodologies Notations Heuristics Design patterns

In particular: Gamma, Helm, Johnson & Vlissides [94]

Formalization?

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Objectives Conceptual:

1. A formal ontology for OOD2. A formal specification language

Patterns Libraries & frameworks

3. Elegance4. Reasoning capabilities

Pragmatic Full integration with existing programming practice Tool support Visual specifications

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Design Models

A Computational Model

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Program & Design Model

class PMButton {}class WinButton {}

void exit() {}

class PMButton {}class WinButton {}

void exit() {}

interface Creator {}

class WinCreator: extends Creator {WinButton_FactoryMethod() {

// Creation:new WinButton;// Invocation: exit();

}}

interface Creator {}

class WinCreator: extends Creator {WinButton_FactoryMethod() {

// Creation:new WinButton;// Invocation: exit();

}}

class PMCreator: extends Creator {PMButton_FactoryMethod() {

// ...new PMButton;

}}

class PMCreator: extends Creator {PMButton_FactoryMethod() {

// ...new PMButton;

}}

PM-creator

Win-creator

Win-button

Win-button-factory-method

exit

PM-button-factory-method

defined-in

defined-in

creator

PM-button

A

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Denotation Function

Given L OOPL, A Denotation: Modelling function

D : L UniverseD , RelationsD

Methods

Invoke

Create

Inherit

Classes

Classes, methods Abstract, Inherit,Create, Call, …

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Axiomatic Semantics

Building Blocks of O-O Design

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Hierarchy

AbstractFactory ConcreteFactories P()Abstract(AbstractFactory)Inherit(ConcreteFactories,AbstractFactory)

AbastractFactory

ConcreteFactories

A

Factories

Factories

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Clans, Selection Operator

PrimitiveOperations1 Classes P()PrimitiveOperation1ClassesClasses

PrimitiveOperation1

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Isomorphic Relations

Factories

CreateProductA

ProductA

Create Factories, ProductA

CreateProductA Create(CreateProductAProducts,

ProductA)

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LePUS

TermsPredicatesOperator

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Terms Constants: Belong to a given domain

EJBContext

Variables: Range over a given domainbean

17 / SameSignature

barx

foo(int)

A::foo(int)

B::foo(int)A::bar()X

A::bar()X

Auxiliary Domains P(X) Power set of X

P(X) {x | x X }

Domain of all hierarchies {h P() | Hierarchy(h)}

Domain of function signatures

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PredicatesR(S,T) Total(R,S,T)

sS tT R(s,t)R(S,T) Isomorphic(R,S,T)

sS tT R(s,t) tT sS R(s,t)

Hierarchy(h) Abstract(r) ch, cr Inherit+(c,r)

Clan(F,C) DefinedIn(F,C) f1,f2F SameSignature(f1,f2)

Tribe(F,C) fF Tribe(f,C)

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Selection Operator Given a signature s, set of signatures S:

sC Selects methods in cC with signature s Result is a clan

SC Selects clans in cC with signature s Result is a tribe

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Specifications in LePUS

Design PatternsObject-Oriented Design

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Factory-Method Pattern

ProductsCreators

factory-methods

ProductsProducts, Creators : FactoryMethods :

Produce(FactoryMethodsCreators,Products)Return(FactoryMethodsCreators,Products)

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Observer Pattern

subject

Observers

Update(subject)concrete-

subject

getState

SetState

attach(observers)

notifyReferenceToMany(subject,Observers)Inherit(subject, concrete-subject)FirstArg(attach,observers)FirstArg(detach,observers)FirstArgupdateobservers,subject)Invoke(SetStateconcrete-observer, notifysubject)Invoke(notifysubject,updateObervers)Invoke(updateObervers,attachsubject)Invoke(updateObervers,detachsubject)Assign(attachsubject,sybject,observers)

subject, concrete-subject : observers : attach, detach, notify, update, get-state : SetState : P()

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Visitor Pattern

Visitors

Visit(Elements)

Elements

accept(Visitors)

Concision: Three isomorphic relations, one total relation,

and many pages of documentation in one

diagram

FirstArg(AcceptElements,Visitors)FirstArg(VisitVisitors,Elements)Invocation(AcceptElements,VisitVisitors)Invocation(VisitVisitors,Elements)

Elements, Visitors : Accept : Visit : P()

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DocumentationTaken from the description of the Enterprise JavaBeans™:

“Every bean obtains an EJBContext object, which is a reference directly to the container”

“A bean's home interface may declare zero or more create() methods, each of which must have corresponding ejbCreate() and ejbPostCreate() methods in the bean class. ”

Bean EJB Context

I

BeanHomeImp

Create Bean

G

ejbCreate

ejbPostCreate

BeanHomeInterface

ICreate Bean

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Enterprise JavaBeans™

java.ejb.EJBObject

Bean

BeanInterface

IMethods

EJBContext

setEntityContext

BeanStub

Methods G

Rem

ote

Methods

I

BeanSkeleton

Methods G

I

Clients

Methods

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Reasoning

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Conformance (also Refinement)

observer

observable

I

Viewsupdate

(Observable)

addObserver(Observer)

notifyObservers

setChanged

ctors

model

Accessors

Mutators

update(Observable)

subject

Observers

Update(subject)concrete-

subject

getState

SetState

attach(observers)

notify

“Model-View-Controller” in Java Swing

... Conforms to the Observer pattern

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creator, product : factory-method : Create(factory-methodfactory, product)Return(factory-methodfactory, product)

Projection

product

factoryfactory-method

product

factoryfactory-method

creator, product : P()factory-method : Create(factory-methodfactory, product)Return(factory-methodfactory, product)

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ProductsCreators

factory-methods

Products

Creators

Factory-Methods

ProductsProducts

Factory Method Vs. Abstract FactoryThe difference is merely in the order of sets

Isomorphisms are preserved

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Two-Tier Programming

Integrating Intentional With Extensional programming

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Multiple Representations

TextViews

observer

observableI

ScrollViews

Update(Observable)

addObserver(Observer)

notifyObservers

C'tormodel

AccessorsMutators

update(Observable)

Update(Observable)

C'tor

subject

observers

update(subject)

attach(observers)

detach(observers)

notify

concrete-subject

Set-state

get-State

public class Observable { public synchronized void addObserver(Observer o) { ... } public void notifyObservers(Object arg) { ... }}

public class Observable { public synchronized void addObserver(Observer o) { ... } public void notifyObservers(Object arg) { ... }}

class MyObservable extends Observable {public void access() { ... }public void mutate() { ... notifyObservers(); }}

class MyObservable extends Observable {public void access() { ... }public void mutate() { ... notifyObservers(); }}

intrface Observer { void update(Observable); }

intrface Observer { void update(Observable); }

class ScrollView extends Scrollbar implements Observer { … }

class ScrollView extends Scrollbar implements Observer { … }

class TextView extends TextField implements Observer {public TextView(Counter c) { ... }public void update(Observable o, Object counter) { ... }}

class TextView extends TextField implements Observer {public TextView(Counter c) { ... }public void update(Observable o, Object counter) { ... }}

Source Code

Pattern

Design Model

observable

observers

update(observable)

attach(observers)

notify

model

Mutators

Accessors

Instance of a pattern

Extensional tier

Intentional tier

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subject

observers

update(subject)

attach(observers)

detach(observers)

notify

concrete-subject

Set-state

get-State

Coordination

TextViews

observer

observableI

ScrollViews

Update(Observable)

addObserver(Observer)

notifyObservers

C'tormodel

AccessorsMutators

update(Observable)

Update(Observable)

C'tor

public class Observable { public synchronized void addObserver(Observer o) { ... } public void notifyObservers(Object arg) { ... }}

public class Observable { public synchronized void addObserver(Observer o) { ... } public void notifyObservers(Object arg) { ... }}

class MyObservable extends Observable {public void access() { ... }public void mutate() { ... notifyObservers(); }}

class MyObservable extends Observable {public void access() { ... }public void mutate() { ... notifyObservers(); }}

intrface Observer { void update(Observable); }

intrface Observer { void update(Observable); }

class ScrollView extends Scrollbar implements Observer { … }

class ScrollView extends Scrollbar implements Observer { … }

class TextView extends TextField implements Observer {public TextView(Counter c) { ... }public void update(Observable o, Object counter) { ... }}

class TextView extends TextField implements Observer {public TextView(Counter c) { ... }public void update(Observable o, Object counter) { ... }}

Source Code

Pattern

Design Model

observable

observers

update(observable)

attach(observers)

notify

model

Mutators

Accessors

Instance of a pattern

Coordination

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Coordination: Part I

TextViews

observer

observableI

ScrollViews

Update(Observable)

addObserver(Observer)

notifyObservers

C'tormodel

AccessorsMutators

update(Observable)

Update(Observable)

C'tor

public class Observable { public synchronized void addObserver(Observer o) { ... } public void notifyObservers(Object arg) { ... }}

public class Observable { public synchronized void addObserver(Observer o) { ... } public void notifyObservers(Object arg) { ... }}

class MyObservable extends Observable {public void access() { ... }public void mutate() { ... notifyObservers(); }}

class MyObservable extends Observable {public void access() { ... }public void mutate() { ... notifyObservers(); }}

intrface Observer { void update(Observable); }

intrface Observer { void update(Observable); }

class ScrollView extends Scrollbar implements Observer { … }

class ScrollView extends Scrollbar implements Observer { … }

class TextView extends TextField implements Observer {public TextView(Counter c) { ... }public void update(Observable o, Object counter) { ... }}

class TextView extends TextField implements Observer {public TextView(Counter c) { ... }public void update(Observable o, Object counter) { ... }}

Source Code

Design Model

Parsing/Reverse engineering

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Coordination: Part II

TextViews

observer

observableI

ScrollViews

Update(Observable)

addObserver(Observer)

notifyObservers

C'tormodel

AccessorsMutators

update(Observable)

Update(Observable)

C'tor

Design Model

observable

observers

update(observable)

attach(observers)

notify

model

Mutators

Accessors

Instance of a pattern

<observers, observer, TextView, ScrollView>

<observers.update,observer.update, TextView.update,

ScrollView.update>

…

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subject

observers

update(subject)

attach(observers)

detach(observers)

notify

concrete-subject

Set-state

get-State

Coordination: Part III

observable

observers

update(observable)

attach(observers)

notify

model

Mutators

Accessors

Pattern

Instance of a pattern

<Observers, Observers><subject, observable><concrete-subject, model><Set-state, Mutators><Observers.update,

Observers.update>…

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Tool Support The Software Architecture Lab, Concordia U. Architectural Reflection projects:

Visualization tool Specifications with a graphic editor

Parser for symbolic specifications Reverse engineering from Java

In collaboration with IBM Research Centre, Haifa

pattern AbstractFactory is FactoryMethods in P2(F), Creators in H, Products in P(H) where tribe (FactoryMethods, Creators), production <-> (FactoryMethods, Products), return_type <-> (FactoryMethods, Products).

pattern AbstractFactory is FactoryMethods in P2(F), Creators in H, Products in P(H) where tribe (FactoryMethods, Creators), production <-> (FactoryMethods, Products), return_type <-> (FactoryMethods, Products).

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Implementation in Prolog LePUS is readily implemented in PROLOG:

Supported activities: Validation Application Recognition Discovery

FactoryMethod(hierarchy_structure (Creators_root, Creators_Leaves), hierarchy_structure (Products_root, Products_Leaves), FactoryMethods) :- clan(FactoryMethods,[Creators_root|Creators_Leaves]), isomorphic(production, FactoryMethods, [Products_root|Products_Leaves]).

FactoryMethod(hierarchy_structure (Creators_root, Creators_Leaves), hierarchy_structure (Products_root, Products_Leaves), FactoryMethods) :- clan(FactoryMethods,[Creators_root|Creators_Leaves]), isomorphic(production, FactoryMethods, [Products_root|Products_Leaves]).

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Limitations “Design Models”: Static properties

Cannot give behavioural specifications

Relations are abstract Cannot represent more than

one relationships between (Journey, Location)

Journey Location

origin

destination

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Future Directions Sample specifications

Common libraries & Frameworks

Behavioural specifications Use Gurevich’s Abstract State Machines (“evolving

algebras”)

Tool support Forward and reverse engineering

Formalization of the visual language Design visual primitives & operators Visual semantics & syntax

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ReferencesD. E. Perry, A. L. Wolf (1992). "Foundation for the Study of

Software Architecture." ACM SIGSOFT Software Engineering Notes Vol. 17, No. 4.

M. Shaw, D. Garlan (1996). Software Architecture: Perspectives on an Emerging Discipline. Prentice Hall.

E. Gamma, R. Helm, R. Johnson, J. Vlissides (1994). Design Patterns: Elements of Reusable Object Oriented Software. Addison-Wesley

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BibliographyFull text: http://www.eden-study.org/

Ontology : A. H. Eden Y. Hirshfeld, "Principles in Formal Specification of Object Oriented Architectures.“CASCON 2001, November 5-8, 2001, Toronto, Canada.

LePUS: A. H. Eden (2001). "Formal Specification of Object-Oriented Design." International Conference on Multidisciplinary Design in Engineering CSME-MDE 2001, November 21-22, 2001, Montreal, Canada.

Visual Notation: A. H. Eden (2002). “Design Schemata.” Submitted: Annals of Software Engineering, Special Volume on Software Visualization.

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Bibliography (Cont.)The Patterns’ Wizard. A. H. Eden, J. Gil, A. Yehudai (1997).

"Precise Specification and Automatic Application of Design Patterns." Proceedings of the Twelve IEEE International Automated Software Engineering Conference (ASE 1997), Lake Tahoe, Nevada Los Alamos, IEEE Computer Society Press, Nov. 3-5, 1997.

Two-Tier Programming. A. H. Eden, J. Jahnke (2002) "Coordinating Software Evolution Via Two-Tier Programming," Coordination 2002, Lecture Notes in Computer Science 2315, pp. 149-159. Berlin: Springer-Verlag.

Intention/Locality. A. H. Eden (2002). “Architecture, Design, Implementation.” Submitted: Journal of Software and System Modeling (SoSyM). Berlin: Springer.