Formal concept analysis based normal forms for class hierarchy design in

object-oriented software development http://www.info.uqam.ca/~godin/ICFCA2003.ppt

Robert Godin, UQAMFirst Conference on "Formal Concept Analysis" DarmstadtFeb. 2003

Collaborators

Rokia Missaoui, Hafedh Mili (UQAM) Guy Mineau (ULaval) Petko Valtchev, Houari Sahraoui (UdeM) Marianne Huchard (LIRMM)

Plan

The problem of class hierarchy design Quality criteria Work on FCA for class hierarchies FCA framework Normal forms (design patterns) for class hierarchies

– Attributes– Methods body/signature/redefinition– Associations

Problem: designing & maintaininggood class hierarchies

Difficult problem (Booch, 1994; Rumbaugh, Blaha, Premerlani, Eddy & Lorensen, 1991) – Large solution space– Evolution– Conflicting criteria

Large body of work– (Godin, Huchard, Roume & Valtchev, 2002)

Development scenarios

Building the hierarchy from scratch using – objects (Lieberherr, Bergstein & Silva-Lepe, 1991) – class specifications (Dvorak, 1994; Godin & Mili, 1993)

Evolution of the class hierarchy to accommodate new requirements– unconstrained class addition (Dvorak, 1994; Godin & Mili, 1993) – addition constrained by backward compatibility

with a previous hierarchy (Rapicault & Napoli, 2001) existing objects (Huchard, 1999)

Reengineering of an existing class hierarchy– from the relation between classes and their attributes/methods (Casais, 1991; Cook, 1992)– using code analysis tools (Dicky, Dony, Huchard & Libourel, 1996; Godin, Mili, Mineau,

Missaoui, Arfi & Chau, 1998)– by applying refactorings (Fowler, 2002; Moore, 1996)– from UML models including associations (Huchard, Roume, Valtchev…)– from access patterns in applications (Snelting & Tip, 2000)– prompted by detecting defects using software metrics (Sahraoui, Godin & Miceli, 2000)

Reengineering procedural code (Sahraoui, Lounis, Melo & Mili, 1999; Tonella, 2001) Merging existing partial hierarchies (Snelting & Tip, 2002)

Formal quality criteria

Minimize redundancy (code duplication)– Maximal factorization

Subclass as specialization Multiple inheritance only if necessary Limit number of classes Guaranteed by FCA framework

Using FCA for class hierarchy

Initial proposal OOPSLA’93 (Godin & Mili, 1993)– Object Oriented Reorganization using GAlois lattices SysteM

LIRMM : ARES incremental alg. (Dicky, Dony, Huchard & Libourel, 1994)– Galois subhierarchy

ISGOOD incremental alg. (Godin, Mineau, Missaoui, 95; Godin & Chau, 2000)

ARES++ : Overloading/extracting specs. from code OOPSLA’96 (Dicky et al., 1996)

Combined with method refactoring GURU OOPSLA’96(Moore, 96) Object database design (Yahia, Lakhal, Bordat & Cicchetti, 1996) Smalltalk tool, exp., metrics (Godin, Mili, Mineau, Missaoui, Arfi & Chau,

1998) Access patterns from applications TOPLAS (Snelting & Tip, 2000) CERES : Java tool, batch alg. (Huchard, Dicky, Leblanc, 2000) Factoring associations (Huchard, Roume, Valtchev, 2002)

FCA framework

Context KK := (G, M, I) G (objects of context)

– classes– example objects– associations

M (attributes of context)– instance variables (OO attributes)

values– methods body/signature– association role– association properties

Relation gIm

From analyst From code From access patterns in applications

Example : class attributes

a b c d e f 1 2 3 4

Class1

af

Class2

abc

Class3

abd

Class4

bde

Reduced labelling of concept lattice

a b c d e f 1 2 3 4

1 2 3 4

a b

cf e

d

Interpretation as class hierarchy : attribute factored lattice form

1 2 3 4

a b

cf e

d

Class1

f

Class2

cClass3 Class4

e

Class7

a

Class5 Class6

d

Class8

b

Class9

Minimize number of classes while preserving other quality criteria

Class1

abc

Class2

abd

Class1

c

Class2

d

Class3

ab

Class1

c

Class2

d

Class3

a

Class4

b

Prune empty classes : FCA object/attribute concepts (Galois subhierarchy, PICH)

1 2 3 4

a b

cf e

d

1 2 3 4

a b

cf e

d

Attribute factored subhierarchy form

1 2 3 4

a b

cf e

d

Class1

f

Class2

cClass3 Class4

e

Class7

a

Class6

d

Class8

b

The case for empty class ?

Method body factored lattice/subhierarchy form

Class1

a1()

Class2

a2()

Class3Class4

c2()

Class5

b2()

Class6

b1()

Class7

c1()

a1 a2 b1 b2 c1 c2 1 2 3 4 5

4 3 5

c2

c1

a1 a2

1 2

b 1

b 2

Class1

a1()

Class2

a2()

Class3

b1()c1()

Class4

b1()c2()

Class5

b2()c1()

Declaration of method signatures

Use many valued attribute for each signature

+ Scaling

a a a1 a2 a a1 a2

a

a1 a2

b

b 1 b 2

c

c1 c2

Derived one-valued context

a b c a a1 a2 b b1 b2 c c1 c2 1 2 3 4 5

a1 a2 b1 b2 c1 c2 1 2 3 4 5

a a a1 a2 a a1 a2

Concept lattice

a b c a a1 a2 b b1 b2 c c1 c2 1 2 3 4 5

4 3 5

b ,c

c2

c1

a

a1 a2

1 2

b 1

b 2

Method declaration and body factored lattice/subhierarchy

4 3 5

b ,c

c2

c1

a

a1 a2

1 2

b 1

b 2

Class1

a1()

Class2

a2()

Class3Class4

c2()

Class5

b2()

Class6

b1()

Class7

c1()

Class8

a()

Class9

b()c()

Method redefinition

By scaling

b

a

a1 a2

b 1

b 2

c

c1

c2

ab a a1 a2 b b1 b2 a a1 a2 b b1 b2

Method redefinition factored lattice/subhierarchy

4

3

5

b ,c ,b 1 ,c1

b 2

a

a1 a21 2

c2

Class1

a1()

Class2

a2()

Class4

c2()

Class5

b2()

Class6

a()

Class3

b()b1()c()c1()

Maximal factorization

H is maximally factorized : if

– x1 in Class1– x2 in Class2– x3 is least upper bound of x1 and x2

then – x3 in superclass of Class1 and Class2

Maximal factorization

Class1

a1()

Class2

a2()

Class4

c2()

Class5

b2()

Class6

a()

Class3

b()b1()c()c1()

Class1

a1()

Class2

a2()

Class3Class4

c2()

Class5

b2()

Class6

b1()

Class7

c1()

Class8

a()

Class9

b()c()

b

a

a1 a2

b 1

b 2

Associations : value of many-valued attribute is an FCA object

a b c d e ass 1 3 2 4 3 4

ass = a b c d e 3 4 1 2 3 4

C3

cd

C1

a

ass

C4

ce

C2

b

ass

First concept lattice : B0

ass = a b c d e 3 4 1 2 3 4

3 4

c

e

a ,a ss :3 a ,a ss :41 2

d

C3

d

C1

a

ass

C4

e

C2

b

ass

C5

c

Relational extension K+ with B0

ass a b c d e 3 4 5 1 2 3 4

C3

d

C1

a

ass

C4

e

C2

b

ass

C5

c

Concept lattice B1 : association factored lattice/subhierarchy forms

ass a b c d e 3 4 5 1 2 3 4

3 4

c

ea ,a ss :3 a ,a ss :41 2

d

ass :5

C3

d

C1

a

ass

C4

e

C2

b

ass

C5

c

C6

ass

Relational context family (RCF)

General framework for set of related contexts– (Huchard, Roume & Valtchev, 2002)

UML – Take into account UML properties (multiplicity,

association classes,…)– One context for classes : K1 – One context for associations : K2

– Mutual enrichment– Iterate until fixed point is reached

Definition of Relational Context Family (RFC)

Definition : Relational context family (RCF)

R s = (KR , AR) KR set of s multi-valued contexts

Ki = (Ai , Oi , Vi , Ji ) and set of relations AR = {j }

j : Or 2Oq

Auxiliairy functions :

i. dom, cod : AR {Oi } 0 ≤ i ≤ s such that for all j : Or 2Oq : a) dom(j ) = Or ,

b) cod(j ) = Oq .

ii. rel : KR 2AR with

rel ( Ki ) = {j | dom(j ) = Oi}

UML exampleStudentnameaddressCollege

Transaction

dD

TransVal

tV

Tenant

nameaddress

Renting

sPmR

Purchase

pCpD

House

type

Rent >

1…*

*

1…**Buy >

Landlord

nameaddress

Context for classes : K1

   GF1 =  GF2 =  GF3 = GFDate = GFValue = GF4 =  

  name adrs col sP pD dD mR pC tV type

Student X X X              

Tenant X X                

Landlord X X                

House                   X

Transaction           X        

TransVal                 X  

Renting       X   X X   X  

Purchase         X X   X X  

Build concept lattice for K1

Tenant-Landlordnameaddress

TransactiondD

RentingsPmR

PurchasepD pC

StudentCollege

Housetype

Rent >1…* *

1…* *Buy >

TransValtV

Context for associations : K2

  name = mo = md =

 

 Nav =

  Rent Buy 1…* * * O-D D-O

Rent X   X X X X X

Buy   X X X X X X

K2 K+2

  name = mo = md =

 

 Nav = to = td = AC =

  Rent Buy1

…* * * O-D D-O Tenant Landlord House Renting Purchase

Rent X   X X X X X X X X

Buy   X X X X X X X X X

Discover AssG1

RentingsPmR

PurchasepD pC

Rent >

1…* * 1…* *

Buy >

1…* *

AssG1 >

to=Tenant td=House td=House

td=House

to=Landlord

K1 K+1

        GFDate = GFValue =   OrigOf = DestOf = ClOf =

 

name

adrs col

sD

pD

dD mR

pC tV

typ

Rent

Buy

AssG1

Rent

Buy

AssG1

Rent

Buy

AssG1

Student X X X                                

Tenant X X                 X   X            

Landlord X X                   X X            

House                   X       X X X

Transaction           X                          

TransVal                 X                    

Renting       X   X X   X               X     X

Purchase         X X   X X                 X     X

Discover new classes

Tenant

TransactiondD

RentingsPmR

PurchasepD pC

StudentCollege

Housetype

Rent >1…* *

1…* *Buy >

TransValtV

NC2

NC4

1…*

*

AssG1 >

NC1 (Person)nameaddress

Landlord

Conclusion

FCA is natural framework for design of class hierarchies

FCA based normal forms for hierarchy design– Attribute, method body, method signature,

redefinition, association factored lattice/hierarchy

Future work– Theoretical : RFC– Tool support

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