Formal concept analysis based normal forms for class

Formal concept analysis based normal forms for class hierarchy design in object-oriented software development http: //www. info. uqam. ca/~godin/ICFCA 2003. ppt Robert Godin, UQAM First Conference on "Formal Concept Analysis" Darmstadt Feb. 2003

Collaborators l l Rokia Missaoui, Hafedh Mili (UQAM) Guy Mineau (ULaval) Petko Valtchev, Houari Sahraoui (Ude. M) Marianne Huchard (LIRMM)

Plan l l l 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 & maintaining good class hierarchies l Difficult problem (Booch, 1994; Rumbaugh, Blaha, Premerlani, Eddy & Lorensen, 1991) – – – l Large solution space Evolution Conflicting criteria Large body of work – (Godin, Huchard, Roume & Valtchev, 2002)

Development scenarios l Building the hierarchy from scratch using – – l 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 l l l Reengineering of an existing class hierarchy – – – l l with a previous hierarchy (Rapicault & Napoli, 2001) existing objects (Huchard, 1999) 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 l Minimize redundancy (code duplication) – l l Maximal factorization Subclass as specialization Multiple inheritance only if necessary Limit number of classes Guaranteed by FCA framework

Using FCA for class hierarchy l Initial proposal OOPSLA’ 93 (Godin & Mili, 1993) – l LIRMM : ARES incremental alg. (Dicky, Dony, Huchard & Libourel, 1994) – l l l l Object Oriented Reorganization using GAlois lattices Syste. M 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 l l Context K : = (G, M, I) G (objects of context) – – – l classes example objects associations M (attributes of context) – instance variables (OO attributes) l – – – values methods body/signature association role association properties

Relation g. Im l l l From analyst From code From access patterns in applications

Example : class attributes

Reduced labelling of concept lattice

Interpretation as class hierarchy : attribute factored lattice form

Minimize number of classes while preserving other quality criteria

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

Attribute factored subhierarchy form

The case for empty class ?

Method body factored lattice/subhierarchy form

Declaration of method signatures l l Use many valued attribute for each signature + Scaling

Derived one-valued context

Concept lattice

Method declaration and body factored lattice/subhierarchy

Method redefinition l By scaling

Method redefinition factored lattice/subhierarchy

Maximal factorization l l H is maximally factorized : if – – – l x 1 in Class 1 x 2 in Class 2 x 3 is least upper bound of x 1 and x 2 then – x 3 in superclass of Class 1 and Class 2

Maximal factorization

Associations : value of manyvalued attribute is an FCA object

First concept lattice : B 0

Relational extension K+ with B 0

Concept lattice B 1 : association factored lattice/subhierarchy forms

Relational context family (RCF) l General framework for set of related contexts – l (Huchard, Roume & Valtchev, 2002) UML – – – Take into account UML properties (multiplicity, association classes, …) One context for classes : K 1 One context for associations : K 2 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 : O r 2 O q Auxiliairy functions : i. dom, cod : AR {Oi } 0 ≤ i ≤ s such that for all j : Or 2 Oq : a) dom( j ) = Or , b) cod( j ) = Oq. ii. rel : KR 2 AR with rel ( Ki ) = { j | dom( j ) = Oi}

UML example Student name address College Renting Tenant name address Transaction s. P m. R 1…* Rent > d. D Landlord Trans. Val t. V name address 1…* Buy > Purchase p. C p. D * House * type

Context for classes : K 1 GF 1 = GF 2 = GF 3 = GFDate = GFValue = GF 4 = name adrs col s. P p. D d. D m. R p. C t. V type Student X X X Tenant X X Landlord X X House X Transaction X Trans. Val X Renting X X Purchase X X

Build concept lattice for K 1 Trans. Val t. V Renting s. P m. R Tenant-Landlord name address Student College Transaction d. D Purchase p. D p. C Rent > 1…* * Buy > * House type

Context for associations : K 2 name = mo = Nav = md = Rent Buy 1…* * * O-D D-O Rent X X X Buy X X X

K 2 K+2 name = mo = md = Nav = Rent Buy 1 …* Rent X X X Buy X X X to = * * O-D D-O Tenant td = Landlord X AC = Renting X X House X X Purchase X

Discover Ass. G 1 > 1…* * td=House Rent > to=Tenant 1…* Renting s. P m. R Buy > * td=House to=Landlord 1…* * Purchase p. D p. C td=House

K 1 K+1 na m e a d r s col Student X X X Tenant X X Landlord X X House Transacti on Trans. Val GFDate = GFValue = Orig. Of = Dest. Of = Cl. Of = Re nt Bu y Ass G 1 Re nt Ass Buy G 1 Re nt Bu y As s. G 1 X X X X X X X X X X s p d D D D m. R p C t. V ty p Renting Purchase

Discover new classes NC 1 (Person) name address Student College Trans. Val t. V Transaction d. D Ass. G 1 > 1…* NC 2 NC 4 Renting s. P m. R Tenant Landlord Purchase p. D p. C * Rent > 1…* * Buy > * House type

Conclusion l l FCA is natural framework for design of class hierarchies FCA based normal forms for hierarchy design – l Attribute, method body, method signature, redefinition, association factored lattice/hierarchy Future work – – Theoretical : RFC Tool support

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