Formal Concept Analysis used for object-oriented software modelling Wolfgang Hesse FB Mathematik und Informatik, Univ. Marburg

FCA-SE 10 Formal Concept Analysis used for object-oriented software modelling Wolfgang Hesse FB Mathematik und Informatik, Univ. Marburg

FCA-SE 20 Contents 1 The role of concepts in software development 2 OO modelling: Aspects, methods and open questions 3 Bridging the gap between use case analysis and class & object modelling 4 FCA used for "crossing perspectives" 5 Other SE applications of FCA 6 Resume References

FCA-SE 30 1 The role of concepts in software development Software development methods support the complex task of.. gathering and analysing requirements.. designing and structuring the software system.. implementing (i.e. programming and integrating) the system.. operating and improving the system Modelling is the central task for finding the adequate system structure to fulfill the requirements Object-oriented modelling builds on concepts formed during analysis of the application domain and to be maintained during system design & implementation

The SW development cycle (acc. to the EOS* model) FCA-SE 40 Analysis Use & Operations Use environment Development environment Design Implementation * (for Evolutionary, Object-oriented Software development) planning, analytic activities synthetic, verifying activities

Concepts everywhere FCA-SE 50 Domain concepts Business concepts Analysis Use & user concepts Maintenance concepts Use & Operations Process concepts Design Implementation System concepts Design & architectural concepts Programming concepts Test & integration concepts

FCA-SE 60 Citations on concepts James Rumbaugh: "The objects in the model should be applicationdomain concepts...." James Martin und James Odell: "Object types are important, because they create conceptual building blocks for designing systems. [...] An object type is a concept." Grady Booch: "Key abstractions are the classes and objects that form the vocabulary of the problem domain." Use Formal Concept Analysis (FCA) to form and evaluate the concepts needed for software development

FCA-SE 70 2 Object-oriented modelling: Aspects and methods Aspects of OO modelling behavioural structural OO methods: ontological support building an OO model and bringing together various aspects. Recent, popular methods start with use cases ( behavioural aspect), recommend to detect objects & classes ( structural aspect), according to the intentions of system users and owners ( ontological aspect).

From use cases to classes & objects FCA-SE 80

FCA-SE 90 From use cases to classes & objects (2) Open questions: Are use cases (formulated in user language) appropriate for finding a good class & object structure? Are there promising alternatives? Where do the candidates for classes & objects come from? Are they already "contained" or "hidden" in the use cases? Is the object list (I. Jacobson) an appropriate "medium"? What are the criteria to choose between class candidates? How can we compare alternative class models? Is all this so easy as some authors suggest? ".. objects are there just for the picking." (B. Meyer in [Mey 88])

FCA-SE 100 Example of a use case diagram Wine trade business Receive order Process order <<include>> Clerk Order missing products <<include>> Determine inv. stock Create deliv. instructions <<include>> Process inc. delivery Define max. & min. stock quantity Process delivery results

Formal Concept Analysis (FCA) FCA-SE 110 A theory for formally describing concepts and their relationships Formal Context (G, M, I ): G (formal) objects ("things") M (formal) attributes I G M Incidence relation A I := { m M g I m for all g A } the set of attributes common to all objects in A B I := { g G g I m for all m B } the set of objects that have all attributes from B Formal Concept (A, B) with A G, B M and A I = B und B I = A. A the extent of a concept B the intent of a concept Sub- / super concept relation (A, B) (C, D) iff A C ( D B)

3 Bridging the gap: The BASE approach FCA-SE 120 Use cases describe functionality handle "things" of the domain "Things" are marked by the domain experts, may occur as classes, objects, attributes, roles, etc... in the forthcoming class model. Our FCA view: "Things" formal objects Use cases formal features

Resulting line diagram FCA-SE 130

FCA-SE 140 Functional perspective (Use cases) Crossing perspectives via FCA general... special... particular Data perspective ("Things") common

FCA-SE 150 Crossing perspectives via FCA (2) - Most general use cases stand top-most. - Special use cases stand lower in the diagram. Upper part shows use case hierarchy (functional perspective) - Most common "things" (class candidates?) stand bottom-most. - Particular "things" (class attributes?) stand higher in the diagram Lower part shows "things" hierarchy (data perspective) Typical questions resulting from FCA analysis: - Why is thing X so high in the diagram? Shouldn't it lie in the scope of use case Y? - Why is (sub-) use case X so low in the diagram? Shouldn't its scope comprise thing Y? - Is node X is good class candidate? Are its sub-nodes good candidates for (OO-) attribute, its super-nodes for (OO-) operations?

FCA-SE 160 Alternative approaches Other possible associations with FCA categories classes formal objects attributes & operations formal features ( e.g. Godin et al. 1998, Snelting & Tip 2000) But: In our case we analyse a forthcoming (not an existing) class structure! It is just our goal to find classes, attributes and operations! use cases "Things" formal objects formal features is a reasonable alternative, - equivalent from a mathematical point of view, - even more "natural" from the use case point of view, -... but less "natural" from an overall SE point of view: functional perspective should be on top of data perspective

FCA-SE 170 Further analyses Implication analysis:. - All use cases covering thing X cover thing Y as well. Is this an indicator of a possible use case refinement? Block relation analysis: - Try to fill up the incidence table in such a way that blocks (rectangles with a total incidence relation) are formed. Each block can be considered as a candidate for a system component (I.e. as a collection of coherent concepts)

FCA-SE 180

FCA-SE 190 Conclusions FCA supports building class & object models from use case descriptions by exposing class candidates, their attributes and operations. Choice between class candidates is done interactively - no automated decisions. FCA analysis illuminates both functional and data perspectives of classes & objects. Implication analysis supports refinement of functional decomposition. Block relation analysis supports modularisation and component structure. FCA is a good basis for the discourse between system owners, users and developers. BASE tool generates concept lattices, suggestions for functional refinement, modularisation and plausibility checks. Additional effort for applying FCA analysis and the BASE tool is marginal.

Goals and aims Formal objects Formal attributes Formal concepts Meaning of order relation References FCA-SE 200 Analysis of class structure Classes Attributes and operations Abstract classes Generalisation Godin et al. [GMM+ 98] Analysis of class structure Program variables Attributes and operations Classes Generalisation Snelting& Tip [S-T 00] Modularisation of legacy systems Program procedures Program variables Modules (of maximal cohesion) Nesting of modules Lindig& Snelting [L-S 97] Configuration analysis Code segments Controlling expressions Configurations Specialisation of configurations Lindig& Snelting [Sne 96], [Lin 98] Searching class libraries Software modules Keywords States during searching Specialisation of search results Lindig [Lin 95] Project control "Things" relevant for projects Project activities States of project progress Grade of project progress Vogt [Vog 97] Finding class candidates "Things" relevant for use cases Use cases Class candidates Specialisation of functionality Düwel& Hesse [Düw 00], [D-H 98]

References FCA-SE 210 [Düw 00] S. Düwel: BASE- ein begriffsbasiertes Analyseverfahren für die Software-Entwicklung, Dissertation, Universität Marburg 2000, http://www.ub.uni-marburg.de/digibib/ediss/welcome.html [D-H 98] S. Düwel, W. Hesse: Identifying Candidate Objects During System Analysis, Proc. CAiSE'98/IFIP 8.1 3 rd Int. Workshop on Evaluation of Modeling Methods in System Analysis and Design (EMMSAD'98), Pisa 1998 [D-H 00] S. Düwel, W. Hesse: Bridging the gap between Use Case Analysis and Class Structure Design by Formal Concept Analysis. In: J. Ebert, U. Frank (Hrsg.): Modelle und Modellierungssprachen in Informatik und Wirtschaftsinformatik. Proc. "Modellierung 2000", pp. 27-40, Fölbach-Verlag, Koblenz 2000 [D-H 03] S. Düwel, W. Hesse: BASE ein begriffsbasiertes Analyseverfahren für die Software- Entwicklung. in: K. Lengnink et. al (Hrsg.) Mathematik für Menschen, Festschrift f. R. Wille, TU Darmstadt 2003 [G-W 98] B. Ganter, R. Wille: Formal Concept Analysis, Mathematical Foundation, Springer 1998 [GMM+ 98] R. Godin et al.: Design of class hierarchies based on concept (Galois) lattices. Theory and Apllication of Object Systems (TOPAS) 4(2), pp. 117-134, 1998 [Jac 93] [Lin 95] [Lin 98] I. Jacobson: Object-Oriented Software Engineering - A Use Case Driven Approach; Revised Printing, Addison- Wesley 1993 C. Lindig: Komponentensuche mit Begriffen, Proceedings Software-technik '95, Braunschweig, S. 67-75, Oktober 1995 C. Lindig: Analyse von Softwarevarianten, Informatik-Bericht 98-04, Technische Universität Braunschweig, Januar 1998

References (cont'd) FCA-SE 220 [L-S 97] C. Lindig, G. Snelting: Assessing Modular Structure of Legacy Code Based on Mathematical Concept Analysis, Proceedings of the International Conference on Software Engineering (ICSE 97), Bo-ston, USA, pp. 349-359; 1997 [L-S 00] C. Lindig, G. Snelting: Formale Begriffsanalyse im Software Engineering. In: [S-W 00] [M-O 92] J. Martin, J. Odell: Object-Oriented Analysis and Design. Prentice Hall 1992 [Mey 88] B. Meyer: Object oriented software construction. Prentice Hall 1988 [Sne 96] G. Snelting: Reengineering of configurations based on mathemati-cal concept analysis, ACM Transactions on Software Engineering and Methodology, 5(2), pp.146--189, April 1996 [S-T 00] G. Snelting, F. Tip: Understanding Class Hierarchies Using Concept Analysis, ACM Transactions on Programming Languages and Systems, pp. 540-582, May 2000 [S-W 00] G. Stumme, R. Wille (Hrsg.): Begriffliche Wissensverarbeitung: Methoden und Anwendungen. Springer 2000 [Vog 97] F. Vogt: Supporting Communication in Software Engineering: An Approach Based on Formal Concept Analysis, Preprint Nr. 1926, Technische Universität Darmstadt, Fachbereich Mathematik, 1997 [Wil 00] R. Wille: Begriffliche Wissensverarbeitung: Theorie und Praxis. Informatik-Spektrum 23.6, pp. 357-369 (2000)