FCA-SE 10

Formal Concept Analysis used for

object-oriented software modelling

Wolfgang HesseFB 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

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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

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The SW development cycle (acc. to the EOS* model)

Use environment

Use & Operations

Implementation

Analysis

Design

planning,analyticactivities

Development environment

synthetic, verifyingactivities* (for Evolutionary,

Object-oriented Software development)

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Concepts everywhere …

Use & Operations

Implementation

Analysis

Design

Domain concepts

Business concepts

System concepts

Programmingconcepts

Design & architectural

concepts

Use & user concepts Maintenance

concepts

Test & integration concepts

Process concepts

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James Rumbaugh: "The objects in the model should be application-domain 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."

Citations on concepts …

Use Formal Concept Analysis (FCA) to form and evaluate the concepts needed for software development

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2 Object-oriented modelling: Aspects and methods

Aspects of OO modelling

OO methods: • 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).

ontological

behavioural structural

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From use cases to classes &

objects

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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])

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Clerk

Wine trade business

Receive order

Process order

Order missing products

Example of a use

case diagram

Determine inv. stock

Create deliv. instructions

Define max. & min. stock quantity

Process deliveryresults

Process inc. delivery

<<include>>

<<include>>

<<include>>

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Formal Concept Analysis (FCA)

AI := { m M | g I m for all g A } the set of attributes common to all objects in A

BI := { 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

AI = B und BI = A .A the extent of a concept B the intent of a concept

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

Sub- / super concept relation(A, B) ≤ (C, D)

iff A C ( D B )

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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

3 Bridging the gap: The BASE approach

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Resulting line diagram

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Crossing perspectives via FCA

...

...

Functional perspective (Use cases)

Data perspective ("Things")

general

special

particular

common

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- 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?

Crossing perspectives via FCA (2)

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Alternative approaches

Other possible associations with FCA categories

• classes formal objectsattributes & 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 formal objects"Things" 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

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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)

Further analyses

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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.

Conclusions

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Goals and aims Formal objects

Formal attributes

Formal concepts

Meaning of order relation

References

Analysis of class structure

Classes Attributes and operations

Abstract classes

Generalisa-tion

Godin et al. [GMM+ 98]

Analysis of class structure

Program variables

Attributes and operations

Classes Generalisa-tion

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

Configura-tions

Specialisa-tion of con-figurations

Lindig& Snelting [Sne 96], [Lin 98]

Searching class libraries

Software modules

Keywords States during searching

Specialisa-tion 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

Specialisa-tion of functionality

Düwel& Hesse [Düw 00], [D-H 98]

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[Düw 00] S. Düwel: BASE- ein begriffsbasiertes Analyseverfahren für die Software-Entwicklung, Disser-tation, 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 3rd 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] I. Jacobson: Object-Oriented Software Engineering - A Use Case Driven Approach; Revised Printing, Addison- Wesley 1993

[Lin 95] C. Lindig: Komponentensuche mit Begriffen, Proceedings Software technik '95, Braunschweig, S. 67-75, Oktober 1995

[Lin 98] C. Lindig: Analyse von Softwarevarianten, Informatik-Bericht 98‑04, Technische Universität Braunschweig, Januar 1998

References

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[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)

References (cont'd)