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Identifying Traits with Formal Concept Analysis
1. Identifying Traits with
Formal Concept Analysis
Adrian Lienhard, Stéphane Ducasse and Gabriela Arévalo
Software Composition Group
University of Berne, Switzerland
2. Overview
“too high”...
...cancelled
duplicated
methods
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3. Overview
“too high”...
...cancelled
duplicated
methods
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6. Background: Traits in a Nutshell
Generic properties
GraphicalObject
Colored Bordered
Circle Polygon
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7. Background: Traits in a Nutshell
Generic properties
GraphicalObject
Colored Bordered
Circle Polygon
ColoredCircle BorderedColoredPol.
Colored Bordered
Colored
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8. Background: Traits in a Nutshell
Generic properties
GraphicalObject
Colored Bordered
Circle Polygon
ColoredCircle BorderedColoredPol. Single inheritance: limited
expressiveness
Colored Bordered
Multiple inheritance:
Colored
complexity
Mixin inheritance: fragility
Goal of traits: reuse mechanism due to linearization
avoiding complexity
ASE‘05 - Identifying Traits with FCA Adrian Lienhard - lienhard@iam.unibe.ch 3 / 16
9. Background: Traits in a Nutshell
Reuse mechanism Trait = “interface with implementation”
complementary to TColored
inheritance [ECOOP’03]
{ }
red rgb
provided green rgb: required
Today in Perl 6, Squeak, =
Scala, Fortress, ... methods methods
hash
...
... ...
ColoredCircle BorderedColoredPol.
trait composition
TColored TBordered
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10. Roadmap
‣ FCA in a nutshell
‣ Approach overview
‣ Illustration of our approach on case study
‣ Evaluation of case study
‣ Conclusion
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11. FCA in a Nutshell
properties
small far moon
Mercur x
elements
y
Mars x x
Jupiter x x
Pluto x x x
Concept: maximal group of elements
based on their common properties
ASE‘05 - Identifying Traits with FCA Adrian Lienhard - lienhard@iam.unibe.ch 6 / 16
12. FCA in a Nutshell
properties
small far moon
Mercur x
elements
y
Mars x x
Jupiter x x
Pluto x x x
Concept: maximal group of elements
based on their common properties
{Mars, Pluto, Jupiter},{moon}
ASE‘05 - Identifying Traits with FCA Adrian Lienhard - lienhard@iam.unibe.ch 6 / 16
13. FCA in a Nutshell
properties
small far moon
Mercur x
elements
y
Mars x x
Jupiter x x
Pluto x x x
Concept: maximal group of elements
based on their common properties
{Mars, Pluto, Jupiter},{moon}
{Pluto, Jupiter},{moon, far}
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14. FCA in a Nutshell
properties Me, Ma, Ju, Pl
small far moon
Mercur x
elements
y
Mars x x Me, Ma, Pl Ma, Ju, Pl
Jupiter x x small moon
Pluto x x x
Ma, Pl Ju, Pl
small, moon moon, far
Concept: maximal group of elements
Pl
based on their common properties
small, moon, far
Concept Lattice
{Mars, Pluto, Jupiter},{moon}
{Pluto, Jupiter},{moon, far}
ASE‘05 - Identifying Traits with FCA Adrian Lienhard - lienhard@iam.unibe.ch 6 / 16
15. FCA in a Nutshell
properties Me, Ma, Ju, Pl
small far moon
Mercur x
elements
y
Mars x x Me, Ma, Pl Ma, Ju, Pl
Jupiter x x small moon
Pluto x x x
Ma, Pl Ju, Pl
small, moon moon, far
Concept: maximal group of elements
Pl
based on their common properties
small, moon, far
Concept Lattice
{Mars, Pluto, Jupiter},{moon} less elements
{Pluto, Jupiter},{moon, far} more properties
ASE‘05 - Identifying Traits with FCA Adrian Lienhard - lienhard@iam.unibe.ch 6 / 16
16. Approach Overview
Stage 1
input generation FCA application filtering manual selection
{
Stage 2
for each class
and trait
input generation FCA application manual selection
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17. Case Study
‣ ST-80 Stream and Collection libraries
‣ Comparison with purely manual refactoring
[OOPSLA’03]
‣ Illustration of our approach on example of
Stream hierarchy...
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18. Generating Input for FCA
Detecting cancellations and duplications Stage 1
Identify real interface of a class taking into account...
...
Stream
Idiom “too high”
next
boolean ‣ implement methods “too
sends message next
int32
...
high” in common superclass
‣ (implicitly) cancel methods
WriteStream ReadStream
in inappropriate subclasses
... ...
next next
... ....
ReadWriteStream
...
next Fact ST-80 Collection library:
... 131 methods too high (~10%), and
of those, 106 implicitly cancelled
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19. Generating Input for FCA
Detecting cancellations and duplications Stage 1
Identify real interface of a class taking into account...
invokes ...
Stream
Idiom “too high”
cancelled next
‣ implement methods “too
boolean
method int32 sends message next
high” in common superclass
...
‣ (implicitly) cancel methods
WriteStream ReadStream
in inappropriate subclasses
... ...
next next
... ....
ReadWriteStream
...
next Fact ST-80 Collection library:
... 131 methods too high (~10%), and
of those, 106 implicitly cancelled
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20. Applying FCA Stage 1
Elements: all concrete classes
Properties: all concrete methods (identifying duplications)
Mapping: method in the real interface of the class
WS, RWS, RS
atEnd
WS, RWS RWS, RS
atEnd, nextPut:, atEnd, next,
next:put: boolean
WS RWS RS
atEnd, nextPut:, atEnd, nextPut:, atEnd, next,
next:put:, next:put:, next, boolean,
contents1 boolean, contents2 contents3
atEnd, nextPut:,
next:put: next,
boolean, contents1,2,3
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21. Filtering Stage 1
‣ reduce properties-sets to delta between
sub-/superconcept
‣ remove concepts with no classes
WS, RWS, RS
atEnd
WS, RWS RWS, RS
nextPut:,
next, boolean
next:put:
WS RWS RS
contents1 contents2 contents3
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22. Selecting Traits and Hierarchy
Reconstruction Stage 1
Partly manual task: deciding whether a
concept becomes a class or a trait
Stream
WriteStream ReadWriteStream ReadStream
TWriteableStream TReadableStream
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23. Invocation Analysis Stage 2
Generating input: analyzing transitive method
invocations of the class/trait
Applying FCA
‣ elements: all methods of the class/trait
‣ properties: (transitive) method invocations
‣ mapping: identifying invocations with methods
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24. Selecting Traits Stage 2
Manual task of selecting traits.
Lattice provides interesting alternatives:
‣ Additional methods in super-concepts
‣ Fewer methods in sub-concepts
Stream
ReadStream ReadWriteStream WriteStream
TReadableStream TWriteableStream
TReadableMultiple TWriteablePutData
TReadableFileIn TWriteablePutCharacter
TWriteableMultiple
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25. Comparison with
Manual Refactoring
Stream library
‣ almost identical result: inheritance reshaping + two
main traits
‣ difference: conceptual vs. functional sub-traits
Collection library
‣ Manual refactoring has identified more traits
‣ Different layers of traits with overriding behavior
‣ Our approach curative, manual approach speculative
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26. Conclusion
‣ Succeeded in curing problems by
restructuring hierarchy with traits (stage 1)
‣ Successful identification of fine-grained traits
also when code is not shared (stage 2).
‣ Limitations:
• Detection based on conceptual meaning of
methods alone not possible
• Missing methods can cause too small traits
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27. Conclusion
‣ Succeeded in curing problems by
restructuring hierarchy with traits (stage 1)
‣ Successful identification of fine-grained traits
also when code is not shared (stage 2).
‣ Limitations:
• Detection based on conceptual meaning of
methods alone not possible
• Missing methods can cause too small traits
Questions?
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28. Refactored Collection
Hierarchy
Legend:
Collection inherits from
composed from
Set SequenceableCollection
SortedCollection OrderedCollection Array
TRemoving- TOrderedSorted- TSequenced-
Elements Common ElementAccess
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