Identifying Traits with Formal Concept Analysis

Identifying Traits with
Formal Concept Analysis
Adrian Lienhard, Stéphane Ducasse and Gabriela Arévalo
Software Composition Group
University of Berne, Switzerland

Overview
“too high”...
...cancelled

duplicated
methods

ASE‘05 - Identifying Traits with FCA Adrian Lienhard - lienhard@iam.unibe.ch 2 / 16

Overview
“too high”...
...cancelled

duplicated
methods traits


Overview
“too high”...
...cancelled
FCA

duplicated
methods traits


Background: Traits in a Nutshell
Generic properties
GraphicalObject
Colored Bordered
Circle Polygon


Generic properties
GraphicalObject
Colored Bordered
Circle Polygon

ColoredCircle BorderedColoredPol.

Colored Bordered
Colored


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

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


Roadmap

‣ FCA in a nutshell
‣ Approach overview
‣ Illustration of our approach on case study
‣ Evaluation of case study
‣ Conclusion


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


FCA in a Nutshell
properties
small far moon
Mercur x
elements

y
Mars x x
Jupiter x x
Pluto x x x


{Mars, Pluto, Jupiter},{moon}


FCA in a Nutshell
properties
small far moon
Mercur x
elements

y
Mars x x
Jupiter x x
Pluto x x x


{Pluto, Jupiter},{moon, far}


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
Pl
small, moon, far

Concept Lattice
{Pluto, Jupiter},{moon, far}


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
Pl
small, moon, far

Concept Lattice
{Mars, Pluto, Jupiter},{moon} less elements
{Pluto, Jupiter},{moon, far} more properties


Approach Overview
Stage 1

input generation FCA application ﬁltering manual selection

{
Stage 2
for each class
and trait
input generation FCA application manual selection


Case Study

‣ ST-80 Stream and Collection libraries
‣ Comparison with purely manual refactoring
[OOPSLA’03]
‣ Illustration of our approach on example of
Stream hierarchy...


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


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


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


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


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


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


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


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


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


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?

Refactored Collection
Hierarchy
Legend:

Collection inherits from
composed from

Set SequenceableCollection

SortedCollection OrderedCollection Array

TRemoving- TOrderedSorted- TSequenced-
Elements Common ElementAccess


Identifying Traits with Formal Concept Analysis

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