Class Analysis with Concept Lattices

1
Class Analysis with Concept Lattices

• Uri Dekel
• Department of Computer Science
• Technion, Haifa, Israel

2
Outline

• Introduction
• Formal Concept Analysis
• Stage I Interface Analysis
• Stage II Implementation Analysis
• Stage III Code Inspection
• Version Comparison
• Overview of other FCA applications

3
Domain

• Understanding and analyzing individual Java
  classes
• Interface (black-box) analysis
• Reducing the learning curve
• Discovering interface problems
• Implementation (white-box) analysis
• Understanding class structure and role of fields
• Discovering implementation problems
• Code review and inspection
• Understanding the purpose of each method from its
  code.
• Ensuring style, quality, and correctness
• Discovering code reuse opportunities
• Version Comparison

4
Problems

• Classes can be very large and complex
• OOP practices promote use of many methods
• Meyers shopping list approach advocates
  completing the interface with syntactic-sugar
  methods
• Rules of software evolution The entropy of
  software artifacts increases with time
• Delocalisation
• Definition order not meaningful

Fact A quarter of all public methods are found
in classes with more than 100 methods !
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Research Question

• Can Formal Concept Analysis (FCA) help alleviate
  some of these problems?
• FCA is a mathematical classification technique
• Helps discover meaningful data in binary
  relations
• Can be visualized with Concept Lattices
• FCA has been applied to many CS and SW problems
• Automatic modularization
• Automatic construction and refinement of class
  hierarchies
• Reverse engineering complex systems
• Smart component repositories

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Formal Concept Analysis

• Input A context ltO,A,Rgt
• O is a set of objects
• A is a set of attributes
• R is a binary relation between O and A
• Mapping Galois Connection
• Common attributes of a set of objects
• Common objects of a set of attributes
• Output Concepts s.t.

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FCA Example

• Field-accesses context of a class
• Objects are fields, attributes are methods,
  relation specifies which methods access each
  field

Context
Concepts
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Concept Lattices

• Partial order
• Defines domination between concepts
• Visualized as a concept lattice

9
Interpreting Class Lattices

• We use only sparse lattices
• Economical but equivalent representation
• Each object introduced in lowest concept
• Each attribute introduced in highest concept
• Interpretation
• Each method uses all fields introducedin the
  same concept or below
• Reveals
• Possible restructuring
• Asymmetry between coordinates

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Field-Accesses Context

• Field usage is critical for understanding a class
• All implementations of an operation use the same
  fields
• Representation changes are rare
• Methods that use the same combination are related
• Can be calculated directly from the .class file
• Allows some reverse engineering without source
  code
• Calculated using standard static analysis
• Currently restricted to accesses inside the class

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Lattices vs. Tables

• The lattice and the accesses table contain
  exactly the same information!
• Advantages of the table
• It is immediately clear what fields are accessed
  by each method.
• Advantages of the lattice
• Related methods appear together. Makes it easier
  to
• Discover what exactly each method does.
• Discover duplicate methods.
• Find inconsistencies.
• Determine level of abstraction.

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Graph example

• Accesses tables (only a part is visible)

13
Graph example (cont.)
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Class Assignment

• Try to find as many problems as possible in the
  Molecule class.
• Examples
• Duplicate methods.
• Different methods that do the same thing (not
  composites!).
• Inconsistencies in types and names between
  methods.
• Asymmetries in the interface.
• Invariants that are violated.
• Methods which do not access the fields you expect
  them to.
• Assume that
• All methods are documented.
• Some methods declare and throw exceptions.

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Zoom-in Zoom-out approach

• Problems
• Concept lattices can be very large
• Number of concepts is bound by
• Polynomial for most real-life contexts
• Linear for 99.5 of classes!
• Elaborate member details are cumbersome
• Solution
• Provide (semi-) automatic zoom in/out tools

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Running Example

• The Molecule class from CDK
• CDK Chemistry Development Kit
• Open source library of chemistry related classes
• Developed at the Max Plank institute in Germany
• Used in chemistry visualization applications
• Why the Molecule class?
• Has a large interface (nearly 75 public members)
• The represented entity is familiar to most people
• Methodology was successfully applied to other
  classes as well

Our methodology revealed several new bugs and
issues !
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Stage I Interface Analysis

• Programming today is a race between software
  engineers striving to build bigger and better
  idiot-proof programs, and the universe trying to
  produce bigger and better idiots. So far, the
  universe is winning
• --Rich Cook
• There are only two industries that refer to
  theircustomers as users
• -- Edward Tufte

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Interface Analysis

• Purpose
• Understand the functionality provided by the
  class
• Map expectations into interface members
• The concept assignment or feature mapping
  problems
• Discover problems
• e.g. missing or superfluous functionality,
  exposed implementation details, inconsistent
  naming
• Methodology
• Methods are partitioned into concepts
• Heuristic for automatic feature categorization
• Zoom-out and reason about overall structure
• Zoom-in and examine specific functionalities

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Preliminaries

• Mapping features to interface members requires
  knowing what the features are
• Tasks
• Surmising abstraction, purpose and role
• Determining vocabulary
• Predicting mandatory- and non-mandatory
  functionality
• Information sources
• Domain-specific knowledge
• Class environment
• E.g. hierarchy, dependencies, etc.
• This step is not unique to concept analysis

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Context Selection

• Only client-visible methods should be used
• Public methods by default, protected if client is
  subclass, default if client is in the same
  package
• All fields are kept to ensure a correct
  partitioning
• Will be removed after the lattice is constructed
• Context parameters (boldface indicates selection)

(bold indicates our selection, F representsdont
care )
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Constructing the Lattice

• The lattice is too cluttered to grasp immediately
• We start zooming-out
• Layers correspond to levels of abstraction

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Simplifying concepts

• We summarize the responsibilities of each concept
  in a quick skim over method signatures
• This process cannot be fully-automated at present
• Still too cluttered !

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Naming Concepts

• Name concepts based on summary
• Use symbolic representations for common
  responsibilities

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Horizontal Decomposition

• Remove top- and bottom- concepts
• Connected components are orthogonal
• Problem with title (on the right) becomes obvious
• Abundance of trivial components implies
  record-like behavior
• Cohesive component requires further analysis

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Abstraction Lattice

• Heuristic for clustering concepts
• Concepts dominated by the same top-layer concepts
  belong in the same cluster

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Match services against expectations

• Functionality search order
• Expected mandatory features
• Expected non-mandatory features
• Unexpected features
• For each functionality
• Mark relevant clusters
• Mark relevant concepts
• Examine each concept
• Example
• Bond management

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Stage II Implementation Analysis

• "There are two ways of constructing a software
  design One way is to make it so simple that
  there are obviously no deficiencies, and the
  other way is to make it so complicated that there
  are no obvious deficiencies. C. A. R.
  Hoare

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Implementation Analysis

• Purpose
• Understand implementation and structure.
• Discover problems
• e.g. redundant fields, bad naming conventions,
  wrongly-implemented operations
• Methodology
• Code is not inspected at this stage!
• All information derived from lattice
• Zoom-in
• Including private fields and methods
• Listing full signatures and introducing classes
• Embedded call-graph

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Embedded Call Graph

• Superposition of call-graph on concept lattice
• A semantics-based CG layout heuristic
• Keeps related methods together while reducing
  crossings
• Helps investigate relations between methods
• e.g. surmise level of abstraction or discover
  wrappers
• Used later for selecting an order for code
  inspection
• Example ECG of Pnt3D

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Investigate Fields

• Examine unused fields
• Might indicate unimplemented stubs or dead
  structure
• Discover the roles of fields
• Easy for trivialcomponents
• Harder for thecohesive one
• Investigateinterdependency
• Naming quality

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Investigate Special Methods

• Methods that (should) use the entire state should
  be in the top concept
• Exceptions can indicate problems
• Zoom-in by adding declaring class details
• Examine methodsthat do not use fields
• e.g. discoverundeclared statics

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Investigate Other Methods

• Ensure symmetry where expected
• e.g. C11 and C13, C10 and C14, C16 and C17
• Ensure methods use expected access patterns
• Add non-publicmethods to lattice

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Stage III Code Inspection

• Real programmers don't document. If it was hard
  to write, it should be hard to understand --A
  nonymous
• Real programmers can write assembly code in any
  language --Larry Wall

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Code Inspection

• Purpose
• Understand functionality which is unclear after
  the previous stages.
• Ensure quality of code and style
• Methodology
• Select an order for effective reading
• Maximizing reading throughput
• Maximizing discovered defects
• Minimizing repetitions

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Code Inspection Problem

• Original source code order not effective
• Co-definitions.
• No incremental order
• All class members are defined simultaneously
• Perturbations to intended order
• Evolution and maintenance
• Language issues (e.g. inheritance)
• Style issues (e.g. public before private)

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Reading Strategy

• Organize methods into groups of related
  functionality and order these groups (global
  order)
• Order the methods inside each group (local order)
• Each concept is a group
• Same-concept methods are similar in purpose,
  semantics and implementation
• Increased prospects of understanding differences
  between methods and discovering redundancies and
  replications
• Less infrastructure (e.g. external libraries) to
  memorize

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Reading Strategy

• Global order (by importance)
• Read each HD component separately
• Each represents an independent functionality
• Read concepts in ascending order of layers
• Exploit similar level of abstraction
• Read concepts of the same cluster together
• Local order (by importance)
• Read methods in topological order
• Use restricted ECG
• Read methods in same ECG component together
• Resolve equivalencies with simplest-first rule

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Inspection Tasks

• Inspection tasks customized for our reading order
• Finding duplicate services inside a concept
• e.g. getDegree and getBondCount
• Identifying code-sharing opportunities
• e.g. overloads of addBond
• Verify that low-level methods are not bypassed
• e.g. getBondCount, getBondAt
• An addition to standardinspection tasks

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Version Comparison

• Zero defects The result of shutting down a
  production line --Kelvin Throop III, "The
  Management Dictionary"

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Version Comparison

• Examine an outline of the differences before the
  actual details
• Example

Differences between the original version of the
Graph class of VGJ (Visualizing Graphs with
Java) and the Technion adaptation of that
class. Originals appear in bold font,
Modifications appear in plain font
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Other applications of FCA
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Hierarchy Construction

• Godin and Mili (93) classified Smalltalk classes
• Objects Names of concrete collection classes
• Attributes Names of messages that these classes
  accept.

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Hierarchy Construction (cont.)

• Output Multiple inheritance class hierarchy

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Hierarchy Construction (cont.)

• There are four types of concepts
• Concrete concepts
• Introduce both attributes and objects
• Intersect concepts
• Introduce objects but no attributes
• Abstract concepts
• Introduce attributes but no objects
• Connector (empty) concepts
• Do not introduce objects or attributes
• Can be removed!

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Hierarchy Construction (cont.)

• Hierarchy after removing connectors and naming
  abstract concepts

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Other Applications

• Modularizing legacy code
• Objects Global variables.
• Attributes Functions.
• Lattice is horizontally decomposed, resulting in
  modules.
• Managing component repositories
• Objects Software components.
• Attributes Text-based properties or features.
• Lattice includes all search paths.

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The End

• Theory is when you know something, but it
  doesn't work. Practice is when something works,
  but you don't know why. Programming combines
  theory and practice Nothing works and you don't
  know why
• -- Anonymous