Automatic Dimension Inference and
Checking for Object-Oriented Programs
Sudheendra Hangal
Monica S. Lam
http://suif.stanford.edu/unifi
International Conference on Software Engineering
Vancouver, Canada
May 20th, 2009

Overview
• A fully automatic dimension inference system
for Java programs
• Diff-based method to detect dimension errors
• Case-study on a 19KLoC program
• UniFi: Usable open-source tool

Dimensionality Checking
Used by physicists
(and high-schoolers)
E.g.
E = m * c;
[M x L2 x T-2 ] vs. [M x L x T-1]
Doesn’t “type check”!

Dimensions are Everywhere
• Program values have dimensions like
id, $, date, port, color, flag, state, mask, count,
message, filename, property, …
and of course, mass, length, time, etc.
• We focus on primitive types and strings
– Hard to define custom types for everything
– No benefit of type-checking

Programmer View
java.awt.MouseWheelEvent
public MouseWheelEvent(Component source,
int id, long when, int modifiers,
int x, int y, int clickCount,
boolean popupTrigger,
int scrollType, int scrollAmount,
int wheelRotation);

Type-checker View
java.awt.MouseWheelEvent
public MouseWheelEvent(Component source,
int id, long when, int modifiers,
int x, int y, int clickCount,
boolean popupTrigger,
int scrollType, int scrollAmount,
int wheelRotation);

Observation
• Programmers use suffixes to capture
dimensions
int proxyPort, backgroundColor;
long startTimeMillis, eventMask;
String inputFilename, serverURL;

Putting Dimensions to Work
How do we get the benefit of dimension
checking in mainstream languages ?
2 ideas:
1) Detect (likely) errors automatically by
diff’ing dimension usage between programs
2) Bootstrap from standard libraries

UniFi’s Core Idea
• Infer dimensions of variables automatically
– Static analysis, type inference techniques
– Standard Java programs, zero annotation burden
• Optional: Examine results
• Compare inferred dimensions across two
programs that have something in common

Results 1
UniFi
Program 1 Inference
Diffs
UniFi
Diff
…
UniFi UniFi
Program 2 Inference GUI
Results 2

Use Cases
• Report changes as the same code evolves
– Nightly builds
– During program maintenance
• Compare against a different configuration
– Different programs using the same library
– 2 different implementations of an interface
– Implementation of a library v/s program using it
– Different programmers’ code

Inference Algorithm
• Input: Java program
• Assigns dimensions to variables
– Initially independent
• Set up constraints between dim. vars
• Solve constraints
• Output: a set of relations between dimension
variables

Inference Example (1)
x = y + z x y z
a < b a b
d[i] i d.length
u = v * w u v * w

Inference Example (2)
int f(x) { return x * x; }
a1 = f(a); a1 a * a
b1 = f(b); b1 b * b
• Context sensitive analysis
– Uses method summaries

OO Constraints
• Subtypes retain supertype interface
– Liskov Substitution Principle
• Constrains dimensions of parameters and
return value of subtype methods
class A { int m( int x ) { … } }
class B extends A { int m( int x ) { … } }

Multiply/Divide Constraints
• Linear equation style expressions for multiply
and divide
– Special handling of java.math libraries
• Solved using Gaussian elimination style
algorithm

Comparing Inferred Dimensions
• Identify common variables
– Same name of field, position of method param,
etc.
• Compare equivalence classes formed by
unification constraints
• Compare Multiply-divide constraints
– Need canonical formulas for dvars
– Make common variables more “stable” than
others
– See paper for details

Case Study: bddbddb
http://sourceforge.net/projects/bddbddb
• Retroactively run over 10 months of active
development
– Oct. 2004 to July 2005, 292 builds
– Approx. 19,000 lines of Java code
• Compared successive nightly builds

Results
• 26 reports, across 19 pairs of builds
• 5 real errors (+ fixes)
• False Positives
– Trivial reasons like field not used
– Probably easy to reduce number

Bug Example
double NO_CLASS = …; // default class id
double NO_CLASS_SCORE = …; // default score
…
double vScore=NO_CLASS, aScore=NO_CLASS;
double vClass=NO_CLASS, aClass=NO_CLASS;
• UniFi detected that independent dimensions
NO_CLASS and NO_CLASS_SCORE merged

Inference Example
double[] distribution = new double[numClasses];
... // compute sum
... // initialize distribution array
for (int i=0; i < NUM_TREES; ++i)
distribution[i] /= sum;
numClasses
distribution.length However: not caught
i since this was in new
NUM_TREES code!

Experiences
• Sometimes bugs indicated by removal of
unification constraint (“error of omission”)
• Dimensionally inconsistent code
– Ignore hashCode(), compareTo()
– Cannot interpret semantically

Experiences
• Types of Errors: Sometimes can be difficult to
root-cause
• Dimensions vs. Units
– May not catch wrong scaling factor…
…but might catch the absence of one (?)

Future Work
• Explore use-cases for UniFi in the wild
• “S.I. Units” for platform libraries
– Using JSR-308 for Java w/understandable names
• An intriguing possibility: Dimension inference
for hardware languages like Verilog

Related Work
• Osprey (Jiang and Su, ICSE ‘06)
• XeLda (Antoniu et al, ICSE '04)
• Type qualifiers (Foster et al, PLDI '99)
• Lackwit (O’Callahan and Jackson, ICSE '97)
• Fortress (Allen et al, OOPSLA '04)

Conclusions
• UniFi is the first dimension inference system
for standard Java programs
– for automatically detecting bugs
– for bootstrapping use of dimensions via libraries
– Many uses waiting to be explored
Open sourced and available from:
http://suif.stanford.edu/unifi
Users and collaborators welcome

Automatic Dimension Inference and
Checking for Object-Oriented Programs
Sudheendra Hangal
Monica S. Lam
http://suif.stanford.edu/unifi
International Conference on Software Engineering
Vancouver, Canada
May 20th, 2009

Backup slides

Bug Example
double[] distribution = new double[numClasses];
... // compute sum and initialize
... // distribution array
for (int i=0; i < NUM_TREES; ++i)
distribution[i] /= sum;
numClasses
distribution.length However: not caught
i
NUM_TREES since this was in new
code!

Dimension Variables
Assign dimension variables (dvars) to
• Fields
• Interfaces: Method Parameters, Return values
• Array elements and lengths
• Local Variables
• Constants
• Result of Multiply/Divide Operations
• Primitive types only

Mechanics
• Bytecode based static analysis
• Scripts to monitor a CVS/SVN repository and
generate diffs
• GUI to view inference results, correlated with
unification points in source code.