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Use of Models in Analysis and Design
Sriram K. Rajamani
Rigorous Software Engineering
Microsoft Research, India
Models
• Abstractions of reality
• All branches of science and engineering use models. Some examples:– Differential equations– State machines
• Models enable conquering complexity– Allow focus on one issue at a time, while
ignoring others
Models in software engineering
• Mainstream mantra:– “Code is truth, and only truth”
• Models are used, but not widely– Requirements capturing (UML):
• Used specialized domains: telcom, automotive, embedded sytstems
– Development tools:• Testing and verification
– Design• Model driven development
This talk
• Use of models in analysis and design– Personal experience
• Analysis:– Extracting analyzable models from source code using
iterative refinement
• Design:– My assessment of state of the art and important
research problems
Models in Analysis
Software Validation
• Large scale reliable software is hard to build and test.
• Different groups of programmers write different components.
• Integration testing is a nightmare.
Property Checking
• Programmer provides redundant partial specifications
• Code is automatically checked for consistency
• Different from proving whole program correctness – Specifications are not complete
Interface Usage Rules
•Rules in documentation–Incomplete, unenforced, wordy
–Order of operations & data access
–Resource management
•Disobeying rules causes bad behavior
–System crash or deadlock
–Unexpected exceptions
–Failed runtime checks
Does a given usage rule hold?
• Checking this is computationally impossible!
• Equivalent to solving Turing’s halting problem (undecidable)
• Even restricted computable versions of the problem (finite state programs) are prohibitively expensive
Why bother?
Just because a problem is undecidable, it doesn’t go away!
Automatic property checking = Study of tradeoffs
• Soundness vs completeness – Missing errors vs reporting false alarms
• Annotation burden on the programmer
• Complexity of the analysis– Local vs Global– Precision vs Efficiency– Space vs Time
Broad classification
• Underapproximations– Testing
• After passing testing, a program may still violate a given property
• Overapproximations– Type checking
• Even if a program satisfies a property, the type checker for the property could still reject it
Current trend
• Confluence of techniques from different fields:– Model checking– Automatic theorem proving– Program analysis
• Significant emphasis on practicality
• Several new projects in academia and industry
Model Checking• Algorithmic exploration of state space of the
system
• Several advances in the past decade: – symbolic model checking– symmetry reductions– partial order reductions– compositional model checking– bounded model checking using SAT solvers
• Most hardware companies use a model checker in the validation cycle
enum {N, T, C} state[1..2]
int turn
init
state[1] = N; state[2] = N
turn = 0
trans
state[i]= N & turn = 0 -> state[i] = T; turn = i
state[i] = N & turn !=0 -> state[i] = T
state[i] = T & turn = i -> state[i] = C
state[i] = C & state[2-i] = N -> state[i] = N
state[i] = C & state[2-i] != N -> state[i] = N; turn = 2-i
N1,N2turn=0
T1,N2turn=1
T1,T2turn=1
C1,N2turn=1
C1,T2turn=1
N1,T2turn=2
T1,T2turn=2
N1,C2turn=2
T1,C2turn=2
N = noncritical, T = trying, C = critical
Model Checking• Strengths
– Fully automatic (when it works)– Computes inductive invariants
• I such that F(I) I
– Provides error traces
• Weaknesses– Scale– Operates only on models
• How do you get from the program to the model?
Theorem proving– Early theorem provers were proof checkers
• They were built to support asssertional reasoning in the Hoare-Dijkstra style
• Cumbersome and hard to use
– Greg Nelson’s thesis in early 80s paved the way for automatic theorem provers• Theory of equality with uninterpreted functions• Theory of lists• Theory of linear arithmetic• Combination of the above !
– Automatic theorem provers based on Nelson’s work are widely used• ESC• Proof Carrying Code
Theory of Equality. • Symbols: =, , f, g, …• Axiomatically defined:
E = E
E2 = E1
E1 = E2
E1 = E2 E2 = E3
E1 = E3
E1 = E2
f(E1) = f(E2)
• Example of a satisfiability problem: g(g(g(x)) = x g(g(g(g(g(x))))) = x g(x) x
• Satisfiability problem decidable in O(n log n)
a : array [1..len] of int;
int max := -MAXINT;i := 1;{ 1 j i. a[j] max}while (i len)
if( a[i] > max) max := a[i];
i := i+1;endwhile{ 1 j len. a[j] max}
( 1 j i. a[j] max) ( i > len)
( 1 j len. a[j]
max}
Automatic theorem proving
• Strengths– Handles unbounded domains naturally– Good implementations for
• equality with uninterpreted functions• linear inequalities• combination of theories
• Weaknesses– Hard to compute fixpoints– Requires inductive invariants
• Pre and post conditions• Loop invariants
Program analysis
• Originated in optimizing compilers– constant propagation– live variable analysis– dead code elimination– loop index optimization
• Type systems use similar analysis• Are the type annotations consistent?
Program analysis• Strengths
– Works on code – Pointer aware– Integrated into compilers– Precision efficiency tradeoffs well studied
• flow (in)sensitive• context (in)sensitive
• Weakenesses– Abstraction is hardwired and done by the
designer of the analysis– Not targeted at property checking
(traditionally)
Model Checking, Theorem Proving and Program Analysis
• Very related to each other
• Different histories– different emphasis– different tradeoffs
• Complementary, in some ways
• Combination can be extremely powerful
What is the key design challenge in a model checker for software?
It is the model!
Model Checking Hardware
Primitive values are booleans
States are boolean vectors of fixed size
Models are finite state machines !!
Characteristics of Software
Primitive values are more complicated– Pointers– Objects
Control flow (transition relation) is more complicated– Functions– Function pointers– Exceptions
States are more complicated – Unbounded graphs over values
Variables are scoped– Locals– Shared scopes
Much richer modularity constructs– Functions– Classes
Sequential C program
Finite state machines
Source code
FSM
modelchecker
Traditional approach
Sequential C program
Finite state machines
Source code
FSM
abstraction
modelchecker
C data structures, pointers,procedure calls, parameter passing,scoping,control flow
Automatic abstraction
Boolean program
Data flow analysis implemented using BDDs
SLAM
Push down model
An optimizing compiler doubles performance every 18 years
-Todd Proebsting
Computing power doubles every 18 months
-Gordon Moore
When I use a model checker, it runs and runs for ever and never comes back… when I use a static analysis tool, it comes back immediately and says “I don’t know”
- Patrick Cousot
Source Code
TestingDevelopment
PreciseAPI Usage Rules
(SLIC)
Software Model Checking
Read forunderstanding
New API rules
Drive testingtools
Defects
100% pathcoverage
Rules
Static Driver VerifierStatic Driver Verifier
SLAM – Software Model Checking
• SLAM innovations– boolean programs: a new model for software– model creation (c2bp)– model checking (bebop)– model refinement (newton)
• SLAM toolkit– built on MSR program analysis infrastructure
SLIC
• Finite state language for stating rules– monitors behavior of C code– temporal safety properties– familiar C syntax
• Suitable for expressing control-dominated properties – e.g. proper sequence of events– can encode data values inside state
State Machine for Locking
Unlocked Locked
Error
Rel Acq
Acq
Rel
state {
enum {Locked,Unlocked}
s = Unlocked;
}
KeAcquireSpinLock.entry {
if (s==Locked) abort;
else s = Locked;
}
KeReleaseSpinLock.entry {
if (s==Unlocked) abort;
else s = Unlocked;
}
Locking Rule in SLIC
prog. P’prog. P
SLIC rule
The SLAM Process
boolean program
pathpredicates
slic
c2bp
bebop
newton
do {KeAcquireSpinLock();
nPacketsOld = nPackets;
if(request){request = request->Next;KeReleaseSpinLock();nPackets++;
}} while (nPackets != nPacketsOld);
KeReleaseSpinLock();
ExampleDoes this code
obey the locking rule?
do {KeAcquireSpinLock();
if(*){
KeReleaseSpinLock();
}} while (*);
KeReleaseSpinLock();
ExampleModel checking boolean program
(bebop)
U
L
L
L
L
U
L
U
U
U
E
do {KeAcquireSpinLock();
nPacketsOld = nPackets;
if(request){request = request->Next;KeReleaseSpinLock();nPackets++;
}} while (nPackets != nPacketsOld);
KeReleaseSpinLock();
ExampleIs error path feasible
in C program?(newton)
U
L
L
L
L
U
L
U
U
U
E
do {KeAcquireSpinLock();
nPacketsOld = nPackets; b = true;
if(request){request = request->Next;KeReleaseSpinLock();nPackets++; b = b ? false : *;
}} while (nPackets != nPacketsOld); !b
KeReleaseSpinLock();
ExampleAdd new predicateto boolean program
(c2bp)b : (nPacketsOld == nPackets)
U
L
L
L
L
U
L
U
U
U
E
do {KeAcquireSpinLock();
b = true;
if(*){
KeReleaseSpinLock();b = b ? false : *;
}} while ( !b );
KeReleaseSpinLock();
b
b
b
b
ExampleModel checking
refined boolean program
(bebop)
b : (nPacketsOld == nPackets)
U
L
L
L
L
U
L
U
U
U
E
b
b
!b
Example
do {KeAcquireSpinLock();
b = true;
if(*){
KeReleaseSpinLock();b = b ? false : *;
}} while ( !b );
KeReleaseSpinLock();
b : (nPacketsOld == nPackets)
b
b
b
b
U
L
L
L
L
U
L
U
U
b
b
!b
Model checking refined
boolean program(bebop)
Observations about SLAM
• Automatic discovery of invariants– driven by property and a finite set of (false) execution paths– predicates are not invariants, but observations– abstraction + model checking computes inductive invariants
(boolean combinations of observations)
• A hybrid dynamic/static analysis– newton executes path through C code symbolically – c2bp+bebop explore all paths through abstraction
• A new form of program slicing– program code and data not relevant to property are dropped– non-determinism allows slices to have more behaviors
Current status of SDV• Runs on 100s of
Windows drivers• Finds several bugs,
proves several properties• SDV now transferred
from MSR to Windows division
• Used to check several DDK and inbox drivers
• Beta Released at WINHEC 2005!
Static Driver Verifier
Static Driver Verifier• Driver: Parallel port device driver • Rule: Checks that driver dispatch routines do not call
IoCompleteRequest(…) twice on the I/O request packet passed to it by the OS or another driver
Call #1
Call #2
SLAM/SDV History (with Tom Ball)• 1999-2001
– foundations, algorithms, prototyping
– papers in CAV, PLDI, POPL, SPIN, TACAS
• March 2002– Bill Gates review
• May 2002– Windows committed to hire two
Ph.D.s in model checking to support Static Driver Verifier
• July 2002– running SLAM on 100+ drivers,
20+ properties
• September 3, 2002– made initial release of SDV to
Windows (friends and family)
• April 1, 2003– made wide release of SDV to
Windows (any internal driver developer)
• September, 2003– team of six in Windows working on
SDV– researchers moving into
“consultant” role
• November, 2003– demonstration at Driver Developer
Conference
• May, 2005– Beta ships at WinHEC 2005!
SLAM
• Boolean program model has proved itself
• Successful for domain of device drivers– control-dominated safety properties– few boolean variables needed to do proof or find real
counterexamples
• Counterexample-driven refinement– terminates in practice– incompleteness of theorem prover not an issue
What is hard?
• Abstracting – from a language with pointers (C) – to one without pointers (boolean programs)
• All side effects need to be modeled by copying (as in dataflow)
• Open environment problem
What stayed fixed?
• Boolean program model
• Basic tool flow
• Repercussions:– newton has to copy between scopes – c2bp has to model side-effects by value-result – finite depth precision on the heap is all
boolean programs can handle
What changed?
• Interface between newton and c2bp
• We now use predicates for doing more things
• refine alias precision via aliasing predicates• newton helps resolve pointer aliasing imprecision
in c2bp
Model Checking, Theorem Proving and Program Analysis
• Very related to each other
• Different histories– different emphasis– different tradeoffs
• Complementary, in some ways
• Combination can be extremely powerful
What worked well?
• Specific domain problem
• Safety properties
• Shoulders & synergies
• Separation of concerns
• Summer interns & visitors
• Strategic partnership with Windows
Predictions• The holy grail of full program verification
has been abandoned. It will probably remain abandoned
• Less ambitious tools like powerful type checkers will emerge and become more widely used
• These tools will exploit ideas from various analysis disciplines
• Tools will alleviate the “chicken-and-egg” problem of writing specifications
Further Reading
See papers, slides from:
http://research.microsoft.com/slam
http://research.microsoft.com/~sriram
GlossaryModel checking Checking properties by systematic exploration of the state-space of a
model. Properties are usually specified as state machines, or using temporal logics
Safety properties Properties whose violation can be witnessed by a finite run of the system. The most common safety properties are invariants
Reachability Specialization of model checking to invariant checking. Properties are specified as invariants. Most common use of model checking. Safety properties can be reduced to reachability.
Boolean programs “C”-like programs with only boolean variables. Invariant checking and reachability is decidable for boolean programs.
Predicate A Boolean expression over the state-space of the program eg. (x < 5)
Predicate abstraction A technique to construct a boolean model from a system using a given set of predicates. Each predicate is represented by a boolean variable in the model.
Weakest precondition The weakest precondition of a set of states S with respect to a statement T is the largest set of states from which executing T, when terminating, always results in a state in S.
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