Spring 2013Program Analysis and Verification

Lecture 1: Introduction

Roman ManevichBen-Gurion University

December 31, 2008

30GB Zunes all over the world fail en masse

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Zune bug 1 while (days > 365) { 2 if (IsLeapYear(year)) { 3 if (days > 366) { 4 days -= 366; 5 year += 1; 6 } 7 } else { 8 days -= 365; 9 year += 1; 10 } 11 }

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Zune bug 1 while (366 > 365) { 2 if (IsLeapYear(2008)) { 3 if (366 > 366) { 4 days -= 366; 5 year += 1; 6 } 7 } else { 8 days -= 365; 9 year += 1; 10 } 11 }

Suggested solution: wait for tomorrow 4

February 25, 1991

On the night of the 25th of February, 1991, a Patriot missile system operating in Dhahran, Saudi Arabia, failed to track and intercept an incoming Scud. The Iraqi missile impacted into an army barracks, killing 28 U.S. soldiers and injuring another 98.

Patriot missile failure

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Patriot bug – rounding error• Time measured in 1/10 seconds• Binary expansion of 1/10:

0.0001100110011001100110011001100....• 24-bit register

0.00011001100110011001100• error of

– 0.0000000000000000000000011001100... binary, or ~0.000000095 decimal

• After 100 hours of operation error is 0.000000095×100×3600×10=0.34

• A Scud travels at about 1,676 meters per second, and so travels more than half a kilometer in this time

Suggested solution: reboot every 10 hours6

August 13, 2003

Billy Gates why do you make this possible ? Stop making moneyand fix your software!!

(W32.Blaster.Worm)

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Windows exploit(s)Buffer Overflow

void foo (char *x) { char buf[2]; strcpy(buf, x); } int main (int argc, char *argv[]) { foo(argv[1]); }

./a.out abracadabraSegmentation fault

Stack grows this way

Memory addresses

Previous frame

Return address

Saved FP

char* x

buf[2]

…

ab

ra

ca

da

br

Buffer overrun exploits int check_authentication(char *password) { int auth_flag = 0; char password_buffer[16];

strcpy(password_buffer, password); if(strcmp(password_buffer, "brillig") == 0) auth_flag = 1; if(strcmp(password_buffer, "outgrabe") == 0) auth_flag = 1; return auth_flag;}int main(int argc, char *argv[]) { if(check_authentication(argv[1])) { printf("\n-=-=-=-=-=-=-=-=-=-=-=-=-=-\n"); printf(" Access Granted.\n"); printf("-=-=-=-=-=-=-=-=-=-=-=-=-=-\n"); } else printf("\nAccess Denied.\n"); }

(source: “hacking – the art of exploitation, 2nd Ed”) 9

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(In)correct usage of APIs Application trend: Increasing number of libraries and APIs

– Non-trivial restrictions on permitted sequences of operations Typestate: Temporal safety properties

– What sequence of operations are permitted on an object?– Encoded as DFA

e.g. “Don’t use a Socket unless it is connected”

init connected closed

err

connect)( close)(

getInputStream)(getOutputStream)(

getInputStream)(getOutputStream)(getInputStream)(

getOutputStream)(

close)(

*

Challengesclass SocketHolder { Socket s; }Socket makeSocket() { return new Socket(); // A }open(Socket l) { l.connect(); }talk(Socket s) { s.getOutputStream()).write(“hello”); }

main() { Set<SocketHolder> set = new HashSet<SocketHolder>(); while(…) { SocketHolder h = new SocketHolder(); h.s = makeSocket(); set.add(h); } for (Iterator<SocketHolder> it = set.iterator(); …) { Socket g = it.next().s; open(g); talk(g); }}

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Testing is not enough

• Observe some program behaviors• What can you say about other behaviors?

• Concurrency makes things worse

• Smart testing is useful– requires the techniques that we will see in the

course

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Static analysis definition

Reason statically (at compile time) about the possible runtime behaviors of a program

“The algorithmic discovery of properties of a program by inspection of its source text1”-- Manna, Pnueli

1 Does not have to literally be the source text, just means w/o running it

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Is it at all doable?x = ?if (x > 0) { y = 42;} else { y = 73; foo();} assert (y == 42);

Bad news: problem is generally undecidable

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universe

Central idea: use approximation

Under Approximation

Exact set of configurations/behaviors

Over Approximation

Goal: exploring program states

initialstates

badstates

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reachablestates

Technique: explore abstract states

initialstates

badstates

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reachablestates

Technique: explore abstract states

initialstates

badstates

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reachablestates

Technique: explore abstract states

initialstates

badstates

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reachablestates

Technique: explore abstract states

initialstates

badstates

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reachablestates

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Sound: cover all reachable states

initialstates

badstates

reachablestates

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Unsound: miss some reachable states

initialstates

badstates

reachablestates

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Imprecise abstraction

initialstates

badstates

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reachablestates

False alarms

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A sound message

x = ?if (x > 0) { y = 42;} else { y = 73; foo();} assert (y == 42); Assertion may be violated

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• Avoid useless result

• Low false alarm rate• Understand where precision is lost

Precision

UselessAnalysis(Program p) { printf(“assertion may be violated\n”);}

Runtime vs. static analysis

Runtime Static analysis

Effectiveness Can miss errorsFinds real errors

Can find rare errorsCan raise false alarms

Cost Proportional to program’s execution

Proportional to program’s complexity

No need to efficiently handle rare cases

Can handle limited classes of programs and still be useful

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Driver’s Source Code in C

PreciseAPI Usage Rules(SLIC)

Defects

100% pathcoverage

Rules

Static Driver Verifier

Environment model

Static Driver Verifier

Bill Gates’ Quote

"Things like even software verification, this has been the Holy Grail of computer science for many decades but now in some very key areas, for example, driver verification we’re building tools that can do actual proof about the software and how it works in order to guarantee the reliability." Bill Gates, April 18, 2002. Keynote address at WinHec 2002

The Astrée Static Analyzer

Patrick CousotRadhia CousotJérôme Feret

Laurent MauborgneAntoine Miné Xavier Rival

ENS France

Objectives of Astrée• Prove absence of errors in safety critical C

code• ASTRÉE was able to prove completely

automatically the absence of any RTE in the primary flight control software of the Airbus A340 fly-by-wire system– a program of 132,000 lines of C analyzed

Objectives of Astrée• Prove absence of errors in safety critical C

code• ASTRÉE was able to prove completely

automatically the absence of any RTE in the primary flight control software of the Airbus A340 fly-by-wire system– a program of 132,000 lines of C analyzed

By Lasse Fuss (Own work) [CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons

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A little about me• History

– Studied B.Sc., M.Sc., Ph.D. at Tel-Aviv University• Research in program analysis with IBM and Microsoft

– Post-doc in UCLA and in UT Austin– Joined Ben-Gurion University this year

• Example research challenges– What’s a good algorithm for automatically discovering (with no

hints) that a program generates a binary tree where all leaves are connected in a list?

– What’s a good algorithm for automatically proving that a parallel program behaves “well”?

– How can we automatically synthesize parallel code that is both correct and efficient?

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Why study program analysis?• Challenging and thought provoking– An approach for dealing with computationally hard

(usually undecidable) problems– Treat programs as mathematical objects

• Understand how to systematically– Design optimizations– Reason about correctness / find bugs (security)

• Some techniques may be applied in other domains– Computational learning– Analysis of biological systems

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What do you get in this course?

• Learn basic principles of static analysis– Understand jargon/papers

• Learn a few advanced techniques– Some principled way of developing analysis– Develop one in a small-scale project

• Put to practice what you learned in logic, automata, programming

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My role

• Teach you theory and practice• Teach you how to think of new techniques

• E-mail: romanm@cs.bgu.ac.il• Office hours: Wednesday 13:00-15:00• Course web-page– Announcements– Forum– …

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Requirements1. Summarize one lecture: 10% of grade– Submit initial summary– Get corrections/suggestions– Submit revised summary

2. Theoretical assignments and programming assignments: 50%– About 8 (some very small)– Must submit all– Must solve all questions– Otherwise re-submit (and get a lower grade)

3. Final project: 40%– Implement a program analyzer for a given component

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How to succeed in this course• Attend all classes• Make sure you understand material in class– Engage by asking questions and raising ideas

• Be on top of assignments– Submit on time– Don’t get stuck or give up on exercises – get help – ask me– Don’t start working on assignments the day before

• Be ethical

Joe (a day before assignment deadline):“I don’t really understand what you want from me in this assignment, can you help me/extend the deadline”?

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The static analysis approach

• Formalize software behavior in a mathematical model (semantics)

• Prove properties of the mathematical model– Automatically, typically with approximation of the

formal semantics

• Develop theory and tools for program correctness and robustness

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Kinds of static analysis• Spans a wide range

– type checking … up to full functional verification

• General safety specifications • Security properties (e.g., information flow)• Concurrency correctness conditions (e.g., absence of data

races, absence of deadlocks, atomicity)• Correct usage of libraries (e.g., typestate)

• Underapproximations useful for bug-finding, test-case generation,…

Static analysis techniques

• Abstract Interpretation• Dataflow analysis

• Constraint-based analysis• Type and effect systems

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Static analysis for verification

program

specification

Abstractcounterexample

Analyzer

Valid

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Relation to program verification

• Fully automatic

• Applicable to a programming language

• Can be very imprecise• May yield false alarms

• Requires specification and loop invariants

• Program specific

• Relatively complete• Provides counter examples• Provides useful documentation• Can be mechanized using

theorem provers

Static Analysis Program Verification

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Verification challenge

main(int i) { int x=3,y=1;

do { y = y + 1; } while(--i > 0) assert 0 < x + y;}

Determine what states can arise during any execution

Challenge: set of states is unbounded

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Abstract Interpretation

main(int i) { int x=3,y=1;

do { y = y + 1; } while(--i > 0) assert 0 < x + y;}

Recipe1) Abstraction2) Transformers3) Exploration

Challenge: set of states is unbounded Solution: compute a bounded representation of (a superset) of program states

Determine what states can arise during any execution

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1) Abstraction

main(int i) { int x=3,y=1;

do { y = y + 1; } while(--i > 0) assert 0 < x + y;}

• concrete state

• abstract state (sign)

: Var Z

#: Var{+, 0, -, ?}

x y i

3 1 7 x y i

+ + +

3 2 6

x y i

… 45

2) Transformers

main(int i) { int x=3,y=1;

do { y = y + 1; } while(--i > 0) assert 0 < x + y;}

• concrete transformer

• abstract transformer

x y i

+ + 0

x y i

3 1 0y = y + 1

x y i

3 2 0

x y i

+ + 0

y = y + 1

+ - 0 + ? 0

+ 0 0 + + 0

+ ? 0 + ? 046

3) Exploration

+ + ? + + ?

x y i

main(int i) { int x=3,y=1;

do { y = y + 1; } while(--i > 0) assert 0 < x + y;}

+ + ?

+ + ?

? ? ?

x y i

+ + ?

+ + ?

+ + ?

+ + ?

+ + ?

+ + ?

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Incompleteness

main(int i) { int x=3,y=1;

do { y = y - 2; y = y + 3; } while(--i > 0) assert 0 < x + y;}

+ ? ?

+ ? ?

x y i

+ ? ?

+ + ?

? ? ?

x y i

+ ? ?

+ ? ?

+ ? ?

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Parity abstraction

challenge: how to find “the right” abstraction

while (x !=1 ) do { if (x % 2) == 0 { x := x / 2; } else { x := x * 3 + 1; assert (x %2 ==0); }}

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How to find “the right” abstraction?

• Pick an abstract domain suited for your property– Numerical domains– Domains for reasoning about the heap– …

• Combination of abstract domains

• Another approach – Abstraction refinement

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Following the recipe (in a nutshell)

1) Abstraction

Concrete state Abstract statex

tn n n

x

t

n

2) Transformers

n

x

t

n

t n

x n

t->n = x

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Example: shape (heap) analysis

tx

n

x

t n

x

t n n

xt n n

xtt

x

ntt

ntx

tx

tx

emp

void stack-init(int i) { Node* x = null;

do {

Node t = malloc(…)

t->n = x;

x = t;

} while(--i>0)

Top = x;

} assert(acyclic(Top))

tx

n n

x

t n n

x

t n n n

xt n n n

xt n n n

top52

x

t n n

tx

n

x

t n

x

t n n

xtt

x

ntt

ntx

tx

tx

emp

xt n

n

xt n

n

n

x

t

n

t n

x n

xt n

n

3) Exploration

x

t n

Top n

ntx Top

tx Top x

t n

Top n

void stack-init(int i) { Node* x = null;

do {

Node t = malloc(…)

t->n = x;

x = t;

} while(--i>0)

Top = x;

}

assert(acyclic(Top))

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Example: polyhedra (numerical) domain

proc MC(n:int) returns (r:int) var t1:int, t2:int; begin if (n>100) then r = n-10; else t1 = n + 11; t2 = MC(t1); r = MC(t2); endif; end

var a:int, b:int; begin b = MC(a); end

What is the result of this program?54

McCarthy 91 function

proc MC (n : int) returns (r : int) var t1 : int, t2 : int;begin /* (L6 C5) top */ if n > 100 then /* (L7 C17) [|n-101>=0|] */ r = n - 10; /* (L8 C14) [|-n+r+10=0; n-101>=0|] */ else /* (L9 C6) [|-n+100>=0|] */ t1 = n + 11; /* (L10 C17) [|-n+t1-11=0; -n+100>=0|] */ t2 = MC(t1); /* (L11 C17) [|-n+t1-11=0; -n+100>=0; -n+t2-1>=0; t2-91>=0|] */ r = MC(t2); /* (L12 C16) [|-n+t1-11=0; -n+100>=0; -n+t2-1>=0; t2-91>=0; r-t2+10>=0; r-91>=0|] */ endif; /* (L13 C8) [|-n+r+10>=0; r-91>=0|] */end

var a : int, b : int;begin /* (L18 C5) top */ b = MC(a); /* (L19 C12) [|-a+b+10>=0; b-91>=0|] */end

if (n>=101) then n-10 else 91

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Some things that should trouble you

• Does a result always exist?• Does the recipe always converge?• How “optimal” is the result?• How do I pick my abstraction?• How do come up with abstract transformers?• Other practical issues– Efficiency– How does it do in practice?

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Change the abstraction to match the program

Abstraction refinement

program

specificationAbstractcounterexample

abstraction AbstractionRefinement counter

example

Verify

Valid

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Recap: program analysis

• Reason statically (at compile time) about the possible runtime behaviors of a program

• use sound overapproximation of program behavior

• abstract interpretation– abstract domain – transformers – exploration (fixed-point computation)

• finding the right abstraction?

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Next lecture:semantics of programming languages

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References• Patriot bug:

– http://www.cs.usyd.edu.au/~alum/patriot_bug.html– Patrick Cousot’s NYU lecture notes

• Zune bug:–

http://www.crunchgear.com/2008/12/31/zune-bug-explained-in-detail/

• Blaster worm:– http://www.sans.org/security-resources/malwarefaq/w32_blast

erworm.php• Interesting CACM article

– http://cacm.acm.org/magazines/2010/2/69354-a-few-billion-lines-of-code-later/fulltext

• Interesting blog post– http://www.altdevblogaday.com/2011/12/24/static-code-analys

is/60