symdiff: leveraging program verification for comparing programs shuvendu lahiri research in software...

SymDiff: Leveraging Program Verification for Comparing Programs

Shuvendu LahiriResearch in Software Engineering (RiSE),

Microsoft Research, Redmond

Jointly withChris Hawblitzel (Microsoft Research, Redmond), Ming

Kawaguchi (UCSD), Henrique Rebelo (UPFE)

VSSE Workshop, 2012

Motivation

Microsoft Confidential

Ensuring compatibility– Programmers spend a large fraction of their time

ensuring (read praying) compatibility after changes

Does my bug-fix introduce a regression?

Does the refactoring change any observable

behavior?

How does the feature addition impact existing

features?

Compatibility: applicationsf() { Print(foo); g(); }

g() { ... Print(foo); }

g() { ... Print(foo); Print(bar); }

New featuresRefactoring

CompilersLibrary APIchanges

Bug fixes

Version Control

Compatibility: Microsoft

• Products– Windows APIs (Win32, ntdll)– Driver development kits– .NET frameworks, Base class library– Compilers (C#, JIT,…)– …..

• Windows updates– Security patches– Bug fixes

Every developer/tester

/auditor

Problem

• Use static analysis to–Improve the productivity of users trying

to ensure compatibility across program changes

• Potential benefits–Agility: fewer regressions, higher confidence in

changes, smarter code review, ..

Challenge

• Equivalence checking is too strong a spec– Most changes modify behavior

• Hard to formalize (separate expected changes from unexpected changes)– Refactoring behaviors intact– Bug fix non-buggy behaviors intact– Feature add existing feature behaviors intact– API change ??– Data change ??– Config changes ??– …

Challenge Opportunity

• Hard to formalize (separate expected changes from unexpected changes)– Refactoring behaviors intact– Bug fix non-buggy behaviors intact– Feature add existing feature behaviors intact– …….

Highlight “unexpected”

changes

Microsoft Confidential

Our approach– Provide a tool for performing semantic diff (diff over

behaviors)

Semantic Diff

Does my bug-fix introduce a regression?

Does the refactoring change any observable

behavior?

How does the feature addition impact existing

features?

Microsoft Confidential

Our approach– Provide a tool for performing semantic diff (diff over

behaviors)

Semantic Diff

Does my bug-fix

introduce a regression?

Does the refactoring change any observable behavior?

How does the feature addition

impact existing features?

What is SymDiff?

A framework to– Leverage and extend program

verification for providing relative correctness

Overview

• Demo• Semantic diff– Tool (in current form)

• An application – Compiler compatibility

• Making SymDiff extensible with contracts– Users can express “expected” changes– Mutual summaries and relative termination

Demo

1. Eval (bug1)2. Eval (func)3. StringCopy (bug fix)4. Recursive example

SymDiff tool

SymDiff

– Apply and extend program verification techniques towards comparing programs–Current form: Checks input/output

partial equivalence

[CAV ’12 tool paper]

SymDiff tool: language independent

SymDiff(Boogie+

Z3)

P1

P2P2≠P1

P1 = P2

Works at Boogie intermediate language

S1C/.NET/

x86/ARM

Boogie

S2C/.NET/

x86/ARM

Boogie

Boogie

• Simple intermediate verification language– [Barnett et al. FMCO’05]

• Commands– x := E //assign– havoc x //change x to an arbitrary value– assert E //if E holds, skip; otherwise, go wrong– assume E // if E holds, skip; otherwise, block– S ; T //execute S, then T– goto L1, L2, … Ln //non-deterministic jump to labels – call x := Foo(e1,e2,..) //procedure call

Boogie (contd.)

• Two types of expressions– Scalars (bool, int, ref, ..)– Arrays ([int]int, [ref]ref, …)

• Array expression sugar for SMT array theory– x[i] := y x := upd(x, i, y)– y := x[i] y := sel(x,i)

• Procedure calls sugar for modular specification

call Foo();assert pre;havoc V;assume post;

procedure Foo();requires pre;ensures post;modifies V;

Basic equivalence checkingvoid swap1(ref int x, ref int y){ int z = x; x = y; y = z;}void swap2(ref int x, ref int y){ x = x + y; y = x - y; x = x - y;}

z0 == x0 &&x1 == y0 &&y1 == z0 &&swap1.x == x1 && swap1.y == y1&&x1' == x0 + y0 &&y1' == x1' – y0 &&x2' == x1' – y1' &&swap2.x == x2' && swap2.y == y1' &&~ (swap1.x == swap2.x && swap1.y == swap2.y)

Z3theorem prover

UNSAT (Equivalent)

SAT (Counterexample)

Handling procedure calls

• Modular checking– Assume “matched” callees are deterministic and

have the same I/O behaviors– Modeled by uninterpreted functions [Necula ‘00, …,

Godlin & Strichman ‘08, …..]• Addition of postcondition for Foo, Foo’

modifies g;free ensures g == UF_Foo_g(x, old(g));free ensures ret == UF_Foo_ret(x, old(g));procedure Foo(x) returns (ret);

modifies g;free ensures g == UF_Foo_g(x, old(g));free ensures ret == UF_Foo_ret(x, old(g));procedure Foo’(x) returns (ret);

Modeling C/Java/C#/x86 Boogie

• Separation of concerns– Front end can be developed independently– Quite a few already exists • HAVOC/VCC for C, Spec#/BCT for .NET, ?? for Java, …

• Heap usually modeled by arrays– x.f := y Heap_f[x] := y

• Challenges– Deterministic modeling of I/O, malloc, …..– The entire heap is passed around

Application: Compiler compatibility

Microsoft Confidential

Compiler validation

X86

ARM

ARM+opt

Source

v1 v2 v3

Versions

X86+opt

v4

Compatibility: x86 vs. x86 example

G01: mov EAX, EDX

G02: and EAX, 255 push EAX mov EDX, 0x100000 call WriteInternalFlag2(int,bool)

__epilog: ret

G01: push ESI mov ESI, EDX

G02: and ESI, 255 push ESI mov EDX, 0x100000 call WriteInternalFlag2(int,bool)

G03: pop ESI ret

v2 v3

X86+opt

254

Large x86 vs. ARM example

Beyond equivalence

Beyond equivalenceType of change Check

Refactoring/Optimizations In1 = In2 Out1’ = Out2’

Bug fix In1 = In2 (Fail1’ || Out1’ = Out2’)

Feature addition In1 = In2 (UnImplemented1’ || Out1’ = Out2’)

Performance optimization In1 = In2 (Measure2’ <= Measure1’)

Differential assertion checking (DAC) (see POPL’12 on “Interleaved Bugs ….”)

In1 = In2 (Fail1’ || ~Fail2’)

Contracts over two programs

• Need an extensible contract mechanism for comparing two programs– Generalization of pre/post conditions

• Why– Allow users to express relative correctness

specifications (e.g. conditional equivalence)– Automated methods may not always suffice (even for

equivalence checking)• Challenge– Should be able to leverage SMT-based program verifiers

Mutual summaries

–A extensible framework for interprocedural program comparison

• Prior work (mostly automated):– Intraprocedural• Translation validation [Pnueli et al. ‘98, Necula ‘00, Zuck

et al. ’05,…]

– Coarse intraprocedural (only track equalities)• Regression verification [Strichman et al. ‘08]

Mutual summaries

– [MSR-TR-2011-112]

• Mutual summaries (MS)• Relative termination (RT)• Dealing with loops and unstructured goto

Example: Feature additionint f1(int x1){ a1 = A1[x2]; a2 = A2[x2]; if (Op[x1] == 0) return Val[x1]; else if (Op[x1] == 1) return f1(a1) + f1(a2); else if (Op[x1] == 2) return f1(a1) - f1(a2); else return 0;}

int f2(int x2, bool isU){ a1 = A1[x2]; a2 = A2[x2]; if (Op[x2] == 0) return Val[x2]; else if (Op[x2] == 1){ if (isU) return uAdd(f2(a1, T), f2(a2, T)); else return f2(a1, F) + f2(a2, F); } else if (Op[x2] == 2){ if (isU) return uSub(f2(a1, T), f2(a2, T)); else return f2(a1, F) – f2(a2, F); } else return 0;}

The programs are equivalent when

isU == False

Mutual summaries

• What is a mutual summary MS(F1, F2)? – An formula over two copies of • parameters, globals (g), returns and next state of globals

(g’)

void F1(int x1){ if(x1 < 100){ g1 := g1 + x1; F1(x1 + 1); }}

void F2(int x2){ if(x2 < 100){ g2 := g2 + 2*x2; F2(x2 + 1); }}

MS(F1, F2): (x1 = x2 && g1 <= g2 && x1 >= 0) ==> g1’ <= g2’

Mutual summaries

• What does a mutual summary MS(F1, F2) mean?– For any pre/post state pairs (s1,t1) of F1, and (s2,t2)

of F2, (s1,t1,s2,t2) satisfy MS(F1,F2)

void F1(int x1){ if(x1 < 100){ g1 := g1 + x1; F1(x1 + 1); }}

void F2(int x2){ if(x2 < 100){ g2 := g2 + 2*x2; F2(x2 + 1); }}

MS(F1, F2): (x1 = x2 && g1 <= g2 && x1 >= 0) ==> g1’ <= g2’

Exampleint f1(int x1){ a1 = A1[x2]; a2 = A2[x2]; if (Op[x1] == 0) return Val[x1]; else if (Op[x1] == 1) return f1(a1) + f1(a2); else if (Op[x1] == 2) return f1(a1) - f1(a2); else return 0;}

int f2(int x2, bool isU){ a1 = A1[x2]; a2 = A2[x2]; if (Op[x2] == 0) return Val[x2]; else if (Op[x2] == 1){ if (isU) return uAdd(f2(a1, T), f2(a2, T)); else return f2(a1, F) + f2(a2, F); } else if (Op[x2] == 2){ if (isU) return uSub(f2(a1, T), f2(a2, T)); else return f2(a1, F) – f2(a2, F); } else return 0;}

MS(f1, f2) = (x1 == x2 && !isU) ==> ret1 == ret2

Checking mutual summaries

• Given F1, F2, MS(F1, F2), define the following procedure:

void CheckMS_F1_F2(int x1, int x2){inline F1(x1);inline F2(x2);

assert MS(F1,F2);}

Modular checking: Instrumentation

1. Add “summary relations” R_F1, and R_F2

void F1(int x1);ensures R_F1(x1, old(g1)/g1, g1/g1’);

2. Use the summary relations to assume mutual summaries at call sites:

axiom (forall x1, g1, g1’, x2, g2, g2’:: {R_F1(x1, g1, g1’), R_F2(x2, g2, g2’)}(R_F1(x1, g1, g1’) && R_F2(x2, g2, g2’)) ==>MS_F1_F2(x1, g1, g1’, x2, g2, g2’));

Leveraging program verifiers

• Mutual Summary checking– Encode using contracts (postconditions), axioms– Verification condition generation (Boogie)– Checking using SMT solver (Z3)

• Next steps– Inferring the mutual summaries

Relative termination

• Specification relating the terminating behaviors of P2 wrt P1

• Not just for proving termination– Required for composing transformations– MS1(f,f’) && MS2(f’,f’’) (MS1 MS2) (f,f’’)– E.g. P_Eq(f,f’) && P_Eq(f’,f’’) P_Eq(f,f’’)

Relative termination condition

• What is a relative termination condition RT(F1, F2)? – An formula over two copies of

• parameters, globals (g)

void F1(int x1){ if(x1 < 100){ g1 := g1 + x1; F1(x1 + 1); }}

void F2(int x2){ if(x2 < 100){ g2 := g2 + 2*x2; F2(x2 + 1); }}

RT(F1, F2): (x1 <= x2)

Relative termination condition

• What does relative termination condition RT(F1, F2) mean? – For pair of inputs states (s1,s2), if F1 terminates on s1,

and (s1,s2) satisfies RT(F1,F2), then F2 terminates on s2

void F1(int x1){ if(x1 < 100){ g1 := g1 + x1; F1(x1 + 1); }}

void F2(int x2){ if(x2 < 100){ g2 := g2 + 2*x2; F2(x2 + 1); }}

RT(F1, F2): (x1 <= x2)

What about loops? int Foo2() { i = 0; if (n > 0) { t = g; v = 3; do2: a[i] := v; i := i + 1; v := v + t; While2: //FLABEL if (i < n) goto do2; } return i;}

int Foo2() { i = 0; if (n > 0) { t = g; v = 3; do2: a[i] := v; i := i + 1; v := v + t; return While2(i, t, v); } return i;}

(int ,int) While2(i2, t2, v2) {i2' := i2;v2' := v2;if (i2' < n) { a2[i2'] := v2'; i2' := i2' + 1; v2' := v2' + t2; return While2(i2', t2,v2');}return (i2‘,v2’);

}

Unrolling optimizationsvoid F2(int i2){ if (i2 < n) { a2[i2] = 1; F2(i2+1); return; } return;}

void F3(int i3){ if (i3 + 1 < n) { a3[i3] := 1; a3[i3+1] := 1; F3(i3+2); return; } if (i3 < n) a3[i3] := 1; return;}

Extra step• Inline F2 once inside F2 to “match up” with F3

MS(F2, F3) = (i2 == i3 && a2 == a3) ==> a2’ == a3’

Using mutual summaries

• Flow1. Specify the FLABELS to remove loops and gotos

into procedures2. Write mutual summaries for pairs of resulting

procedures3. Specify the inlining limit (if needed)

Express translation validation proofs of many compiler optimizations

– Copy propagation – Constant propagation – Common sub-expression

elimination – Partial redundancy

elimination – Loop invariant code

hoisting – Conditional speculation – Speculation

– Software pipelining – Loop unswitching – Loop unrolling – Loop peeling – Loop splitting – Loop alignment – Loop interchange – Loop reversal – Loop skewing – Loop fusion – Loop distribution

[Kundu, Tatlock, Lerner ‘09]

Order of updates differ in two versions

A nice example that uses MS, RT

void A(ref x){ if(x != nil){ A(next[x]); D(x); }}

next: ref ref; data: ref int;

void B(ref x){ if(x != nil){ D(x); B(next[x]); }}

void C(ref x){ ref i := x; if(i != nil){Do: D(i); i := next[i]; if (i != nil)

goto Do; }}

void D(ref x){ data[x] := U(data[x]);}

Recursive Tail-recursive Do-while

Overview

DemoSemantic diff– Tool (in current form)

An application – Compiler compatibility

Making SymDiff extensible with contracts– Mutual summaries and relative termination– General contracts for comparing programs

In summary

• Checking compatibility (statically) is a huge opportunity– Both formalizing the problem– Tools/techniques to solve it

• Likely to have impact on development cycle– Existing static analysis tools has failed to do so cost-

effectively, in spite of all the progress• Combining with dynamic analysis– To generate test cases when possible, or aid testing

achieve higher differential coverage

Resources

• SymDiff website

http://research.microsoft.com/symdiff/

• Binary release soon!– Contains C front end