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SymDiff: Leveraging Program Verification for Comparing Programs Shuvendu Lahiri Research in Software Engineering (RiSE), Microsoft Research, Redmond Contributors: Chris Hawblitzel (Microsoft Research, Redmond), Ming Kawaguchi (UCSD), Henrique Rebelo (UPFE), Rahul Sharma (Stanford)

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Motivation

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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?

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Compatibility: applications f() { Print(foo); g(); } g() {... Print(foo); } f() { Print(foo); g(); } g() {... Print(foo); } g() {... Print(foo); Print(bar); } g() {... Print(foo); Print(bar); } New features Refactoring Compilers Library API changes Bug fixes Version Control

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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

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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,..

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Main challenge 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 ?? – … Equivalence checking is too strong a spec – Most changes modify behavior

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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

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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?

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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?

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What is SymDiff? A framework to – Leverage and extend program verification for providing relative correctness

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Overview Demo Equivalence checking – Application: Compiler compatibility Differential assertion checking Making SymDiff extensible with contracts – Users can express “expected” changes Ongoing works

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Demo 1.Eval (bug1) 2.StringCopy (bug fix) 3.RtlString (regression)

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SymDiff tool

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SymDiff – Apply and extend program verification techniques towards comparing programs – Current form: Checks input/output partial equivalence Terminating executions from the same input result in the same output [CAV ’12 tool paper]

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SymDiff tool: language independent SymDiff (Boogie+ Z3) P1 P2 ≠ P1 = P2 Works at Boogie intermediate language S1 C/.NET/ x86/ARM Boogie S2 C/.NET/ x86/ARM Boogie

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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

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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;

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Basic equivalence checking void 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) Z3 theorem prover UNSAT (Equivalent) SAT (Counterexample)

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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);

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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

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Application: Compiler compatibility

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Compiler validation X86 ARM ARM+opt Source v1v2v3 Versions X86+opt v4

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Compatibility: x86 vs. x86 example G01: mov EAX, EDX G02: and EAX, 255 push EAX mov EDX, 0x call WriteInternalFlag2(int,bool) __epilog: ret G01: mov EAX, EDX G02: and EAX, 255 push EAX mov EDX, 0x call WriteInternalFlag2(int,bool) __epilog: ret G01: push ESI mov ESI, EDX G02: and ESI, 255 push ESI mov EDX, 0x call WriteInternalFlag2(int,bool) G03: pop ESI ret G01: push ESI mov ESI, EDX G02: and ESI, 255 push ESI mov EDX, 0x call WriteInternalFlag2(int,bool) G03: pop ESI ret v2v3 X86+opt 254

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Compatibility: x86 vs. x86 example

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Large x86 vs. ARM example

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Summary of results Compiler tool took heavy dependency on the semantic diff tool for testing the compilers The compiler team found and fixed 12 bugs False alarm varies by configuration – Month to month (x86-x86, ARM-ARM): ~2-3% – Optimized vs. Unoptimized: ~19% – X86 vs. ARM: ~29% Root cause analysis was crucial – Bucketed between 50-96% (depending on configuration) – MAXSAT based rootcause analysis compares poorly Comparable to results of translator validators

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Beyond equivalence

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Type of changeCheck Refactoring/OptimizationsIn1 = In2 Out1’ = Out2’ Bug fixIn1 = In2 (Fail1’ || Out1’ = Out2’) Feature additionIn1 = In2 (UnImplemented1’ || Out1’ = Out2’) Performance optimizationIn1 = In2 (Measure2’ <= Measure1’) Differential assertion checking (DAC) In1 = In2 (Fail1’ || ~Fail2’)

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Differential assertion checking (DAC) – [POPL’12, Interleaved bugs and underspecified harnesses] Given two programs V1 and V2 – Each program has an assertion A Traditionally: Does there exist an “input” n – for which V1(n) is not OK (violates A) DAC: Does there exist an input n – For which V1(n) is OK (for all/some internal choice) – And V2(n) is not OK Highlight warnings more relevant to the changes

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Cost-benefit tradeoff in DAC Sound analysis: – Callee can crash – Compute equality information as a prepass Local analysis: Local analysis – Callee cannot crash – Compute equality information as a prepass Bogus analysis: Bogus analysis – Assume callees are equivalent and do not crash

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Preliminary evaluation Compared different versions of Windows DDK (Vista vs. Win7) – Instrumented drivers with null pointer asserts Implemented single program local analysis Constructed joint program

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Results on DDK

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DAC evaluation DAC helps reduce the set of false alarms compared to single version checking Challenges remain to reduce false alarms

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Mutual summaries: Making Symdiff extensible

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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

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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]

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Mutual summaries – [MSR-TR ] Mutual summaries (MS) Relative termination (RT) Dealing with loops and unstructured goto

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Example: Feature addition int 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

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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 = 0) ==> g1’ <= g2’

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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 = 0) ==> g1’ <= g2’

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Example int 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

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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); }

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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’) );

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Leveraging program verifiers Mutual Summary checking – Encode using contracts (postconditions), axioms – Verification condition generation (Boogie) – Checking using SMT solver (Z3) Future work – Inferring the mutual summaries

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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’’)

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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)

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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)

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What about loops? int Foo2() { i = 0; if (n > 0) { t = g; v = 3; do2: a[i] := v; i := i + 1; v := v + t; //FLABEL 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’); }

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Unrolling optimizations void 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’

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Using mutual summaries Flow 1.Specify the FLABELS to remove loops and gotos into procedures 2.Write mutual summaries for pairs of resulting procedures 3.Specify the inlining limit (if needed)

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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

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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

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Overview Demo Equivalence checking Application: Compiler compatibility Differential assertion checking Making SymDiff extensible with contracts Users can express “expected” changes Ongoing works

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SMT theory of array isomorphism – Required to deal with out of order mallocs Inferring mutual summaries automatically MAXSAT based root cause analysis

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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

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Resources SymDiff website Binary release available! – Contains C front end RiSE website for trying tools

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Questions

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Research challenges Difficult for changes across – Loop boundaries (use loop unrolling) – Procedure boundaries (try use inlining) – Module boundaries (??) Assumptions – procedure names/parameters/globals remain the same – underlying runtime or external APIs are the same and deterministic – object layouts are the same – single threaded executions

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Deployment challenges Requires more than just the source code – Need to be able to build Need source depot integration – Currently need both versions to be in two directories Approximation due to modeling of C/C#/x86 – false positives/negatives as the modeling will never be perfect Need some user guidance for bug-fixes/features – Tell the tool what the assertion/feature was

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Questions

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