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Verifying invariants in object-oriented programs

Verifying invariants in object-oriented programs . K. Rustan M. Leino Microsoft Research, Redmond, WA, USA. Joint work with Mike Barnett, Robert DeLine, Manuel Fahndrich, and Wolfram Schulte. ‥. Computer Science Colloquium ETH Zurich 24 Nov 2003. Vision.

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Verifying invariants in object-oriented programs

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  1. Verifying invariants in object-oriented programs K. Rustan M. Leino Microsoft Research, Redmond, WA, USA Joint work with Mike Barnett, Robert DeLine, Manuel Fahndrich, and Wolfram Schulte ‥ Computer Science ColloquiumETH Zurich24 Nov 2003

  2. Vision Record design decisions + Utilize automatic checking= Detect errors and improve maintainability

  3. A# and Boogie:Programmer's view A# A# compiler Other .NETcompilers C# C# compiler MSIL Boogie Warnings

  4. Boogie: under the hood MSIL translator Inferenceengine BoogiePL weakest-preconditiongenerator verification condition Theoremprover Warnings

  5. Boogie technologyand research • Programming methodology • model for writing code and specifications • Inference • abstract domains over heap structures • Verification-condition generation • formulas that are “efficient” for theorem prover

  6. Invariants: straw man Object invariants hold on public method boundaries and are shorthands for pre/post-conditions class T { // field declarations ... invariantJ ; T(...)requires Pmodifies vensures Q { … } method m(...)requires Rmodifies wensures T { … } … class T { // field declarations ... T(...)requires Pmodifies vensures Q∧ J { … } method m(...)requires R ∧ Jmodifies wensures T∧ J { … } …

  7. Invariants, example class T { privateint x, y ;invariant0 ≦ x < y ; public T() { x = 0 ; y = 1 ; } publicmethod m()modifies x, y {assert y-x ≧ 0 ; x = x + 3 ; y = 4 * y ; } … class T { privateint x, y ; public T()ensures0 ≦ x < y { x = 0 ; y = 1 ; } publicmethod m()requires0 ≦ x < ymodifies x, y ensures0 ≦ x < y {assert y-x ≧ 0 ; x = x + 3 ; y = 4 * y ; } …

  8. Invariants, problems class T { privateint x, y ;invariant 0 ≦ x < y ; public T() { x = 0 ; y = 1 ; } publicmethod m()modifies x, y {assert y-x ≧ 0 ; x = x + 3 ; y = 4 * y ; } … class T { privateint x, y ; public T()ensures 0 ≦ x < y { x = 0 ; y = 1 ; } publicmethod m()requires 0 ≦ x < y modifies x, y ensures 0 ≦ x < y {assert y-x ≧ 0 ; x = x + 3 ; y = 4 * y ; } … callers are expected to establish property about internal data structure

  9. Invariants, problems class T { privateint x, y ;invariant 0 ≦ x < y ; public T() { x = 0 ; y = 1 ; } publicmethod m()modifies x, y {assert y-x ≧ 0 ; x = x + 3 ; y = 4 * y ; } … class T { privateint x, y ; public T()ensures 0 ≦ x < y { x = 0 ; y = 1 ; } publicmethod m()requires 0 ≦ x < ymodifies x, y ensures 0 ≦ x < y {assert y-x ≧ 0 ; x = x + 3 ; y = 4 * y ; } … possible solution (?): callers don’t need to be checked for this precondition—it holds automatically!

  10. Invariants, problems class T { privateint x, y ;invariant 0 ≦ x < y ; public T() { x = 0 ; y = 1 ; } publicmethod m()modifies x, y {assert y-x ≧ 0 ; x = x + 3 ; y = 4 * y ; } … class T { privateint x, y ; public T()ensures 0 ≦ x < y { x = 0 ; y = 1 ; } publicmethod m() requires 0 ≦ x < y modifies x, y ensures 0 ≦ x < y {assert y-x ≧ 0 ; x = x + 3 ; y = 4 * y ; } … invariant does not hold here

  11. Invariants, problems class T { privateint x, y ;invariant 0 ≦ x < y ; public T() { x = 0 ; y = 1 ; } public method m()modifies x, y {assert y-x ≧ 0 ; x = x + 3 ; y = 4 * y ; } … class T { privateint x, y ; public T()ensures 0 ≦ x < y { x = 0 ; y = 1 ; } publicmethod m() requires 0 ≦ x < y modifies x, y ensures 0 ≦ x < y {assert y-x ≧ 0 ; x = x + 3 ;p(...) ; y = 4 * y ; } … invariant does not hold here, so what if p calls m?!

  12. The problem of specifying modifications class Kitchen {private Dishes d ; private bool hasGarbage ;private Stove s ;private Light l ; ... publicmethod SpiffUp()modifies hasGarbage, s.foodPieces, s.big.sufaceColor, … { d.Clean() ; hasGarbage = false ; s.Wipe() ; l.TurnOff() ; ... } class Stove {private Burner big ;private Burner small ;privateint foodPieces ;private Knob[] knobs ; ... publicmethod Wipe()modifies foodPieces, big.surfaceColor, … { big.Polish() ; small.Polish() ; foodPieces = 0 ; ... } these lists are long, and they mention private state

  13. The problem of specifying modifications class Kitchen {private Dishes d ; private bool hasGarbage ;private Stove s ;private Light l ; ... publicmethod SpiffUp()modifieshasGarbage, s.foodPieces, s.big.sufaceColor, … { d.Clean() ; hasGarbage = false ; s.Wipe() ; l.TurnOff() ; ... } class Stove {private Burner big ;private Burner small ;privateint foodPieces ;private Knob[] knobs ; ... publicmethod Wipe()modifiesfoodPieces, big.surfaceColor, … { big.Polish() ; small.Polish() ; foodPieces = 0 ; ... } possible solution (?):don’t need to declare modifications of private state—it can’t be observed anyhow

  14. The problem of specifying modifications class Kitchen {private Dishes d ; private bool hasGarbage ;private Stove s ;private Light l ; ... publicmethod SpiffUp()modifies { d.Clean() ; hasGarbage = false ; s.Wipe() ; assert ￢hasGarbage ; l.TurnOff() ; ... } class Stove {private Burner big ;private Burner small ;privateint foodPieces ;private Knob[] knobs ; ... publicmethod Wipe()modifies { big.Polish() ; small.Polish() ; foodPieces = 0 ; ... } SpiffUp treats Wipe as if Wipe modified nothing, so what if Wipe calls a method in Kitchen that sets hasGarbage to true?!

  15. Soundness of verification • Soundness = verification finds all errors • Soundness follows from: • pre- and postconditions are the same for caller and callee • Note: In addition to soundness, we want something usable

  16. Methodology • object invariant declaration • class T { int x, y ;invariant x < y ; • special variable st: {Invalid, Valid} • Idea: program invariant (∀o ･ o.st = Invalid ∨ Inv(o)) • st is changed by commands pack andunpack for any o: T, we writeInv(o)≡ o.x < o.y holds at everyprogram point!

  17. pack and unpack • pack o ≡assert o.st = Invalid ;assert Inv(o) ; o.st := Valid • unpack o ≡assert o.st = Valid ; o.st := Invalid

  18. Example receiver parameter(“this”, “self”, “current”) class T {int x, y ;invariant 0 ≦ x < y ; method init(t)requires t.st = Invalidmodifies t.st, t.x, t.yensures t.st = Valid { t.x := 0 ; t.y := 1 ;pack t } method m(t)requires t.st = Validmodifies t.x, t.y {unpack t ; t.x := t.x + 3 ; t.y := 4 * t.y ;pack t }

  19. Program invariant (∀o ･ o.st = Invalid ∨ Inv(o)) • x := new(T)≡ ... ; assume x.st = Invalid • pack o≡ ... ; assert Inv(o) ; o.st := Valid • unpack o≡ ... ; o.st := Invalid • o.f := E≡ assert o.st = Invalid ; ... • Inv(o) can mention only the fields of o

  20. Methodology, summary • invariant ... • st: {Invalid, Valid} • pack, unpack • modifications of o.f require o.st=Invalid • Inv(o) can mention only the fields of o • (∀o ･ o.st = Invalid ∨ Inv(o))

  21. Methodology, extended • component declarations • class Kitchen {component Stove s ; • st: {Invalid, Valid, Committed} • Idea: program invariant(∀o ･ o.st=Invalid ∨ (Inv(o) ∧ (∀p∈Comp(o) ･ p.st=Committed))) • pack o and unpack o change st for o and o's components for any k: Kitchen, we havek.s ∈ Comp(k)

  22. pack and unpack, extended • pack o ≡assert o.st = Invalid ∧ Inv(o) ;assert (∀p ∈ Comp(o) ･ p.st=Valid) ; o.st := Valid ;foreachp ∈ Comp(o)do p.st :=Committed ; • unpack o ≡assert o.st = Valid ;foreachp ∈ Comp(o)do p.st=Valid ; o.st := Invalid ;

  23. Example class Stove {method Wipe(s)requires s.st=Valid … class Kitchen { method SpiffUp(k)requires k.st=Valid … {unpack k ; k.d.Clean() ; k.s.Wipe() ;pack k } Committed Committed Dishes Committed Committed Stove s d Committed k Kitchen Valid

  24. Example class Stove {method Wipe(s)requires s.st=Valid … class Kitchen { method SpiffUp(k)requires k.st=Valid … {unpack k ; k.d.Clean() ; k.s.Wipe() ;pack k } Committed Committed Dishes Committed Committed Valid Stove s d Committed Valid k Kitchen Valid Invalid

  25. Program invariant (∀o ･ o.st=Invalid ∨ (Inv(o) ∧ (∀p∈Comp(o) ･ p.st=Committed))) • x := new(T)≡ ... ; assume x.st=Invalid • pack o, unpack o • o.f := E≡ assert o.st=Invalid ; ... • Inv(o) can mention only the fields of o andof o.p for any component field p

  26. Extended methodology, summary • invariant ... • component ... • st: {Invalid, Valid, Committed} • pack, unpack • modifications of o.f require o.st=Invalid • Inv(o) can mention only the fields of o and of o.p for any component field p • (∀o ･ o.st=Invalid ∨ (Inv(o) ∧ (∀p∈Comp(o) ･ p.st=Committed)))

  27. Verification system • We let st be used in method specifications (requires, modifies, ensures) • We must address the Problem of Specifying Modifications

  28. A heap model • Heap is a two-dimensional “array” class T { f: U; g: V; ... } • x := o.f = x := Heap[o, f] • o.f := E = Heap[o, f] := E

  29. Meaning of modifies • modifies w =modifies Heapensures (∀o,f ･ Heap[o,f] = Heap0[o,f] ∨ (o,f) ∈ w0 ) viewed as set of object/field-name pairs

  30. Meaning of modifies • modifies w =modifies Heapensures (∀o,f ･ Heap[o,f] = Heap0[o,f] ∨ (o,f) ∈ w0 ∨ ￢Heap0[o,alloc] )

  31. Meaning of modifies • modifies w =modifies Heapensures (∀o,f ･ Heap[o,f] = Heap0[o,f] ∨ (o,f) ∈ w0 ∨ ￢Heap0[o,alloc] ∨ Heap0[o,st]=Committed )

  32. Example class Stove {method Wipe(s)requires s.st=Validmodifies s.foodPieces class Kitchen { method SpiffUp(k)requires k.st=Validmodifies k.hasGarbage {unpack k ; k.d.Clean() ; k.hasGarbage := false ; k.s.Wipe() ;assert￢k.hasGarbage ;pack k }

  33. Another example method m(p)requires p.st=Committed{var y, z in y := p.x ; z := sqrt(49) ;assert y = p.xend}

  34. Soundness • Pre- and postconditions are the same for callers and callees, so verification system is sound!

  35. Related work • rep types in CLU • dynamically checked invariants in Eiffel • valid idiom in ESC/Modula-3 • universe types and invariants in Muller's thesis • invariant declarations in ESC/Java and JML • (implicit) pack/unpack operations in Vault and Fugue • capability calculus • ownership types • locking and monitor disciplines in concurrent programming ‥

  36. Conclusions • Invariants different from pre/post-conditions • Resulting program invariants hold at every program point • Uses pack/unpack commands, but good defaults can be constructed for these • No linear type system • Components are not unique references—objects (pointers) can freely be copied • Fields can freely be read • No additional features of abstraction needed to support the specification of modifications • Sound ‥

  37. Further research challenges • experience, understanding of limits • extensions to support more good programs(joint work with Peter Muller) ‥

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