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Verification of object-oriented programs with invariants

Verification of object-oriented programs with invariants. Mike Barnett, Robert DeLine, Manuel Fahndrich , K. Rustan M. Leino, Wolfram Schulte. ¨. Formal techniques for Java-like programs Darmstadt, Germany 21 July 2003. Example problem.

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Verification of object-oriented programs with invariants

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  1. Verification of object-oriented programs with invariants Mike Barnett, Robert DeLine, Manuel Fahndrich, K. Rustan M. Leino, Wolfram Schulte ¨ Formal techniques for Java-like programsDarmstadt, Germany21 July 2003

  2. Example problem class T {int x, y;invariant x < y; publicvoid m(U u) { x++; u.p(); y++; } invariant assumed to hold invariant may not hold problem if p calls back into T invariant re-established

  3. Wanted:Methodology for invariants • Ideal methodology: • easy to understand • statically and modularly checkable • identifies all errors in a program • permits all good programs

  4. Invariant declarations–one per subclass Y y = new Y(); class W extends V {int a;int[] b; invariant a ≤ b.length; … Y X W V class V extends U { P p;invariant p ≠ null; … U T Object

  5. Special field inv keeps track of which invariants hold o o o • Declarations and statements of programminglanguage determine when inv is changed • The associated invariants are checked when inv increases • To prevent established invariants from having to bere-checked, one can treat fields in and below o.inv asread-only W W W V V V U U U T T T Object Object Object o.inv == ⊥ o.inv == U o.inv == W== typeof(o) “o is consistent”

  6. inv can be used inmethod specifications class T {int x, y;invariant x < y; publicvoid m()requiresinv == T; {int[] a = newint[y-x]; … } meaning: (∀t:T ･ t.inv <: T ⇒ t.x < t.y) invariant holds here (checked at call sites)

  7. inv can be used inmethod specifications class T {int x, y;invariant x < y; publicvoid m()requiresinv == typeof(this); {int[] a = newint[y-x]; … } meaning: (∀t:T ･ t.inv <: T ⇒ t.x < t.y) invariant holds here (checked at call sites)

  8. Exposed vs. owned o o o o owned W W W W V V V V U U U U T T T T Object Object Object Object o.inv == W o.inv == ⊥ o.inv == U o.inv == W consistent consistent exposed owned • Only consistent objects can be owned • Special field exposed keeps track of exposed/owned • exposed can be used in method specifications

  9. Components Q Object R W q P x 26 Object V p U T Object

  10. Components Q Object • Component fields are declared as such • Component fields are not necessarily unique references R q P x 26 Object p U T Object

  11. Components Q Object • When inv is increased to U, then U’s components are checked to be consistent (p.inv == typeof(p)) and are subsequently un-exposed owned R q P x 26 Object p U T Object o.inv == T o.inv == U

  12. Components Q Object • Decreasing inv below U exposes U’s components owned R q P x 26 Object p U T Object o.inv == T o.inv == U

  13. Fields of componentscan be mentioned in invariants k Q Object g h R q P x 26 Object p class U {… invariant x ≤ p.g ∧ p.g == p.h; invariant x ≤ q.k; U T Object • Fields of owned (un-exposed) objects are not allowed to be mutated

  14. License to modify • A field o.f can be modified only when o.exposed holds • A method m is allowed a net effect on a field o.f (including o.inv and o.exposed) only if: • o.f appears in the modifies clause of m, or • o was not allocated on entry to m, or • o was not exposed on entry to m new

  15. Method calls may change fields of un-exposed objects o owned g h R P x 26 Object p class U {… invariant x ≤ p.g ∧ p.g == p.h; U T Object

  16. Related work • rep types in CLU • valid idiom in ESC/Modula-3 • (implicit) pack/unpack operations in Vault and Fugue • capability calculus • ownership types • invariant declarations in ESC/Java and JML • locking and monitor disciplines in concurrent programming

  17. Conclusions exposed inv Object • Simple! • inv, exposed, identification of components, protocol for changing inv/exposed • object references can always be copied • but objects can have just one owner • fields can always be read • but curbed expectations about the values read • frame problem solved without abstraction (e.g., data groups) • Want: • experience, understanding of limits • extensions to support more good programs • more detailed comparison with other work

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