Insertion into Doubly-Linked List

(Figure of doubly-linked list of size 3.)


   assume P;
   if (first == null) {
     first = n; = null;
     n.prev = null;
   } else { = first;
     first.prev = n;
     n.prev = null;
     first = n;
   assert Q;

Where $P$ is

   n \neq null\ \land  \\
   next(n) = null \land prev(n)=null\ \land \\
   prev(first) = null\ \land \ Q

and where $Q$ is

   \forall x.\forall y. prev(x)=y\ \ \rightarrow \\
   \qquad (y \neq null \rightarrow next(y)=x)\ \land \\
   \qquad (y = null \land x \neq null \rightarrow (\forall z. next(z) \neq x))

Corresponding Jahob file (call it

We can check the add method by:

jahob.opt -method Simple.add -usedp cvcl

How can we build a verification conditions for such programs?

  • we need to be able to reason about data structures (objects, references, arrays)

Illustration of phases in Jahob system when loop invariants are specified:

  • source code
  • syntax tree
  • jast: simplified statements (use option -jast to see it)
  • ast: guarded commands with loops (use option -ast to see it)
  • sast (use option -sast to see it):
    • eliminating loops with loop invariants by translation to guarded commands (as in Backward VCG with Loops)
    • incorporate preconditions and postconditions using assume and assert
  • compute weakest precondition with respect to 'true' - this is verification condition (VC)
  • simplify VC, split into multiple formulas, eliminate easily provable formulas
    • use -v to view the remaining formulas
  • use theorem provers to prove the resulting formulas
    • some of the provers: cvcl (make symbolic link to cvc3), z3, SPASS, E, Vampire, BAPA, Isabelle (see also –help)

In general, system also deals with:

  • specification variables (shorthands and ghost variables)
  • loop invariant inference