Automatic Reasoning on Recursive Data-Structures with Sharing

We consider the problem of automatically verifying programs which manipulate arbitrary data structures. Our specification language is expressive, contains a notion of \emph{separation}, and thus enables a precise specification of \emph{frames}. The main contribution then is a program verification method which combines strongest postcondition reasoning in the form symbolic execution, unfolding recursive definitions of the data structure in question, and a new frame rule to achieve \emph{local reasoning} so that proofs can be compositional. Finally, we present an implementation of our verifier, and demonstrate automation on a number of representative programs. In particular, we present the first automatic proof of a classic graph marking algorithm, paving the way for dealing with a class of programs which traverse a complex data structure.