A Framework for Inductive Proofs of Data Structures

We consider the problem of automated program verification with emphasis on reasoning about dynamically manipulated data structures. We begin with an existing specification language which has two key features: (a) the use of explicit heap variables, and (b) user defined recursive properties in a wrapper logic language. The language provides a new-level of expressiveness for specifying properties of heap manipulations. The main contribution, however, is an algorithm to automatically prove verification conditions when formulas in the specification language are used as assertions in programs. More precisely, we consider verification of heap manipulating programs that combines user written modular contracts and loop invariants with completely automated theorem proving of the resulting verification conditions. The key feature of the algorithm is the ability to automatically employ induction proof steps with respect to dynamically generated induction hypotheses. Though necessarily still incomplete, the algorithm provides a new level of automation.