Invariants synthesis over a combined domain for automated program verification

Program invariants such as loop invariants and method specifications ( a.k.a. procedural summaries) are key components in program verification. Such invariants are usually manually specified by users before passed as inputs to a program verifier. The process of manually annotating programs with such invariants is tedious and error-prone and can significantly hinder the level of automation in program verification. Although invariant synthesis techniques have made noticeable progress in reducing the burden of user annotations; when it comes to automated verification of memory safety and functional correctness for heap-manipulating programs, it remains a rather challenging task to discover program specifications and invariants automatically, due to the complexity of aliasing and mutability of data structures. In this paper, we present invariant synthesis algorithms for the following scenarios: i) to synthesise a missing loop invariant, ii) to refine given pre/post shape templates to complete pre/post-conditions, iii) to infer a missing precondition, iv) to calculate a missing postcondition, given a precondition. The proposed analyses are based on abstract interpretation and are built over an abstract domain combining separation, numerical and multi-set (bag) information. Our inference mechanisms are equipped with newly designed abstraction, join, widening and abduction operations. Initial prototypical experiments have shown that they are viable and powerful enough to discover interesting useful invariants for non-trivial programs.