Formal Reasoning Using an Iterative Approach with an Integrated Web IDE

This paper summarizes our experience in communicating the elements of reasoning about correctness, and the central role of formal specifications in reasoning about modular, component-based software using a language and an integrated Web IDE designed for the purpose. Our experience in using such an IDE, supported by a 'push-button' verifying compiler in a classroom setting, reveals the highly iterative process learners use to arrive at suitably specified, automatically provable code. We explain how the IDE facilitates reasoning at each step of this process by providing human readable verification conditions (VCs) and feedback from an integrated prover that clearly indicates unprovable VCs to help identify obstacles to completing proofs. The paper discusses the IDE's usage in verified software development using several examples drawn from actual classroom lectures and student assignments to illustrate principles of design-by-contract and the iterative process of creating and subsequently refining assertions, such as loop invariants in object-based code.Comment: In Proceedings F-IDE 2015, arXiv:1508.0338

Uni-Prover: A Universal Automated Prover for Specificationally Rich Languages

Formal software verification systems must be designed to adapt to growth in the scope and complexity of software, driven by expanding capabilities of computer hardware and domain of potential usage. They must provide specification languages that are flexible and rich enough to allow software developers to write precise and comprehensible specifications for a full spectrum of object-based software components. Rich specification languages allow for arbitrary extensions to the library of mathematical theories, and critically, verification of programs with such specifications require a universal automated prover. Most existing verification systems either incorporate specification languages limited to first-order logic, which lacks the richness necessary to write adequate specifications, or provide automated provers covering only a fixed collection of mathematical theories, which lack the compass to specify and verify sophisticated object-based software. This dissertation presents an overall design of Uni-Prover, a universal automated prover for atomic sequents to verify software specified with rich languages. Such a prover is a necessary element of any adequate automated verification system of the future. The design contains components to accommodate changes or upgrades that may happen. The congruence class registry at the center of Uni-Prover handles all core manipulations necessary to verify programs, and it includes a multi-level organization for effective searching of the registry. The full functional behavior of the registry component is described mathematically, and a prototype implementation is given. Additionally, the contiguous instantiation strategy, a strategy that requires neither user-supplied heuristics nor triggers when instantiating universally quantified theorems in any theory, is detailed to minimize verification steps by avoiding the proliferation of sequents in the instantiation process