Toward Automated Verification of Model Transformations: A Case Study of Analysis of Refactoring Business Process Models

Verification of the transformations is a fundamental issue for applying them in real world solutions. We have previously proposed a formalization to declaratively describe model transformations and proposed an approach for the verification. Our approach consists of a reasoning system that works on the formal transformation description and deduction rules for the system. The reasoning system can automatically generate the proof of some properties. In this paper, we present a case study, to demonstrate our approach of automated verification of model transformations in a multi-paradigm environment

Formalization, Mechanization and Automation of G\"odel's Proof of God's Existence

G\"odel's ontological proof has been analysed for the first-time with an unprecedent degree of detail and formality with the help of higher-order theorem provers. The following has been done (and in this order): A detailed natural deduction proof. A formalization of the axioms, definitions and theorems in the TPTP THF syntax. Automatic verification of the consistency of the axioms and definitions with Nitpick. Automatic demonstration of the theorems with the provers LEO-II and Satallax. A step-by-step formalization using the Coq proof assistant. A formalization using the Isabelle proof assistant, where the theorems (and some additional lemmata) have been automated with Sledgehammer and Metis.Comment: 2 page

Checking Zenon Modulo Proofs in Dedukti

Dedukti has been proposed as a universal proof checker. It is a logical framework based on the lambda Pi calculus modulo that is used as a backend to verify proofs coming from theorem provers, especially those implementing some form of rewriting. We present a shallow embedding into Dedukti of proofs produced by Zenon Modulo, an extension of the tableau-based first-order theorem prover Zenon to deduction modulo and typing. Zenon Modulo is applied to the verification of programs in both academic and industrial projects. The purpose of our embedding is to increase the confidence in automatically generated proofs by separating untrusted proof search from trusted proof verification.Comment: In Proceedings PxTP 2015, arXiv:1507.0837

Tableaux Modulo Theories Using Superdeduction

We propose a method that allows us to develop tableaux modulo theories using the principles of superdeduction, among which the theory is used to enrich the deduction system with new deduction rules. This method is presented in the framework of the Zenon automated theorem prover, and is applied to the set theory of the B method. This allows us to provide another prover to Atelier B, which can be used to verify B proof rules in particular. We also propose some benchmarks, in which this prover is able to automatically verify a part of the rules coming from the database maintained by Siemens IC-MOL. Finally, we describe another extension of Zenon with superdeduction, which is able to deal with any first order theory, and provide a benchmark coming from the TPTP library, which contains a large set of first order problems.Comment: arXiv admin note: substantial text overlap with arXiv:1501.0117

Automated verification of refinement laws

Demonic refinement algebras are variants of Kleene algebras. Introduced by von Wright as a light-weight variant of the refinement calculus, their intended semantics are positively disjunctive predicate transformers, and their calculus is entirely within first-order equational logic. So, for the first time, off-the-shelf automated theorem proving (ATP) becomes available for refinement proofs. We used ATP to verify a toolkit of basic refinement laws. Based on this toolkit, we then verified two classical complex refinement laws for action systems by ATP: a data refinement law and Back's atomicity refinement law. We also present a refinement law for infinite loops that has been discovered through automated analysis. Our proof experiments not only demonstrate that refinement can effectively be automated, they also compare eleven different ATP systems and suggest that program verification with variants of Kleene algebras yields interesting theorem proving benchmarks. Finally, we apply hypothesis learning techniques that seem indispensable for automating more complex proofs

An experimental Study using ACSL and Frama-C to formulate and verify Low-Level Requirements from a DO-178C compliant Avionics Project

Safety critical avionics software is a natural application area for formal verification. This is reflected in the formal method's inclusion into the certification guideline DO-178C and its formal methods supplement DO-333. Airbus and Dassault-Aviation, for example, have conducted studies in using formal verification. A large German national research project, Verisoft XT, also examined the application of formal methods in the avionics domain. However, formal methods are not yet mainstream, and it is questionable if formal verification, especially formal deduction, can be integrated into the software development processes of a resource constrained small or medium enterprise (SME). ESG, a Munich based medium sized company, has conducted a small experimental study on the application of formal verification on a small portion of a real avionics project. The low level specification of a software function was formalized with ACSL, and the corresponding source code was partially verified using Frama-C and the WP plugin, with Alt-Ergo as automated prover. We established a couple of criteria which a method should meet to be fit for purpose for industrial use in SME, and evaluated these criteria with the experience gathered by using ACSL with Frama-C on a real world example. The paper reports on the results of this study but also highlights some issues regarding the method in general which, in our view, will typically arise when using the method in the domain of embedded real-time programming.Comment: In Proceedings F-IDE 2015, arXiv:1508.0338