Towards Generic Monitors for Object-Oriented Real-Time Maude Specifications

Non-Functional Properties (NFPs) are crucial in the design of software. Specification of systems is used in the very first phases of the software development process for the stakeholders to make decisions on which architecture or platform to use. These specifications may be an- alyzed using different formalisms and techniques, simulation being one of them. During a simulation, the relevant data involved in the anal- ysis of the NFPs of interest can be measured using monitors. In this work, we show how monitors can be parametrically specified so that the instrumentation of specifications to be monitored can be automatically performed. We prove that the original specification and the automati- cally obtained specification with monitors are bisimilar by construction. This means that the changes made on the original system by adding monitors do not affect its behavior. This approach allows us to have a library of possible monitors that can be safely added to analyze different properties, possibly on different objects of our systems, at will.Universidad de Málaga, Campus de Excelencia Internacional Andalucía Tech. Spanish MINECO/FEDER project TIN2014-52034-R, NSF Grant CNS 13-19109

Recursive Definitions of Monadic Functions

Using standard domain-theoretic fixed-points, we present an approach for defining recursive functions that are formulated in monadic style. The method works both in the simple option monad and the state-exception monad of Isabelle/HOL's imperative programming extension, which results in a convenient definition principle for imperative programs, which were previously hard to define. For such monadic functions, the recursion equation can always be derived without preconditions, even if the function is partial. The construction is easy to automate, and convenient induction principles can be derived automatically.Comment: In Proceedings PAR 2010, arXiv:1012.455

The Matrix Reproved (Verification Pearl)

International audienceIn this paper we describe a complete solution for the first challenge of the VerifyThis 2016 competition held at the 18th ETAPS Forum. We present the proof of two variants for the multiplication of matrices: a naive version using three nested loops and the Strassen's algorithm. The proofs are conducted using the Why3 platform for deductive program verification, and automated theorem provers to discharge proof obligations. In order to specify and prove the two multiplication algorithms , we develop a new Why3 theory of matrices and apply the proof by reflection methodology

An open extensible tool environment for Event-B

Abstract. We consider modelling indispensable for the development of complex systems. Modelling must be carried out in a formal notation to reason and make meaningful conjectures about a model. But formal modelling of complex systems is a difficult task. Even when theorem provers improve further and get more powerful, modelling will remain difficult. The reason for this that modelling is an exploratory activity that requires ingenuity in order to arrive at a meaningful model. We are aware that automated theorem provers can discharge most of the onerous trivial proof obligations that appear when modelling systems. In this article we present a modelling tool that seamlessly integrates modelling and proving similar to what is offered today in modern integrated development environments for programming. The tool is extensible and configurable so that it can be adapted more easily to different application domains and development methods.

Foundational extensible corecursion: a proof assistant perspective

This paper presents a formalized framework for defining corecursive functions safely in a total setting, based on corecursion up-to and relational parametricity. The end product is a general corecursor that allows corecursive (and even recursive) calls under “friendly” operations, including constructors. Friendly corecursive functions can be registered as such, thereby increasing the corecursor’s expressiveness. The metatheory is formalized in the Isabelle proof assistant and forms the core of a prototype tool. The corecursor is derived from first principles, without requiring new axioms or extensions of the logic

Type-and-Scope Safe Programs and Their Proofs

We abstract the common type-and-scope safe structure fromcomputations on lambda-terms that deliver, e.g., renaming, substitution, evaluation, CPS-transformation, and printing witha name supply. By exposing this structure, we can prove generic simulation and fusion lemmas relating operations built this way. This work has been fully formalised in Agda

A Foundational View on Integration Problems

The integration of reasoning and computation services across system and language boundaries is a challenging problem of computer science. In this paper, we use integration for the scenario where we have two systems that we integrate by moving problems and solutions between them. While this scenario is often approached from an engineering perspective, we take a foundational view. Based on the generic declarative language MMT, we develop a theoretical framework for system integration using theories and partial theory morphisms. Because MMT permits representations of the meta-logical foundations themselves, this includes integration across logics. We discuss safe and unsafe integration schemes and devise a general form of safe integration

Isabelle/PIDE as Platform for Educational Tools

The Isabelle/PIDE platform addresses the question whether proof assistants of the LCF family are suitable as technological basis for educational tools. The traditionally strong logical foundations of systems like HOL, Coq, or Isabelle have so far been counter-balanced by somewhat inaccessible interaction via the TTY (or minor variations like the well-known Proof General / Emacs interface). Thus the fundamental question of math education tools with fully-formal background theories has often been answered negatively due to accidental weaknesses of existing proof engines. The idea of "PIDE" (which means "Prover IDE") is to integrate existing provers like Isabelle into a larger environment, that facilitates access by end-users and other tools. We use Scala to expose the proof engine in ML to the JVM world, where many user-interfaces, editor frameworks, and educational tools already exist. This shall ultimately lead to combined mathematical assistants, where the logical engine is in the background, without obstructing the view on applications of formal methods, formalized mathematics, and math education in particular.Comment: In Proceedings THedu'11, arXiv:1202.453

Integrated Reasoning and Proof Choice Point Selection in the Jahob System – Mechanisms for Program Survival

In recent years researchers have developed a wide range of powerful automated reasoning systems. We have leveraged these systems to build Jahob, a program specification, analysis, and verification system. In contrast to many such systems, which use a monolithic reasoning approach, Jahob provides a general integrated reasoning framework, which enables multiple automated reasoning systems to work together to prove the desired program correctness properties. We have used Jahob to prove the full functional correctness of a collection of linked data structure implementations. The automated reasoning systems are able to automatically perform the vast majority of the reasoning steps required for this verification. But there are some complex verification conditions that they fail to prove. We have therefore developed a proof language, integrated into the underlying imperative Java programming language, that developers can use to control key choice points in the proof search space. Once the developer has resolved these choice points, the automated reasoning systems are able to complete the verification. This approach appropriately leverages both the developer’s insight into the high-level structure of the proof and the ability of the automated reasoning systems to perform the mechanical steps required to prove the verification conditions. Building on Jahob’s success with this challenging program verification problem, we contemplate the possibility of verifying the complete absence of fatal errors in large software systems. We envision combining simple techniques that analyze the vast majority of the program with heavyweight techniques that analyze those more sophisticated parts of the program that may require arbitrarily sophisticated reasoning. Modularity mechanisms such as abstract data types enable the sound division of the program for this purpose. The goal is not a completely correct program, but a program that can survive any remaining errors to continue to provide acceptable service

A coinductive semantics of the Unlimited Register Machine

We exploit (co)inductive specifications and proofs to approach the evaluation of low-level programs for the Unlimited Register Machine (URM) within the Coq system, a proof assistant based on the Calculus of (Co)Inductive Constructions type theory. Our formalization allows us to certify the implementation of partial functions, thus it can be regarded as a first step towards the development of a workbench for the formal analysis and verification of both converging and diverging computations