There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

物件導向軟體之架構(Object-Oriented Software Construction)探討

ing WS1S Systems to Verify Parameterized Networks . . . . . . . . . . . . 188 Kai Baukus, Saddek Bensalem, Yassine Lakhnech and Karsten Stahl FMona: A Tool for Expressing Validation Techniques over Infinite State Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 J.-P. Bodeveix and M. Filali Transitive Closures of Regular Relations for Verifying Infinite-State Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 Bengt Jonsson and Marcus Nilsson Diagnostic and Test Generation Using Static Analysis to Improve Automatic Test Generation . . . . . . . . . . . . . 235 Marius Bozga, Jean-Claude Fernandez and Lucian Ghirvu Efficient Diagnostic Generation for Boolean Equation Systems . . . . . . . . . . . . 251 Radu Mateescu Efficient Model-Checking Compositional State Space Generation with Partial Order Reductions for Asynchronous Communicating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 Jean-Pierre Krimm and Laurent Mounier Checking for CFFD-Preorder with Tester Processes . . . . . . . . . . . . . . . . . . . . . . . 283 Juhana Helovuo and Antti Valmari Fair Bisimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Thomas A. Henzinger and Sriram K. Rajamani Integrating Low Level Symmetries into Reachability Analysis . . . . . . . . . . . . . 315 Karsten Schmidt Model-Checking Tools Model Checking Support for the ASM High-Level Language . . . . . . . . . . . . . . 331 Giuseppe Del Castillo and Kirsten Winter Table of

Tools and Algorithms for the Construction and Analysis of Systems. Proc. TACAS 2009

Traditionally, the full verification of a program's functional correctness has been obtained with pen and paper or with interactive proof assistants, whereas only reduced verification tasks, such as extended static checking, have enjoyed the automation offered by satisfiability-modulo-theories (SMT) solvers. More recently, powerful SMT solvers and well-designed program verifiers are starting to break that tradition, thus reducing the effort involved in doing full verification.

This paper gives a tour of the language and verifier Dafny, which has been used to verify the functional correctness of a number of challenging pointer-based programs. The paper describes the features incorporated in Dafny, illustrating their use by small examples and giving a taste of how they are coded for an SMT solver. As a larger case study, the paper shows the full functional specification of the Schorr-Waite algorithm in Dafny.

/pdf/dafny-an-automatic-program-verifier-for-functional-2trag0l49s.pdf

Dafny: an automatic program verifier for functional correctness

This article provides a detailed description of the automatic theorem prover Simplify, which is the proof engine of the Extended Static Checkers ESC/Java and ESC/Modula-3. Simplify uses the Nelson--Oppen method to combine decision procedures for several important theories, and also employs a matcher to reason about quantifiers. Instead of conventional matching in a term DAG, Simplify matches up to equivalence in an E-graph, which detects many relevant pattern instances that would be missed by the conventional approach. The article describes two techniques, error context reporting and error localization, for helping the user to determine the reason that a false conjecture is false. The article includes detailed performance figures on conjectures derived from realistic program-checking problems.

https://www.hpl.hp.com/techreports/2003/HPL-2003-148.pdf

Simplify: a theorem prover for program checking

The ultimate goal of program verification is not the theory behind the tools or the tools themselves, but the application of the theory and tools in the software engineering process. Our society relies on the correctness of a vast and growing amount of software. Improving the software engineering process is an important, long-term goal with many steps. Two of those steps are the KeY tool and this KeY book.

The material is presented on an advanced level suitable for graduate courses and, of course, active researchers with an interest in verification. The underlying verification paradigm is deductive verification in an expressive program logic. The logic used for reasoning about programs is not a minimalist version suitable for theoretical investigations, but an industrial-strength version. The first-order part is equipped with a type system for modelling of object hierarchies, with underspecification, and with various built-in theories. The program logic covers full Java Card (plus a bit more such as multi-dimensional arrays, characters, and long integers). A lot of emphasis is thereby put on specification, including two widely-used object-oriented specification languages (OCL and JML) and even an interface to natural language generation. The generation of proof obligations from specified code is discussed at length. The book is rounded off by two substantial case studies that are included and presented in detail.

https://www.springer.com/cda/content/document/productFlyer/productFlyer-WEST_978-3-540-68977-5.pdf?SGWID=0-0-1297-173712406-bookseller

Verification of Object-Oriented Software. the Key Approach

This paper presents ABS, an abstract behavioral specification language for designing executable models of distributed object-oriented systems. The language combines advanced concurrency and synchronization mechanisms for concurrent object groups with a functional language for modeling data. ABS uses asynchronous method calls, interfaces for encapsulation, and cooperative scheduling of method activations inside concurrent objects. This feature combination results in a concurrent object-oriented model which is inherently compositional. We discuss central design issues for ABS and formalize the type system and semantics of Core ABS, a calculus with the main features of ABS. For Core ABS, we prove a subject reduction property which shows that well-typedness is preserved during execution; in particular, "method not understood" errors do not occur at runtime for well-typed ABS models. Finally, we briefly discuss the tool support developed for ABS.

ABS: a core language for abstract behavioral specification

KeY is a tool that provides facilities for formal specification and verification of programs within a commercial platform for UML based software development. Using the KeY tool, formal methods and object-oriented development techniques are applied in an integrated manner. Formal specification is performed using the Object Constraint Language (OCL), which is part of the UML standard. KeY provides support for the authoring and formal analysis of OCL constraints. The target language of KeY based development is Java Card DL, a proper subset of Java for smart card applications and embedded systems. KeY uses a dynamic logic for Java Card DL to express proof obligations, and provides a state-of-the-art theorem prover for interactive and automated verification. Apart from its integration into UML based software development, a characteristic feature of KeY is that formal specification and verification can be introduced incrementally.

The KeY tool

Preface. Introduction M. Fitting. Tableau Methods for Classical Propositional Logic M. D'Agostino. First-Order Tableau Methods R. Letz. Equality and Other Theories B. Beckert. Tableaux for Intuitionistic Logics A. Waaler, L. Wallen. Tableau Methods for Modal and Temporal Logics R. Gore. Tableau Methods for Substructural Logics M. D'Agostino, et al. Tableaux for Nonmonotonic Logics N. Olivetti. Tableaux for Many-valued Logics R. Hahnle. Implementing Semantic Tableaux J. Posegga, P. Schmitt. A Bibliography on Analytic Tableaux Theorem Proving G. Wrightson. Index.

Handbook of tableau methods

Static analysis of software with deductive methods is a highly dynamic field of research on the verge of becoming a mainstream technology in software engineering. It consists of a large portfolio of - mostly fully automated - analyses: formal verification, test generation, security analysis, visualization, and debugging. All of them are realized in the state-of-art deductive verification framework KeY. This book is the definitive guide to KeY that lets you explore the full potential of deductive software verification in practice. It contains the complete theory behind KeY for active researchers who want to understand it in depth or use it in their own work. But the book also features fully self-contained chapters on the Java Modeling Language and on Using KeY that require nothing else than familiarity with Java. All other chapters are accessible for graduate students (M.Sc. level and beyond). The KeY framework is free and open software, downloadable from the book companion website which contains also all code examples mentioned in this book.

Reiner Hähnle

Papers

Verification of Object-Oriented Software. the Key Approach

ABS: a core language for abstract behavioral specification

The KeY tool

Handbook of tableau methods

Deductive Software Verification - The KeY Book