Programming language elements for correctness proofs

Formal methods are not used widely in industrial software development, because the overhead of formally proving program properties is generally not acceptable. In this paper we present an ongoing research project to make the construction of such proofs easier by embedding the proof system into a compiler. Using the introduced new programming language, the programmer writes formal specification first. The specification is to be refined using stepwise refinement which results in a proof. The compiler checks this proof and generates the corresponding program in a traditional programming language. The resulting code automatically fulfills the requirements of the specification. In this paper we present language elements to build specification statements and proofs. We give a short overview on the metaprogramming techniques of the language that support the programmer's work. Using a formal model we give the semantics of specification statements and refinements. We also prove the soundness of the basic algorithms of the compiler

Verification of systolic arrays: a stream functional approach

Journal ArticleWe illustrate that the verification of systolic architectures can be carried out using techniques developed in the context of verification of programs. This is achieved by a decomposition of the original problem into separately proving the correctness of the data representation and of the individual processing elements in the systolic architecture. By expressing a processing element as a function on a stream of data we are able to utilize standard proof techniques from programming language theory. This decomposition leads to relatively straightforward proofs of the properties of the systolic architecture. We illustrate the techniques via a substantial example, the proof of the correctness of a linear-time systolic architecture for computing the gcd of polynomials. Although this architecture has been designed a few years ago, a formal proof of correctness has not hitherto appeared in the literature

Trustworthy Refactoring via Decomposition and Schemes: A Complex Case Study

Widely used complex code refactoring tools lack a solid reasoning about the correctness of the transformations they implement, whilst interest in proven correct refactoring is ever increasing as only formal verification can provide true confidence in applying tool-automated refactoring to industrial-scale code. By using our strategic rewriting based refactoring specification language, we present the decomposition of a complex transformation into smaller steps that can be expressed as instances of refactoring schemes, then we demonstrate the semi-automatic formal verification of the components based on a theoretical understanding of the semantics of the programming language. The extensible and verifiable refactoring definitions can be executed in our interpreter built on top of a static analyser framework.Comment: In Proceedings VPT 2017, arXiv:1708.0688

Towards correct-by-construction product variants of a software product line: GFML, a formal language for feature modules

Software Product Line Engineering (SPLE) is a software engineering paradigm that focuses on reuse and variability. Although feature-oriented programming (FOP) can implement software product line efficiently, we still need a method to generate and prove correctness of all product variants more efficiently and automatically. In this context, we propose to manipulate feature modules which contain three kinds of artifacts: specification, code and correctness proof. We depict a methodology and a platform that help the user to automatically produce correct-by-construction product variants from the related feature modules. As a first step of this project, we begin by proposing a language, GFML, allowing the developer to write such feature modules. This language is designed so that the artifacts can be easily reused and composed. GFML files contain the different artifacts mentioned above.The idea is to compile them into FoCaLiZe, a language for specification, implementation and formal proof with some object-oriented flavor. In this paper, we define and illustrate this language. We also introduce a way to compose the feature modules on some examples.Comment: In Proceedings FMSPLE 2015, arXiv:1504.0301

Modal logics for reasoning about object-based component composition

Component-oriented development of software supports the adaptability and maintainability of large systems, in particular if requirements change over time and parts of a system have to be modified or replaced. The software architecture in such systems can be described by components and their composition. In order to describe larger architectures, the composition concept becomes crucial. We will present a formal framework for component composition for object-based software development. The deployment of modal logics for defining components and component composition will allow us to reason about and prove properties of components and compositions

Specifying Reusable Components

Reusable software components need expressive specifications. This paper outlines a rigorous foundation to model-based contracts, a method to equip classes with strong contracts that support accurate design, implementation, and formal verification of reusable components. Model-based contracts conservatively extend the classic Design by Contract with a notion of model, which underpins the precise definitions of such concepts as abstract equivalence and specification completeness. Experiments applying model-based contracts to libraries of data structures suggest that the method enables accurate specification of practical software

Fifty years of Hoare's Logic

We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin