精化演算支撑工具PRT的研究

1 引言精化演算是一种数学表示法和若干规则的集合,用于从程序规约推导出命令式程序。精化是从抽象程序向具体程序转换的过程,其中包含程序的正确性证明。精化的程序开发方法比对已有程序进行验证以保证程序正确性的方法更有效。通过精化演算中的转换规则可以演算出精化的程序。利用精化演算从规约导出程序的过程由大量步骤构成,非常适合利用机器工具进行辅助。本文对精化工具进行了需求分析和功能分析,研究了一个新的精化工具PRT(Program Refinement Tool)并与现有的一些工具进行了比较。     

基于时序约束建模的自动精化和组合工具

为提供更优质的使用Event-B形式化方法建模混合系统的工具,根据混合系统的时序约束建模方法,其能够很好刻画混合系统建模中的时间相关性质并且支持精化和组合,提出基于它的自动筛选、精化和组合的方法.开发对应的自动精化和组合的工具链,工具链包含模型检测、自动精化和组合、模型证明等一系列功能并拥有用户友好的界面.给出一个使用工具的案例介绍和应用此工具.     

Petri网结点精化及其应用

在Petri网精化概念的基础上,给出一种解决Petri网结点爆炸问题的方法,该方法针对精化的定义,从库所和变迁的约束条件入手,分析结点精化的可行性和方法,并给出证明。该方法的建立为今后利用Petri网进行建模提供了必要帮助。     

基于Event-B 方法的多应用智能卡的建模与开发

Event-B是一种基于集合论和谓词逻辑的形式化系统语言,能够采用精化策略为系统建立逐渐精化的模型。提出了如何将Event B应用到实际工业领域的方法,包括重写需求、建立抽象模型及逐层精化三个步骤。首先从环境、功能、性质三个主要方面重写需求,明确精化策略;然后利用形式化方法建立抽象模型并验证该模型;最后,在正确的抽象模型上按照精化策略添加需求、逐层精化,并对每层模型进行验证,基于满足需求的最后一层模型,可进一步利用工具完成代码自动生成。该方法学采用精化理论,以逐层递增的方式明确被开发系统的需求及性质,并进行形式化建模与验证,确保了模型的正确性。为了说明该方法学的可行性,以真正工业界的多应用智能卡为实例,基于Event-B方法及其工具平台Rodin给出了该方法在实际建模及验证过程中的应用。     

基于Event-B方法的安全协议设计、建模与验证

随着软件精化验证方法以及Isabella/HOL、VCC等验证工具不断取得进展,研究者们开始采用精化方法和验证工具设计、建模安全协议和验证安全协议源程序的正确性.在介绍Event-B方法和验证工具Isabella/HOL、VCC的基础上,综述了基于Event-B方法的安全协议形式化设计、建模与源程序验证的典型研究工作,主要包括从需求规范到消息传递形式协议的安全协议精化设计、基于TPM（trusted platform module）的安全协议应用的精化建模以及从消息传递形式协议到代码的源程序精化验证.     

基于遗传规划的行为模型精化方法

行为模型的精化是软件工程中的基于模型驱动开发的关键问题.基于针对环境的形式化行为模型和形式化方法中的精化理论,提出了一种基于遗传规划的行为模型的自动精化方法.该方法将精化看作可执行的基本操作的组合过程.首先通过分析抽象行为的后置条件公式,执行基于逻辑归约的精化方法,从而生成循环结构和其他简单新行为的描述.然后利用基于遗传规划的精化方法对新行为继续精化,直到产生的程序最终由基本操作构成.由于传统的遗传规划方法对选择结构难以演化,提出了组合终止条件的概念.通过测试组合终止条件,选择结构也能较好的产生.最后以排序问题为例,给出实际的演化过程,结果说明该方法具有较强的可行性.事实上该方法适用于任何由若干基本操作组合以完成复杂操作的问题求解过程.     

一种从面向对象Z规约到代码的精化演算方法

COOZ(complete object-oriented Z)的优势在于精确描述大型程序的规约.COOZ本身的结构 不支持精化演算,这限制了COOZ的应用能力,使COOZ难以作为完整的方法应用于软件的开发. 将精化演算引入COOZ,弥补了COOZ在设计和实现阶段的不足,同时也消除了规约与实现之间在 结构和表示方法上的完全分离,使程序开发在一个完整的框架下平滑进行.该文提出了基于CO OZ和精化演算的软件开发模型,通过实例讨论了数据精化和操作精化问题.在精化演算实现技 术方面构造了一种数据精化算子,提出一     

一种基于构件演算的主动构件精化方法

现代构件系统通常包含多个并发执行的主动构件,这使得验证构件系统的正确性变得十分困难.通过对构件演算进行扩展,提出了一种主动构件的精化方法.在构件接口层引入契约.契约使用卫式设计描述公共方法和主动活动的功能规约.通过一对发散、失败集合定义契约的动态行为,并利用发散、失败集合之间的包含关系定义契约间的精化关系.证明了应用仿真技术确认契约精化关系的定理.定义构件的语义为其需求接口契约到其服务接口契约的函数,以此为基础,可以通过契约的精化来证明构件的精化.给出了构件的组装规则.在构件系统自底向上的构造过程中,应用构件的精化方法和组装规则可以保证最终系统的正确性.     

形式化方法B的精化

形式化方法B支持从抽象规约到实现的完整的开发过程，用于开发安全关键的软件系统。给出了B方法精化的定义后，介绍了抽象机的精化过程与方法，结合实例分析了仅使用前向精化的普通精化规则的不完整性，通过引入反向精化提供了完备的精化理论，二者联合起来能够证明任何正确的精化。     

一种新的多分辨率模型表示方法

提出了一种简洁高效的多分辨率模型表示方法MRM,该方法能对网格简化或精化过程进行编码,并在此基础上实现了一个多分辨率造型与编辑系统。该系统能为给定的模型生成多分辨率表示,并支持对模型的分辨率进行编辑,统一地完成有选择地精化和简化操作。     

A Program Refinement Tool

The refinement calculus for the development of programs from specifications is well suited to mechanised support. We review the requirements for tool support of refinement as gleaned from our experience with existing refinement tools, and report on the design and implementation of a new tool to support refinement based on these requirements. The main features of the new tool are close integration of refinement and proof in a single tool (the same mechanism is used for both), good management of the refinement context, an extensible theory base that allows the tool to be adapted to new application domains, and a flexible user interface. Received June 1997 / Accepted in revised form June 1998     

Superposition refinement of reactive systems

Superposition refinement enhances an algorithm by superposing one computation mechanism onto another mechanism, in a way that preserves the behavior of the original mechanism. Superposition seems to be particularly well suited to the development of parallel and distributed programs: an originally simple sequential algorithm can be extended with mechanisms that distribute control and state information to many processes, thus permitting efficient parallel execution of the algorithm. We will show in this paper how superposition of reactive systems is expressed in the refinement calculus. We illustrate the power of this method by a case study, showing how a distributed broadcasting system is derived through a sequence of superposition refinements.     

Refinement calculus: A basis for translation validation,debugging and certification

In this paper, we show how refinement calculus provides a basis for translation validation of optimized programs written in high level languages. Towards such a direction, we shall provide a generalized proof rule for establishing refinement of source and target programs for which one need not have to know the underlying program transformations. Our method is supported by a semi-automatic tool that uses a theorem prover for validating the verification conditions. We further show that the translation validation infrastructure provides an effective basis for deriving semantic debuggers and illustrate the development of a simple debugger for optimized programs using this approach using Prolog. A distinct advantage of semantic debugging is that it permits the user to change values at run-time only when the values are consistent with the underlying semantics.     

Exits in the refinement calculus

Although many programming languages contain exception handling mechanisms, their formal treatment — necessary for rigorous development — can be complex. Nevertheless, this paper presents a simple incorporation ofexit commands and exception blocks into a rigorous program development method. The refinement calculus, chosen for the exercise, is a method of developing imperative programs. It is based on weakest preconditions, although they are not used explicitly during program construction; they merely justify the general method. In the style of the refinement calculus, program development laws are given that introduce and allow the manipulation ofexits. The soundness of the new laws is shown using weakest preconditions (as for the existing refinement calculus laws). The extension of weakest preconditions needed to handleexits is a variation on earlier work of Cristian; the variation is necessary to handle nondeterminism.     

Refinement and the Z Schema Calculus

It is well known that the principal operators in the Z schema calculus are not monotonic with respect to refinement, which limits their usefulness in software development. The usual reaction to this observation is to remove all schema operators before performing any kind of refinement, or to move to a different formalism such as B or the refinement calculus. This paper examines the interaction between refinement and the schema calculus more closely, showing exactly how non-monotonicity arises, and identifying various conditions under which components of schema expressions can be safely replaced by their refinements. This analysis uses a decomposition of the standard refinement relation into two simpler relations that allow us to study refinements that modify a specification in different ways.     

A Logic for Schema-Based Program Development

We show how a theory of specification refinement and program development can be constructed as a conservative extension of our existing logic for Z. The resulting system can be set up as a development method for a Z-like specification language, or as a generalisation of a refinement calculus (with a novel semantics). In addition to the technical development we illustrate how the theory can be used in practice.     

A tactic language for refinement of state-rich concurrent specifications

Circus is a refinement language in which specifications define both data and behavioural aspects of concurrent systems using a combination of Z and CSP. Its refinement theory and calculus are distinctive, but since refinements may be long and repetitive, the practical application of this technique can be hard. Useful strategies have been identified, described, and used, and by documenting them as tactics, they can be expressed and repeatedly applied as single transformation rules. Here, we present ArcAngelC, a language for defining such tactics; we present the language, its semantics, and its application in the formalisation of an existing strategy for verification of Ada implementations of control systems specified by Simulink diagrams. We also discuss its mechanisation in a theorem prover, ProofPower-Z.     

一种从Z到精化演算的软件开发方法

一、引言形式化方法的研究和应用已有二十多年的历史,源于Dijkstra和Hoare的程序验证以及Scott、stratchey等人的程序语义研究,指为保证复杂系统的可靠性,以数学为基础对其进行精确描述和验证的语言、技术和工具。形式化方法的关键在于形式规约语言。通过语法和语义有严格数学定义的形式规约语言对系统及其各方面性能的描述,产生系统的形式规约,可以帮助开发者获得对所描述系统的深刻理解,并通     

Components as coalgebras: The refinement dimension

This paper characterises refinement of state-based software components modelled as pointed coalgebras for some Set endofunctors. The proposed characterisation is parametric on a specification of the underlying behaviour model introduced as a strong monad. This provides a basis to reason about (and transform) state-based software designs. In particular, it is shown how refinement can be applied to the development of the inequational subset of a calculus of generic software components.     

Real-time refinement in Manna and Pnueli's temporal logic

A refinement calculus for the development of real-time systems is presented. The calculus is based upon a wide-spectrum language called TAM (the Temporal Agent Model), within which both functional and timing properties can be expressed in either abstract or concrete terms. A specification oriented semantics is given for the language. Program development is considered as a refinement process i.e. thecalculation of a structured program from an unstructured specification. An example program is developed.