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     

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。     

一种基于Z和精化演算的形式化开发方法

通过分析Z和精化演算各自的特点,本文提出了一种使两者无缝集成的形式化开发方法。该方法利用Z良好的描述特性和扩充的类机制,将系统规约直妆定义成精化演算中的抽象程序,然后用精化规则对抽象程序逐步精化,直到可执行程序。最后给出了一个简单例子。     

用Petri网描述程序精化中的循环不变式

形式化方法把程序看成规范,形式化开发方法包括形式规范和规范(程序)的精化.精化演算方法能够通过演算的方式,把规范逐步精化为程序.然而,演化的过程依赖于开发人员的经验,整个过程全部都是手动的.形式化方法的最高目标是软件自动化,使得能从规范自动开发出正确的程序.因而用Petri网来描述程序精化中的循环不变式,希望以此作为软件自动化的一个探索.     

用Petri网描述程序精化中的循环不变式

形式化方法把程序看成规范,形式化开发方法包括形式规范和规范（程序）的精化。精化演算方法能够通过演算的方式,把规范逐步精化为程序。然而,演化的过程依赖于开发人员的经验,整个过程全部都是手动的。形式化方法的最高目标是软件自动化,使得能从规范自动开发出正确的程序。因而用Petri网来描述程序精化中的循环不变式,希望以此作为软件自动化的一个探索。     

一种将设计模式用于程序精化演算的并行程序设计方法研究

并行程序设计是并行计算的难点之一。提出了一种将设计模式用于程序精化演算的并行程序设计方法。它通过在Z语言的Schema演算体系中扩充并行的概念和表示，使用设计模式，将问题求解和并行开发的知识进行形式化的定义与描述，通过扩充的Schema演算将其与模型规范进行复合，逐步精化得到抽象并行程序。通过实例对这一方法进行了详细的描述。     

精化演算支撑工具的分析

利用精化演算的方法开发软件,其过程由巨大数量的小步骤构成,由手工完成极其烦琐,也极容易出错。因此,利用机器辅助工具的支持是必要的。在分析现有的精化工具的基础上,我们提出了一个用于软件形式化开发的精化工具RT(RefinementTool),对精化工具进行了需求分析和功能分析。在精化工具的设计中,分析了精化工具的设计目标、总体结构、精化与证明的表示方法、用户界面和工具的扩充性等问题,通过对精化和证明的表示方法的分析,提出了一种精化与证明的表示相结合的方法。     

互逆主义程序精化——程序精化从形式化到半自动化的发展

Carroll Morgan的规则精化方法是一种典型的程序精化方法,是一种形式方法.本文用互逆主义逻辑对其进行了改造将其中的精化法则改造成为逻辑定理,以二层假言推理和小前提逆二层单准正向证明系统为推理规则,使得程序精化从形式化发展为半自动化.     

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.     

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.     

OOZE求精技术自动化的探讨

文中立足于一种Ｚ的面向对象扩充广谱语言ＯＯＺＥ，研究其从软件规格说明到可执行程序求精过程的自动化技术，重点讨论了数据求精技术，对Ｚ中的几种复合数据类型及其嵌套结构，ＯＯＺＥ中的类结构提出了相应的自动求精规则，同时给出了采用自动化技术进行操作求精的一般步骤。     

A formal software development approach using refinement calculus

The advantage of COOZ(Complete Object-Oriented Z) is to specify large scale software,but it does not support refinement calculus.Thus its application is comfined for software development.Including refinement calculus into COOZ overcomes its disadvantage during design and implementation.The separation between the design and implementation for structure and notation is removed as well .Then the software can be developed smoothly in the same frame.The combination of COOZ and refinement calculus can build object-oriented frame,in which the specification in COOZ is refined stepwise to code by calculus.In this paper,the development model is established.which is based on COOZ and refinement calculus.Data refinement is harder to deal with in a refinement tool than ordinary algorithmic refinement,since data refinement usually has to be done on a large program component at once.As to the implementation technology of refinement calculus,the data refinement calculator is constructed and an approach for data refinement which is based on data refinement calculus and program window inference is offered.     

The Automated Refinement of a Requirements Domain Theory

The specification and management of requirements is widely considered to be one of the most important yet most problematic activities in software engineering. In some applications, such as in safety critical areas or knowledge-based systems, the construction of a requirements domain theory is regarded as an important part of this activity. Building and maintaining such a domain theory, however, requires a large investment and a range of powerful validation and maintenance tools. The area of theory refinement is concerned with the use of training data to automatically change an existing theory so that it better fits the data. Theory refinement techniques, however, have not been extensively used in applications because of the problems in scaling up their underlying algorithms.In our work we have applied theory refinement to assist in the problem of validation and maintenance of a requirements theory concerning separation standards in the North East Atlantic. In this paper we describe an implemented refinement algorithm, which processes a logic program automatically generated from the theory. We overcame the size and expressiveness problems typically encountered when applying theory refinement to a logic program of this kind by designing focused, composite refinement operators within the algorithm. These operators modify the auto-generated logic program by generalising or specialising clauses containing ordinal relations—that is relations which operate on totally ordered data.     

Encoding, Decoding and Data Refinement

Data refinement is the systematic replacement of a data structure with another one in program development. Data refinement between program statements can on an abstract level be described as a commutativity property where the abstraction relationship between the data structures involved is represented by an abstract statement (a decoding). We generalise the traditional notion of data refinement by defining an encoding operator that describes the least (most abstract) data refinement with respect to a given abstraction. We investigate the categorical and algebraic properties of encoding and describe a number of special cases, which include traditional notions of data refinement. The dual operator of encoding is decoding, which we investigate and give an intuitive interpretation to. Finally we show a number of applications of encoding and decoding. Received May 1999 / Accepted in revised form November 2000     

Program development by inductive stepwise refinement

A constructive method of program development is presented. It seeks to unify two important ideas about program development. Namely that programming is a goal-oriented activity and that there should be a correspondence between data and program structures. The latter concept is seen to be extensible beyond the data processing context in which it was originally proposed. Induction provides the vehicle for program development by stepwise refinement, with the final program being constructed by application of a sequence of progressively more powerful generalizations. The design process employed guarantees the correctness of the final program provided that each of the refinement steps have been correctly taken. The method is illustrated by a number of samples.     

Unification: A case-study in data refinement

In this paper, the Z notation is used to develop a small theory of terms and substitutions within which a simple unification algorithm can be specified and proved correct. Particular emphasis is placed on the use of Z's mathematical data types to simplify the development and structure of this theory. The correctness of an abstract version of the algorithm is proved first; this version operates on substitutions by composition. Then data refinement is used to show that the substitutions can be represented by binding functions that make composition a particularly efficient operation. The approach taken in this paper is compared with the approaches of three previous papers based on VDM.The contribution of this paper is to show how data refinement can be used to explain the design decisions behind a non-trivial program, and to provide a point of comparison between Z and VDM approaches to the same problem.     

Verifying Contextual Refinement with Ownership Transfer

Contextual refinement is a compositional approach to compositional verification of concurrent objects.There has been much work designing program logics to prove the contextual refinement between the object implementation and its abstract specification.However,these program logics for contextual refinement verification cannot support objects with resource ownership transfer,which is a common pattern in many concurrent objects,such as the memory management module in OS kernels,which transfers the allocated memory block between the object and clients.In this paper,we propose a new approach to give abstract and implementation independent specifications to concurrent objects with ownership transfer.We also design a program logic to verify contextual refinement of concurrent objects w.r.t.their abstract specifications.We have successfully applied our logic to verifying an implementation of the memory management module,where the implementation is an appropriately simplified version of the original version from a real-world preemptive OS kernel.     

Data refinement and singleton failures refinement are not equivalent

In this paper, we give simple example abstract data types, with atomic operations, that are related by data refinement under a definition used widely in the literature, but these same abstract data types are not related by singleton failure refinement. This contradicts results found in the literature.     

Program families: Program construction by context independent refinements

The concept of program families is a generalisation of the conventional stepwise refinement paradigm. We formalise program families by allowing Hoare-triplets to be parameterized. Next we derive a simple calculus to develop programs which are known a priori to be correct with respect to explicitly formulated pre- and postconditions.

Program families deal with at least two important problems of conventional refinement steps, i.e. program families are not context dependent and they apply just as well to top-down decomposition as to the bottom-up or middle-out approach. It turns out that the meaning of a pseudostatement in the context of program families is quite different from its meaning in the conventional refinement process.

A couple of examples illustrate the technique: the 1000 primes problem, a palindrome filter and a sorting routine.

The discussion relates program families to Morgan's refinement calculus, Knuth' literate programming and Soloway's programming plans.