Trace 演算

文章定义了基于踪迹(trace)的逻辑语言L_Trace,它是一阶线性时序逻辑语言的扩充,同时也是“对象演算”研究工作的基础.Trace演算所述的“对象”用来刻画具有内部状态和外部行为的动态实体,语法上由对象标记表示.对象标记Ω=(S,F,A,E)包含4个部分:数据类型S、函数F、属性A和动作E.Σ=(S,F)构成通常代数规范意义下的标记,可将动作看成一广义数据类型,从而得到标记Σ的动作扩充ΣE.对象标记的语义解释结构由关于标记ΣE的代数、映射和动作与踪迹的关系定义.ΣE-代数给出关于数据参数的解释;映射给出属性在动作踪迹中所取的值;而动作与踪迹的关系则给出执行一有限踪迹以后该动作是否允许执行.在定义了Trace演算的语法和语义之后,文章给出了Trace演算的公理系统及其可靠性证明.     

Action演算中动作之间数据流分析方法及其实现

一前言 Action演算簇(action calculi)作为描述一大类并发交互行为模型的数学框架[1,2],是具有某些相同特性的一类演算的集合,其中一个具体的演算称为action演算.Action演算可以有三种不同的表示方式,其中分子形式可以说是项代数的形式的一种范式,体现了一种自然的、模块化的表达方式,非常适合于程序设计.     

命令式语言的高阶Action演算表示

Action演算簇（action calculi)是一种抽象的数学结构，已经表明它可以表示λ演算，进程代数，γ演算以及函数式语言等。作为Action演算族的进一步应用，针对一个典型的顺序命令式语言SIL，充分利用Action演算的可扩充性，定义了一个具体的Action演算AC（KSIL），同时为了给出循环计算的表示引入了高阶性，给出了SIL的AC（KSIL），语义，并证明了SIL的操作语义与AC（KSIL）语义之间的对应关系，最后讨论了顺序机制的控制及其控制规则定义方法，不仅表明Action演算可以方便地表示顺序计算，而且也证明了Action演算强大的描述能力。     

基于余归纳的最小Kripke结构的求解

状态空间爆炸问题是模型检测的最大障碍.从余归纳（特别是余代数）的角度研究了这个问题.用余归纳的方法证明：（1） 对于任意给定的一类Kripke结构（记为K）,在互模拟等价意义下K中最小Kripke结构（记为K₀）的存在唯一性.K₀描述了K中所有Kripke结构的行为而且没有冗余的状态;（2） 对于任意的M∈K（M可能包含无穷多个状态）,在互模拟等价意义下的相对于（M且基于K₀）的最小Kripke结构（记为K_M）的存在唯一性.由此提出一种求解K_M的算法,并用Ocaml予以简单实现.其应用之一在于可以用状态空间更小的K_M代替M进行模型检测.该方法可自然地推广到基于其他类型函子的余代数结构.     

描述逻辑ALC中关于伪子概念极小改变的R-演算

AGM公设是用于信念修正的（被一个单一信念修正）,而DP公设是用于迭代修正的（被一个有限的信念序列修正）.李未给出了对于R-构型（configuration）△|Γ的R-演算,其中,△是一个原子公式或原子公式否定的集合,而Γ是一个有限的公式集合.为了在修正过程中能够保留断言中尽可能多的信息,将考虑一种新的极小改变的定义：伪子概念极小改变（≤-极小改变）,其中,≤是一种伪子概念的关系;之后,在此基础上给出一种新的R-演算T^DL,它是关于≤-极小改变可靠和完备的,使得△|Γ在T^DL中可以被约减为一个理论△∪Θ（记作├_T^DL △|Γ⇒△,Θ）当且仅当Θ是Γ关于△的一个≤-极小改变.     

利用MODIS数据估计中国黄东海区域测深参数

目的 现有关于漫衰减系数的研究大多是在490 nm波段建立反演模型,且未将相关研究与机载激光雷达测深能力建立联系,本文尝试获取测深参数532 nm漫衰减系数K_d(532)和透明度SD(Secchi disk depth),为机载双色激光雷达测深能力的评估和飞行方案的制定提供了重要技术参数。方法 首先分析了测深参数532 nm漫衰减系数K_d(532)和透明度SD对于评估机载双色激光系统测深能力的重要性。利用2003年春季中国黄东海区域的实测光学数据,对现有的漫衰减系数反演模式进行改进,建立了K_d(532)和K_d(490)=的线性关系以及SD和K_d(532)的幂函数关系。结果 根据2003年春季MODIS的490 nm漫衰减系数产品和上述函数关系获取了K_d(532)和SD参数。结论 本文获取测深参数K_d(532)和SD的方法能够用来有效评估该区域机载激光雷达的测深能力,准确性和精度依赖于实测光学数据的精度、分布和数量以及MODIS的K_d(490)产品的准确性。     

基于类型理论的领域数据建模和验证及案例

数据作为软件系统的主要处理对象,其规范性有助于软件系统的设计开发和软件系统之间的数据交换。本文面向行业数据规范及其验证,提出了一种基于类型理论的领域数据建模语言（DDML）和领域建模方法（DDMM）。DDML语言通过定义类型和项的语法和语义,描述领域数据类型和对象的结构,通过定义类型规则及其类型检查算法判定任意项t：T?。DDMM给出了领域数据建模的方法,即构建K₁（原子类型）、K₂（数据元）、K₃（数据元目录）三层框架,生成表示K3层数据元目录之间关系的类型规则。在此基础上,给出了数据元目录序列的定义及其正确性判定算法。基于上述方法,实现了一种领域数据建模工具原型系统,并通过领域数据建模与自动验证的一个实际案例,完成了一个较大规模行业数据规范的制定与验证。     

一个并发对象演算

由于缺乏一个为人们接受的描述并发对象系统语义的形式化模型,开发面向对象程序设计语言的开发受到了很大的制约,为了给并发面向对象程序设计定义一个公共的语义框架,人们分别以π演算和ａｃｔｏｒ模型为基础进行了研究。     

基于Pi演算的跨组织工作流建模研究

传统的工作流建模方法主要用于描述组织内部流程,因而难以描述跨组织工作流面向流程、组合、抽象、涉及多个自治系统通信合作的新特点.针对此问题,提出了一种基于Pi演算的跨组织工作流建模方法,利用Pi演算的并发计算操作符,将跨组织业务流程建模为一组自治且并发执行的组织内子流程的组合,子流程建模为组织内本地流程定义和组织间控制约束的组合.基于Pi演算的弱互相似理论,验证了两个跨组织子流程外部行为的相等性,用于帮助组织内私有流程的外部抽象.基于该方法建立的跨组织工作流模型在子流程间建立了一种松耦合的关系,适用于动态的跨组织环境,同时基于严格的形式化方法,便于分析和验证.     

类型化π演算的双代数语义

证明互模拟同余通常冗长且易出错.双代数为解决该问题提供统一的框架:若行为函子保持弱回拉,共代数范畴到基范畴的忘却函子有右伴函子,则最大共代数互模拟同余.但已有双代数理论建模类型化π演算存在以下困难:行为函子不保持弱回拉,进程互模拟与共代数互模拟不一致.为解决以上两个问题,用稠密拓扑导出布尔范畴作为语义范畴,令行为函子保持弱回拉;定义一类行为函子,使最大进程互模拟与最大共代数互模拟一致,而迟语义和早语义对应的行为函子属于该类函子.进而给出π演算最大进程互模拟同余的双代数模型,为进一步应用双代数框架对其他复杂演算建模奠定了理论基础.     

Calculi for interaction

Action structures have previously been proposed as an algebra for both the syntax and the semantics of interactive computation. Here, a class of concrete action structures called action calculi is identified, which can serve as a non-linear syntax for a wide variety of models of interactive behaviour. Each action in an action calculus is represented as an assembly of molecules; the syntactic binding of names is the means by which molecules are bound together. A graphical form, action graphs, is used to aid presentation. One action calculus differs from another only in its generators, called controls. Action calculi generalise a previously defined action structure for the -calculus. Several extensions to are given as action calculi, giving essentially the same power as the -calculus. An action calculus is also given for the typed -calculus, and for Petri nets parametrized on their places and transitions. An equational characterization of action calculi is given: each action calculus is the quotient of a term algebra by certain equations. The terms are generated by a set of operators, including those basic to all action structures as well as the controls specific to ; the equations are the basic axioms of action structures together with four additional axiom schemata. Received May 12, 1995 / August 7, 1995     

Calculi for interaction

Action structures have previously been proposed as an algebra for both the syntax and the semantics of interactive computation. Here, a class of concrete action structures calledaction calculi is identified, which can serve as a non-linear syntax for a wide variety of models of interactive behaviour. Each action in an action calculus is represented as an assembly ofmolecules; the syntactic binding ofnames is the means by which molecules are bound together. A graphical form,action graphs, is used to aid presentation. One action calculus differs from another only in its generators, calledcontrols. Action calculi generalise a previously defined action structure PIC for the π- calculus. Several extensions to PIC are given as action calculi, giving essentially the same power as the π-calculus. An action calculus is also given for the typed λ-calculus, and for Petri nets parametrized on their places and transitions. An equational characterization of action calculi is given: each action calculusA is the quotient of a term algebra by certain equations. The terms are generated by a set of operators, including those basic to all action structures as well as the controls specific toA; the equations are the basic axioms of action structures together with four additional axiom schemata.     

A functional presentation of Pi calculus

From the very beginning process algebra introduced the dichotomy between channels and processes. This dichotomy prevails in all present process calculi. The situation is in contrast to that withlambda calculus which has only one class of entities-the lambda terms. We introduce in this papera process calculus called Lamp in which channels are process names. The language is more uniform than existing process calculi in two aspects-. First it has a unified treatment of channels and processes.There is only one class of syntactical entities-processes. Second it has a unified presentation ofboth first order and higher order process calculi. The language is functional in the sense that lambda calculus is functional. Two bisimulation equivalences, barbed and closed bisimilarities, are proved to coincide.A natural translation from Pi calculus to Lamp is shown to preserve both operational and algebraic semantics. The relationship between lazy lambda calculus and Lamp is discussed.     

Barbed Congruence of Asymmetry and Mismatch

The X calculus is a model of concurrent and mobile systems. It emphasizes that communications are information exchanges. In the paper, two constructions are incorporated into the framework of the chi calculus, which are asymmetric communication and mismatch condition widely used in applications. Since the barbed bisimilarity has proved its generality and gained its popularity as an effective approach to generating a reasonable observational equivalence, we study both the operational and algebraic properties of the barbed bisimilarity in this enriched calculus. The investigation supports an improved understanding of the bisimulation behaviors of the model. It also gives a general picture of how the two constructions affect the observational theory.     

Types and full abstraction for polyadic π-calculus

A type system for terms of the monadic π-calculus is introduced and used to obtain a full-abstraction result for the translation of the polyadic π-calculus into the monadic calculus: well-sorted terms of the polyadic calculus are barbed congruent iff their translations are typed barbed congruent.     

Algebraic computational models of OR-parallel execution of Prolog

A specification of the OR-parallel execution of Prolog programs, using CHOCS (calculus of higher order communicating systems) [24], is presented in the paper. A translation is defined from Prolog programs and goals to CHOCS processes: the execution of the CHOCS process corresponding to a goal mimics the OR-parallel execution of the original Prolog goal. In the translation, clauses and predicate definitions of a Prolog program correspond to processes. To model OR-parallelism, the processes , corresponding to clauses (having the same head predicate ) start their execution concurrently, but, in order to respect the depth-first search rule, each is guarded by the termination of the executions of processes 's, . The computational model is proved correct with respect to the semantics of Prolog, as given in [4, 5]. Our model, because of its algebraic specification, can be easily used to prove properties of the parallel execution of Prolog programs. Moreover, the model exploits the maximum degree of parallelism, by giving the Prolog solutions in parallel, without any order among them. However, this model, being close to the Prolog semantics definition, contains sources of inefficiency which make it unpractical as a guide for the implementation. To overcome these problems, a new computational model is defined. This model is obtained by modifications of the basic one and thus its correctness can be easily proved. Finally, we show how to obtain models of different real implementations of OR-parallel Prolog by slight modification of the new model. The relations among all these models, in terms of parallelism degree, are studied by using the concepts of bisimulation and simulation, developed for concurrent calculi. Received: 5 May 1995 / 28 May 1996     

Preface: Special Issue on Interpolation

This paper presents a mechanisation of psi-calculi, a parametric framework for modelling various dialects of process calculi including (but not limited to) the pi-calculus, the applied pi-calculus, and the spi calculus. psi-calculi are significantly more expressive, yet their semantics is as simple in structure as the semantics of the original pi-calculus. Proofs of meta-theoretic properties for psi-calculi are more involved, however, not least because psi-calculi (unlike simpler calculi) utilise binders that bind multiple names at once. The mechanisation is carried out in the Nominal Isabelle framework, an interactive proof assistant designed to facilitate formal reasoning about calculi with binders. Our main contributions are twofold. First, we have developed techniques that allow efficient reasoning about calculi that bind multiple names in Nominal Isabelle. Second, we have adopted these techniques to mechanise substantial results from the meta-theory of psi-calculi, including congruence properties of bisimilarity and the laws of structural congruence. To our knowledge, this is the most extensive formalisation of process calculi mechanised in a proof assistant to date.     

Shallow Linear Action Graphs and their Embeddings

Action calculi, which generalise process calculi such as Petri nets, π-calculusand ambient calculus, have been presented in terms of action graphs. We here offer linear action graphs as a primitive basis for action calculi. This paper presents the category of embeddings of undirected linear action graphs without nesting, using a novel form of graphical reasoning which simplifies some otherwise complex manipulations in regular algebra. The results are adapted in a few lines to directed graphs. This work is part of a long-term search for a uniform behavioural theory for process calculi. Received October 2000 / Accepted in revised form April 2001     

Modelling Calculi with Name Mobility using Graphs with Equivalences

In the theory of graph rewriting, the use of coalescing rules, i.e., of rules which besides deleting and generating graph items, can coalesce some parts of the graph, turns out to be quite useful for modelling purposes, but, at the same time, problematic for the development of a satisfactory partial order concurrent semantics for rewrites. Rewriting over graphs with equivalences, i.e., (typed hyper)-graphs equipped with an equivalence over nodes provides a technically convenient replacement of graph rewriting with coalescing rules, for which a truly concurrent semantics can be easily defined. The expressivity of such a formalism is tested in a setting where coalescing rules typically play a basic role: the encoding of calculi with name passing as graph rewriting systems. Specifically, we show how the (monadic fragment) of the solo calculus, one of the dialect of those calculi whose distinctive feature is name fusion, can be encoded as a rewriting system over graph with equivalences.     

Concurrent Nets: A Study of Prefixing in Process Calculi

We introduce the calculus of concurrent nets as an extension of the fusion calculus in which usual prefixing is replaced by arbitrary monotonic guards. Then we use this formalism to describe the prefixing policy of standard calculi as a particular form of communication. By developing a graphical syntax, we sharpen the geometric intuition and finally we provide an encoding of these guards as causality in the prefix-free fragment, in the spirit of the encoding of the fusion calculus into solos by Laneve and Victor, proving that communication by fusion is expressive enough to implement arbitrary monotonic guards.