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Mathematical Operational Semantics for Data-Passing Processes

数据传递过程的数学运算语义

基本信息

批准号：
EP/E042414/1
负责人：
Samuel Staton
金额：
$ 26.66万
依托单位：
University of Cambridge
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2007
资助国家：
英国
起止时间：
2007 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FE042414%2F1
关键词：
Mathematical Operational Semantics Data Passing

项目摘要

Operational semantics is concerned with ascribing meaning to computer programs by formally describing their evolution. A formal description of a programming language is crucial if one is to prove properties of programs. One may wish to prove that a program meets a specification: for instance, that it has no security flaws; that it interacts correctly with other systems; or that the values it computes are correct. When one specifies an operational semantics for a programming language, it is usually necessary to prove some basic properties in order to ensure the validity of reasoning techniques. These properties have to be established for every new language that is considered, and whenever an existing language is changed.We use the term 'Mathematical Operational Semantics' (MOS) to describe the process of understanding techniques from operational semantics at an abstract level. A primary motivation for this line of research is that procedures from operational semantics, at times lengthy and ad hoc, can be understood from a basic structuralist viewpoint. A second, more pragmatic motivation is that theorems that are established at this abstract level have the chance of wider application in quite general contexts. With this second motivation in mind, it is helpful to see work in MOS as occuring at three levels. The highest, most abstract and general level, is concerned with theorems of category theory, which is a powerful framework for studying mathematical concepts and structures in an abstract and general way. The intermediate level involves devising category-theoretic models for particular kinds of system. The lowest level is the level at which most operational semanticists work, and involves particular logical frameworks for reasoning about particular systems.My proposal is to make progress at all three of these levels. I will take, as a case study, the data-passing process calculi. These calculi are basic programming languages for systems that involve concurrency and communication of structured data. For instance, if one allows the names of communication channels to themselves be communicated, then a kind of mobility arises. Another kind of structured data involves encryption; process calculi involving this kind of data have been used to model security aspects of systems.At the lowest, concrete level, the proposed work involves deriving new theorems about data-passing systems from the general results. To do this it will be necessary to investigate logical frameworks that are suitable for reasoning about data-passing systems. Frameworks of this sort are of interest to researchers in other fields, such as those interested in the formalisation of large scale programming systems. Theorems that will be extracted will be of the form: if a data-passing system is specified in a certain way, then certain properties will hold . The results will hold for data-passing systems in general. They will be tested against various semantics that have been proposed in the literature.Research at the intermediate level will involve category-theoretic models of data-passing. I will investigate the extent to which existing models and results can be considered in the category-theoretic domain. In this way the field of data-passing will be given a more unified theory.At the highest level of abstraction, my proposed work will involve devising abstract forms of some complex proof principles. I will focus on two topics: firstly, techniques for higher-order systems -- these are systems that can receive programs as data; secondly, I will investigate ways of combining proof techniques. This research will give rise to a better, more principled understanding of the processes involved in these proof methods, and will give rise to new, concrete techniques of immediate relevance to the operational semantics community.

操作语义学关注的是通过形式化描述计算机程序的演变来赋予其意义。如果要证明程序的性质，编程语言的形式化描述是至关重要的。人们可能希望证明程序符合规范：例如，它没有安全缺陷；它能与其他系统正确交互；或者它计算的值是正确的。当为编程语言指定操作语义时，通常有必要证明一些基本属性，以确保推理技术的有效性。必须为所考虑的每一种新语言以及更改现有语言时建立这些属性。我们使用术语“数学操作语义”（MOS）来描述从抽象层面上的操作语义理解技术的过程。这条研究路线的主要动机是，从操作语义学的过程，有时是冗长和临时的，可以从基本结构主义的观点来理解。第二个更实用的动机是，在这种抽象水平上建立的定理有机会在相当普遍的情况下得到更广泛的应用。考虑到第二个动机，将MOS中的工作分为三个层次是有帮助的。最高、最抽象、最一般的层次是范畴论定理，范畴论是一个以抽象和一般的方式研究数学概念和结构的强大框架。中间层次涉及为特定类型的系统设计范畴理论模型。最低的层次是大多数操作语义学家工作的层次，它涉及对特定系统进行推理的特定逻辑框架。我的建议是在这三个层面都取得进展。我将以数据传递过程演算为例进行研究。这些演算是涉及并发性和结构化数据通信的系统的基本编程语言。例如，如果允许通信通道的名称自己进行通信，那么就会产生一种移动性。另一种结构化数据涉及加密；涉及这类数据的过程演算已被用于系统安全方面的建模。在最低的、具体的层面上，建议的工作包括从一般结果中推导出关于数据传递系统的新定理。为此，有必要研究适合于对数据传递系统进行推理的逻辑框架。这类框架对其他领域的研究人员很有兴趣，比如对大规模编程系统的形式化感兴趣的研究人员。将提取的定理将是这样的形式：如果数据传递系统以某种方式指定，那么某些属性将保持不变。结果一般适用于数据传递系统。它们将针对文献中提出的各种语义进行测试。中级层次的研究将涉及数据传递的范畴论模型。我将研究在何种程度上现有的模型和结果可以考虑范畴论领域。通过这种方式，数据传递领域将被赋予一个更统一的理论。在抽象的最高层次上，我建议的工作将包括设计一些复杂证明原则的抽象形式。我将重点关注两个主题：首先，高阶系统的技术——这些系统可以接收程序作为数据；其次，我将探讨结合证明技术的方法。这项研究将对这些证明方法中涉及的过程产生更好、更有原则性的理解，并将产生与操作语义社区直接相关的新的、具体的技术。