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.

操作语义涉及通过正式描述计算机程序的演变来赋予计算机程序含义。如果要证明程序的属性，编程语言的正式描述至关重要。人们可能希望证明一个程序符合规范：例如，它没有安全缺陷；它与其他系统正确交互；或者它计算的值是正确的。当人们为一种编程语言指定一种操作语义时，通常需要证明一些基本属性，以确保推理技术的有效性。必须为每一种所考虑的新语言以及每当现有语言发生更改时建立这些属性。我们使用术语“数学操作语义”（MOS）来描述在抽象级别上从操作语义理解技术的过程。这一研究方向的主要动机是，来自操作语义的过程，有时是冗长的和临时的，可以从基本结构主义的观点来理解。第二个更务实的动机是，在这个抽象层面上建立的定理有机会在相当普遍的背景下得到更广泛的应用。考虑到第二个动机，将 MOS 中的工作视为发生在三个级别上是有帮助的。最高、最抽象和一般的层次涉及范畴论定理，它是以抽象和一般的方式研究数学概念和结构的强大框架。中级涉及为特定类型的系统设计范畴论模型。最低级别是大多数操作语义学家工作的级别，并且涉及用于推理特定系统的特定逻辑框架。我的建议是在所有这三个级别上取得进展。我将以数据传递过程演算作为案例研究。这些演算是涉及结构化数据的并发和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本身被传达，那么就会出现一种移动性。另一种结构化数据涉及加密；涉及此类数据的过程演算已用于对系统的安全方面进行建模。在最低、具体的层面上，所提出的工作涉及从一般结果中推导出有关数据传递系统的新定理。为此，有必要研究适合推理数据传递系统的逻辑框架。此类框架引起了其他领域的研究人员的兴趣，例如那些对大规模编程系统的形式化感兴趣的人。将提取的定理将采用以下形式：如果以某种方式指定数据传递系统，则某些属性将成立。结果通常适用于数据传递系统。它们将根据文献中提出的各种语义进行测试。中级研究将涉及数据传递的类别理论模型。我将研究现有模型和结果在范畴论领域中的考虑程度。这样，数据传递领域将被赋予更统一的理论。在最高抽象层次上，我提出的工作将涉及设计一些复杂证明原理的抽象形式。我将重点讨论两个主题：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，我将研究结合证明技术的方法。这项研究将使人们对这些证明方法所涉及的过程有更好、更有原则的理解，并将产生与操作语义社区直接相关的新的、具体的技术。