Parametricity, Abstraction and Objects

9804087数据抽象是程序设计的核心问题，而“参数”是这一概念的数学形式化。使用参数化法，只要客户端程序可观察到的行为相同，就可以争辩说，导出类型和操作的两个程序模块是等价的。在这个项目中，乌迪·雷迪教授与伦敦玛丽女王和韦斯特菲尔德的彼得·奥赫恩教授共同研究了参变量理论的关键问题。所涉及的问题包括找到包含各种编程语言现象及其数学模型的参数化抽象框架，将参数化和子类型类型系统集成，以及将这些结果应用于具有可变状态的面向对象编程的建模。这项研究跨越了理论和实践问题，从抽象的范畴框架到类型系统和实用推理原则。所解决的问题对于将参数化与多年来发展起来的大量编程理论相结合至关重要。奥赫恩教授在参数理论方面的专业知识将补充雷迪在研究局部变量的数据抽象方面的工作。这种合作提高了他们解决共同感兴趣的问题的研究效率。*

9804087 Data abstraction is of central concern in program design while ``parametricity'' is a mathematical formalization of this concept. Using parametricity, one can argue that two program modules that export types and operations are equivalent as long as the behavior observable by client programs is the same. In this project, Prof. Uday Reddy addresses key issues of parametricity theory in joint research with Prof. Peter O'Hearn at Queen Mary and Westfield, London. The issues addressed include finding an abstract framework for parametricity that encompasses various programming language phenomena and their mathematical models, integrating parametricity with subtyping type systems, and the application of these results for modeling object-oriented programming with mutable state. The research spans theoretical and practical issues, ranging from abstract categorical frameworks to type systems and practical reasoning principles. The issues addressed are of vital importance for integrating parametricity with the vast body of programming theory developed over the years. Prof. O'Hearn's expertise in parametricity theory will complement Reddy's work in the study of data abstraction aspects of local variables. This collaboration enhances their research effectiveness in addressing issues of mutual interest.***