SHF: Small: SEQUBE: A Sequent Calculus Foundation for High- Level and Intermediate Programming Languages

SHF：小型：SEQUBE：高级和中级编程语言的顺序微积分基础

• 批准号: 1423617
• 负责人: Zena Ariola
• 金额: $ 50万
• 依托单位: University of Oregon Eugene
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-07-01 至 2019-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1423617&HistoricalAwards=false
• 关键词: SHF; Small; SEQUBE; Sequent; Calculus

Title: SHF:Small:SEQUBE:A Sequent Calculus Foundation for High-Level and Intermediate Programming LanguagesModern programming languages are complex. They provide sophisticated control mechanisms, offer a combination of different programming paradigms (e.g., functional or object-oriented), and allow the definition of infinite objects and processes (e.g., servers or operating systems). To have assurance in our software, it is fundamentally important to have a simple and intuitive framework for reasoning about and experimenting with programs that use these features: both for programming language designers and implementors, as well as for programmers who need to prove safety properties of critical applications.Traditionally, the lambda-calculus has served as a foundation for writing and proving properties of programs. The intellectual merit of this research consists of developing an alternative model of programs based on the sequent calculus. Instead of starting from a core language and layering features on top as needed, the new model naturally includes these features from the beginning. Like the lambda-calculus, the sequent-based model originates from logic, but is rooted in the concept of duality that provides two ways to approach problems, where one is often more familiar. Additionally, the sequent-based model provides a new way to organize intermediate languages used in compilers to aid program optimization and analysis.The broader impact of the research consists of providing a vehicle for disseminating knowledge between different communities. Since the new model includes both the functional and object-oriented paradigms naturally as duals, it provides a logical interpretation of languages, such as Scala, that merge the two approaches. In addition, the research will explore ways to incorporate reasoning about infinite processes and computational effects in a proof assistant. Lastly, an emphasis on duality is beneficial for education; given two possible explanations, students can be introduced to the more familiar one first when introducing difficult ideas, while using existing knowledge and intuition to explore new concepts.

标题：SHF：小：SEQUBE：高级和中级编程语言的顺序微积分基础现代编程语言是复杂的。它们提供了复杂的控制机制，提供了不同编程范式的组合（例如，函数式的或面向对象的），并且允许定义无限对象和过程（例如，服务器或操作系统）。 为了保证软件的安全性，我们必须有一个简单直观的框架来推理和实验使用这些特性的程序：无论是对于编程语言的设计者和实现者，还是对于需要证明关键应用程序的安全性的程序员。传统上，微积分是编写和证明程序属性的基础。这项研究的智力价值包括开发一个替代模型的程序的基础上的微积分。 新模型不是从核心语言开始，然后根据需要将功能分层，而是从一开始就自然地包含这些功能。像微积分一样，基于序列的模型起源于逻辑，但植根于对偶的概念，提供了两种方法来处理问题，其中一种通常更熟悉。此外，基于序列的模型提供了一种新的方式来组织编译器中使用的中间语言，以帮助程序优化和分析。由于新模型自然地包含了函数式和面向对象范式，因此它提供了对语言（如Scala）的逻辑解释，将这两种方法合并在一起。此外，该研究还将探索如何将关于无限过程和计算效果的推理纳入证明助手中。最后，强调二元性对教育是有益的;给出两种可能的解释，在介绍困难的想法时，学生可以先介绍更熟悉的一种，同时利用现有的知识和直觉探索新的概念。