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

标题：SHF：Small：SEQUBE：高级和中级编程语言的顺序演算基础现代编程语言是复杂的。它们提供复杂的控制机制，提供不同编程范例的组合(例如，功能或面向对象)，并允许定义无限的对象和进程(例如，服务器或操作系统)。为了在我们的软件中有保证，拥有一个简单而直观的框架来推理和试验使用这些功能的程序是至关重要的：对于编程语言设计者和实现者，以及对于需要证明关键应用程序的安全属性的程序员来说。传统上，lambda演算一直作为编写和证明程序性质的基础。这项研究的智力价值在于开发了一种基于顺序演算的替代程序模型。新的模型不是从一种核心语言开始，然后根据需要将功能分层，而是从一开始就自然地包括这些功能。像lambda演算一样，基于顺序的模型起源于逻辑，但植根于二元性的概念，该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法来组织编译器中使用的中间语言，以帮助程序优化和分析。研究的更广泛的影响包括提供在不同社区之间传播知识的工具。由于新模型自然包括函数式和面向对象范例，因此它提供了对合并了这两种方法的语言(如Scala)的逻辑解释。此外，这项研究还将探索如何在证明助手中整合关于无限过程和计算效果的推理。最后，强调二元性对教育是有益的；给出两种可能的解释，学生可以在介绍困难的想法时首先被介绍给更熟悉的一种，同时利用现有的知识和直觉来探索新的概念。

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.