Formalizing CCS and π-calculus in Guarded Cubical Agda

IF 0.7 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Journal of Logical and Algebraic Methods in Programming Pub Date : 2023-02-01 DOI:10.1016/j.jlamp.2022.100846

Niccolò Veltri , Andrea Vezzosi

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引用次数: 1

Abstract

Dependent type theories with guarded recursion have shown themselves suitable for the development of denotational semantics of programming languages. In particular, Ticked Cubical Type Theory (TCTT) has been used to show that, for guarded labeled transition systems (GLTS), interpretation into the denotational semantics maps bisimilar processes to equal values. In fact the two notions are proved equivalent, allowing one to reason about equality in place of bisimilarity.

We extend that result to the Calculus of Communicating Systems (CCS) and the π-calculus. For the latter, we pick early congruence as the syntactic notion of equivalence between processes, showing that denotational models based on guarded recursive types can handle the dynamic creation of channels that goes beyond the scope of GLTSs.

Hence we present fully abstract denotational models for CCS and the early π-calculus, formalized as an extended example for Guarded Cubical Agda: a novel implementation of Ticked Cubical Type Theory based on Cubical Agda.

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保护立方体Agda中CCS和π演算的形式化

具有保护递归的依赖类型理论已经表明它们适合于编程语言的指称语义的发展。特别是，Ticked Cubical Type Theory（TCTT）已经被用来表明，对于保护标记的转换系统（GLTS），对指称语义的解释将双相似过程映射到相等的值。事实上，这两个概念被证明是等价的，允许人们用平等来代替双重性。我们将这个结果推广到通信系统微积分（CCS）和π演算。对于后者，我们选择早期同余作为过程之间等价的句法概念，表明基于保护递归类型的指称模型可以处理超出GLTS范围的通道的动态创建。因此，我们为CCS和早期π演算提出了完全抽象的指称模型，形式化为保护立体派阿格达的扩展示例：基于立体派阿格达的Ticked Cubical Type Theory的新颖实现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Logical and Algebraic Methods in Programming COMPUTER SCIENCE, THEORY & METHODS-LOGIC

CiteScore

2.60

自引率

22.20%

发文量

期刊介绍： The Journal of Logical and Algebraic Methods in Programming is an international journal whose aim is to publish high quality, original research papers, survey and review articles, tutorial expositions, and historical studies in the areas of logical and algebraic methods and techniques for guaranteeing correctness and performability of programs and in general of computing systems. All aspects will be covered, especially theory and foundations, implementation issues, and applications involving novel ideas.