Environmental Bisimulations for Higher-Order Languages

D. Sangiorgi, N. Kobayashi, Eijiro Sumii
{"title":"Environmental Bisimulations for Higher-Order Languages","authors":"D. Sangiorgi, N. Kobayashi, Eijiro Sumii","doi":"10.1145/1889997.1890002","DOIUrl":null,"url":null,"abstract":"Developing a theory of bisimulation in higher-order languages can be hard. Particularly challenging can be: (1) the proof of congruence, as well as enhancements of the bisimulation proof method with \"up-to context\" techniques, and (2) obtaining definitions and results that scale to languages with different features. To meet these challenges, we present environmental bisimulations, a form of bisimulation for higher-order languages, and its basic theory. We consider four representative calculi: pure lambda-calculi (call-by-name and call-by-value), call-by-value lambda-calculus with higher-order store, and then higher-order pi-calculus. In each case: we present the basic properties of environmental bisimilarity, including congruence; we show that it coincides with contextual equivalence; we develop some up-to techniques, including up-to context, as examples of possible enhancements of the associated bisimulation method. Unlike previous approaches (such as applicative bisimulations, logical relations, Sumii-Pierce-Koutavas-Wand), our method does not require induction/indices on evaluation derivation/steps (which may complicate the proofs of congruence, transitivity, and the combination with up-to techniques), or sophisticated methods such as Howe's for proving congruence. It also scales from the pure lambda-calculi to the richer calculi with simple congruence proofs.","PeriodicalId":137827,"journal":{"name":"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"164","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1889997.1890002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 164

Abstract

Developing a theory of bisimulation in higher-order languages can be hard. Particularly challenging can be: (1) the proof of congruence, as well as enhancements of the bisimulation proof method with "up-to context" techniques, and (2) obtaining definitions and results that scale to languages with different features. To meet these challenges, we present environmental bisimulations, a form of bisimulation for higher-order languages, and its basic theory. We consider four representative calculi: pure lambda-calculi (call-by-name and call-by-value), call-by-value lambda-calculus with higher-order store, and then higher-order pi-calculus. In each case: we present the basic properties of environmental bisimilarity, including congruence; we show that it coincides with contextual equivalence; we develop some up-to techniques, including up-to context, as examples of possible enhancements of the associated bisimulation method. Unlike previous approaches (such as applicative bisimulations, logical relations, Sumii-Pierce-Koutavas-Wand), our method does not require induction/indices on evaluation derivation/steps (which may complicate the proofs of congruence, transitivity, and the combination with up-to techniques), or sophisticated methods such as Howe's for proving congruence. It also scales from the pure lambda-calculi to the richer calculi with simple congruence proofs.
高阶语言的环境双仿真
在高阶语言中发展双模拟理论是很困难的。特别具有挑战性的可能是:(1)同余性的证明,以及使用“up-to - context”技术增强双模拟证明方法,以及(2)获得可扩展到具有不同特征的语言的定义和结果。为了应对这些挑战,我们提出了环境双模拟,一种高阶语言的双模拟形式,以及它的基本理论。我们考虑了四种有代表性的演算:纯lambda演算(按名称和按值调用)、高阶存储的按值调用lambda演算和高阶pi演算。在每种情况下:我们提出了环境双相似性的基本性质,包括同余性;我们证明了它与语境对等是一致的;我们开发了一些up-to技术,包括up-to上下文,作为相关双仿真方法可能增强的示例。与以前的方法(如应用双模拟、逻辑关系、sumi - pierre - koutavas - wand)不同,我们的方法不需要在评估推导/步骤上的归纳/索引(这可能使同余、传递性和与最新技术的结合的证明复杂化),也不需要像Howe证明同余的复杂方法。它也可以从纯的λ微积分扩展到具有简单同余证明的更丰富的微积分。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信