The Essence of Generalized Algebraic Data Types

IF 2.2 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Proceedings of the ACM on Programming Languages Pub Date : 2024-01-05 DOI:10.1145/3632866
Filip Sieczkowski, Sergei Stepanenko, Jonathan Sterling, L. Birkedal
{"title":"The Essence of Generalized Algebraic Data Types","authors":"Filip Sieczkowski, Sergei Stepanenko, Jonathan Sterling, L. Birkedal","doi":"10.1145/3632866","DOIUrl":null,"url":null,"abstract":"This paper considers direct encodings of generalized algebraic data types (GADTs) in a minimal suitable lambda-calculus. To this end, we develop an extension of System Fω with recursive types and internalized type equalities with injective constant type constructors. We show how GADTs and associated pattern-matching constructs can be directly expressed in the calculus, thus showing that it may be treated as a highly idealized modern functional programming language. We prove that the internalized type equalities in conjunction with injectivity rules increase the expressive power of the calculus by establishing a non-macro-expressibility result in Fω, and prove the system type-sound via a syntactic argument. Finally, we build two relational models of our calculus: a simple, unary model that illustrates a novel, two-stage interpretation technique, necessary to account for the equational constraints; and a more sophisticated, binary model that relaxes the construction to allow, for the first time, formal reasoning about data-abstraction in a calculus equipped with GADTs.","PeriodicalId":20697,"journal":{"name":"Proceedings of the ACM on Programming Languages","volume":"5 29","pages":"695 - 723"},"PeriodicalIF":2.2000,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the ACM on Programming Languages","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3632866","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 0

Abstract

This paper considers direct encodings of generalized algebraic data types (GADTs) in a minimal suitable lambda-calculus. To this end, we develop an extension of System Fω with recursive types and internalized type equalities with injective constant type constructors. We show how GADTs and associated pattern-matching constructs can be directly expressed in the calculus, thus showing that it may be treated as a highly idealized modern functional programming language. We prove that the internalized type equalities in conjunction with injectivity rules increase the expressive power of the calculus by establishing a non-macro-expressibility result in Fω, and prove the system type-sound via a syntactic argument. Finally, we build two relational models of our calculus: a simple, unary model that illustrates a novel, two-stage interpretation technique, necessary to account for the equational constraints; and a more sophisticated, binary model that relaxes the construction to allow, for the first time, formal reasoning about data-abstraction in a calculus equipped with GADTs.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
广义代数数据类型的本质
本文探讨了在最小合适的λ演算法中对广义代数数据类型(GADT)进行直接编码的问题。为此,我们开发了一个具有递归类型和内部化类型等价性的系统 Fω 扩展,其中包含注入式常量类型构造函数。我们展示了如何在微积分中直接表达 GADT 和相关的模式匹配构造,从而证明它可以被视为高度理想化的现代函数式编程语言。我们通过在 Fω 中建立一个非宏可表达性结果,证明了内部化类型等价与注入性规则的结合提高了微积分的表达能力,并通过语法论证证明了系统的类型健全性。最后,我们为我们的微积分建立了两个关系模型:一个是简单的一元模型,它展示了一种新颖的两阶段解释技术,这是解释等式约束所必需的;另一个是更复杂的二元模型,它放宽了构造,首次允许在配备了GADT的微积分中对数据抽象进行形式推理。
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 去求助
来源期刊
Proceedings of the ACM on Programming Languages
Proceedings of the ACM on Programming Languages Engineering-Safety, Risk, Reliability and Quality
CiteScore
5.20
自引率
22.20%
发文量
192
期刊最新文献
ReLU Hull Approximation An Axiomatic Basis for Computer Programming on the Relaxed Arm-A Architecture: The AxSL Logic The Essence of Generalized Algebraic Data Types Explicit Effects and Effect Constraints in ReML Indexed Types for a Statically Safe WebAssembly
×
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
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1