对名义Scott域的完全抽象

Steffen Lösch, A. Pitts
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引用次数: 4

摘要

我们在标称集内发展了一个领域理论,并提出了从这种方法中可以获得的编程语言结构和结果。这一发展是基于轨道有限子集的概念,即一个标称集合的子集,它既被有限支持又被包含在有限多个轨道中。这一概念在Bojanczyk等人最近关于无限语言上的自动机的研究计划中表现突出,我们的结果建立了他们的工作与拓扑紧致性特征之间的联系,在一个完全不同的环境中,winskkel和Turner发现了拓扑紧致性,作为并发性的名义领域理论的一部分。我们利用这个联系导出了名义集合内的斯科特域的概念。名称上的存在量化泛函和名称上的“确定描述”泛函在适合名义斯科特域的意义上是紧凑的。将它们与parallel-or一起添加到具有名称抽象和局部作用域名称的递归定义高阶函数的编程语言中,我们证明了名义Scott域的完全抽象结果,类似于Plotkin关于PCF和传统Scott域的经典结果:两个程序短语在所有上下文中具有相同的可观察操作行为,当且仅当它们表示名义Scott域模型的相等元素。这是我们所知道的第一个具有局部名称的高阶函数的完整抽象结果,它使用基于普通外延函数的域理论,而不是使用更内蕴的游戏语义方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Full abstraction for nominal Scott domains
We develop a domain theory within nominal sets and present programming language constructs and results that can be gained from this approach. The development is based on the concept of orbit-finite subset, that is, a subset of a nominal sets that is both finitely supported and contained in finitely many orbits. This concept appears prominently in the recent research programme of Bojanczyk et al. on automata over infinite languages, and our results establish a connection between their work and a characterisation of topological compactness discovered, in a quite different setting, by Winskel and Turner as part of a nominal domain theory for concurrency. We use this connection to derive a notion of Scott domain within nominal sets. The functionals for existential quantification over names and `definite description' over names turn out to be compact in the sense appropriate for nominal Scott domains. Adding them, together with parallel-or, to a programming language for recursively defined higher-order functions with name abstraction and locally scoped names, we prove a full abstraction result for nominal Scott domains analogous to Plotkin's classic result about PCF and conventional Scott domains: two program phrases have the same observable operational behaviour in all contexts if and only if they denote equal elements of the nominal Scott domain model. This is the first full abstraction result we know of for higher-order functions with local names that uses a domain theory based on ordinary extensional functions, rather than using the more intensional approach of game semantics.
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