V2EX domain theory

Domain Theory

定义 / Definition

域论:数学与理论计算机科学中的一个分支,用偏序集合(尤其是完备偏序集等结构)来刻画“信息的逐步逼近”,常用于描述递归、无穷计算过程与程序语义(尤其是指称语义)中的不动点语义。

发音 / Pronunciation (IPA)

/domen θiri/

例句 / Examples

Domain theory is used to model recursion in programming languages.
域论用于对编程语言中的递归进行建模。

Using domain theory, we can give a denotational semantics where the meaning of a recursive function is defined as a least fixed point in a suitable ordered structure.
借助域论,我们可以给出指称语义:在合适的有序结构中,把递归函数的含义定义为一个最小不动点。

词源 / Etymology

“domain”原意为“领域、范围”,在数学语境里可指“取值域/对象的集合”;“theory”是“理论”。在20世纪6070年代,Dana Scott 等人发展出该理论,用来为 λ 演算与递归程序提供严谨的数学语义基础,因此“domain theory”逐渐固定为这一专门领域的名称。

相关词 / Related Words

文献作品 / Notable Works

  • Continuous Lattices and Domains(Gierz, Hofmann, Keimel, Lawson, Mislove, Scott)
  • Domains and Lambda-Calculi(Roberto M. Amadio, Pierre-Louis Curien)
  • The Formal Semantics of Programming Languages: An Introduction(Glynn Winskel)
  • “Outline of a Mathematical Theory of Computation”(Dana Scott, 技术报告/论文,常被视为域论与程序语义的重要早期文本)
  • “Toward a Mathematical Semantics for Computer Languages”(Strachey & Scott 相关研究传统中的代表性论文与报告)
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