Quasi-prime algebraic domains
Quasi-prime algebraic domains
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DOI：
10.1016/0304-3975(95)00133-6
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发表时间：
1996-02-26
影响因子：
1.1
通讯作者：
Zhang, GQ
中科院分区：
文献类型：
--
作者：
Zhang, GQ
本文的目的是介绍一类新的域，称为准素数代数域。我们证明这个类是用于编程语言的指称语义的一个很好的候选者。这是通过展示准素数代数域上的指称语义通常所需的许多构造来实现的。在第一部分中，我们通过研究线性函数对非素数代数域的影响来激发拟素数和拟素数代数域的概念。在第二部分中，我们通过将准素数代数域表示为不可约信息系统来研究它们的类别。我们引入具有拟线性函数的拟质数代数域的对称幺半闭范畴。我们进一步证明，使用通常的斯科特连续函数作为态射，准素数代数域是笛卡尔闭的。在第三部分中，我们证明了饱和拟素数代数域的存在性，并介绍了求解拟素数代数域中域方程的框架。例如，然后可以给出具有自反准素数代数域的非类型化 lambda 演算的模型。
The purpose of this paper is to introduce a new class of domains called quasi-prime algebraic domains. We show that this class is a good candidate for the purpose of denotational semantics of programming languages. This is achieved by exhibiting many constructions usually needed for denotational semantics on quasi-prime algebraic domains. In the first part we motivate the notion of quasi-primes and quasi-prime algebraic domains by studying the effect of linear functions on domains that are not prime algebraic. In the second part we study categories of quasi-prime algebraic domains by representing them as irreducible information systems. We introduce a symmetric monoidal closed category of quasi-prime algebraic domains with quasi-linear functions. We show further that with the usual Scott continuous functions as morphisms, quasi-prime algebraic domains are cartesian closed. In the third part we show the existence of a saturated quasi-prime algebraic domain, and introduce a framework for solving domain equations in quasi-prime algebraic domains. It is then possible to give, for example, a model for the un-typed lambda calculus with a reflexive quasi-prime algebraic domain.