编程语言语义的可计算性概念

H. Egli, R. Constable
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引用次数: 57

摘要

本文讨论了程序设计语言语义中的数学问题及其对递归函数理论的影响。我们定义了连续更高类型上的可计算性概念(适用于所有类型),并证明了它与有效算子的等价性。这个结果表明,我们的可计算运算符可以数学地(即扩展地)建模任何可以在操作语义中完成的事情。这些适用于语义学的新的递归理论概念也允许我们构建包含所有且仅包含可计算元素的微积分的Scott模型。根据初始cpo的选择,我们的一般理论产生了严格确定或任意非确定对象(并行性)的理论。本文的第二部分是形式理论的发展。第一部分给出了研究的动机,并与相关工作进行了比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Computability concepts for programming language semantics
This paper is about mathematical problems in programming language semantics and their influence on recursive function theory. We define a notion of computability on continuous higher types (for all types) and show its equivalence to effective operators. This result shows that our computable operators can model mathematically (i.e. extensionally) everything that can be done in an operational semantics. These new recursion theoretic concepts which are appropriate to semantics also allow us to construct Scott models for the &lgr;-calculus which contain all and only computable elements. Depending on the choice of the initial cpo, our general theory yields a theory for either strictly determinate or else arbitrary non-deterministic objects (parallelism). The formal theory is developed in part II of this paper. Part I gives motivation and comparison with related work.
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