Discrete Lawvere Theories
Discrete Lawvere Theories
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离散劳维尔理论
DOI：
10.1007/11548133_22
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
J. Power
中科院分区：
文献类型：
--
作者：
J. Power
本文引入了离散可列Lawvere V-理论的概念，并研究了它的构造，离散可列Lawvere V-理论的概念扩展了普通可列Lawvere理论的概念，它允许普通可列Lawvere理论的homset成为行为良好的公理定义范畴（如ω-cpo）的homobject。每一个离散的可数的Lawvere V-理论诱导V-丰富的单子，相当于一个强单子，在V.我们表明，离散可数的Lawvere V-理论允许我们模拟所有领先的例子，计算效果以外的延续，他们是封闭的建设和，张量和分配张量，这是基本的方式，其中一个结合这样的效果。我们还表明，离散可数的Lawvere V-理论下采取的图像是封闭的，允许一个治疗观察作为一个数学原始的建模效果。
We introduce the notion of discrete countable Lawvere V-theory and study constructions that may be made on it. The notion of discrete countable Lawvere V-theory extends that of ordinary countable Lawvere theory by allowing the homsets of an ordinary countable Lawvere theory to become homobjects of a well-behaved axiomatically defined category such as that of ω-cpo's. Every discrete countable Lawvere V-theory induces a V-enriched monad, equivalently a strong monad, on V. We show that discrete countable Lawvere V-theories allow us to model all the leading examples of computational effects other than continuations, and that they are closed under constructions of sum, tensor and distributive tensor, which are the fundamental ways in which one combines such effects. We also show that discrete countable Lawvere V-theories are closed under taking an image, allowing one to treat observation as a mathematical primitive in modelling effects.