Applications of Categories in Computer Science: On clubs and data-type constructors
Applications of Categories in Computer Science: On clubs and data-type constructors
复制标题
范畴在计算机科学中的应用：关于俱乐部和数据类型构造函数
DOI：
--
复制
发表时间：
1992
期刊：
影响因子：
--
通讯作者：
G. M. Kelly
中科院分区：
文献类型：
--
作者：
G. M. Kelly
引言图对称monoidal封闭范畴证明交换的Mac巷和作者在[19]是图（广义）自然变换。为了理解这些结果与自由结构模型之间的联系，作者在[13]和[14]中引入了俱乐部的概念，[15]中进一步发展了俱乐部的概念，并在[16]和其他地方应用于其他连贯性问题。俱乐部的概念似乎适用于一个范畴的几种不同的结构，但仍然只适用于有限的几种。在试图了解其自然的限制，作者制定了一个一般概念的“俱乐部”，作为一个单子与某些性质，不一定对猫现在，但任何范畴有限的限制。1978年的研讨会报告[17]中对此有一个简要的描述，但从未发表;作者怀疑是否有足够的例子来使其引起普遍兴趣。然而，在1990年和1991年期间，我们有幸与我们在悉尼的研究团队一起罗宾·科基特（Robin Cockett），他致力于将范畴理论应用于计算机科学。在我们研讨会的演讲中，他提请注意与数据类型有关的某些类型的单子，这些单子具有特殊的属性：他称它们为形状单子，但实际上它们正是上述抽象意义上的俱乐部的例子。在这种情况下，似乎应该把那些旧的观念放下，并以各种方式来完成它们，特别是关于丰富的单子。
Introduction The diagrams for symmetric monoidal closed categories proved commutative by Mac Lane and the author in [19] were diagrams of (generalized) natural transformations. In order to understand the connexion between these results and free models for the structure, the author introduced in [13] and [14] the notion of club , which was further developed in [15] and applied later to other coherence problems in [16] and elsewhere. The club idea seemed to apply to several diverse kinds of structure on a category, but still to only a restricted number of kinds. In an attempt to understand its natural limits, the author worked out a general notion of “club”, as a monad with certain properties, not necessarily on Cat now, but on any category with finite limits. A brief account of this was included in the 1978 Seminar Report [17], but was never published; the author doubted that there were enough examples to make it of general interest. During 1990 and 1991, however, we were fortunate to have with our research team at Sydney Robin Cockett, who was engaged in applying category theory to computer science. In lectures to our seminar he called attention to certain kinds of monads involved with data types, which have special properties : he was calling them shape monads , but in fact they are precisely examples of clubs in the abstract sense above. In these circumstances it seems appropriate to set down those old ideas after all, and to complete them in various ways, in particular as regards enriched monads.