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 题名: The Category-Theoretic Solution of Recursive Domain Equations 作者: M. B. Smyth ; G. D. Plotkin 关键词: Domains ; semantics ; data-types ; category ; partial-order ; fixed-point ; computability 刊名: SIAM Journal on Computing 发表日期: 1982 卷: 11, 期:4, 页:761-783 收录类别: 其他 合作性质: 其它 摘要: Recursive specifications of domains plays a crucial role in denotational semantics as developed by Scott and Strachey and their followers. The purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place. The idea is to follow the well-known analogy between partial orders and categories, generalizing from least fixed-points of continuous functions over cpos to initial ones of continuous functors over $\omega$-categories. To apply these general ideas we introduce Wand's ${\bf O}$-categories where the morphism-sets have a partial order structure and which include almost all the categories occurring in semantics. The idea is to find solutions in a derived category of embeddings and we give order-theoretic conditions which are easy to verify and which imply the needed categorical ones. The main tool is a very general form of the limit-colimit coincidence remarked by Scott. In the concluding section we outline how compatibility considerations are to be included in the framework. A future paper will show how Scott's universal domain method can be included too. 语种: 英语 内容类型: 期刊论文 URI标识: http://ir.iscas.ac.cn/handle/311060/1358 Appears in Collections: 软件所图书馆_期刊论文

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 Recommended Citation: M. B. Smyth,G. D. Plotkin. The Category-Theoretic Solution of Recursive Domain Equations[J]. SIAM Journal on Computing,1982-01-01,11(4):761-783.
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