The Category-Theoretic Solution of Recursive Domain Equations
文献类型：期刊论文
| 作者 | M. B. Smyth ; G. D. Plotkin |
| 刊名 | SIAM Journal on Computing
 |
| 出版日期 | 1982 |
| 卷号 | 11期号:4页码:761-783 |
| 关键词 | Domains semantics data-types category partial-order fixed-point computability |
| 合作状况 | 其它 |
| 中文摘要 | 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. |
| 收录类别 | 其他 |
| 语种 | 英语 |
| 公开日期 | 2010-05-14 |
| 源URL | [http://124.16.136.157/handle/311060/1358]  |
| 专题 | 软件研究所_软件所图书馆_期刊论文 |
| 推荐引用方式 GB/T 7714 | M. B. Smyth,G. D. Plotkin. The Category-Theoretic Solution of Recursive Domain Equations[J]. SIAM Journal on Computing,1982,11(4):761-783. |
| APA | M. B. Smyth,&G. D. Plotkin.(1982).The Category-Theoretic Solution of Recursive Domain Equations.SIAM Journal on Computing,11(4),761-783. |
| MLA | M. B. Smyth,et al."The Category-Theoretic Solution of Recursive Domain Equations".SIAM Journal on Computing 11.4(1982):761-783. |
入库方式： OAI收割
来源：软件研究所
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