| The Category-Theoretic Solution of Recursive Domain Equations |
| M. B. Smyth; G. D. Plotkin
|
| 1982
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| 发表期刊 | SIAM Journal on Computing
 |
| 卷号 | 11期号:4页码:761-783 |
| 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
|
| 合作性质 | 其它
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| 关键词 | Domains
Semantics
Data-types
Category
Partial-order
Fixed-point
Computability
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| 语种 | 英语
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| 内容类型 | 期刊论文
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| URI标识 | http://ir.iscas.ac.cn/handle/311060/1358
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| 专题 | 中国科学院软件研究所
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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.
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| 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.
|
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