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| The Category-Theoretic Solution of Recursive Domain Equations | |
| M. B. Smyth; G. D. Plotkin | |
| 1982 | |
| Source | SIAM Journal on Computing
 |
| Volume | 11Issue:4Pages:761-783 |
| English Abstract | 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. |
| Indexed Type | 其他 |
| Cooperation Status | 其它 |
| Keyword | Domains Semantics Data-types Category Partial-order Fixed-point Computability |
| Language | 英语 |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/1358 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation 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. |
| Files in This Item: | ||||||
| File Name/Size | DocType | Version | Access | License | ||
| bj01149966.pdf（902KB） | 开放获取 | License | Application Full Text | |||
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