Mathematical semantics of the internal structure of algorithms
| Project/Area Number |
19700012
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Fundamental theory of informatics
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| Research Institution | Hosei University |
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Principal Investigator |
KURATA Toshihiko Hosei University, 経営学部, 教授 (40311899)
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| Project Period (FY) |
2007 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥3,140,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥540,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2007: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | プログラム意味論 / ラムダ計算 / 型理論 / 層論 / 領域理論 / 外延性 / 高階遂次性 / Kripkeモデル / 2階直観主義命題論理 / 完備Heyting代数 / 完全性定理 / Stone双対性 / 完備半順序集合 |
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| Research Abstract |
As a result of this research, we introduced a new notion of sheaves of complete partially ordered sets from the ordinary definition of sheavs of sets, which is given by replacing the category Sets of sets and functions with the category Cpos of complete partially ordered sets and continuous functions. The framework so obtained allows us to have the cartesian closed category Cpos(X) in which we can develop various structures for denotational semantics of programming languages excluding the condition of extensionality. This is because of a number of desirable features of Cpos(X) in order to interpret flexible syntactical devices of programming languages.
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Report
(6 results)
Research Products
(13 results)
