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Types and Programming Languages习题的参考解答及思考(第12章)

CloseToZero 发布于 2022-12-15
第12章 章节12.1 练习12.1.1 题目: Where do we fail if we attempt to prove normalization by a straightforward induction on the size of a well-typed term? 解答: 在处理使用求值规则E-APPABS的情况会出问题,
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 数学, 类型理论

Types and Programming Languages习题的参考解答及思考(第11章)

CloseToZero 发布于 2022-12-08
第11章 章节11.2 练习11.2.1 题目: Is there a way of constructing a sequence of terms \( \text{t}_1, \text{t}_2, \dots \), in the simply typed lambda-calculus with only the base type Unit, such that, for each \( n \), the term \( \text{t}_n \) as size at most \( O(n) \) but requires at least
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 数学, 类型理论

Types and Programming Languages习题的参考解答及思考(第9章)

CloseToZero 发布于 2022-12-06
第9章 章节9.2 练习9.2.1 题目: The pure simply typed lambda-calculus with no base types is actually degenerate, in the sense that it has no well-typed terms at all. Why? 解答: 去掉基础类型后,类型\( \text{T} \)的语法只剩下: \[ \text{T} ::=
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 数学, 类型理论

Types and Programming Languages习题的参考解答及思考(第8章)

CloseToZero 发布于 2022-12-05
第8章 章节8.2 练习8.2.3 题目: Prove that every subterm of a well-typed term is well typed. 证明: \( \forall \)类型良好的项\( \text{t}: \text{R} \),我们对\( \text{t} \)的形式进行分类讨论: 如果\
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 数学, 类型理论

Types and Programming Languages习题的参考解答及思考(第6章)

CloseToZero 发布于 2022-11-27
第6章 章节6.1 练习6.1.1 题目: For each of the following combinators \( \text{c}_0 = \lambda \text{s. } \lambda \text{z. } \text{z} \); \( \text{c}_2 = \lambda \text{s. } \lambda \text{z. } \text{s (s z)} \); \( \text{plus} = \lambda \text{m. } \lambda \text{n. } \lambda \text{s. } \lambda \text{z. } \text{m s (n s z)} \) \(
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 数学, 类型理论

Types and Programming Languages习题的参考解答及思考(第5章)

CloseToZero 发布于 2022-11-19
第5章 章节5.2 练习5.2.1 题目: Define logical \( \text{or} \) and \( \text{not} \) functions. 解答: 逻辑或函数:\( \text{or} = \lambda \text{b. } \lambda \text{c. } \text{b tru c} \) 逻辑非函数:\( \text{not} = \lambda \text{b. } \text{b fls tru} \) 练习
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 数学, 类型理论
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