协定
发表于 2025-3-30 09:12:55
* Extraction and Imperative Programming, provide an efficient environment to execute them. It is better to rely on the usual programming tools (compilers, abstract machines, and so on) to provide this environment. The . system simply provides ways to translate formal developments into conventional programming languages.
CLASH
发表于 2025-3-30 16:22:18
** Foundations of Inductive Types,this function may have a dependent type, and some of its arguments may be parameters. The constructors may be constants or functions, possibly with a dependent type, their arguments may or may not be in the inductive type, and these arguments may themselves be functions. In this section, we want to study the limits of this freedom.
产生
发表于 2025-3-30 19:00:37
Propositions and Proofs,In this chapter we introduce the reasoning techniques used in ., starting with a very reduced fragment of logic, ., where formulas are exclusively constructed using propositional variables and implication.
ventilate
发表于 2025-3-30 21:13:36
* Functions and Their Specifications,We gave an informal presentation of certified programs in Chap. 1. Given a relation . of .→.→Prop, we want to produce a function that maps any . in . to a value . in . together with a proof of “.” (a .).
遣返回国
发表于 2025-3-31 01:39:39
* A Case Study,In Chap. 10, we described succinctly the principle of the extraction mechanism. This chapter contains a simple case study to illustrate the subtle links between the sorts Prop and Set. In particular, we can develop and extract certified programs that provide reasonable efficiency, thanks to our knowledge of the extraction process.
STEER
发表于 2025-3-31 08:20:25
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连词
发表于 2025-3-31 11:03:20
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CRAFT
发表于 2025-3-31 15:37:18
* General Recursion,Structural recursion is powerful, especially in combination with higher-order definitions, as we have seen in the example of Ackermann’s function. Nevertheless, it is not always adapted to describe algorithms where termination is difficult to express as structural recursion with respect to one of the arguments.
hidebound
发表于 2025-3-31 17:50:17
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Intact
发表于 2025-3-31 22:06:35
The Future of Energy, universal increase in quality of life and by the development of emerging economies. The world’s energy consumption has more than doubled since 1973; it could even be tripled by the end of the century. Although the planet’s main fossil fuels—oil, natural gas, and coal—are being depleted, they still