Titlebook: Interactive Theorem Proving and Program Development; Coq’Art: The Calculu Yves Bertot,Pierre Castéran Textbook 2004 Springer-Verlag Berlin

协定

* 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

** 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

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

* 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

* 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.

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连词

CRAFT

* 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

Intact

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