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

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Yves Bertot,Pierre Castéranase. ...This volume contains detailed introductions to human syntactic processing as well as to German syntax which will be helpful especially for readers less familiar with psycholinguistics and with Germanic.978-90-481-7111-8978-1-4020-4344-4Series ISSN 1873-0043 Series E-ISSN 2215-1788

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Interactive Theorem Proving and Program Development978-3-662-07964-5Series ISSN 1862-4499 Series E-ISSN 1862-4502

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Yves Bertot,Pierre CastéranFirst book providing the theoretical foundations.A broad spectrum of applications of the theorem proving system Coq.Includes supplementary material:

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Texts in Theoretical Computer Science. An EATCS Serieshttp://image.papertrans.cn/i/image/470579.jpg

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,Dependent Products , Pandora’s Box,tions. This limitation disappears with the introduction of a new type construct, called the .. This construct generalizes the arrow . → . which represents functional types or implications depending on the sort of . and .. With dependent products we can build functions where the result type depends on the argument.

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Everyday Logic,ems. Interpreting types as formulas and terms as proofs works well and makes it possible to reduce the problem of verifying formal proofs to the problem of verifying that some terms are well-typed. This chapter takes a more pragmatic point of view and shows how we can use tactics to make the logical reasoning easier.

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Inductive Data Types,cursive type definitions found in most functional programming languages. However, the possibility of mixing recursive types and dependent products makes the inductive types of . much more precise and expressive, up to the point where they can also be used to describe pure logic programming, in other words the primitive kernel of ..

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