Type Theory and Formal Proof 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Rob Nederpelt 作者

Cambridge University Press

译者

2014-10-31 出版日期

490 页数

USB 80.00 价格

Hardcover

丛书系列

9781107036505 图书编码

Type Theory and Formal Proof 在线电子书图书标签: 类型论计算机编程语言理论 lambda-calculus 证明论类型系统逻辑学语言学

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发表于2024-11-24

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Type Theory and Formal Proof 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

Type Theory and Formal Proof 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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感觉自己在另一本书下面的装B评论中说的不对，类型论和范畴论区别很大，后者更接近方法论，前者更接近逻辑。本身就是在逻辑悖论中提出，不同的类型系统也比较类似各种逻辑系统。只是逻辑系统中的证明也可以看成是类型，于是我理解的类型论更接近于对操作规则的数学建模。而拉马达演算对于数理逻辑中的每个分支都是重要的。类型论、集合论、模型论等等确实更接近于哲学。只是在现代计算机程序语言的研究中，类型论得以新生。但正如没有完美的逻辑系统，所以也不存在什么作为数学基础的类型系统。但正是这些不完美与不存在，才是其学科内部的全动力。只是我已经不再把他们当成数学内容了。P.S.那个叫Coq的辅助证明系统，取名那位您认真的！

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Type Theory and Formal Proof 在线电子书著者简介

Rob Nederpelt was Lecturer in Logic for Computer Science until his retirement. Currently he is a guest researcher in the Faculty of Mathematics and Computer Science at Eindhoven University of Technology, The Netherlands.

Herman Geuvers is Professor in Theoretical Informatics at the Radboud University Nijmegen, and Professor in Proving with Computer Assistance at Eindhoven University of Technology, both in The Netherlands.

Type Theory and Formal Proof 在线电子书图书目录

Type Theory and Formal Proof 在线电子书 pdf 下载 txt下载 epub 下载 mobi 在线电子书下载

Type Theory and Formal Proof 在线电子书图书描述

Type theory is a fast-evolving field at the crossroads of logic, computer science and mathematics. This gentle step-by-step introduction is ideal for graduate students and researchers who need to understand the ins and outs of the mathematical machinery, the role of logical rules therein, the essential contribution of definitions and the decisive nature of well-structured proofs. The authors begin with untyped lambda calculus and proceed to several fundamental type systems culminating in the well-known and powerful Calculus of Constructions. The book also covers the essence of proof checking and proof development, and the use of dependent type theory to formalize mathematics. The only prerequisites are a good knowledge of undergraduate algebra and analysis. Carefully chosen examples illustrate the theory throughout. Each chapter ends with a summary of the content, some historical context, suggestions for further reading and a selection of exercises to help readers familiarize themselves with the material.

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