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Formal mathematics
来自开放百科 - 灰狐
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*[https://www.cs.utexas.edu/users/hunt/class/2021-fall/cs389r/vega-equations-new.pdf Theorems from CDS4LTL (Expanded)] Calculational Deductive System for Linear Temporal Logic（线性时态逻辑的计算演绎系统） | *[https://www.cs.utexas.edu/users/hunt/class/2021-fall/cs389r/vega-equations-new.pdf Theorems from CDS4LTL (Expanded)] Calculational Deductive System for Linear Temporal Logic（线性时态逻辑的计算演绎系统） | ||
*[https://www21.in.tum.de/teaching/lambda/WS21/assets/lecture-notes.pdf Lambda Calculus] [https://www21.in.tum.de/teaching.html Teaching - Chair for Logic and Verification] | *[https://www21.in.tum.de/teaching/lambda/WS21/assets/lecture-notes.pdf Lambda Calculus] [https://www21.in.tum.de/teaching.html Teaching - Chair for Logic and Verification] | ||
| + | *[https://www.kth.se/social/files/596318bc56be5bfdc343d436/itp-course.pdf Interactive Theorem Proving (ITP) Course] | ||
==书籍== | ==书籍== | ||
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image:isabelle-on-windows.png|Isabelle | image:isabelle-on-windows.png|Isabelle | ||
image:Erlang-Henk-Pure-Type-System.png|Erlang定义的Henk纯类型系统 | image:Erlang-Henk-Pure-Type-System.png|Erlang定义的Henk纯类型系统 | ||
| + | image:Mathematical-vs-Formal-Proof.png|Mathematical vs. Formal Proof | ||
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2022年10月15日 (六) 00:58的版本
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您可以在Wikipedia上了解到此条目的英文信息 Formal mathematics Thanks, Wikipedia. |
Formal mathematics 形式化数学
目录 |
简介
ML (Meta language -> Mathematics language) 很有寓意，ML 实力体现在编译器构建、自动化定理证明和形式化验证等。
理论
项目
- Coq Univalent Mathematics
- Agda Univalent mathematics in Agda
- ACL2
- Isabelle
- Prolog logic programming language
- OCaml Zarith library 对任意精度（arbitrary-precision）的整数进行算术和逻辑运算
- Lean mathlib Lean
- IsarMathLib Proofs by humans, for humans, formally verified by Isabelle/ZF proof assistant
- lean-gym Lean
- Calculating Programs
- Charity is a categorical programming language
- Groupoid Infinity Institute 研究所正在做数学的形式化，其形式化编程语言称为 Anders 1.3.0，是立方体类型系统（cubical type systems）的 CCHM/HTS 变体（variant ）Groupoid @ GitHub
- Henk: Pure Type System 是带有通用量词（universal quantifier）和宇宙无穷数量（infinity number of universes）的最小语言，用于一致的类型检查和规范化（consistent typechecking and normalization） made by Erlang
- Anders is a Modal HoTT proof assistant, written in OCaml and Pug.
- e language
文档
两千多年来，几何学一直是公理方法、逻辑和形式化的一个重要试验场。本幻灯片（66页PDF）将回顾几何学的历史、公理学、以及计算机辅助证明和证明检查的使用。
- Speaking Logic Type Theory A Brief Tutorial on the PVS Interactive Proof Assistant
- Formal Mathematics Statement Curriculum Learning
- ETPS: A System to Help Students Write Formal Proofs
- Theorems from CDS4LTL (Expanded) Calculational Deductive System for Linear Temporal Logic（线性时态逻辑的计算演绎系统）
- Lambda Calculus Teaching - Chair for Logic and Verification
- Interactive Theorem Proving (ITP) Course
书籍
- 《Implementing Mathematics with The Nuprl Proof Development System》
- 《Mathematical Proofs: A Transition to Advanced Mathematics》 Gary Chartrand, Albert D. Polimeni, Ping Zhang
STEM
这是有关形式化方法、形式化技术的课程，质量很高。基于形式逻辑的技术，如模型检查、可满足性、静态分析和自动定理证明在建模、分析、验证等方面都有广泛应用。课程每年更新，已经有11年了（SSFT11 - SSFT22）。
图集
Isabelle
Erlang定义的Henk纯类型系统
Mathematical vs. Formal Proof
链接
- Metamath
- vdash a formal math wiki
- Formalized Mathematics IsarMathLib Blog
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