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Formal mathematics
来自开放百科 - 灰狐
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| + | *[https://fm.csl.sri.com/SSFT21/speaklogicV10.pdf Speaking Logic] [https://fm.csl.sri.com/SSFT21/TypeTheory.pdf Type Theory] [https://fm.csl.sri.com/SSFT21/CAS2017.pdf A Brief Tutorial on the PVS Interactive Proof Assistant] | ||
*[https://cdn.openai.com/papers/Formal_Mathematics_Statement_Curriculum_Learning__ICML_2022.pdf Formal Mathematics Statement Curriculum Learning] | *[https://cdn.openai.com/papers/Formal_Mathematics_Statement_Curriculum_Learning__ICML_2022.pdf Formal Mathematics Statement Curriculum Learning] | ||
*[https://gtps.math.cmu.edu/etps-report-pdf.pdf ETPS: A System to Help Students Write Formal Proofs] | *[https://gtps.math.cmu.edu/etps-report-pdf.pdf ETPS: A System to Help Students Write Formal Proofs] | ||
2022年10月12日 (三) 15:03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
- 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）
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
图集
Isabelle
Erlang定义的Henk纯类型系统
链接
- Metamath
- vdash a formal math wiki
- Formalized Mathematics IsarMathLib Blog
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