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Formal mathematics
来自开放百科 - 灰狐
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*[[Prolog]] logic programming language | *[[Prolog]] logic programming language | ||
| + | *[https://github.com/ocaml/Zarith OCaml Zarith library] 对任意精度（arbitrary-precision）的整数进行算术和逻辑运算 | ||
*[https://github.com/leanprover-community/mathlib Lean mathlib] [[Lean]] | *[https://github.com/leanprover-community/mathlib Lean mathlib] [[Lean]] | ||
*[https://isarmathlib.org/ IsarMathLib] Proofs by humans, for humans, formally verified by [[Isabelle]]/ZF proof assistant | *[https://isarmathlib.org/ IsarMathLib] Proofs by humans, for humans, formally verified by [[Isabelle]]/ZF proof assistant | ||
2022年10月10日 (一) 10:01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
- 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
- e language
文档
- Formal Mathematics Statement Curriculum Learning
- ETPS: A System to Help Students Write Formal Proofs
书籍
- 《Implementing Mathematics with The Nuprl Proof Development System》
- 《Mathematical Proofs: A Transition to Advanced Mathematics》 Gary Chartrand, Albert D. Polimeni, Ping Zhang
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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