Formal mathematics

2022年10月12日 (三) 09:05的版本

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

简介

What is Formal Math?

Open Provable Foundation

数理逻辑/数学证明

Formalized Mathematics

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

• homotopy type theory (HoTT) and Cubical type theory

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
• Anders is a Modal HoTT proof assistant, written in OCaml and Pug.
• e language

文档

• 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

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