Formal mathematics

2022年10月12日 (三) 15:03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

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。

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

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 ==文档==
+*[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://gtps.math.cmu.edu/etps-report-pdf.pdf ETPS: A System to Help Students Write Formal Proofs]