principia
hs-to-coq
| principia | hs-to-coq | |
|---|---|---|
| 10 | 2 | |
| 198 | 74 | |
| - | - | |
| 2.7 | 0.0 | |
| 10 months ago | 24 days ago | |
| TeX | Coq | |
| GNU General Public License v3.0 only | MIT License |
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principia
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Principia Mathematica in modern notation.
You can check it out here: https://www.principiarewrite.com/
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It took Russell and that other guy 360 pages to prove that 1+1=2. That's how rigorous math is.
It's crazy to think that we didn't really know for sure whether 1+1=2 until ~1910, yet it's true. That's when Bernard Russell (best known for Russell's teapot, exposing a logical fallacy in Christianity) and some other dude actually proved it from axioms. They laid out the foundation of 1+1 in a book called Principia Mathematica. They worked so rigorously that it took them 360 pages to even prove something as basic as 1+1=2 using the axiomatic method. If you want to use a modern tool like Coq to verify 1+1=2, then the best way of doing this is to formalize Principia Mathematica in Coq.
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Which is the most abstract and bizzare book of mathematics you have ever came across?
There are people trying to make it more readable.
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Ask HN: Would prog. language look like if that was designed by no-programmer
Principia
A work from the early 20th century, mathematics, logic.
I think some expert called Bertrand Russell's and A.N. Whitehead's "Principia Mathematica" initiative a "bizarre" piece of work, when seen from the perspective of a programming language designer.
I can't make a qualified statement about this, as I am neither a mathematician nor a language designer. And I cannot find the exact quote on the internet, sorry. Just saying.
In code? See for yourself :
https://www.principiarewrite.com/
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Hacker News top posts: Dec 6, 2021
Whitehead and Russell’s Principia rewritten in Coq\ (44 comments)
- Whitehead and Russell’s Principia rewritten in Coq
- The Principia Rewrite: Whitehead and Russell’s Principia Rewritten in Coq
hs-to-coq
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Do you use Idris or Coq, and why?
There is even a project that converts Haskell to Coq.
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agda2hs, verify your haskell code in agda?
PS: Obligatory plug for hs-to-coq.
What are some alternatives?
Coq-Equations - A function definition package for Coq
Agda - Agda is a dependently typed programming language / interactive theorem prover.
Transformer-in-Transformer - An Implementation of Transformer in Transformer in TensorFlow for image classification, attention inside local patches
UniMath - This coq library aims to formalize a substantial body of mathematics using the univalent point of view.
inform7-ide - A design system for interactive fiction based on natural language.
notes
cycle-cloud - Repository to allow collaboration between Cycle Labs Cloud community in support of the community.
CompCert - The CompCert formally-verified C compiler
mathlib - Lean 3's obsolete mathematical components library: please use mathlib4
magmide - A dependently-typed proof language intended to make provably correct bare metal code possible for working software engineers.
planckforth - Bootstrapping a Forth interpreter from hand-written tiny ELF binary. Just for fun.
agda2hs - Compiling Agda code to readable Haskell