Coq type-theory Projects

Coq-HoTT

4 1,213 9.8 Coq

A Coq library for Homotopy Type Theory

Project mention: What do we mean by "the foundations of mathematics"? | news.ycombinator.com | 2023-11-01

https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_t... :
> * Today, Zermelo–Fraenkel set theory [ZFC], with the historically controversial axiom of choice (AC) included, is the standard form of axiomatic set theory and as such is the most common* foundation of mathematics.
Foundation of mathematics: https://en.wikipedia.org/wiki/Foundations_of_mathematics
Implementation of mathematics in set theory:
> The implementation of a number of basic mathematical concepts is carried out in parallel in ZFC (the dominant set theory) and in NFU, the version of Quine's New Foundations shown to be consistent by R. B. Jensen in 1969 (here understood to include at least axioms of Infinity and Choice).
> What is said here applies also to two families of set theories: on the one hand, a range of theories including Zermelo set theory near the lower end of the scale and going up to ZFC extended with large cardinal hypotheses such as "there is a measurable cardinal"; and on the other hand a hierarchy of extensions of NFU which is surveyed in the New Foundations article. These correspond to different general views of what the set-theoretical universe is like
IEEE-754 specifies that float64s have ±infinity and specify ZeroDivisionError. Symbolic CAS with MPFR needn't be limited to float64s.
HoTT in CoQ: Coq-HoTT: https://github.com/HoTT/Coq-HoTT
leanprover-community/mathlib4//

proofs

5 285 8.9 Coq

My personal repository of formally verified mathematics.

Project mention: A Taste of Coq and Correct Code by Construction | news.ycombinator.com | 2023-09-03

If you're already familiar with a functional programming language like Haskell or OCaml, you have the prerequisite knowledge to work through my Coq tutorial here: https://github.com/stepchowfun/proofs/tree/main/proofs/Tutor...
My goal with this tutorial was to introduce the core aspects of the language (dependent types, tactics, etc.) in a "straight to the point" kind of way for readers who are already motivated to learn it. If you've heard about proof assistants like Coq or Lean and you're fascinated by what they can do, and you just want the TL;DR of how they work, then this tutorial is written for you.
Any feedback is appreciated!

WorkOS

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The modern identity platform for B2B SaaS. The APIs are flexible and easy-to-use, supporting authentication, user identity, and complex enterprise features like SSO and SCIM provisioning.

NOTE: The open source projects on this list are ordered by number of github stars. The number of mentions indicates repo mentiontions in the last 12 Months or since we started tracking (Dec 2020).