Coq type-theory

Open-source Coq projects categorized as type-theory

Coq type-theory Projects

  • Coq-HoTT

    A Coq library for Homotopy Type Theory

  • Project mention: What do we mean by "the foundations of mathematics"? | | 2023-11-01 :

    > * 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:

    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:


  • proofs

    My personal repository of formally verified mathematics.

  • Project mention: A Taste of Coq and Correct Code by Construction | | 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:

    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!

  • InfluxDB

    Power Real-Time Data Analytics at Scale. Get real-time insights from all types of time series data with InfluxDB. Ingest, query, and analyze billions of data points in real-time with unbounded cardinality.

    InfluxDB logo
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).

Coq type-theory related posts

  • A Taste of Coq and Correct Code by Construction

    3 projects | | 3 Sep 2023
  • Will Computers Redefine the Roots of Math?

    6 projects | | 30 Jun 2023
  • Formally Verifying Rust's Opaque Types

    2 projects | | 1 Aug 2022
  • What is the benefit of using a text editor like MikTex, Texmaker, etc. over Overleaf?

    1 project | /r/LaTeX | 1 Apr 2021


Project Stars
1 Coq-HoTT 1,221
2 proofs 286

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