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Coq-HoTT Alternatives
Similar projects and alternatives to Coq-HoTT
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path_semantics
A research project in path semantics, a re-interpretation of functions for expressing mathematics
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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.
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WorkOS
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.
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UniMath
This coq library aims to formalize a substantial body of mathematics using the univalent point of view.
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TypeTopology
Logical manifestations of topological concepts, and other things, via the univalent point of view.
NOTE:
The number of mentions on this list indicates mentions on common posts plus user suggested alternatives.
Hence, a higher number means a better Coq-HoTT alternative or higher similarity.
Coq-HoTT reviews and mentions
Posts with mentions or reviews of Coq-HoTT.
We have used some of these posts to build our list of alternatives
and similar projects. The last one was on 2023-11-01.
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What do we mean by "the foundations of mathematics"?
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//
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Will Computers Redefine the Roots of Math?
For those interested in formalisation of homotopy type theory, there are several (more or less) active and developed libraries. To mention a few:
UniMath (https://github.com/UniMath/UniMath, mentioned in the article)
Coq-HoTT (https://github.com/HoTT/Coq-HoTT)
agda-unimath (https://unimath.github.io/agda-unimath/)
cubical agda (https://github.com/agda/cubical)
All of these are open to contributions, and there are lots of useful basic things that haven't been done and which I think would make excellent semester projects for a cs/math undergrad (for example).
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Homotopy Type Theory
HoTT is somewhat independent of the choice of proof assistant.
Coq: https://github.com/HoTT/HoTT
Lean: https://github.com/gebner/hott3
idk what you mean by "blue screened", or results being on the way. afaict most of the non-foundational work present (what I assume you mean by "results") in these libraries are basic properties of basic mathematical concepts being rebuilt on HoTT.
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What is the benefit of using a text editor like MikTex, Texmaker, etc. over Overleaf?
The major one for me is version control (git). Imaging having to write a book like HoTT without having revisions and easy way to work on your changes without interfering with anyone else's work and then easily merging everything together.
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A note from our sponsor - WorkOS
workos.com | 26 Apr 2024
Stats
Basic Coq-HoTT repo stats
4
1,213
9.8
7 days ago
HoTT/Coq-HoTT is an open source project licensed under GNU General Public License v3.0 or later which is an OSI approved license.
The primary programming language of Coq-HoTT is Coq.
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