redtt VS cubical

Compare redtt vs cubical and see what are their differences.

redtt

"Between the darkness and the dawn, a red cube rises!": a proof assistant for cartesian cubical type theory (by RedPRL)
cubical-type-theory proof-assistant type-theory Ocaml
Source Code
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cubical

An experimental library for Cubical Agda (by agda)
Agda cubical-type-theory Library
Source Code
agda.github.io
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redtt cubical
2 3
199 421
0.0% 1.0%
0.0 8.5
about 2 years ago 3 days ago
OCaml Agda
Apache License 2.0 GNU General Public License v3.0 or later
The number of mentions indicates the total number of mentions that we've tracked plus the number of user suggested alternatives.
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redtt

Posts with mentions or reviews of redtt. We have used some of these posts to build our list of alternatives and similar projects. The last one was on 2021-02-11.

cubical

Posts with mentions or reviews of cubical. We have used some of these posts to build our list of alternatives and similar projects. The last one was on 2023-06-30.
  • Will Computers Redefine the Roots of Math?
    6 projects | news.ycombinator.com | 30 Jun 2023
    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).

  • Homotopy Type Theory
    3 projects | news.ycombinator.com | 23 Jun 2021
  • Cubical Type Theory?
    2 projects | /r/dependent_types | 11 Feb 2021
    In the case of transpension, it seems like one of the uses is proving something about a path in inductive types by cases on an abstract point along that path. For instance, right now, the way that you prove that a path in A + B is either a path in A or a path in B is to define a family by cases and then transport like here. But I think transpension might let you just do cases on a formal intermediate point directly, which would be much simpler.

What are some alternatives?

When comparing redtt and cubical you can also consider the following projects:

cooltt - 😎TT

Coq-HoTT - A Coq library for Homotopy Type Theory

sml-redprl - The People's Refinement Logic

hott3 - HoTT in Lean 3

Agda - Agda is a dependently typed programming language / interactive theorem prover.

nqthm - nqthm - the original Boyer-Moore theorem prover, from 1992

UniMath - This coq library aims to formalize a substantial body of mathematics using the univalent point of view.

mathlib - Lean 3's obsolete mathematical components library: please use mathlib4

pasv - The Pascal-F Verifier

redtt vs cooltt cubical vs Coq-HoTT redtt vs sml-redprl cubical vs hott3 redtt vs Agda cubical vs nqthm cubical vs UniMath cubical vs mathlib cubical vs pasv