UniMath
cubical
UniMath | cubical | |
---|---|---|
2 | 3 | |
915 | 424 | |
1.0% | 1.7% | |
9.5 | 8.5 | |
1 day ago | 5 days ago | |
Coq | Agda | |
GNU General Public License v3.0 or later | GNU General Public License v3.0 or later |
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UniMath
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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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Are There People Doing Formal Math In Berlin?
I just wonder if there are any irl meetups of people involved with formalizing mathematics, I thought that it would be a cool hobby to pick up (with some background in math and programming) but the existing libraries, like MathLib, TypeTopology or UniMath look a bit intimidating...
cubical
-
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).
- Homotopy Type Theory
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Cubical Type Theory?
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?
analysis - Mathematical Components compliant Analysis Library
Coq-HoTT - A Coq library for Homotopy Type Theory
math-comp - Mathematical Components
redtt - "Between the darkness and the dawn, a red cube rises!": a proof assistant for cartesian cubical type theory
hott3 - HoTT in Lean 3
nqthm - nqthm - the original Boyer-Moore theorem prover, from 1992
TypeTopology - Logical manifestations of topological concepts, and other things, via the univalent point of view.
mathlib - Lean 3's obsolete mathematical components library: please use mathlib4
hs-to-coq - Convert Haskell source code to Coq source code.
pasv - The Pascal-F Verifier