HoTT VS lean

Compare HoTT vs lean and see what are their differences.

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HoTT lean
2 2
1,032 1,915
2.1% -
9.4 0.0
13 days ago over 1 year ago
Coq C++
GNU General Public License v3.0 or later Apache License 2.0
The number of mentions indicates the total number of mentions that we've tracked plus the number of user suggested alternatives.
Stars - the number of stars that a project has on GitHub. Growth - month over month growth in stars.
Activity is a relative number indicating how actively a project is being developed. Recent commits have higher weight than older ones.
For example, an activity of 9.0 indicates that a project is amongst the top 10% of the most actively developed projects that we are tracking.

HoTT

Posts with mentions or reviews of HoTT. We have used some of these posts to build our list of alternatives and similar projects. The last one was on 2021-06-23.

lean

Posts with mentions or reviews of lean. We have used some of these posts to build our list of alternatives and similar projects. The last one was on 2021-03-26.
  • Mathematics: our overlooked ability
    1 project | reddit.com/r/agi | 30 Apr 2021
    I have spent a good deal of time trying to formalize elementary mathematics and computer science textbooks in the Lean Theorem Prover, and in trying to extend and improve Lean to make the process easier. I have been able to translate entire chapters of several textbooks into Lean in a natural way, with every line of Lean seemingly isomorphic to the informal presentation. However, once in a while I will hit a statement or proof step that may seem simple to me but that requires a major refactor, or adding new features to Lean itself, or just seems like a brick wall. My brain is able to perform massive refactorings of mathematical knowledge and abstractions, synthesize the equivalent of tens of thousands of lines of tricky and performance-critical software, and maybe even expand the logic I am effectively operating in, all in the blink of an eye.
  • How do I get back into math?
    3 projects | reddit.com/r/math | 26 Mar 2021
    However, mathlib makes some weird design choices. For example, (semi)groups are defined using multiplicative notation -- and then immediately followed by an entire section giving the exact same definitions using additive notation! The claimed reason for this is that the more abstract approach is inconvenient for automation. I did it in Coq using the abstract approach, and indeed, noticed that doing so broke automation, which I then worked around in various ways. But it's just weird to me as a mathematician to have additive and multiplicative groups be different objects, so I wouldn't want to do it the Lean way come hell or high water. The Lean approach causes practical difficulties as well: you have to prove every theorem about groups twice. In some cases (e.g. product groups), you have to prove every theorem FOUR times. Ugh.

What are some alternatives?

When comparing HoTT and lean you can also consider the following projects:

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

FStar - Verification system for effectful programs

cubical - An experimental library for Cubical Agda

arend-lib