cubicaltt
sml-redprl
| cubicaltt | sml-redprl | |
|---|---|---|
| 3 | 1 | |
| 557 | 225 | |
| - | - | |
| 2.3 | 10.0 | |
| 7 months ago | over 1 year ago | |
| Haskell | Standard ML | |
| MIT License | MIT License |
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cubicaltt
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Let's collect relatively new research programming languages in this thread
- cubicialtt a programming language based on cubical type theory in which univalence from homotopy type theory isn't an axiom but a theorem
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How and where to learn the latest mathematical concepts?
If you’re interested in programming languages specifically, the current state of the art is called Cubical Type Theory. CuTT has lots of flavours and the community hasn’t coalesced around a single design. The paper I personally found easiest to digest was the “ABCFHL” paper, but I’d recommend reading it alongside the original CCHM paper. None of the publications made an ounce of sense to me until after I’d digested Favonia’s YouTube channel, Mortberg’s lecture notes and this other series of lectures from Harper (particularly the final one).
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Plato’s Cave Found in Mathematics
I updated the blog post to include some people in academia who contributed. I've been interacting with Kent Palmer and Sylvester James Gates, Jr. The latter held lectures about the philosophy of mathematics. I've been using work inspired by Vladimir Voevodsky, e.g. cubicaltt (https://github.com/mortberg/cubicaltt), which is also performed by academics.
sml-redprl
What are some alternatives?
Coq-HoTT - A Coq library for Homotopy Type Theory
cooltt - 😎TT
redtt - "Between the darkness and the dawn, a red cube rises!": a proof assistant for cartesian cubical type theory
jasmin - Language for high-assurance and high-speed cryptography
coq - Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs.
karamel - KaRaMeL is a tool for extracting low-level F* programs to readable C code
anders - 🧊 Модальний гомотопічний верифікатор математики
proofs - My personal repository of formally verified mathematics.
cogent - Cogent Project
Agda - Agda is a dependently typed programming language / interactive theorem prover.