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dannypsnl authored Nov 27, 2024
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Expand Up @@ -20,7 +20,7 @@ An experimental proof assistant for synthetic ∞-categories.

## About this project

This project has started with the idea of bringing Riehl and Shulman's 2017 paper [1] to "life" by implementing a proof assistant based on their type theory with shapes. Currently an early prototype with an [online playground](https://rzk-lang.github.io/rzk/develop/playground/) is available. The current implementation is capable of checking various formalisations. Perhaps, the largest formalisations are available in two related projects: <https://rzk-lang.github.com/sHoTT> and <https://github.com/emilyriehl/yoneda>. `sHoTT` project (originally a fork of the yoneda project) aims to cover more formalisations in simplicial HoTT and ∞-categories, while `yoneda` project aims to compare different formalisations of the Yoneda lemma.
This project has started with the idea of bringing Riehl and Shulman's 2017 paper [1] to "life" by implementing a proof assistant based on their type theory with shapes. Currently an early prototype with an [online playground](https://rzk-lang.github.io/rzk/develop/playground/) is available. The current implementation is capable of checking various formalisations. Perhaps, the largest formalisations are available in two related projects: <https://rzk-lang.github.io/sHoTT> and <https://github.com/emilyriehl/yoneda>. `sHoTT` project (originally a fork of the yoneda project) aims to cover more formalisations in simplicial HoTT and ∞-categories, while `yoneda` project aims to compare different formalisations of the Yoneda lemma.

Internally, `rzk` uses a version of second-order abstract syntax allowing relatively straightforward handling of binders (such as lambda abstraction). In the future, `rzk` aims to support dependent type inference relying on E-unification for second-order abstract syntax [2].
Using such representation is motivated by automatic handling of binders and easily automated boilerplate code. The idea is that this should keep the implementation of `rzk` relatively small and less error-prone than some of the existing approaches to implementation of dependent type checkers.
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