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yacctt's Introduction

yacctt: Yet Another Cartesian Cubical Type Theory

This is an extremely experimental implementation of a cartesian cubical type theory based on https://arxiv.org/abs/1712.01800 written by Anders Mörtberg and Carlo Angiuli. It is mainly meant as proof of concept and for experimentation with new cubical features and ideas.

It is based on the code base of https://github.com/mortberg/cubicaltt/.

yacctt's People

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silky hardentoo 5ht eamon-otuathail chrisfischer samtoth drruisseau

yacctt's Issues

Is there a general way to derive these computation rules?

I saw

yacctt/Eval.hs

Lines 428 to 433 in 72cf547

Ter (Sum _ n nass) env
| n `elem` ["nat","Z","bool"] -> return u -- hardcode hack
| otherwise -> error $ "coe sum: " ++ show n
Ter (HSum _ n nass) env
| n `elem` ["S1","S2","S3"] -> return u -- hardcode hack
| otherwise -> error "coe hsum"

Is it that you are too lazy to implement the general case, or is it an open problem?

How is eta rule for VType is implemented?

Hello.

From the implementation I failed to find how eta rule for VType is implemented. It seems to me at least it is essential for some computation rules to be correct.

It seems to me that the conversion checking in yacctt is syntax directed, but lambda term is not domain-free. open variables needs to have it's type because we need to have infer for path type application rules.

In my implementation https://github.com/molikto/mlang/blob/master/shared/shared/src/main/scala/mlang/core/Unify.scala#L381 I can get type directed eta rules for all types except VType, because VType don't really terminate unfolding in a type directed way.

So what's the best conversion checking for cartisian cubical type theory? It seems both syntax-directed way and type directed way has its slight problems

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