Apprentice
1.3K posts

Apprentice
@monadivalence
Type theory daisuki! Profile picture by @sealily___
Katılım Şubat 2023
274 Takip Edilen210 Takipçiler

A piece of code (a quotient inductive type) in
arxiv.org/abs/2502.20496
can be written in Aya. Note that the one-linear function `paint` and `strip` are mutually-recursive with `RBTree`.
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@michael_kove @tekbog Thank you for saying this so I don't have to make a reply myself.
I'm glad that monkeys have finally found the right tool, though.
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@TheEduardoRFS @krismicinski @onehappyfellow That's why I implemented them in my set-level language, to become a better syntax for quotients
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@TheEduardoRFS @krismicinski @onehappyfellow Cubical Agda is indeed a lot of fun. I love higher inductive types
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@TheEduardoRFS @onehappyfellow @krismicinski Quotients are not higher. They're still set-level, but in a syntactically more interesting way
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@monadivalence @onehappyfellow @krismicinski Same, I think the dependent type theory and "respecting" the equality is the useful bits.
But as long as you're dealing with traditional data types you're in usually set-level type theory anyway.
And even for the higher bits, you're often dealing with quotients only.
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@scheminglunatic @krismicinski @TheEduardoRFS @onehappyfellow There isn't a path between them imo. Code is usually about set-level structures. I barely notice any interesting homotopy amongst program equivalence
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@onehappyfellow @krismicinski @TheEduardoRFS My current conclusion is that they will help you understand dependent type theory, which is helpful. But when you reason about programs, you still want to use a Set-level type theory, as opposed to these which I refer to as higher (-dimensional) type theory
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@krismicinski @monadivalence @TheEduardoRFS i don't mind the thread flowing away from the topic as long as it's interesting
it'd be cool to understand what univalence/hott/ctt bring into verifying program correctness, even if I don't end up using it
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@onehappyfellow @TheEduardoRFS Tbh if you *just* want to learn about univalence, cubical Agda probably won't help
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@TheEduardoRFS i really need to learn cubical Agda don't I?
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@theodorvaryag Though I mostly disagree with this guy
Haskell is indeed C++ in FP
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