owo-lang / rfcs

RFCs: Feature requests, discussions, etc.
MIT License
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Wanted basic features #2

Open ice1000 opened 5 years ago

ice1000 commented 5 years ago
ice1000 commented 5 years ago
ice1000 commented 5 years ago
ice1000 commented 5 years ago

owo-lang/OwO#5 Redy!

ice1000 commented 5 years ago
ice1000 commented 5 years ago
ice1000 commented 5 years ago
ice1000 commented 5 years ago
ice1000 commented 5 years ago

Cubical Type Theories?

ice1000 commented 5 years ago
ice1000 commented 5 years ago

I don't want typeclass/type instance as language component.

ice1000 commented 5 years ago
ice1000 commented 5 years ago
ice1000 commented 5 years ago
ice1000 commented 5 years ago
anqurvanillapy commented 5 years ago

What about n-truncated types like HoTT-Agda's to introduce hProp/hSet, make identity types and homotopy equivalence equivalent, and axiom K a theorem for hSet.

ice1000 commented 5 years ago

What about n-truncated types like HoTT-Agda's to introduce hProp/hSet, make identity types and homotopy equivalence equivalent, and axiom K a theorem for hSet.

It has already been covered as Prop and Proof Irrelevance

ice1000 commented 5 years ago
anqurvanillapy commented 5 years ago

It's an urge to give a research about the ability of modeling HoTT by UTT, since the base standard library of OwO should start with things like in HoTT-Agda's n-truncated types, since then we can easily model h-props and h-sets by postulating different axioms, and even forget about UA when modelling all the groupoids.

anqurvanillapy commented 5 years ago

And I will leave a comment about the design of record-like stuff, since I think Agda's (co-)inductive records are weird to construct...

ice1000 commented 5 years ago

Yes, forget about record constructors. We'll use copatterns to replace record constructors!

ice1000 commented 5 years ago

After a little study about cutt, I'd say proof irrelevance is no longer useful when we have path types.