Open ice1000 opened 5 years ago
owo-lang/OwO#5 Redy!
open {{ ... }}
Cubical Type Theories?
I don't want typeclass/type instance as language component.
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
.
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 forhSet
.
It has already been covered as Prop
and Proof Irrelevance
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.
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...
Yes, forget about record constructors. We'll use copatterns to replace record constructors!
After a little study about cutt, I'd say proof irrelevance is no longer useful when we have path types.