[Agda] [ cubical ] : Questions on PathP on Sets.
Apostolis Xekoukoulotakis
apostolis.xekoukoulotakis at gmail.com
Fri Sep 15 05:16:14 CEST 2017
The definition of PathP when it is a path between sets does not make sense
to me.
Here is an example :
```
module test where
open import PathPrelude
-- fun : ∀{ℓ} → {A B : Set ℓ} → A ≡ B → A → B
-- fun eq a = transp eq a
fun2 : ∀{ℓ} → {A B : Set ℓ} → A ≡ B → A → B
fun2 eq a = transp (λ i → eq i) a
fun3 : ∀{ℓ} → {A B : Set ℓ} → A ≡ B → A → B
fun3 eq a = {!!} -- C-u C-u C-c C-,
```
eq ' s type is :
```
eq : PathP (λ _ → Set .ℓ) .A .B
```
but the defintion of PathP is :
```
PathP : ∀ {ℓ} (A : I → Set ℓ) → A i0 → A i1 → Set ℓ
```
which means A B must be elements of Sets, not Sets.
Of course A ≡ B is a path inside Set ℓ , thus the definition of PathP makes
no sense with regards to Sets.
Another problem I am experiencing that might be related is that A=B
requires to be eta-abstracted to work like in the fun/fun2 case.
I also wonder why I cannot fill the hole with ```r i``` here :
https://github.com/xekoukou/cubical-demo/blob/agda-mailing-list/Univalence.agda#L115
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