Path types - Type Theory

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Giovanni Santiago

So I'm trying to learn cubical type theory (specifically to use cubical agda), and there's one point that feels like I almost grasp it but not quite, and that's what exactly PathP is. I think I have a sort of intuition, so I wanted to ask if it's valid.

Is the difference between

p: I -> Type
PathP p (p i0) (p i1)

analogous to the difference between

B: A -> Type
Pi x. B x?


I believe so. At least, it seems to be typed similarly.