[Agda] [newbie] universe levels and BUILTIN EQUALITY

Martin Stone Davis martin.stone.davis at gmail.com
Wed Jan 4 21:58:07 CET 2017


It's possible to define a kind of EQUALITY sorted in any universe we 
want. For example, Set₀:

data _≡_ {a} {A : Set a} (x : A) : A → Set₀
  where refl : x ≡ x

However, to be declarable as BUILTIN, the sort needs to be Set a. Why is 
it that way? It seems, to my naive eye, that it would be somehow simpler 
or more conservative to have it at the lowest level possible. What bad 
things would happen if it were required to be Set₀?



More information about the Agda mailing list