[Agda] type:type locally?

[Thorsten Altenkirch]

I can switch off positivity checking locally by saying

{-# NO_POSITIVITY_CHECK #-}

But I can’t say

{-# TYPE-IN-TYPE #-}
data Prop : Set
T : Prop → Set

data Prop where
  pi : (A : Set)(b : A → Prop) → Prop

T (pi A b) = (x : A) → T (b x)

Or is there a difference syntax? This would be useful for a simple-minded encoding of the calculus of constructions.

Thorsten

P.S. I know I can avoid this by adding another level:

data Prop : Set
T : Prop → Set
data U : Set
El : U → Set

{-# NO_POSITIVITY_CHECK #-}
data U where
  prop : U
  pi : (a : U)(b : El a → U) → U
  emb : Prop → U

El prop = Prop
El (pi a b) = (x : El a) → El (b x)
El (emb p) = T p

data Prop where
  pi : (a : U)(b : El a → Prop) → Prop

T (pi a b) = (x : El a) → T (b x)



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