content: {-# LANGUAGE TemplateHaskell, RankNTypes, TypeOperators, DataKinds,
               PolyKinds, TypeFamilies, GADTs, TypeInType #-}
  
  module RAE_T32a where
  
  import Data.Kind
  
  data family Sing (k :: Type) :: k -> Type
  
  data TyArr' (a :: Type) (b :: Type) :: Type
  type TyArr (a :: Type) (b :: Type) = TyArr' a b -> Type
  type family (a :: TyArr k1 k2) @@ (b :: k1) :: k2
  data TyPi' (a :: Type) (b :: TyArr a Type) :: Type
  type TyPi (a :: Type) (b :: TyArr a Type) = TyPi' a b -> Type
  type family (a :: TyPi k1 k2) @@@ (b :: k1) :: k2 @@ b
  $(return [])
  
  data MkStar (p :: Type) (x :: TyArr' p Type)
  type instance MkStar p @@ x = Type
  $(return [])
  
  data Sigma (p :: Type) (r :: TyPi p (MkStar p)) :: Type where
    Sigma ::
      forall (p :: Type) (r :: TyPi p (MkStar p)) (a :: p) (b :: r @@@ a).
      Sing Type p -> Sing (TyPi p (MkStar p)) r -> Sing p a -> Sing (r @@@ a) b -> Sigma p r
  $(return [])
  
  data instance Sing Sigma (Sigma p r) x where
    SSigma ::
      forall (p :: Type) (r :: TyPi p (MkStar p)) (a :: p) (b :: r @@@ a)
      (sp :: Sing Type p) (sr :: Sing (TyPi p (MkStar p)) r) (sa :: Sing p a) (sb :: Sing (r @@@ a) b).
      Sing (Sing (r @@@ a) b) sb ->
      Sing (Sigma p r) ('Sigma sp sr sa sb)
  
  -- I (RAE) believe this last definition is ill-typed.
  