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{-# LANGUAGE GADTs #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE DataKinds, PolyKinds #-}
module T14040a where
import Data.Kind
data family Sing (a :: k)
data WeirdList :: Type -> Type where
WeirdNil :: WeirdList a
WeirdCons :: a -> WeirdList (WeirdList a) -> WeirdList a
data instance Sing (z :: WeirdList a) where
SWeirdNil :: Sing WeirdNil
SWeirdCons :: Sing w -> Sing wws -> Sing (WeirdCons w wws)
elimWeirdList :: forall (a :: Type) (wl :: WeirdList a)
(p :: forall (x :: Type). x -> WeirdList x -> Type).
Sing wl
-> (forall (y :: Type). p _ WeirdNil)
-> (forall (z :: Type) (x :: z) (xs :: WeirdList (WeirdList z)).
Sing x -> Sing xs -> p _ xs
-> p _ (WeirdCons x xs))
-> p _ wl
elimWeirdList SWeirdNil pWeirdNil _ = pWeirdNil
elimWeirdList (SWeirdCons (x :: Sing (x :: z))
(xs :: Sing (xs :: WeirdList (WeirdList z))))
pWeirdNil pWeirdCons
= pWeirdCons @z @x @xs x xs
(elimWeirdList @(WeirdList z) @xs @p xs pWeirdNil pWeirdCons)
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