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{-# LANGUAGE AllowAmbiguousTypes #-}
{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE ExistentialQuantification #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeInType #-}
{-# LANGUAGE TypeOperators #-}
module T14038 where
import Data.Kind (Type)
data family Sing (a :: k)
data instance Sing (z :: [a]) where
SNil :: Sing '[]
SCons :: Sing x -> Sing xs -> Sing (x:xs)
data TyFun :: Type -> Type -> Type
type a ~> b = TyFun a b -> Type
infixr 0 ~>
type family Apply (f :: k1 ~> k2) (x :: k1) :: k2
type a @@ b = Apply a b
infixl 9 @@
data FunArrow = (:->) -- ^ '(->)'
| (:~>) -- ^ '(~>)'
class FunType (arr :: FunArrow) where
type Fun (k1 :: Type) arr (k2 :: Type) :: Type
class FunType arr => AppType (arr :: FunArrow) where
type App k1 arr k2 (f :: Fun k1 arr k2) (x :: k1) :: k2
type FunApp arr = (FunType arr, AppType arr)
instance FunType (:->) where
type Fun k1 (:->) k2 = k1 -> k2
instance AppType (:->) where
type App k1 (:->) k2 (f :: k1 -> k2) x = f x
instance FunType (:~>) where
type Fun k1 (:~>) k2 = k1 ~> k2
instance AppType (:~>) where
type App k1 (:~>) k2 (f :: k1 ~> k2) x = f @@ x
infixr 0 -?>
type (-?>) (k1 :: Type) (k2 :: Type) (arr :: FunArrow) = Fun k1 arr k2
elimList :: forall (a :: Type) (p :: [a] -> Type) (l :: [a]).
Sing l
-> p '[]
-> (forall (x :: a) (xs :: [a]). Sing x -> Sing xs -> p xs -> p (x:xs))
-> p l
elimList = elimListPoly @(:->)
elimListTyFun :: forall (a :: Type) (p :: [a] ~> Type) (l :: [a]).
Sing l
-> p @@ '[]
-> (forall (x :: a) (xs :: [a]). Sing x -> Sing xs -> p @@ xs -> p @@ (x:xs))
-> p @@ l
elimListTyFun = elimListPoly @(:~>) @_ @p
elimListPoly :: forall (arr :: FunArrow) (a :: Type) (p :: ([a] -?> Type) arr) (l :: [a]).
FunApp arr
=> Sing l
-> App [a] arr Type p '[]
-> (forall (x :: a) (xs :: [a]). Sing x -> Sing xs -> App [a] arr Type p xs -> App [a] arr Type p (x:xs))
-> App [a] arr Type p l
elimListPoly SNil pNil _ = pNil
elimListPoly (SCons x (xs :: Sing xs)) pNil pCons = pCons x xs (elimListPoly @arr @a @p @xs xs pNil pCons)
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