Incredibly slow type-level Nub

Nub.hs

{-# LANGUAGE DataKinds #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-}
module Nub where

import Data.Proxy
import Data.Type.Bool
import GHC.TypeLits

-- | Remove duplicates from a type-level list.
type family Nub xs where
  Nub '[] = '[]
  Nub (x ': xs) = x ': Nub (Remove x xs)

type family Remove x xs where
  Remove x '[]       = '[]
  Remove x (x ': ys) =      Remove x ys
  Remove x (y ': ys) = y ': Remove x ys

class KnownNats ns where
  natVals :: proxy ns -> [Integer]

instance KnownNats '[] where
  natVals _ = []

instance (KnownNat n, KnownNats ns) => KnownNats (n ': ns) where
  natVals _ = natVal (Proxy :: Proxy n) : natVals (Proxy :: Proxy ns)

type Example = '[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 1, 1, 1, 1]

exampleVals :: [Integer]
exampleVals = natVals (Proxy :: Proxy (Nub Example))