I was wondering if it is possible to sort types in hakell and if so what language extension I should use. Not sure if
this is possible but here is my attempt:

(I'm aware I don't need so many pragmas

{-# LANGUAGE GADTs #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE TypeSynonymInstances #-}
data Z=Z deriving (Show)
data S i=S i deriving (Show)
data family N a
type family Add n m
type instance Add Z m = m
type instance Add m Z = m
type instance Add (S n) (S m) = S (S (Add n m))
--14
type family LT a b
data Cat=Cat
data Dog=Dog
data Fish=Fish
type family Sort a --19
data And a b=And a b

type instance LT Dog Z = Cat
type instance LT Fish Z = Dog
type instance LT a (S i) = LT (LT a Z) i
type instance Sort (And a (LT a i))=And (LT a i) a

I get the following error:

  Illegal type synonym family application in instance: And a (LT a i)
  In the type synonym instance declaration for 'Sort'
Failed, modules loaded: none,