{-# LANGUAGE TypeSynonymInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE TypeFamilies #-}

module MyLang where

import Prelude (($),(.))
import qualified Prelude as P

import Generic.Data.Bool
import Generic.Data.Num

newtype MyLang a = ML {unML :: a}

type Bool = MyLang (TBool MyLang)
type Number a = MyLang (TNum MyLang a)
type Integer = Number P.Integer

instance BoolC MyLang where
  data TBool MyLang = MyTrue | MyFalse
  true  = ML MyTrue
  false = ML MyFalse
  bool t _ (ML MyTrue) = t
  bool _ e (ML MyFalse) = e

instance (P.Num a) => Num MyLang a where
  data TNum MyLang a = MyNumber a
  fromInteger = ML . MyNumber . P.fromInteger
  abs = liftNum P.abs
  signum = liftNum P.signum
  (+) = liftNum2 (P.+)
  (-) = liftNum2 (P.-)
  (*) = liftNum2 (P.*)
  negate = liftNum P.negate

liftNum f (ML (MyNumber a)) = ML $ MyNumber $ f a
liftNum2 f (ML (MyNumber a)) (ML (MyNumber b)) = ML $ MyNumber $ f a b

test :: Integer
test = if' true (3 + 4) (4)