{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}
module Language.Symantic.Type.Tuple where

import Data.Maybe (isJust)
import Data.Type.Equality ((:~:)(Refl))

import Language.Symantic.Type.Common
import Language.Symantic.Type.Fun
import Language.Symantic.Type.Bool
import Language.Symantic.Type.Var

-- * Type 'Type_Tuple2'
-- | The 'Tuple' type.
data Type_Tuple2 root h where
	Type_Tuple2 :: root h_a
	            -> root h_b
	            -> Type_Tuple2 root (h_a, h_b)

type instance Root_of_Type      (Type_Tuple2 root) = root
type instance Error_of_Type ast (Type_Tuple2 root) = No_Error_Type

instance -- Eq_Type
 Eq_Type root =>
 Eq_Type (Type_Tuple2 root) where
	eq_type (Type_Tuple2 a1 b1) (Type_Tuple2 a2 b2)
	 | Just Refl <- a1 `eq_type` a2
	 , Just Refl <- b1 `eq_type` b2
	 = Just Refl
	eq_type _ _ = Nothing
instance -- Eq
 Eq_Type root =>
 Eq (Type_Tuple2 root h) where
	x == y = isJust $ eq_type x y
instance -- String_from_Type
 String_from_Type root =>
 String_from_Type (Type_Tuple2 root) where
	string_from_type (Type_Tuple2 a b) =
		"Tuple (" ++ string_from_type a ++
		 ", " ++ string_from_type b ++ ")"
instance -- Show
 String_from_Type root =>
 Show (Type_Tuple2 root h) where
	show = string_from_type

-- | Convenient alias to include a 'Type_Tuple2' within a type.
type_tuple2
 :: Type_Root_Lift Type_Tuple2 root
 => root h_a
 -> root h_b
 -> root (h_a, h_b)
type_tuple2 a b = type_root_lift (Type_Tuple2 a b)

-- * Type 'Type_Fun_Bool_Tuple2'
-- | Convenient alias.
type Type_Fun_Bool_Tuple2 lam
 = Type_Root (Type_Alt Type_Var
             (Type_Alt (Type_Fun lam)
             (Type_Alt Type_Bool
                       Type_Tuple2)))