{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}
module Language.Symantic.Type.Int 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_Int'
-- | The 'Int' type.
data Type_Int (root:: * -> *) h where
	Type_Int :: Type_Int root Int
type instance Root_of_Type      (Type_Int root) = root
type instance Error_of_Type ast (Type_Int root) = No_Error_Type

instance -- Type_Eq
 Type_Eq (Type_Int root) where
	type_eq Type_Int Type_Int = Just Refl
instance -- Eq
 Eq (Type_Int root h) where
	x == y = isJust $ x `type_eq` y
instance -- String_from_Type
 String_from_Type (Type_Int root) where
	string_from_type Type_Int = "Int"
instance -- Show
 Show (Type_Int root h) where
	show = string_from_type
instance Type_Constraint Eq (Type_Int root) where
	type_constraint _c Type_Int = Just Dict
instance Type_Constraint Ord (Type_Int root) where
	type_constraint _c Type_Int = Just Dict

-- | Convenient alias to include a 'Type_Int' within a type.
type_int :: Type_Root_Lift Type_Int root => root Int
type_int = type_root_lift Type_Int

-- * Type 'Type_Fun_Int'
-- | Convenient alias.
type Type_Fun_Int lam
 = Type_Root (Type_Alt  Type_Var
             (Type_Alt (Type_Fun lam)
                        Type_Int))

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