{-# LANGUAGE DefaultSignatures #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}
-- | Expression for 'Int'.
module Language.LOL.Symantic.Expr.Int where

import Data.Proxy (Proxy(..))

import Language.LOL.Symantic.Type
import Language.LOL.Symantic.Expr.Common
import Language.LOL.Symantic.Expr.Lambda
import Language.LOL.Symantic.Repr.Dup
import Language.LOL.Symantic.Trans.Common

-- * Class 'Sym_Int'

-- | Symantic.
class Sym_Int repr where
	int ::      Int -> repr Int
	neg :: repr Int -> repr Int
	add :: repr Int -> repr Int -> repr Int
	
	default int :: Trans t repr =>        Int -> t repr Int
	default neg :: Trans t repr => t repr Int -> t repr Int
	default add :: Trans t repr => t repr Int -> t repr Int -> t repr Int
	int = trans_lift . int
	neg = trans_map1 neg
	add = trans_map2 add

instance -- Sym_Int Dup
 ( Sym_Int r1
 , Sym_Int r2
 ) => Sym_Int (Dup r1 r2) where
	int x = int x `Dup` int x
	neg (x1 `Dup` x2) = neg x1 `Dup` neg x2
	add (x1 `Dup` x2) (y1 `Dup` y2) = add x1 y1 `Dup` add x2 y2

-- * Type 'Expr_Int'
-- | Expression.
data Expr_Int (root:: *)
type instance Root_of_Expr      (Expr_Int root)      = root
type instance Type_of_Expr      (Expr_Int root)      = Type_Int
type instance Sym_of_Expr       (Expr_Int root) repr = Sym_Int repr
type instance Error_of_Expr ast (Expr_Int root)      = No_Error_Expr

-- ** Type 'Expr_Lambda_Int'
-- | Convenient alias.
type Expr_Lambda_Int lam = Expr_Root (Expr_Alt (Expr_Lambda lam) Expr_Int)

-- | Convenient alias around 'expr_from'.
expr_lambda_int_from
 :: forall lam ast.
 Expr_from ast (Expr_Lambda_Int lam)
 => Proxy lam
 -> ast
 -> Either (Error_of_Expr ast (Expr_Lambda_Int lam))
           (Exists_Type_and_Repr (Type_Root_of_Expr (Expr_Lambda_Int lam))
                                 (Forall_Repr (Expr_Lambda_Int lam)))
expr_lambda_int_from _lam ast =
	expr_from (Proxy::Proxy (Expr_Lambda_Int lam)) ast
	 Context_Empty $ \ty (Forall_Repr_with_Context repr) ->
		Right $ Exists_Type_and_Repr ty $
			Forall_Repr $ repr Context_Empty