{-# LANGUAGE DefaultSignatures #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
-- | Expression for 'Applicative'.
module Language.Symantic.Expr.Applicative where

import Control.Applicative (Applicative)
import Data.Proxy (Proxy(..))
import Data.Type.Equality ((:~:)(Refl))
import Prelude hiding (Applicative(..))

import Language.Symantic.Type
-- import Language.Symantic.Repr.Dup
import Language.Symantic.Trans.Common
import Language.Symantic.Expr.Common
import Language.Symantic.Expr.Lambda
import Language.Symantic.Expr.Functor

class Sym_Applicative repr where
	pure  :: Applicative f => repr a -> repr (f a)
	-- (*>)  :: Applicative f => repr (f a) -> repr (f b) -> repr (f b)
	-- (<*)  :: Applicative f => repr (f a) -> repr (f b) -> repr (f a)
	
	default pure :: (Trans t repr, Applicative f) => t repr a -> t repr (f a)
	pure = trans_map1 pure

class Sym_Functor lam repr => Sym_Applicative_Lam lam repr where
	(<*>) :: Applicative f => repr (f (Lambda lam a b)) -> repr (f a) -> repr (f b)
	-- (*>)  :: Applicative f => repr (f a) -> repr (f b) -> repr (f b)
	-- (<*)  :: Applicative f => repr (f a) -> repr (f b) -> repr (f a)
	
	default (<*>) :: (Trans t repr, Applicative f) => t repr (f (Lambda lam a b)) -> t repr (f a) -> t repr (f b)
	-- default (*>)  :: (Trans t, Applicative f) => t repr (f a) -> t repr (f b) -> t repr (f b)
	-- default (<*)  :: (Trans t, Applicative f) => t repr (f a) -> t repr (f b) -> t repr (f a)
	(<*>) = trans_map2 (<*>)

-- * Type 'Expr_Applicative'
-- | Expression.
data Expr_Applicative (lam:: * -> *) (root:: *)
type instance Root_of_Expr      (Expr_Applicative lam root)      = root
type instance Type_of_Expr      (Expr_Applicative lam root)      = No_Type
type instance Sym_of_Expr       (Expr_Applicative lam root) repr = (Sym_Applicative repr, Sym_Applicative_Lam lam repr)
type instance Error_of_Expr ast (Expr_Applicative lam root)      = No_Error_Expr

-- * Class 'Type1_from'
-- | Parse given @ast@ into a 'Root_of_Type',
-- or return an 'Error_of_Type'.
class Type1_from ast (ty:: * -> *) where
	type1_from
	 :: Proxy ty
	 -> ast
	 -> (forall h. (Root_of_Type ty h -> Root_of_Type ty h)
	            -> Either (Error_of_Type ast (Root_of_Type ty)) ret)
	 ->            Either (Error_of_Type ast (Root_of_Type ty)) ret

pure_from
 :: forall root ty lam ast hs ret.
 ( ty ~ Type_Root_of_Expr (Expr_Applicative lam root)
 , Eq_Type (Type_Root_of_Expr root)
 , Type1_from ast (Type_of_Expr root)
 , Expr_from ast root
 , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
                   (Error_of_Expr ast root)
 , Root_of_Expr root ~ root
 , Constraint1_Type Functor_with_Lambda ty
 , Constraint1_Type Applicative ty
 ) => ast -> ast
 -> Expr_From ast (Expr_Applicative lam root) hs ret
pure_from ast_f ast_a ex ast ctx k =
 -- pure :: Applicative f => a -> f a
	case type1_from (Proxy::Proxy ty_root)
	 ast_f (Right . Exists_Type1) of
	 Left err -> Left $ error_expr ex $ Error_Expr_Type err ast
	 Right (Exists_Type1 ty_f) ->
		expr_from (Proxy::Proxy root) ast_a ctx $
		 \(ty_a::Type_Root_of_Expr root h_a) (Forall_Repr_with_Context a) ->
		let ty_fa = (Type_Root $ ty_f $ Type_Type1 f ty_a) in
		check_constraint1_type ex (Proxy::Proxy Applicative) ast ty_fa $ \Dict ->
		k ty_fa $ Forall_Repr_with_Context $
		 \c -> pure (a c)

ltstargt_from
 :: forall root ty lam ast hs ret.
 ( ty ~ Type_Root_of_Expr (Expr_Applicative lam root)
 , Eq_Type (Type_Root_of_Expr root)
 , Expr_from ast root
 , Type_Lift   (Type_Fun lam) (Type_of_Expr root)
 , Type_Unlift (Type_Fun lam) (Type_of_Expr root)
 , Type_Unlift1 (Type_of_Expr root)
 , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
                   (Error_of_Expr ast root)
 , Root_of_Expr root ~ root
 , Constraint1_Type Applicative ty
 ) => ast -> ast
 -> Expr_From ast (Expr_Applicative lam root) hs ret
ltstargt_from ast_g ast_fa ex ast ctx k =
 -- (<*>) :: Applicative f => f (a -> b) -> f a -> f b
	expr_from (Proxy::Proxy root) ast_g ctx $
	 \(ty_fg::Type_Root_of_Expr root h_fg) (Forall_Repr_with_Context fg) ->
	expr_from (Proxy::Proxy root) ast_fa ctx $
	 \(ty_fa::Type_Root_of_Expr root h_fa) (Forall_Repr_with_Context fa) ->
	check_type1 ex ast ty_fg $ \(Type_Type1 _f (ty_g::Type_Root_of_Expr root h_g), _) ->
	check_type_fun ex ast ty_g $ \(ty_g_a `Type_Fun` ty_g_b
	 :: Type_Fun lam (Type_Root_of_Expr root) h_g) ->
	check_type1 ex ast ty_fa $ \(Type_Type1 f ty_fa_a, Type_Lift1 ty_f) ->
	check_constraint1_type ex (Proxy::Proxy Applicative) ast ty_fa $ \Dict ->
	check_eq_type ex ast ty_g_a ty_fa_a $ \Refl ->
	k (Type_Root $ ty_f $ Type_Type1 f ty_g_b) $ Forall_Repr_with_Context $
	 \c -> (<*>) (fg c) (fa c)