{-# LANGUAGE DefaultSignatures #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# OPTIONS_GHC -fno-warn-orphans #-}
-- | Expression for 'List'.
module Language.Symantic.Expr.List where

import Data.Proxy (Proxy(..))
import Data.Type.Equality ((:~:)(Refl))

import Language.Symantic.Type
import Language.Symantic.Trans.Common
import Language.Symantic.Expr.Common
import Language.Symantic.Expr.Lambda
import Language.Symantic.Expr.Functor
import Language.Symantic.Expr.Applicative

-- * Class 'Sym_List_Lam'
-- | Symantic.
class Sym_List repr where
	list_empty :: repr [a]
	list_cons  :: repr a -> repr [a] -> repr [a]
	list       :: [repr a] -> repr [a]
	
	default list_empty :: Trans t repr => t repr [a]
	default list_cons  :: Trans t repr => t repr a -> t repr [a] -> t repr [a]
	default list       :: Trans t repr => [t repr a] -> t repr [a]
	list_empty = trans_lift list_empty
	list_cons  = trans_map2 list_cons
	list l     = trans_lift $ list (trans_apply Prelude.<$> l)
-- | Symantic requiring a 'Lambda'.
class Sym_List_Lam lam repr where
	list_filter
	 :: repr (Lambda lam a Bool)
	 -> repr [a]
	 -> repr [a]
	
	default list_filter
	 :: Trans t repr
	 => t repr (Lambda lam a Bool)
	 -> t repr [a]
	 -> t repr [a]
	list_filter = trans_map2 list_filter

-- * Type 'Expr_List'
-- | Expression.
data Expr_List (lam:: * -> *) (root:: *)
type instance Root_of_Expr      (Expr_List lam root)      = root
type instance Type_of_Expr      (Expr_List lam root)      = Type_List
type instance Sym_of_Expr       (Expr_List lam root) repr = (Sym_List repr, Sym_List_Lam lam repr)
type instance Error_of_Expr ast (Expr_List lam root)      = No_Error_Expr

instance Constraint_Type1 Functor_with_Lambda (Type_Type1 [] root) where
	constraint_type1 _c (Type_Type1 _ _) = Just Dict
instance Constraint_Type1 Applicative_with_Lambda (Type_Type1 [] root) where
	constraint_type1 _c (Type_Type1 _ _) = Just Dict

-- | Parsing utility to check that the given type is a 'Type_List'
-- or raise 'Error_Expr_Type_mismatch'.
check_type_list
 :: forall ast ex root ty h ret.
 ( root ~ Root_of_Expr ex
 , ty ~ Type_Root_of_Expr ex
 , Lift_Type   Type_List (Type_of_Expr root)
 , Unlift_Type Type_List (Type_of_Expr root)
 , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
                   (Error_of_Expr ast root)
 )
 => Proxy ex -> ast -> ty h
 -> (Type_List ty h -> Either (Error_of_Expr ast root) ret)
 -> Either (Error_of_Expr ast root) ret
check_type_list ex ast ty k =
	case unlift_type $ unType_Root ty of
	 Just ty_l -> k ty_l
	 Nothing -> Left $
		error_expr ex $
		Error_Expr_Type_mismatch ast
		 (Exists_Type (type_list $ type_var SZero
		 :: Type_Root_of_Expr ex [Zero]))
		 (Exists_Type ty)

-- | Parse 'list_empty'.
list_empty_from
 :: forall root lam ty ty_root ast hs ret.
 ( ty ~ Type_Root_of_Expr (Expr_List lam root)
 , ty_root ~ Type_Root_of_Expr root
 , Type_from ast ty_root
 , Lift_Type_Root Type_List ty_root
 , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
                   (Error_of_Expr ast root)
 , Root_of_Expr root ~ root
 ) => ast
 -> Expr_From ast (Expr_List lam root) hs ret
list_empty_from ast_ty_a ex ast _ctx k =
	either (\err -> Left $ error_expr ex $ Error_Expr_Type err ast) id $
	type_from (Proxy::Proxy ty_root) ast_ty_a $ \ty_a -> Right $
	k (type_list ty_a) $ Forall_Repr_with_Context $
		const list_empty

-- | Parse 'list_cons'.
list_cons_from
 :: forall root lam ty ast hs ret.
 ( ty ~ Type_Root_of_Expr (Expr_List lam root)
 , Eq_Type (Type_Root_of_Expr root)
 , Expr_from ast root
 , Lift_Type   Type_List (Type_of_Expr root)
 , Unlift_Type Type_List (Type_of_Expr root)
 , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
                   (Error_of_Expr ast root)
 , Root_of_Expr root ~ root
 ) => ast -> ast
 -> Expr_From ast (Expr_List lam root) hs ret
list_cons_from ast_a ast_l ex ast ctx k =
	expr_from (Proxy::Proxy root) ast_a ctx $
	 \(ty_a::Type_Root_of_Expr root h_a) (Forall_Repr_with_Context a) ->
	expr_from (Proxy::Proxy root) ast_l ctx $
	 \(ty_l::Type_Root_of_Expr root h_l) (Forall_Repr_with_Context l) ->
	check_type_list ex ast ty_l $ \(Type_Type1 _ ty_l_a) ->
	check_eq_type ex ast ty_a ty_l_a $ \Refl ->
	k (type_list ty_a) $ Forall_Repr_with_Context $
		\c -> list_cons (a c) (l c)

-- | Parse 'list'.
list_from
 :: forall root lam ex ty ty_root ast hs ret.
 ( ty ~ Type_Root_of_Expr (Expr_List lam root)
 , ty_root ~ Type_Root_of_Expr root
 , ex ~ Expr_List lam root
 , Eq_Type (Type_Root_of_Expr root)
 , Type_from ast ty_root
 , Expr_from ast root
 , Lift_Type   Type_List (Type_of_Expr root)
 , Unlift_Type Type_List (Type_of_Expr root)
 , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
                   (Error_of_Expr ast root)
 , Root_of_Expr root ~ root
 , Root_of_Type ty_root ~ ty_root
 ) => ast -> [ast]
 -> Expr_From ast ex hs ret
list_from ast_ty_a ast_as =
	case type_from (Proxy::Proxy ty_root)
	 ast_ty_a (Right . Exists_Type) of
	 Left err -> \ex ast _ctx _k -> Left $ error_expr ex $ Error_Expr_Type err ast
	 Right (Exists_Type ty_a) -> go ty_a [] ast_as
	where
	go :: Type_Root_of_Expr root ty_a
	   -> [Forall_Repr_with_Context root hs ty_a]
	   -> [ast]
	   -> Expr_From ast (Expr_List lam root) hs ret
	go ty_a as [] _ex _ast _ctx k =
		k (type_list ty_a) $ Forall_Repr_with_Context $
			\c -> list ((\(Forall_Repr_with_Context a) -> a c) Prelude.<$> reverse as)
	go ty_a as (ast_x:ast_xs) ex ast ctx k =
		expr_from (Proxy::Proxy root) ast_x ctx $
		 \(ty_x::Type_Root_of_Expr root h_x) x ->
		check_eq_type ex ast ty_a ty_x $ \Refl ->
		go ty_a (x:as) ast_xs ex ast ctx k

-- | Parse 'list_filter'.
list_filter_from
 :: forall root lam ty ty_root ast hs ret.
 ( ty ~ Type_Root_of_Expr (Expr_List lam root)
 , ty_root ~ Type_of_Expr root
 , Eq_Type (Type_Root_of_Expr root)
 , Expr_from ast root
 , Lift_Type   Type_Bool      ty_root
 , Lift_Type   (Type_Fun lam) ty_root
 , Unlift_Type (Type_Fun lam) ty_root
 , Lift_Type   Type_List      ty_root
 , Unlift_Type Type_List      ty_root
 , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
                   (Error_of_Expr ast root)
 , Root_of_Expr root ~ root
 ) => ast -> ast
 -> Expr_From ast (Expr_List lam root) hs ret
list_filter_from ast_f ast_l ex ast ctx k =
	expr_from (Proxy::Proxy root) ast_f ctx $
	 \(ty_f::Type_Root_of_Expr root h_f) (Forall_Repr_with_Context f) ->
	expr_from (Proxy::Proxy root) ast_l ctx $
	 \(ty_l::Type_Root_of_Expr root h_l) (Forall_Repr_with_Context l) ->
	check_type_fun ex ast ty_f $ \(ty_f_a `Type_Fun` ty_f_b
	 :: Type_Fun lam (Type_Root_of_Expr root) h_f) ->
	check_eq_type ex ast type_bool ty_f_b $ \Refl ->
	check_type_list ex ast ty_l $ \(Type_Type1 _ ty_l_a) ->
	check_eq_type ex ast ty_f_a ty_l_a $ \Refl ->
	k ty_l $ Forall_Repr_with_Context $
	 \c -> list_filter (f c) (l c)