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

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

import Language.Symantic.Repr.Dup
import Language.Symantic.Trans.Common
import Language.Symantic.Type
import Language.Symantic.Expr.Common
import Language.Symantic.Expr.Eq

-- * Class 'Sym_Ord'
-- | Symantic.
class Sym_Eq repr => Sym_Ord repr where
	compare :: Ord a => repr a -> repr a -> repr Ordering
	default compare :: (Trans t repr, Ord a)
	                => t repr a -> t repr a -> t repr Ordering
	compare = trans_map2 compare

instance (Sym_Ord r1, Sym_Ord r2) => Sym_Ord (Dup r1 r2) where
	compare (x1 `Dup` x2) (y1 `Dup` y2) =
		compare x1 y1 `Dup`
		compare x2 y2

-- * Type 'Expr_Ord'
-- | Expression.
data Expr_Ord (root:: *)
type instance Root_of_Expr      (Expr_Ord root)      = root
type instance Type_of_Expr      (Expr_Ord root)      = No_Type
type instance Sym_of_Expr       (Expr_Ord root) repr = (Sym_Ord repr)
type instance Error_of_Expr ast (Expr_Ord root)      = No_Error_Expr

compare_from
 :: forall root ty ast hs ret.
 ( ty ~ Type_Root_of_Expr (Expr_Ord root)
 , Type_Root_Lift Type_Ordering (Type_Root_of_Expr root)
 , Eq_Type (Type_Root_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
 , Constraint_Type Ord ty
 ) => ast -> ast
 -> Expr_From ast (Expr_Ord root) hs ret
compare_from ast_x ast_y ex ast ctx k =
	expr_from (Proxy::Proxy root) ast_x ctx $
	 \(ty_x::Type_Root_of_Expr root h_x) (Forall_Repr_with_Context x) ->
	expr_from (Proxy::Proxy root) ast_y ctx $
	 \(ty_y::Type_Root_of_Expr root h_y) (Forall_Repr_with_Context y) ->
	check_eq_type ex ast ty_x ty_y $ \Refl ->
	check_constraint_type ex (Proxy::Proxy Ord) ast ty_x $ \Dict ->
		k type_ordering $ Forall_Repr_with_Context $
		 \c -> x c `compare` y c