{-# LANGUAGE DefaultSignatures #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}
-- | Expression for /lambda abstraction/s
-- in /Higher-Order Abstract Syntax/ (HOAS).
module Language.LOL.Symantic.Expr.Lambda where

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

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

-- * Class 'Sym_Lambda'

-- | Symantic.
--
-- NOTE: argument @arg@ and result @res@ of 'Lambda'
-- wrapped inside 'lam': to control the calling
-- in the 'Repr_Host' instance.
--
-- NOTE: the default definitions supplied for:
-- 'app', 'inline', 'val' and 'lazy'
-- are there to avoid boilerplate code
-- when writting 'Trans' instances which
-- do not need to alterate those methods.
class (lam ~ Lambda_from_Repr repr) => Sym_Lambda lam repr where
	-- | This type constructor is used like
	-- the functional dependency: @repr -> lam@
	-- (ie. knowing @repr@ one can determine @lam@)
	-- in order to avoid to introduce a 'Proxy' @lam@
	-- in 'let_inline', 'let_val' and 'let_lazy'.
	--
	-- Distinguishing between @lam@ and @repr@ is used to maintain
	-- the universal polymorphism of @repr@ in 'Expr_from',
	-- the downside with this however is that
	-- to be an instance of 'Sym_Lambda' for all @lam@,
	-- the @repr@ type of an interpreter
	-- has to be parameterized by @lam@,
	-- even though it does not actually need @lam@ to do its work.
	--
	-- Basically this means having sometimes to add a type annotation
	-- to the interpreter call to specify @lam@.
	type Lambda_from_Repr repr :: {-lam-}(* -> *)
	
	-- | Lambda application.
	app :: repr (Lambda lam arg res) -> repr arg -> repr res
	
	-- | /Call-by-name/ lambda.
	inline :: (repr arg -> repr res) -> repr (Lambda lam arg res)
	-- | /Call-by-value/ lambda.
	val    :: (repr arg -> repr res) -> repr (Lambda lam arg res)
	-- | /Call-by-need/ lambda (aka. /lazyness/): lazy shares its argument, no matter what.
	lazy   :: (repr arg -> repr res) -> repr (Lambda lam arg res)
	
	default app    :: Trans t repr => t repr (Lambda lam arg res) -> t repr arg -> t repr res
	default inline :: Trans t repr => (t repr arg -> t repr res) -> t repr (Lambda lam arg res)
	default val    :: Trans t repr => (t repr arg -> t repr res) -> t repr (Lambda lam arg res)
	default lazy   :: Trans t repr => (t repr arg -> t repr res) -> t repr (Lambda lam arg res)
	app  f x = trans_lift $ trans_apply f `app` trans_apply x
	inline f = trans_lift $ inline $ trans_apply . f . trans_lift
	val    f = trans_lift $ val    $ trans_apply . f . trans_lift
	lazy   f = trans_lift $ lazy   $ trans_apply . f . trans_lift
	
	-- | Convenient 'inline' wrapper.
	let_inline
	 :: Sym_Lambda lam repr
	 => repr var -> (repr var -> repr res) -> repr res
	let_inline x y = inline y `app` x
	-- | Convenient 'val' wrapper.
	let_val
	 :: Sym_Lambda lam repr
	 => repr var -> (repr var -> repr res) -> repr res
	let_val x y = val y `app` x
	-- | Convenient 'lazy' wrapper.
	let_lazy
	 :: Sym_Lambda lam repr
	 => repr var -> (repr var -> repr res) -> repr res
	let_lazy x y = lazy y `app` x

infixl 5 `app`

instance -- Sym_Lambda Dup
 ( Sym_Lambda lam r1
 , Sym_Lambda lam r2
 ) => Sym_Lambda lam (Dup r1 r2) where
	type Lambda_from_Repr (Dup r1 r2) = Lambda_from_Repr r1
	app (f1 `Dup` f2) (x1 `Dup` x2) = app f1 x1 `Dup` app f2 x2
	inline f = dup1 (inline f) `Dup` dup2 (inline f)
	val    f = dup1 (val f)    `Dup` dup2 (val f)
	lazy   f = dup1 (lazy f)   `Dup` dup2 (lazy f)

-- * Type 'Expr_Lambda'
-- | Expression.
data Expr_Lambda (lam:: * -> *) (root:: *)
type instance Root_of_Expr      (Expr_Lambda lam root)      = root
type instance Type_of_Expr      (Expr_Lambda lam root)      = Type_Fun lam
type instance Sym_of_Expr       (Expr_Lambda lam root) repr = Sym_Lambda lam repr
type instance Error_of_Expr ast (Expr_Lambda lam root)      = Error_Expr_Lambda ast

var_from
 :: forall ast lam root hs ret.
 ( Type_from ast (Type_Root_of_Expr root)
 , Error_Expr_Lift (Error_Expr_Lambda ast)
                   (Error_of_Expr ast root)
 , Root_of_Expr root ~ root
 ) => Text -> Expr_From ast (Expr_Lambda lam root) hs ret
var_from name _px_ex ast = go
	where
	go :: forall ex hs'. (ex ~ (Expr_Lambda lam root))
	 => Context (Lambda_Var (Type_Root_of_Expr ex)) hs'
	 -> ( forall h. Type_Root_of_Expr ex h
	    -> Forall_Repr_with_Context ex hs' h
	    -> Either (Error_of_Expr ast (Root_of_Expr ex)) ret )
	 ->    Either (Error_of_Expr ast (Root_of_Expr ex)) ret
	go c k' =
		case c of
		 Context_Empty -> Left $ error_expr_lift $
			Error_Expr_Lambda_Var_unbound name ast
		 Lambda_Var n ty `Context_Next` _ | n == name ->
			k' ty $ Forall_Repr_with_Context $
			 \(repr `Context_Next` _) -> repr
		 _ `Context_Next` ctx' ->
			go ctx' $ \ty (Forall_Repr_with_Context repr) ->
				k' ty $ Forall_Repr_with_Context $
				 \(_ `Context_Next` c') -> repr c'

app_from
 :: forall ty ast lam root hs ret.
 ( ty ~ Type_Root_of_Expr root
 , Type_from ast ty
 , Expr_from ast root
 , Type_Root_Lift (Type_Fun lam) ty
 , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
                   (Error_of_Expr ast root)
 , Type_Unlift (Type_Fun lam) (Type_of_Expr root)
 , Root_of_Expr root ~ root
 ) => ast -> ast
 -> Expr_From ast (Expr_Lambda lam root) hs ret
app_from ast_lam ast_arg_actual px_ex ast ctx k =
	expr_from (Proxy::Proxy root) ast_lam ctx $
	 \(ty_lam::Type_Root_of_Expr root h_lam) (Forall_Repr_with_Context lam) ->
	expr_from (Proxy::Proxy root) ast_arg_actual ctx $
	 \(ty_arg_actual::Type_Root_of_Expr root h_arg_actual)
	  (Forall_Repr_with_Context arg_actual) ->
		case type_unlift $ unType_Root ty_lam of
		 Nothing -> Left $
			error_expr px_ex $
			Error_Expr_Type_mismatch ast
			 (Exists_Type (type_var SZero `type_fun` type_var (SSucc SZero)
			 :: Type_Root_of_Expr (Expr_Lambda lam root) (lam Zero -> lam (Succ Zero))))
			 (Exists_Type ty_lam)
		 Just (ty_arg_expected `Type_Fun` ty_res
		  :: Type_Fun lam (Type_Root_of_Expr root) h_lam) ->
			when_type_eq px_ex ast
			 ty_arg_expected ty_arg_actual $ \Refl ->
				k ty_res $ Forall_Repr_with_Context $
				 \c -> lam c `app` arg_actual c

lam_from
 :: forall ty ast lam root hs ret.
 ( ty ~ Type_Root_of_Expr root
 , Type_from ast ty
 , Expr_from ast root
 , Type_Root_Lift (Type_Fun lam) ty
 , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
                   (Error_of_Expr ast root)
 , Root_of_Expr root ~ root
 ) => (forall repr arg res
      . Sym_Lambda lam repr
      => (repr arg -> repr res)
      -> repr (Lambda lam arg res))
 -> Text -> ast -> ast
 -> Expr_From ast (Expr_Lambda lam root) hs ret
lam_from lam name ast_ty_arg ast_body px_ex ast ctx k =
	case type_from
	 (Proxy::Proxy (Type_Root_of_Expr root))
	 ast_ty_arg (Right . Exists_Type) of
	 Left err -> Left $ error_expr px_ex $ Error_Expr_Type err ast
	 Right (Exists_Type (ty_arg::Type_Root_of_Expr root h_arg)) ->
		expr_from (Proxy::Proxy root) ast_body
		 (Lambda_Var name ty_arg `Context_Next` ctx) $
		 \(ty_res::Type_Root_of_Expr root h_res) (Forall_Repr_with_Context res) ->
			k (ty_arg `type_fun` ty_res
			 :: Root_of_Type (Type_Root_of_Expr root)
			                 (Lambda lam h_arg h_res)) $
			Forall_Repr_with_Context $
			 \c -> lam $
				 \arg -> res (arg `Context_Next` c)

let_from
 :: forall ty ast lam root hs ret.
 ( ty ~ Type_Root_of_Expr root
 , Type_from ast ty
 , Expr_from ast root
 , Type_Root_Lift (Type_Fun lam) ty
 , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
                   (Error_of_Expr ast root)
 , Root_of_Expr root ~ root
 ) => (forall repr var res. Sym_Lambda lam repr
      => repr var -> (repr var -> repr res) -> repr res)
 -> Text -> ast -> ast
 -> Expr_From ast (Expr_Lambda lam root) hs ret
let_from let_ name ast_var ast_body _px_ex _ast ctx k =
	expr_from (Proxy::Proxy root) ast_var ctx $
	 \(ty_var::Type_Root_of_Expr root h_var) (Forall_Repr_with_Context var) ->
		expr_from (Proxy::Proxy root) ast_body
		 (Lambda_Var name ty_var `Context_Next` ctx) $
		 \(ty_res::Type_Root_of_Expr root h_res) (Forall_Repr_with_Context res) ->
			k ty_res $ Forall_Repr_with_Context $
			 \c -> let_ (var c) $
				 \arg -> res (arg `Context_Next` c)

-- * Type 'Error_Expr_Lambda'
data Error_Expr_Lambda ast
 =   Error_Expr_Lambda_Var_unbound Lambda_Var_Name ast
 deriving (Eq, Show)