{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-}
{-# OPTIONS_GHC -fno-warn-orphans #-}
module Language.Symantic.Type.Type0 where

import Data.Maybe (isJust)
import Data.Proxy
import Data.Type.Equality ((:~:)(Refl))
import GHC.Prim (Constraint)

import Language.Symantic.Lib.Data.Peano
import Language.Symantic.Type.Root
import Language.Symantic.Type.Alt
import Language.Symantic.Type.Error

-- ** Type 'Dict'
-- | 'Dict' captures the dictionary of a 'Constraint':
-- pattern matching on the 'Dict' constructor
-- brings the 'Constraint' into scope.
data Dict :: Constraint -> * where
	Dict :: c => Dict c

-- * Type 'No_Type'
-- | A discarded type.
data No_Type (root:: * -> *) h
 =   No_Type (root h)
 deriving (Eq, Show)

-- * Class 'Eq_Type'
-- | Test two types for equality,
-- returning an Haskell type-level proof
-- of the equality when it holds.
class Eq_Type (ty:: * -> *) where
	eq_type :: forall h1 h2. ty h1 -> ty h2 -> Maybe (h1 :~: h2)
instance -- Type_Root
 Eq_Type (ty (Type_Root ty)) =>
 Eq_Type (Type_Root ty) where
	eq_type (Type_Root x) (Type_Root y) = x `eq_type` y
instance -- Eq Type_Root
 Eq_Type (Type_Root ty) =>
 Eq (Type_Root ty h) where
	x == y = isJust $ x `eq_type` y
instance -- Type_Alt
 ( Eq_Type (curr root)
 , Eq_Type (next root)
 ) => Eq_Type (Type_Alt curr next root) where
	eq_type (Type_Alt_Curr x) (Type_Alt_Curr y) = x `eq_type` y
	eq_type (Type_Alt_Next x) (Type_Alt_Next y) = x `eq_type` y
	eq_type _ _ = Nothing
instance -- Eq Type_Alt
 ( Eq_Type (curr root)
 , Eq_Type (next root)
 ) => Eq (Type_Alt curr next root h) where
	x == y = isJust $ x `eq_type` y

-- * Class 'Constraint_Type'
-- | Test if a type satisfies a given 'Constraint',
-- returning an Haskell type-level proof
-- of that satisfaction when it holds.
class Constraint_Type (c:: * -> Constraint) (ty:: * -> *) where
	constraint_type :: forall h. Proxy c -> ty h -> Maybe (Dict (c h))
	constraint_type _c _ = Nothing
instance -- Type_Root
 Constraint_Type c (ty (Type_Root ty)) =>
 Constraint_Type c (Type_Root ty) where
	constraint_type c (Type_Root ty) = constraint_type c ty
instance -- Type_Alt
 ( Constraint_Type c (curr root)
 , Constraint_Type c (next root)
 ) => Constraint_Type c (Type_Alt curr next root) where
	constraint_type c (Type_Alt_Curr ty) = constraint_type c ty
	constraint_type c (Type_Alt_Next ty) = constraint_type c ty

-- * Class 'Type_from'
-- | Parse given @ast@ into a 'Root_of_Type',
-- or return an 'Error_of_Type'.
--
-- NOTE: making a distinction between @ty@ and 'Root_of_Type'@ ty@,
-- instead of having only a @root@ variable
-- is what enables to define many instances, one per type.
class Type_from ast (ty:: * -> *) where
	type_from
	 :: Proxy ty
	 -> ast
	 -> (forall 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
instance -- Type_Root
 ( Eq_Type (Type_Root ty)
 , Type_from ast (ty (Type_Root ty))
 , Root_of_Type (ty (Type_Root ty)) ~ Type_Root ty
 ) => Type_from ast (Type_Root ty) where
	type_from _ty = type_from (Proxy::Proxy (ty (Type_Root ty)))
instance -- Type_Alt
 ( Eq_Type (curr root)
 , Type_from ast (curr root)
 , Type_from ast (next root)
 , Root_of_Type (curr root) ~ root
 , Root_of_Type (next root) ~ root
 , Unlift_Error_Type (Error_Type ast) (Error_of_Type ast root)
 ) => Type_from ast (Type_Alt curr next root) where
	type_from _ty ast k =
		case type_from (Proxy::Proxy (curr root)) ast (Right . k) of
		 Right ret -> ret
		 Left err ->
			case unlift_error_type err of
			 Just (Error_Type_Unsupported_here (_::ast)) ->
				type_from (Proxy::Proxy (next root)) ast k
			 _ -> Left err

-- * Class 'String_from_Type'
-- | Return a 'String' from a type.
class String_from_Type ty where
	string_from_type :: ty h -> String
instance -- Type_Root
 String_from_Type (ty (Type_Root ty)) =>
 String_from_Type (Type_Root ty) where
	string_from_type (Type_Root ty) = string_from_type ty
instance -- Show Type_Root
 String_from_Type (Type_Root ty) =>
 Show (Type_Root ty h) where
	show = string_from_type
instance -- Type_Alt
 ( String_from_Type (curr root)
 , String_from_Type (next root)
 ) => String_from_Type (Type_Alt curr next root) where
	string_from_type (Type_Alt_Curr t) = string_from_type t
	string_from_type (Type_Alt_Next t) = string_from_type t

-- * Type 'Type_Type0'
-- | A type of kind @*@.
data Type_Type0 px (root:: * -> *) h where
	Type_Type0 :: px -> Type_Type0 px root (Host0_of px)

type instance Root_of_Type      (Type_Type0 px root) = root
type instance Error_of_Type ast (Type_Type0 px root) = No_Error_Type

instance -- Eq_Type
 Eq_Type (Type_Type0 (Proxy h0) root) where
	eq_type Type_Type0{} Type_Type0{} = Just Refl
instance -- Eq_Type
 Eq_Type (Type_Type0 EPeano root) where
	eq_type (Type_Type0 p1)
	        (Type_Type0 p2)
	 | p1 == p2
	 = Just Refl
	eq_type _ _ = Nothing
instance -- Eq
 Eq_Type (Type_Type0 px root) =>
 Eq (Type_Type0 px root h) where
	x == y = isJust $ x `eq_type` y
instance -- Show
 String_from_Type (Type_Type0 (Proxy h0) root) =>
 Show (Type_Type0 (Proxy h0) root h0) where
	show = string_from_type
instance Eq h0 => Constraint_Type Eq (Type_Type0 (Proxy h0) root) where
	constraint_type _c Type_Type0{} = Just Dict
instance Ord h0 => Constraint_Type Ord (Type_Type0 (Proxy h0) root) where
	constraint_type _c Type_Type0{} = Just Dict

-- | Convenient alias to include a 'Type_Type0' within a type.
type_type0 :: forall root h0. Lift_Type_Root (Type_Type0 (Proxy h0)) root => root h0
type_type0 = lift_type_root (Type_Type0 (Proxy::Proxy h0))

-- ** Type family 'Host0_of'
type family Host0_of px :: *
type instance Host0_of (Proxy h0) = h0

-- ** Type 'Lift_Type'
-- | Apply 'Peano_of_Type' on 'Lift_TypeP'.
type Lift_Type ty tys
 =   Lift_TypeP (Peano_of_Type ty tys) ty tys
instance
 Lift_Type ty root =>
 Lift_Type_Root ty (Type_Root root) where
	lift_type_root = Type_Root . lift_type

-- *** Type 'Peano_of_Type'
-- | Return a 'Peano' number derived from the location
-- of a given type within a given type stack,
-- which is used to avoid @OverlappingInstances@.
type family Peano_of_Type
 (ty::  (* -> *) -> * -> *)
 (tys:: (* -> *) -> * -> *) :: * where
	Peano_of_Type ty    ty                   = Zero
	Peano_of_Type ty    (Type_Alt ty   next) = Zero
	Peano_of_Type other (Type_Alt curr next) = Succ (Peano_of_Type other next)

-- *** Class 'Lift_TypeP'
-- | Lift a given type to the top of a given type stack including it,
-- by constructing the appropriate sequence of 'Type_Alt_Curr' and 'Type_Alt_Next'.
class Lift_TypeP (p:: *) ty tys where
	lift_typeP :: forall (root:: * -> *) h. Proxy p -> ty root h -> tys root h
instance Lift_TypeP Zero curr curr where
	lift_typeP _ = id
instance Lift_TypeP Zero curr (Type_Alt curr next) where
	lift_typeP _ = Type_Alt_Curr
instance
 Lift_TypeP p other next =>
 Lift_TypeP (Succ p) other (Type_Alt curr next) where
	lift_typeP _ = Type_Alt_Next . lift_typeP (Proxy::Proxy p)

-- | Convenient wrapper around 'lift_typeP',
-- passing it the 'Peano' number from 'Peano_of_Type'.
lift_type
 :: forall ty tys (root:: * -> *) h.
 Lift_Type ty tys =>
 ty root h -> tys root h
lift_type = lift_typeP (Proxy::Proxy (Peano_of_Type ty tys))

-- ** Type 'Unlift_Type'
-- | Apply 'Peano_of_Type' on 'Unlift_TypeP'.
type Unlift_Type ty tys
 =   Unlift_TypeP (Peano_of_Type ty tys) ty tys

-- *** Class 'Unlift_TypeP'
-- | Try to unlift a given type out of a given type stack including it,
-- by deconstructing the appropriate sequence of 'Type_Alt_Curr' and 'Type_Alt_Next'.
class Unlift_TypeP (p:: *) ty tys where
	type_unliftN :: forall (root:: * -> *) h. Proxy p -> tys root h -> Maybe (ty root h)
instance Unlift_TypeP Zero curr curr where
	type_unliftN _ = Just
instance Unlift_TypeP Zero curr (Type_Alt curr next) where
	type_unliftN _ (Type_Alt_Curr x) = Just x
	type_unliftN _ (Type_Alt_Next _) = Nothing
instance
 Unlift_TypeP p other next =>
 Unlift_TypeP (Succ p) other (Type_Alt curr next) where
	type_unliftN _ (Type_Alt_Next x) = type_unliftN (Proxy::Proxy p) x
	type_unliftN _ (Type_Alt_Curr _) = Nothing

-- | Convenient wrapper around 'type_unliftN',
-- passing it the 'Peano' number from 'Peano_of_Type'.
unlift_type
 :: forall ty tys (root:: * -> *) h.
 Unlift_Type ty tys =>
 tys root h -> Maybe (ty root h)
unlift_type = type_unliftN (Proxy::Proxy (Peano_of_Type ty tys))

-- * Type 'Exists_Type'
-- | Existential data type wrapping the index of a type.
data Exists_Type ty
 = forall h. Exists_Type (ty h)
instance -- Eq
 Eq_Type ty =>
 Eq (Exists_Type ty) where
	Exists_Type xh == Exists_Type yh =
		isJust $ xh `eq_type` yh
instance -- Show
 String_from_Type ty =>
 Show (Exists_Type ty) where
	show (Exists_Type ty) = string_from_type ty

-- * Type 'Exists_Type_and_Repr'
data Exists_Type_and_Repr ty repr
 =   forall h.
     Exists_Type_and_Repr (ty h) (repr h)