{-# LANGUAGE UndecidableInstances #-}
{-# OPTIONS_GHC -fno-warn-orphans #-}
-- | Symantic for 'Bool'.
module Language.Symantic.Lib.Bool where

import Control.Monad
import Prelude hiding ((&&), not, (||))
import qualified Data.Bool as Bool
import qualified Data.Text as Text

import Language.Symantic
import Language.Symantic.Lib.Function ()

-- * Class 'Sym_Bool'
type instance Sym Bool = Sym_Bool
class Sym_Bool term where
	bool ::      Bool -> term Bool
	not  :: term Bool -> term Bool
	(&&) :: term Bool -> term Bool -> term Bool; infixr 3 &&
	(||) :: term Bool -> term Bool -> term Bool; infixr 2 ||
	xor  :: term Bool -> term Bool -> term Bool; infixr 2 `xor`
	xor x y = (x || y) && not (x && y)
	
	default bool :: Sym_Bool (UnT term) => Trans term =>      Bool -> term Bool
	default not  :: Sym_Bool (UnT term) => Trans term => term Bool -> term Bool
	default (&&) :: Sym_Bool (UnT term) => Trans term => term Bool -> term Bool -> term Bool
	default (||) :: Sym_Bool (UnT term) => Trans term => term Bool -> term Bool -> term Bool
	
	bool = trans . bool
	not  = trans1 not
	(&&) = trans2 (&&)
	(||) = trans2 (||)

-- Interpreting
instance Sym_Bool Eval where
	bool = Eval
	not  = liftM Bool.not
	(&&) = liftM2 (Bool.&&)
	(||) = liftM2 (Bool.||)
instance Sym_Bool View where
	bool o = View $ \_p _v -> Text.pack (show o)
	not    = view1 "not"
	(&&)   = viewInfix "&&"    (infixR 3)
	(||)   = viewInfix "||"    (infixR 2)
	xor    = viewInfix "`xor`" (infixR 2)
instance (Sym_Bool r1, Sym_Bool r2) => Sym_Bool (Dup r1 r2) where
	bool b = bool b `Dup` bool b
	not    = dup1 @Sym_Bool not
	(&&)   = dup2 @Sym_Bool (&&)
	(||)   = dup2 @Sym_Bool (||)
	xor    = dup2 @Sym_Bool xor

-- Transforming
instance (Sym_Lambda term, Sym_Bool term) => Sym_Bool (BetaT term) where
	xor = trans2 xor

-- Typing
instance ClassInstancesFor Bool where
	proveConstraintFor _ (TyApp _ (TyConst _ _ q) c)
	 | Just HRefl <- proj_ConstKiTy @_ @Bool c
	 = case () of
		 _ | Just Refl <- proj_Const @Bounded q -> Just Dict
		   | Just Refl <- proj_Const @Enum    q -> Just Dict
		   | Just Refl <- proj_Const @Eq      q -> Just Dict
		   | Just Refl <- proj_Const @Ord     q -> Just Dict
		   | Just Refl <- proj_Const @Show    q -> Just Dict
		 _ -> Nothing
	proveConstraintFor _c _q = Nothing
instance TypeInstancesFor Bool

-- Compiling
instance Gram_Term_AtomsFor src ss g Bool
instance (Source src, SymInj ss Bool) => ModuleFor src ss Bool where
	moduleFor = ["Bool"] `moduleWhere`
	 [ "False" := teBool False
	 , "True"  := teBool True
	 , "not"   := teBool_not
	 , "and" `withInfixR` 3 := teBool_and
	 , "or"  `withInfixR` 2 := teBool_or
	 , "xor" `withInfixR` 2 := teBool_xor
	 ]

-- ** 'Type's
tyBool :: Source src => LenInj vs => Type src vs Bool
tyBool = tyConst @(K Bool) @Bool

-- ** 'Term's
teBool :: Source src => SymInj ss Bool => Bool -> Term src ss ts '[] (() #> Bool)
teBool b = Term noConstraint tyBool $ teSym @Bool $ bool b

teBool_not :: TermDef Bool '[] (() #> (Bool -> Bool))
teBool_not = Term noConstraint (tyBool ~> tyBool) $ teSym @Bool $ lam1 not

teBool_and, teBool_or, teBool_xor :: TermDef Bool '[] (() #> (Bool -> Bool -> Bool))
teBool_and = Term noConstraint (tyBool ~> tyBool ~> tyBool) $ teSym @Bool $ lam2 (&&)
teBool_or  = Term noConstraint (tyBool ~> tyBool ~> tyBool) $ teSym @Bool $ lam2 (||)
teBool_xor = Term noConstraint (tyBool ~> tyBool ~> tyBool) $ teSym @Bool $ lam2 xor