symantic-lib/Language/Symantic/Lib/Bool.hs

   1 {-# LANGUAGE UndecidableInstances #-}
   2 {-# OPTIONS_GHC -fno-warn-orphans #-}
   3 -- | Symantic for 'Bool'.
   4 module Language.Symantic.Lib.Bool where
   5
   6 import Control.Monad
   7 import Data.Proxy
   8 import Prelude hiding ((&&), not, (||))
   9 import qualified Data.Bool as Bool
  10 import qualified Data.Text as Text
  11
  12 import Language.Symantic
  13 import Language.Symantic.Lib.Function ()
  14
  15 -- * Class 'Sym_Bool'
  16 type instance Sym (Proxy Bool) = Sym_Bool
  17 class Sym_Bool term where
  18         bool ::      Bool -> term Bool
  19         not  :: term Bool -> term Bool
  20         (&&) :: term Bool -> term Bool -> term Bool; infixr 3 &&
  21         (||) :: term Bool -> term Bool -> term Bool; infixr 2 ||
  22         xor  :: term Bool -> term Bool -> term Bool; infixr 2 `xor`
  23         xor x y = (x || y) && not (x && y)
  24
  25         default bool :: Sym_Bool (UnT term) => Trans term =>      Bool -> term Bool
  26         default not  :: Sym_Bool (UnT term) => Trans term => term Bool -> term Bool
  27         default (&&) :: Sym_Bool (UnT term) => Trans term => term Bool -> term Bool -> term Bool
  28         default (||) :: Sym_Bool (UnT term) => Trans term => term Bool -> term Bool -> term Bool
  29
  30         bool = trans . bool
  31         not  = trans1 not
  32         (&&) = trans2 (&&)
  33         (||) = trans2 (||)
  34
  35 -- Interpreting
  36 instance Sym_Bool Eval where
  37         bool = Eval
  38         not  = liftM Bool.not
  39         (&&) = liftM2 (Bool.&&)
  40         (||) = liftM2 (Bool.||)
  41 instance Sym_Bool View where
  42         bool o = View $ \_p _v -> Text.pack (show o)
  43         not    = view1 "not"
  44         (&&)   = viewInfix "&&"    (infixR 3)
  45         (||)   = viewInfix "||"    (infixR 2)
  46         xor    = viewInfix "`xor`" (infixR 2)
  47 instance (Sym_Bool r1, Sym_Bool r2) => Sym_Bool (Dup r1 r2) where
  48         bool b = bool b `Dup` bool b
  49         not    = dup1 @Sym_Bool not
  50         (&&)   = dup2 @Sym_Bool (&&)
  51         (||)   = dup2 @Sym_Bool (||)
  52         xor    = dup2 @Sym_Bool xor
  53
  54 -- Transforming
  55 instance (Sym_Lambda term, Sym_Bool term) => Sym_Bool (BetaT term) where
  56         xor = trans2 xor
  57
  58 -- Typing
  59 instance ClassInstancesFor Bool where
  60         proveConstraintFor _ (TyApp _ (TyConst _ _ q) c)
  61          | Just HRefl <- proj_ConstKiTy @_ @Bool c
  62          = case () of
  63                  _ | Just Refl <- proj_Const @Bounded q -> Just Dict
  64                    | Just Refl <- proj_Const @Enum    q -> Just Dict
  65                    | Just Refl <- proj_Const @Eq      q -> Just Dict
  66                    | Just Refl <- proj_Const @Ord     q -> Just Dict
  67                    | Just Refl <- proj_Const @Show    q -> Just Dict
  68                  _ -> Nothing
  69         proveConstraintFor _c _q = Nothing
  70 instance TypeInstancesFor Bool
  71
  72 -- Compiling
  73 instance Gram_Term_AtomsFor src ss g Bool
  74 instance (Source src, Inj_Sym ss Bool) => ModuleFor src ss Bool where
  75         moduleFor = ["Bool"] `moduleWhere`
  76          [ "False" := teBool False
  77          , "True"  := teBool True
  78          , "not"   := teBool_not
  79          , "and" `withInfixR` 3 := teBool_and
  80          , "or"  `withInfixR` 2 := teBool_or
  81          , "xor" `withInfixR` 2 := teBool_xor
  82          ]
  83
  84 -- ** 'Type's
  85 tyBool :: Source src => Inj_Len vs => Type src vs Bool
  86 tyBool = tyConst @(K Bool) @Bool
  87
  88 -- ** 'Term's
  89 teBool :: Source src => Inj_Sym ss Bool => Bool -> Term src ss ts '[] (() #> Bool)
  90 teBool b = Term noConstraint tyBool $ teSym @Bool $ bool b
  91
  92 teBool_not :: TermDef Bool '[] (() #> (Bool -> Bool))
  93 teBool_not = Term noConstraint (tyBool ~> tyBool) $ teSym @Bool $ lam1 not
  94
  95 teBool_and, teBool_or, teBool_xor :: TermDef Bool '[] (() #> (Bool -> Bool -> Bool))
  96 teBool_and = Term noConstraint (tyBool ~> tyBool ~> tyBool) $ teSym @Bool $ lam2 (&&)
  97 teBool_or  = Term noConstraint (tyBool ~> tyBool ~> tyBool) $ teSym @Bool $ lam2 (||)
  98 teBool_xor = Term noConstraint (tyBool ~> tyBool ~> tyBool) $ teSym @Bool $ lam2 xor