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

   1 {-# LANGUAGE UndecidableInstances #-}
   2 {-# OPTIONS_GHC -fno-warn-orphans #-}
   3 -- | Symantic for 'Num'.
   4 module Language.Symantic.Lib.Num where
   5
   6 import Control.Monad (liftM, liftM2)
   7 import Data.Proxy
   8 import Data.Type.Equality ((:~:)(Refl))
   9 import Prelude (Num)
  10 import Prelude hiding (Num(..))
  11 import qualified Data.Function as Fun
  12 import qualified Prelude
  13
  14 import Language.Symantic.Parsing
  15 import Language.Symantic.Typing
  16 import Language.Symantic.Compiling
  17 import Language.Symantic.Interpreting
  18 import Language.Symantic.Transforming
  19 import Language.Symantic.Lib.Lambda
  20
  21 -- * Class 'Sym_Num'
  22 class Sym_Num term where
  23         abs         :: Num n => term n -> term n
  24         negate      :: Num n => term n -> term n
  25         signum      :: Num n => term n -> term n
  26         (+)         :: Num n => term n -> term n -> term n; infixl 6 +
  27         (-)         :: Num n => term n -> term n -> term n; infixl 6 -
  28         (*)         :: Num n => term n -> term n -> term n; infixl 7 *
  29         fromInteger :: Num n => term Integer -> term n
  30
  31         default abs         :: (Trans t term, Num n) => t term n -> t term n
  32         default negate      :: (Trans t term, Num n) => t term n -> t term n
  33         default signum      :: (Trans t term, Num n) => t term n -> t term n
  34         default (+)         :: (Trans t term, Num n) => t term n -> t term n -> t term n
  35         default (-)         :: (Trans t term, Num n) => t term n -> t term n -> t term n
  36         default (*)         :: (Trans t term, Num n) => t term n -> t term n -> t term n
  37         default fromInteger :: (Trans t term, Num n) => t term Integer -> t term n
  38
  39         abs         = trans_map1 abs
  40         negate      = trans_map1 negate
  41         signum      = trans_map1 signum
  42         (+)         = trans_map2 (+)
  43         (-)         = trans_map2 (-)
  44         (*)         = trans_map2 (*)
  45         fromInteger = trans_map1 fromInteger
  46
  47 type instance Sym_of_Iface (Proxy Num) = Sym_Num
  48 type instance TyConsts_of_Iface (Proxy Num) = Proxy Num ': TyConsts_imported_by (Proxy Num)
  49 type instance TyConsts_imported_by (Proxy Num) =
  50  '[ Proxy Integer
  51  ]
  52
  53 instance Sym_Num HostI where
  54         abs         = liftM Prelude.abs
  55         negate      = liftM Prelude.negate
  56         signum      = liftM Prelude.signum
  57         (+)         = liftM2 (Prelude.+)
  58         (-)         = liftM2 (Prelude.-)
  59         (*)         = liftM2 (Prelude.*)
  60         fromInteger = liftM Prelude.fromInteger
  61 instance Sym_Num TextI where
  62         abs         = textI1 "abs"
  63         negate      = textI1 "negate"
  64         signum      = textI1 "signum"
  65         (+)         = textI_infix "+" (infixB L 6)
  66         (-)         = textI_infix "-" (infixL 6)
  67         (*)         = textI_infix "*" (infixB L 7)
  68         fromInteger = textI1 "fromInteger"
  69 instance (Sym_Num r1, Sym_Num r2) => Sym_Num (DupI r1 r2) where
  70         abs         = dupI1 @Sym_Num abs
  71         negate      = dupI1 @Sym_Num negate
  72         signum      = dupI1 @Sym_Num signum
  73         (+)         = dupI2 @Sym_Num (+)
  74         (-)         = dupI2 @Sym_Num (-)
  75         (*)         = dupI2 @Sym_Num (*)
  76         fromInteger = dupI1 @Sym_Num fromInteger
  77
  78 instance
  79  ( Read_TyNameR TyName cs rs
  80  , Inj_TyConst cs Num
  81  ) => Read_TyNameR TyName cs (Proxy Num ': rs) where
  82         read_TyNameR _cs (TyName "Num") k = k (ty @Num)
  83         read_TyNameR _rs raw k = read_TyNameR (Proxy @rs) raw k
  84 instance Show_TyConst cs => Show_TyConst (Proxy Num ': cs) where
  85         show_TyConst TyConstZ{} = "Num"
  86         show_TyConst (TyConstS c) = show_TyConst c
  87
  88 instance Proj_TyConC cs (Proxy Num)
  89 data instance TokenT meta (ts::[*]) (Proxy Num)
  90  = Token_Term_Num_abs         (EToken meta ts)
  91  | Token_Term_Num_negate      (EToken meta ts)
  92  | Token_Term_Num_signum      (EToken meta ts)
  93  | Token_Term_Num_add         (EToken meta ts)
  94  | Token_Term_Num_sub         (EToken meta ts)
  95  | Token_Term_Num_mul         (EToken meta ts)
  96  | Token_Term_Num_fromInteger (EToken meta '[Proxy Token_Type])
  97 deriving instance (Eq meta, Eq_Token meta ts) => Eq (TokenT meta ts (Proxy Num))
  98 deriving instance (Show meta, Show_Token meta ts) => Show (TokenT meta ts (Proxy Num))
  99
 100 instance -- CompileI
 101  ( Read_TyName TyName cs
 102  , Inj_TyConst        cs Num
 103  , Inj_TyConst        cs (->)
 104  , Inj_TyConst        cs Integer
 105  , Proj_TyCon         cs
 106  , Compile cs is
 107  ) => CompileI cs is (Proxy Num) where
 108         compileI tok ctx k =
 109                 case tok of
 110                  Token_Term_Num_abs    tok_a -> op1_from tok_a abs
 111                  Token_Term_Num_negate tok_a -> op1_from tok_a negate
 112                  Token_Term_Num_signum tok_a -> op1_from tok_a signum
 113                  Token_Term_Num_add    tok_a -> op2_from tok_a (+)
 114                  Token_Term_Num_sub    tok_a -> op2_from tok_a (-)
 115                  Token_Term_Num_mul    tok_a -> op2_from tok_a (*)
 116                  Token_Term_Num_fromInteger tok_ty_a ->
 117                         -- fromInteger :: Num a => Integer -> a
 118                         compile_Type tok_ty_a $ \(ty_a::Type cs a) ->
 119                         check_Kind
 120                          (At Nothing SKiType)
 121                          (At (Just tok_ty_a) $ kind_of ty_a) $ \Refl ->
 122                         check_TyCon (At (Just tok_ty_a) (ty @Num :$ ty_a)) $ \TyCon ->
 123                         k (ty @Integer ~> ty_a) $ Term $
 124                                 Fun.const $ lam fromInteger
 125                 where
 126                 op1_from tok_a
 127                  (op::forall term a. (Sym_Num term, Num a)
 128                          => term a -> term a) =
 129                  -- abs    :: Num a => a -> a
 130                  -- negate :: Num a => a -> a
 131                  -- signum :: Num a => a -> a
 132                         compile tok_a ctx $ \ty_a (Term x) ->
 133                         check_TyCon (At (Just tok_a) (ty @Num :$ ty_a)) $ \TyCon ->
 134                         k ty_a $ Term $
 135                          \c -> op (x c)
 136                 op2_from tok_a
 137                  (op::forall term a. (Sym_Num term, Num a)
 138                          => term a -> term a -> term a) =
 139                  -- (+) :: Num a => a -> a -> a
 140                  -- (-) :: Num a => a -> a -> a
 141                  -- (*) :: Num a => a -> a -> a
 142                         compile tok_a ctx $ \ty_a (Term x) ->
 143                         check_TyCon (At (Just tok_a) (ty @Num :$ ty_a)) $ \TyCon ->
 144                         k (ty_a ~> ty_a) $ Term $
 145                          \c -> lam $ \y -> op (x c) y
 146 instance -- TokenizeT
 147  Inj_Token meta ts Num =>
 148  TokenizeT meta ts (Proxy Num) where
 149         tokenizeT _t = mempty
 150          { tokenizers_infix = tokenizeTMod []
 151                  [ tokenize1 "abs"    infixN5 Token_Term_Num_abs
 152                  , tokenize1 "negate" infixN5 Token_Term_Num_negate
 153                  , tokenize1 "signum" infixN5 Token_Term_Num_signum
 154                  , tokenize1 "+" (infixB L 6) Token_Term_Num_add
 155                  , tokenize1 "-" (infixL 6) Token_Term_Num_sub
 156                  , tokenize1 "*" (infixB L 7) Token_Term_Num_mul
 157                  , (TeName "fromInteger",) ProTok_Term
 158                          { protok_term = \meta -> ProTokPi $ \a ->
 159                                 ProTokTe $ inj_EToken meta $ Token_Term_Num_fromInteger a
 160                          , protok_fixity = infixN5
 161                          }
 162                  ]
 163          , tokenizers_prefix = tokenizeTMod []
 164                  [ tokenize1 "-"   (Prefix 10) Token_Term_Num_negate
 165                  ]
 166          }
 167 instance Gram_Term_AtomsT meta ts (Proxy Num) g