Language/Symantic/Expr/From.hs

   1 {-# LANGUAGE ConstraintKinds #-}
   2 {-# LANGUAGE DataKinds #-}
   3 {-# LANGUAGE DefaultSignatures #-}
   4 {-# LANGUAGE FlexibleContexts #-}
   5 {-# LANGUAGE FlexibleInstances #-}
   6 {-# LANGUAGE GADTs #-}
   7 {-# LANGUAGE KindSignatures #-}
   8 {-# LANGUAGE MultiParamTypeClasses #-}
   9 {-# LANGUAGE OverloadedStrings #-}
  10 {-# LANGUAGE Rank2Types #-}
  11 {-# LANGUAGE ScopedTypeVariables #-}
  12 {-# LANGUAGE TypeFamilies #-}
  13 {-# LANGUAGE TypeOperators #-}
  14 {-# LANGUAGE UndecidableInstances #-}
  15 module Language.Symantic.Expr.From where
  16
  17 import Data.Maybe (fromMaybe)
  18 import Data.Monoid
  19 import Data.Proxy (Proxy(..))
  20 import Data.Text (Text)
  21 import qualified Data.Text as Text
  22 import Data.Type.Equality ((:~:)(Refl))
  23 import GHC.Prim (Constraint)
  24
  25 import Language.Symantic.Type
  26 import Language.Symantic.Expr.Root
  27 import Language.Symantic.Expr.Alt
  28 import Language.Symantic.Expr.Error
  29 import Language.Symantic.Trans.Common
  30 import Language.Symantic.Repr
  31
  32 -- * Class 'Expr_From'
  33 -- | Parse given @ast@ into
  34 -- a 'Type_Root_of_Expr' and
  35 -- a 'Forall_Repr_with_Context',
  36 -- or return an 'Error_of_Expr'.
  37 class Expr_From ast (ex:: *) where
  38         expr_from :: ExprFrom ast ex hs ret
  39 instance -- Expr_From
  40  ( Expr_From ast (ex (Expr_Root ex))
  41  , Root_of_Expr (ex (Expr_Root ex)) ~ Expr_Root ex
  42  ) => Expr_From ast (Expr_Root ex) where
  43         expr_from _ex ctx ast k =
  44                 expr_from (Proxy::Proxy (ex (Expr_Root ex)))
  45                  ctx ast $ \ty (Forall_Repr_with_Context repr) ->
  46                 k ty (Forall_Repr_with_Context repr)
  47 instance -- Expr_From
  48  ( Expr_From ast (curr root)
  49  , Expr_From ast (next root)
  50  , Root_of_Expr (curr root) ~ root
  51  , Root_of_Expr (next root) ~ root
  52  , Error_Expr_Unlift (Error_Expr (Error_of_Type ast (Type_Root_of_Expr root))
  53                                  (Type_Root_of_Expr root) ast)
  54                      (Error_of_Expr ast root)
  55  ) => Expr_From ast (Expr_Alt curr next root) where
  56         expr_from _ex ctx ast k =
  57                 case expr_from (Proxy::Proxy (curr root)) ctx ast $
  58                  \ty (Forall_Repr_with_Context repr) ->
  59                         Right $ k ty (Forall_Repr_with_Context repr) of
  60                  Right ret -> ret
  61                  Left err ->
  62                         case error_expr_unlift err of
  63                          Just (Error_Expr_Unsupported_here _
  64                           :: Error_Expr (Error_of_Type ast (Type_Root_of_Expr root))
  65                                         (Type_Root_of_Expr root) ast) ->
  66                                 expr_from (Proxy::Proxy (next root)) ctx ast $
  67                                  \ty (Forall_Repr_with_Context repr) ->
  68                                 k ty (Forall_Repr_with_Context repr)
  69                          _ -> Left err
  70
  71 -- ** Type 'ExprFrom'
  72 -- | Convenient type synonym defining a parser.
  73 type ExprFrom ast ex hs ret
  74  = Proxy ex
  75  -- ^ Select the 'Expr_From' instance.
  76  -> ast
  77  -- ^ The input data to parse.
  78  -> Lambda_Context (Lambda_Var (Type_Root_of_Expr ex)) hs
  79  -- ^ The bound variables in scope and their types:
  80  -- held in the heterogeneous list @hs@,
  81  -- from the closest including lambda abstraction to the farest.
  82  -> ( forall h
  83     .  Type_Root_of_Expr ex h
  84     -> Forall_Repr_with_Context ex hs h
  85     -> Either (Error_of_Expr ast (Root_of_Expr ex)) ret )
  86  -- ^ The accumulating continuation.
  87  ->    Either (Error_of_Expr ast (Root_of_Expr ex)) ret
  88
  89 -- ** Type 'Lambda_Context'
  90 -- | GADT for a typing context,
  91 -- accumulating an @item@ at each lambda;
  92 -- used to accumulate object-types (in 'Expr_From')
  93 -- or host-terms (in 'Repr_Host')
  94 -- associated with the 'Lambda_Var's in scope.
  95 data Lambda_Context :: (* -> *) -> [*] -> * where
  96         Lambda_Context_Empty :: Lambda_Context item '[]
  97         Lambda_Context_Next  :: item h
  98                              -> Lambda_Context item hs
  99                              -> Lambda_Context item (h ': hs)
 100 infixr 5 `Lambda_Context_Next`
 101
 102 -- ** Type 'Lambda_Var'
 103 -- | Join a name and a type.
 104 --
 105 -- This data type is used to handle lambda variables by name
 106 -- (instead of DeBruijn indices for instance).
 107 data Lambda_Var ty h
 108  =   Lambda_Var Lambda_Var_Name (ty h)
 109 type Lambda_Var_Name = Text
 110
 111 -- ** Type 'Forall_Repr_with_Context'
 112 -- | A data type embedding a universal quantification
 113 -- over an interpreter @repr@
 114 -- and qualified by the symantics of an expression.
 115 --
 116 -- Moreover the expression is abstracted by a 'Lambda_Context'
 117 -- built at parsing time to build a /Higher-Order Abstract Syntax/ (HOAS)
 118 -- for lambda abstractions.
 119 --
 120 -- This data type is used to keep a parsed expression polymorphic enough
 121 -- to stay interpretable by different interpreters.
 122 --
 123 -- NOTE: 'Sym_of_Expr'@ ex repr@
 124 -- is needed to be able to use symantic methods of the parsed expression
 125 -- into a 'Forall_Repr_with_Context'@ ex@.
 126 --
 127 -- NOTE: 'Sym_of_Expr'@ (@'Root_of_Expr'@ ex) repr@
 128 -- is needed to be able to use an expression
 129 -- out of a 'Forall_Repr_with_Context'@ (@'Root_of_Expr'@ ex)@
 130 -- into a 'Forall_Repr_with_Context'@ ex@,
 131 -- which happens when a symantic method includes a polymorphic type
 132 -- and thus calls: 'expr_from'@ (Proxy::Proxy (@'Root_of_Expr'@ ex))@.
 133 --
 134 -- NOTE: 'Sym_Lambda_Lam repr@
 135 -- is needed to be able to parse partially applied functions
 136 -- (when their type is knowable).
 137 data Forall_Repr_with_Context ex hs h
 138  =   Forall_Repr_with_Context
 139  (   forall repr. ( Sym_of_Expr ex repr
 140                   , Sym_of_Expr (Root_of_Expr ex) repr
 141                   , Sym_Lambda_Lam repr
 142                   ) => Lambda_Context repr hs -> repr h )
 143
 144 -- ** Type 'Forall_Repr'
 145 -- | 'Forall_Repr_with_Context' applied on a 'Lambda_Context'.
 146 data Forall_Repr ex h
 147  =   Forall_Repr
 148  { unForall_Repr :: forall repr
 149                  .  ( Sym_of_Expr ex repr
 150                     , Sym_of_Expr (Root_of_Expr ex) repr
 151                     , Sym_Lambda_Lam repr )
 152                  => repr h }
 153
 154 -- * Class 'Sym_Lambda_Lam'
 155 class Sym_Lambda_Lam repr where
 156         -- | /Lambda abstraction/.
 157         lam :: (repr arg -> repr res) -> repr ((->) arg res)
 158         default lam :: Trans t repr
 159          => (t repr arg -> t repr res) -> t repr ((->) arg res)
 160         lam f = trans_lift $ lam $ trans_apply . f . trans_lift
 161 instance Sym_Lambda_Lam Repr_Host where
 162         lam f = Repr_Host (unRepr_Host . f . Repr_Host)
 163 instance Sym_Lambda_Lam Repr_Text where
 164         lam f =
 165                 Repr_Text $ \p v ->
 166                         let p' = Precedence 1 in
 167                         let x = "x" <> Text.pack (show v) in
 168                         paren p p' $ "\\" <> x <> " -> "
 169                          <> unRepr_Text (f (Repr_Text $ \_p _v -> x)) p' (succ v)
 170 instance (Sym_Lambda_Lam r1, Sym_Lambda_Lam r2) => Sym_Lambda_Lam (Repr_Dup r1 r2) where
 171         lam f = repr_dup_1 (lam f) `Repr_Dup` repr_dup_2 (lam f)
 172
 173 -- ** Type family 'Sym_of_Expr'
 174 -- | The symantic of an expression.
 175 type family Sym_of_Expr (ex:: *) (repr:: * -> *) :: Constraint
 176 type instance Sym_of_Expr (Expr_Root ex) repr
 177  =            Sym_of_Expr (ex (Expr_Root ex)) repr
 178 type instance Sym_of_Expr (Expr_Alt curr next root) repr
 179  = ( Sym_of_Expr (curr root) repr
 180    , Sym_of_Expr (next root) repr
 181    )
 182
 183 -- * Checks
 184
 185 -- | Parsing utility to check that two types are equal,
 186 -- or raise 'Error_Expr_Type_mismatch'.
 187 check_type0_family
 188  :: forall ast ex ta root ty h ret.
 189  ( root ~ Root_of_Expr ex
 190  , ty ~ Type_Root_of_Expr ex
 191  , Type0_Family ta ty
 192  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 193                    (Error_of_Expr ast root)
 194  ) => Proxy ta -> Proxy ex -> ast -> ty h
 195  -> (ty (Host_of_Type0_Family ta h) -> Either (Error_of_Expr ast root) ret)
 196  -> Either (Error_of_Expr ast root) ret
 197 check_type0_family ta ex ast ty k =
 198         case type0_family ta ty of
 199          Just t -> k t
 200          Nothing -> Left $ error_expr ex $
 201                 Error_Expr_Type (error_type_lift $ Error_Type_No_Type_Family ast) ast
 202
 203 -- | Parsing utility to check that two types are equal,
 204 -- or raise 'Error_Expr_Type_mismatch'.
 205 check_type0_eq
 206  :: forall ast ex root ty x y ret.
 207  ( root ~ Root_of_Expr ex
 208  , ty ~ Type_Root_of_Expr ex
 209  , Type0_Eq ty
 210  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 211                    (Error_of_Expr ast root)
 212  ) => Proxy ex -> ast -> ty x -> ty y
 213  -> (x :~: y -> Either (Error_of_Expr ast root) ret)
 214  -> Either (Error_of_Expr ast root) ret
 215 check_type0_eq ex ast x y k =
 216         case x `type0_eq` y of
 217          Just Refl -> k Refl
 218          Nothing -> Left $ error_expr ex $
 219                 Error_Expr_Type_mismatch ast
 220                  (Exists_Type0 x)
 221                  (Exists_Type0 y)
 222
 223 -- | Parsing utility to check that two 'Type1' are equal,
 224 -- or raise 'Error_Expr_Type_mismatch'.
 225 check_type1_eq
 226  :: forall ast ex root ty h1 h2 a1 a2 ret.
 227  ( root ~ Root_of_Expr ex
 228  , ty ~ Type_Root_of_Expr ex
 229  , Type1_Eq ty
 230  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 231                    (Error_of_Expr ast root)
 232  )
 233  => Proxy ex -> ast -> ty (h1 a1) -> ty (h2 a2)
 234  -> (h1 :~: h2 -> Either (Error_of_Expr ast root) ret)
 235  -> Either (Error_of_Expr ast root) ret
 236 check_type1_eq ex ast h1 h2 k =
 237         case h1 `type1_eq` h2 of
 238          Just Refl -> k Refl
 239          Nothing -> Left $ error_expr ex $
 240                 Error_Expr_Type_mismatch ast
 241                  (Exists_Type0 h1)
 242                  (Exists_Type0 h2)
 243
 244 -- | Parsing utility to check that a 'Type0' or higher
 245 -- is an instance of a given 'Constraint',
 246 -- or raise 'Error_Expr_Constraint_missing'.
 247 check_type0_constraint
 248  :: forall ast ex c root ty h ret.
 249  ( root ~ Root_of_Expr ex
 250  , ty ~ Type_Root_of_Expr ex
 251  , Type0_Constraint c ty
 252  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 253                    (Error_of_Expr ast root)
 254  )
 255  => Proxy ex -> Proxy c -> ast -> ty h
 256  -> (Dict (c h) -> Either (Error_of_Expr ast root) ret)
 257  -> Either (Error_of_Expr ast root) ret
 258 check_type0_constraint ex c ast ty k =
 259         case type0_constraint c ty of
 260          Just Dict -> k Dict
 261          Nothing -> Left $ error_expr ex $
 262                 Error_Expr_Constraint_missing ast
 263                  {-(Exists_Dict c)-}
 264                  -- FIXME: not easy to report the constraint
 265                  -- and still support 'Eq' and 'Show' deriving.
 266                  (Exists_Type0 ty)
 267
 268 -- | Parsing utility to check that a 'Type1' or higher
 269 -- is an instance of a given 'Constraint',
 270 -- or raise 'Error_Expr_Constraint_missing'.
 271 check_type1_constraint
 272  :: forall ast ex c root ty h a ret.
 273  ( root ~ Root_of_Expr ex
 274  , ty ~ Type_Root_of_Expr ex
 275  , Type1_Constraint c ty
 276  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 277                    (Error_of_Expr ast root)
 278  ) => Proxy ex -> Proxy c -> ast -> ty (h a)
 279  -> (Dict (c h) -> Either (Error_of_Expr ast root) ret)
 280  -> Either (Error_of_Expr ast root) ret
 281 check_type1_constraint ex c ast ty k =
 282         case type1_constraint c ty of
 283          Just Dict -> k Dict
 284          Nothing -> Left $ error_expr ex $
 285                 Error_Expr_Constraint_missing ast
 286                  (Exists_Type0 ty)
 287
 288 -- | Parsing utility to check that the given type is at least a 'Type1'
 289 -- or raise 'Error_Expr_Type_mismatch'.
 290 check_type1
 291  :: forall ast ex root ty h ret.
 292  ( root ~ Root_of_Expr ex
 293  , ty ~ Type_Root_of_Expr ex
 294  , Type1_Unlift (Type_of_Expr root)
 295  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 296                    (Error_of_Expr ast root)
 297  ) => Proxy ex -> ast -> ty h
 298  -> (forall (t1:: *).
 299      ( Type1 t1 ty h
 300      , Type1_Lift t1 ty (Type_Var0 :|: Type_Var1 :|: Type_of_Expr root)
 301      ) -> Either (Error_of_Expr ast root) ret)
 302  -> Either (Error_of_Expr ast root) ret
 303 check_type1 ex ast ty k =
 304         (`fromMaybe` type1_unlift (unType_Root ty) (Just . k)) $
 305         Left $
 306                 error_expr ex $
 307                 Error_Expr_Type_mismatch ast
 308                  (Exists_Type0 (type_var1 SZero (type_var0 SZero)
 309                  :: ty (Var1 Var0)))
 310                  (Exists_Type0 ty)
 311
 312 -- * Parsers
 313
 314 -- | Like 'expr_from' but for a root expression.
 315 root_expr_from
 316  :: forall ast root.
 317  ( Expr_From ast root
 318  , Root_of_Expr root ~ root
 319  ) => Proxy root -> ast
 320  -> Either (Error_of_Expr ast root)
 321            (Exists_Type0_and_Repr (Type_Root_of_Expr root)
 322                                   (Forall_Repr root))
 323 root_expr_from _ex ast =
 324         expr_from (Proxy::Proxy root) ast
 325          Lambda_Context_Empty $ \ty (Forall_Repr_with_Context repr) ->
 326                 Right $ Exists_Type0_and_Repr ty $
 327                         Forall_Repr $ repr Lambda_Context_Empty
 328
 329 -- | Parse a literal.
 330 lit_from
 331  :: forall ty lit ex ast hs ret.
 332  ( ty ~ Type_Root_of_Expr ex
 333  , Read lit
 334  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 335                    (Error_of_Expr ast (Root_of_Expr ex))
 336  ) => (forall repr. Sym_of_Expr ex repr => lit -> repr lit)
 337  -> ty lit -> Text
 338  -> ExprFrom ast ex hs ret
 339 lit_from lit ty_lit toread ex ast _ctx k =
 340         case read_safe toread of
 341          Left err -> Left $ error_expr ex $ Error_Expr_Read err ast
 342          Right (i::lit) -> k ty_lit $ Forall_Repr_with_Context $ const $ lit i
 343
 344 -- | Parse a unary class operator.
 345 class_op1_from
 346  :: forall root ty cl ex ast hs ret.
 347  ( ty ~ Type_Root_of_Expr ex
 348  , root ~ Root_of_Expr ex
 349  , Type0_Eq ty
 350  , Expr_From ast root
 351  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 352                    (Error_of_Expr ast root)
 353  , Root_of_Expr root ~ root
 354  , Type0_Constraint cl ty
 355  ) => (forall lit repr. (cl lit, Sym_of_Expr ex repr) => repr lit -> repr lit)
 356  -> Proxy cl -> ast
 357  -> ExprFrom ast ex hs ret
 358 class_op1_from op cl ast_x ex _ast ctx k =
 359         expr_from (Proxy::Proxy root) ast_x ctx $ \ty_x (Forall_Repr_with_Context x) ->
 360         check_type0_constraint ex cl ast_x ty_x $ \Dict ->
 361         k ty_x $ Forall_Repr_with_Context (op . x)
 362
 363 -- | Parse a binary class operator.
 364 class_op2_from
 365  :: forall root ty cl ex ast hs ret.
 366  ( ty ~ Type_Root_of_Expr ex
 367  , root ~ Root_of_Expr ex
 368  , Type0_Eq ty
 369  , Expr_From ast root
 370  , Type0_Constraint cl ty
 371  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 372                    (Error_of_Expr ast root)
 373  , Root_of_Expr root ~ root
 374  ) => (forall lit repr. (cl lit, Sym_of_Expr ex repr) => repr lit -> repr lit -> repr lit)
 375  -> Proxy cl -> ast -> ast
 376  -> ExprFrom ast ex hs ret
 377 class_op2_from op cl ast_x ast_y ex ast ctx k =
 378         expr_from (Proxy::Proxy root) ast_x ctx $ \ty_x (Forall_Repr_with_Context x) ->
 379         expr_from (Proxy::Proxy root) ast_y ctx $ \ty_y (Forall_Repr_with_Context y) ->
 380         check_type0_constraint ex cl ast_x ty_x $ \Dict ->
 381         check_type0_constraint ex cl ast_y ty_y $ \Dict ->
 382         check_type0_eq ex ast ty_x ty_y $ \Refl ->
 383         k ty_x $ Forall_Repr_with_Context $
 384          \c -> x c `op` y c
 385
 386 -- | Parse a binary class operator, partially applied.
 387 class_op2_from1
 388  :: forall root ty cl ex ast hs ret.
 389  ( ty ~ Type_Root_of_Expr ex
 390  , root ~ Root_of_Expr ex
 391  , Type0_Eq ty
 392  , Type0_Constraint cl ty
 393  , Type0_Lift Type_Fun (Type_of_Expr root)
 394  , Expr_From ast root
 395  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 396                    (Error_of_Expr ast root)
 397  , Root_of_Expr root ~ root
 398  ) => (forall lit repr. (cl lit, Sym_of_Expr ex repr) => repr lit -> repr lit -> repr lit)
 399  -> Proxy cl -> ast
 400  -> ExprFrom ast ex hs ret
 401 class_op2_from1 op cl ast_x ex _ast ctx k =
 402         expr_from (Proxy::Proxy root) ast_x ctx $ \ty_x (Forall_Repr_with_Context x) ->
 403         check_type0_constraint ex cl ast_x ty_x $ \Dict ->
 404         k (type_fun ty_x ty_x) $ Forall_Repr_with_Context $
 405          \c -> lam $ \y -> x c `op` y
 406
 407 -- | Parse a unary operator.
 408 op1_from
 409  :: forall root ty lit ex ast hs ret.
 410  ( ty ~ Type_Root_of_Expr ex
 411  , root ~ Root_of_Expr ex
 412  , Type0_Eq ty
 413  , Expr_From ast root
 414  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 415                    (Error_of_Expr ast root)
 416  , Root_of_Expr root ~ root
 417  ) => (forall repr. Sym_of_Expr ex repr => repr lit -> repr lit)
 418  -> ty lit -> ast
 419  -> ExprFrom ast ex hs ret
 420 op1_from op ty_lit ast_x ex ast ctx k =
 421         expr_from (Proxy::Proxy root) ast_x ctx $ \ty_x (Forall_Repr_with_Context x) ->
 422         check_type0_eq ex ast ty_lit ty_x $ \Refl ->
 423         k ty_x $ Forall_Repr_with_Context (op . x)
 424
 425 -- | Parse a unary operator, partially applied.
 426 op1_from0
 427  :: forall root ty lit ex ast hs ret.
 428  ( ty ~ Type_Root_of_Expr ex
 429  , root ~ Root_of_Expr ex
 430  , Type0_Eq ty
 431  , Type0_Lift Type_Fun (Type_of_Expr root)
 432  , Expr_From ast root
 433  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 434                    (Error_of_Expr ast root)
 435  , Root_of_Expr root ~ root
 436  ) => (forall repr. Sym_of_Expr ex repr => repr lit -> repr lit)
 437  -> ty lit
 438  -> ExprFrom ast ex hs ret
 439 op1_from0 op ty_lit _ex _ast _ctx k =
 440         k (type_fun ty_lit ty_lit) $ Forall_Repr_with_Context $
 441          \_c -> lam op
 442
 443 -- | Parse a binary operator.
 444 op2_from
 445  :: forall root ty lit ex ast hs ret.
 446  ( ty ~ Type_Root_of_Expr ex
 447  , root ~ Root_of_Expr ex
 448  , Type0_Eq ty
 449  , Expr_From ast root
 450  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 451                    (Error_of_Expr ast root)
 452  , Root_of_Expr root ~ root
 453  ) => (forall repr. Sym_of_Expr ex repr => repr lit -> repr lit -> repr lit)
 454  -> ty lit -> ast -> ast
 455  -> ExprFrom ast ex hs ret
 456 op2_from op ty_lit ast_x ast_y ex ast ctx k =
 457         expr_from (Proxy::Proxy root) ast_x ctx $ \ty_x (Forall_Repr_with_Context x) ->
 458         expr_from (Proxy::Proxy root) ast_y ctx $ \ty_y (Forall_Repr_with_Context y) ->
 459         check_type0_eq ex ast ty_lit ty_x $ \Refl ->
 460         check_type0_eq ex ast ty_lit ty_y $ \Refl ->
 461         k ty_x $ Forall_Repr_with_Context $
 462          \c -> x c `op` y c
 463
 464 -- | Parse a binary operator, partially applied.
 465 op2_from1
 466  :: forall root ty lit ex ast hs ret.
 467  ( ty ~ Type_Root_of_Expr ex
 468  , root ~ Root_of_Expr ex
 469  , Type0_Eq ty
 470  , Type0_Lift Type_Fun (Type_of_Expr root)
 471  , Expr_From ast root
 472  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 473                    (Error_of_Expr ast root)
 474  , Root_of_Expr root ~ root
 475  ) => (forall repr. Sym_of_Expr ex repr => repr lit -> repr lit -> repr lit)
 476  -> ty lit -> ast
 477  -> ExprFrom ast ex hs ret
 478 op2_from1 op ty_lit ast_x ex ast ctx k =
 479         expr_from (Proxy::Proxy root) ast_x ctx $ \ty_x (Forall_Repr_with_Context x) ->
 480         check_type0_eq ex ast ty_lit ty_x $ \Refl ->
 481                 k (type_fun ty_x ty_x) $ Forall_Repr_with_Context $
 482                  \c -> lam $ \y -> x c `op` y
 483
 484 -- | Parse a binary operator, partially applied.
 485 op2_from0
 486  :: forall root ty lit ex ast hs ret.
 487  ( ty ~ Type_Root_of_Expr ex
 488  , root ~ Root_of_Expr ex
 489  , Type0_Eq ty
 490  , Type0_Lift Type_Fun (Type_of_Expr root)
 491  , Expr_From ast root
 492  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
 493                    (Error_of_Expr ast root)
 494  , Root_of_Expr root ~ root
 495  ) => (forall repr. Sym_of_Expr ex repr => repr lit -> repr lit -> repr lit)
 496  -> ty lit
 497  -> ExprFrom ast ex hs ret
 498 op2_from0 op ty_lit _ex _ast _ctx k =
 499         k (type_fun ty_lit $ type_fun ty_lit ty_lit) $ Forall_Repr_with_Context $
 500          \_c -> lam $ \x -> lam $ \y -> x `op` y