Language/LOL/Symantic/Expr/Lambda.hs

   1 {-# LANGUAGE FlexibleContexts #-}
   2 {-# LANGUAGE FlexibleInstances #-}
   3 {-# LANGUAGE GADTs #-}
   4 {-# LANGUAGE MultiParamTypeClasses #-}
   5 {-# LANGUAGE OverloadedStrings #-}
   6 {-# LANGUAGE Rank2Types #-}
   7 {-# LANGUAGE ScopedTypeVariables #-}
   8 {-# LANGUAGE TypeFamilies #-}
   9 {-# LANGUAGE UndecidableInstances #-}
  10 module Language.LOL.Symantic.Expr.Lambda where
  11
  12 import Data.Proxy (Proxy(..))
  13 import Data.Type.Equality ((:~:)(Refl))
  14
  15 import Language.LOL.Symantic.AST
  16 import Language.LOL.Symantic.Type
  17 import Language.LOL.Symantic.Expr.Common
  18 import Language.LOL.Symantic.Repr.Dup
  19
  20 -- * Class 'Sym_Lambda'
  21
  22 -- | /Tagless-final symantics/ for /lambda abstraction/
  23 -- in /higher-order abstract syntax/ (HOAS),
  24 -- and with argument @arg@ and result @res@ of 'Lambda'
  25 -- wrapped inside 'lam': to control the calling
  26 -- in the 'Repr_Host' instance.
  27 class (lam ~ Lambda_from_Repr repr) => Sym_Lambda lam repr where
  28         -- | This type constructor is used like
  29         -- the functional dependency: @repr -> lam@
  30         -- (ie. knowing @repr@ one can determine @lam@)
  31         -- in order to avoid to introduce a 'Proxy' @lam@
  32         -- in 'let_inline', 'let_val' and 'let_lazy'.
  33         --
  34         -- Distinguishing between @lam@ and @repr@ is used to maintain
  35         -- the universal polymorphism of @repr@ in 'Sym_from',
  36         -- the downside with this however is that
  37         -- to be an instance of 'Sym_Lambda' for all @lam@,
  38         -- the @repr@ type of an interpreter
  39         -- has to be parameterized by @lam@,
  40         -- even though it does not actually need @lam@ to do its work.
  41         --
  42         -- Basically this means having sometimes to add a type annotation
  43         -- to the interpreter call to specify @lam@.
  44         type Lambda_from_Repr repr :: {-lam-}(* -> *)
  45
  46         -- | Lambda application.
  47         app :: repr (Lambda lam arg res) -> repr arg -> repr res
  48
  49         -- | /Call-by-name/ lambda.
  50         inline :: (repr arg -> repr res) -> repr (Lambda lam arg res)
  51         -- | /Call-by-value/ lambda.
  52         val    :: (repr arg -> repr res) -> repr (Lambda lam arg res)
  53         -- | /Call-by-need/ lambda (aka. /lazyness/): lazy shares its argument, no matter what.
  54         lazy   :: (repr arg -> repr res) -> repr (Lambda lam arg res)
  55
  56         -- | Convenient 'inline' wrapper.
  57         let_inline
  58          :: Sym_Lambda lam repr
  59          => repr arg -> (repr arg -> repr res) -> repr res
  60         let_inline x y = inline y `app` x
  61         -- | Convenient 'val' wrapper.
  62         let_val
  63          :: Sym_Lambda lam repr
  64          => repr arg -> (repr arg -> repr res) -> repr res
  65         let_val x y = val y `app` x
  66         -- | Convenient 'lazy' wrapper.
  67         let_lazy
  68          :: Sym_Lambda lam repr
  69          => repr arg -> (repr arg -> repr res) -> repr res
  70         let_lazy x y = lazy y `app` x
  71
  72 infixl 5 `app`
  73
  74 instance -- Sym_Lambda Dup
  75  ( Sym_Lambda lam r1
  76  , Sym_Lambda lam r2
  77  ) => Sym_Lambda lam (Dup r1 r2) where
  78         type Lambda_from_Repr (Dup r1 r2) = Lambda_from_Repr r1
  79         app (f1 `Dup` f2) (x1 `Dup` x2) = app f1 x1 `Dup` app f2 x2
  80         inline f = dup1 (inline f) `Dup` dup2 (inline f)
  81         val    f = dup1 (val f)    `Dup` dup2 (val f)
  82         lazy   f = dup1 (lazy f)   `Dup` dup2 (lazy f)
  83
  84 -- * Type 'Expr_Lambda'
  85 data Expr_Lambda (lam:: * -> *) (root:: *)
  86 type instance Root_of_Expr (Expr_Lambda lam root) = root
  87 type instance Type_of_Expr (Expr_Lambda lam root) = Type_Fun lam
  88 type instance Sym_of_Expr (Expr_Lambda lam root) repr = Sym_Lambda lam repr
  89 type instance Error_of_Expr ast (Expr_Lambda lam root)
  90  = Error_Expr_Lambda (Error_of_Type ast (Type_Root_of_Expr root))
  91                      (Type_Root_of_Expr root)
  92                      ast
  93  -- NOTE: require UndecidableInstances.
  94
  95 instance -- Sym_from AST Expr_Lambda
  96  ( Type_from AST (Type_Root_of_Expr root)
  97  , Sym_from AST root
  98
  99  , Type_Root_Lift (Type_Fun lam) (Type_Root_of_Expr root)
 100  , Error_Type_Lift (Error_Type_Fun AST)
 101                    (Error_of_Type AST (Type_Root_of_Expr root))
 102  , Error_Expr_Lift (Error_Expr_Lambda (Error_of_Type AST (Type_Root_of_Expr root))
 103                                       (                   Type_Root_of_Expr root)
 104                                       AST)
 105                    (Error_of_Expr AST root)
 106
 107  , Type_Unlift (Type_Fun lam) (Type_of_Expr root)
 108
 109  , Root_of_Expr root ~ root
 110  ) => Sym_from AST (Expr_Lambda lam root) where
 111         sym_from _px_ex ctx ast k =
 112                 case ast of
 113                  AST "var" asts ->
 114                         case asts of
 115                          [AST name []] -> go ctx k
 116                                 where
 117                                 go
 118                                  :: forall hs ret
 119                                  . Context (Var root) hs
 120                                  -> ( forall h
 121                                     .  Type_Root_of_Expr root h
 122                                     -> Forall_Repr_with_Context (Expr_Lambda lam root) hs h
 123                                     -> Either (Maybe (Error_of_Expr AST root)) ret )
 124                                  -> Either (Maybe (Error_of_Expr AST root)) ret
 125                                 go c k' =
 126                                         case c of
 127                                          Context_Empty -> Left $ Just $ error_lambda_lift $
 128                                                 Error_Expr_Lambda_Var_unbound name ast
 129                                          Var n ty `Context_Next` _ | n == name ->
 130                                                 k' ty $ Forall_Repr_with_Context $
 131                                                  \(repr `Context_Next` _) -> repr
 132                                          _ `Context_Next` ctx' ->
 133                                                 go ctx' $ \ty (Forall_Repr_with_Context repr) ->
 134                                                         k' ty $ Forall_Repr_with_Context $
 135                                                          \(_ `Context_Next` c') -> repr c'
 136                          _ -> Left $ Just $ error_lambda_lift $
 137                                 Error_Expr_Fun_Wrong_number_of_arguments 1 ast
 138                  AST "app" asts ->
 139                         case asts of
 140                          [ast_lam, ast_arg_actual] ->
 141                                 sym_from (Proxy::Proxy root) ctx ast_lam $
 142                                  \(ty_lam::Type_Root_of_Expr root h_lam) (Forall_Repr_with_Context lam) ->
 143                                 sym_from (Proxy::Proxy root) ctx ast_arg_actual $
 144                                  \(ty_arg_actual::Type_Root_of_Expr root h_arg_actual)
 145                                   (Forall_Repr_with_Context arg_actual) ->
 146                                         case type_unlift $ unType_Root ty_lam of
 147                                          Just (ty_arg_expected `Type_Fun` ty_res
 148                                           :: Type_Fun lam (Type_Root_of_Expr root) h_lam) ->
 149                                                 case ty_arg_expected `type_eq` ty_arg_actual of
 150                                                  Just Refl ->
 151                                                         k ty_res $ Forall_Repr_with_Context $
 152                                                          \c -> lam c `app` arg_actual c
 153                                                  Nothing -> Left $ Just $ error_lambda_lift $
 154                                                         Error_Expr_Fun_Argument_mismatch
 155                                                          (Exists_Type ty_arg_expected)
 156                                                          (Exists_Type ty_arg_actual) ast
 157                                          Nothing -> Left $ Just $ error_lambda_lift $
 158                                                 Error_Expr_Lambda_Not_a_lambda ast
 159                          _ -> Left $ Just $ error_lambda_lift $
 160                                 Error_Expr_Type
 161                                  (error_type_lift $
 162                                         Error_Type_Fun_Wrong_number_of_arguments 2 ast
 163                                  ) ast
 164                  AST "inline" asts -> lambda_from asts inline
 165                  AST "val"    asts -> lambda_from asts val
 166                  AST "lazy"   asts -> lambda_from asts lazy
 167                  _ -> Left Nothing
 168                 where
 169                 lambda_from asts
 170                  (lam::forall repr arg res. Sym_Lambda lam repr
 171                      => (repr arg -> repr res) -> repr (Lambda lam arg res)) =
 172                         case asts of
 173                          [AST name [], ast_ty_arg, ast_body] ->
 174                                 case type_from (Proxy::Proxy (Type_Root_of_Expr root)) ast_ty_arg
 175                                  (Right . Exists_Type) of
 176                                  Left Nothing -> Left Nothing
 177                                  Left (Just err) -> Left $ Just $ error_lambda_lift $ Error_Expr_Type err ast
 178                                  Right (Exists_Type (ty_arg::Type_Root_of_Expr root h_arg)) ->
 179                                         sym_from (Proxy::Proxy root)
 180                                          (Var name ty_arg `Context_Next` ctx) ast_body $
 181                                          \(ty_res::Type_Root_of_Expr root h_res) (Forall_Repr_with_Context res) ->
 182                                                 k (ty_arg `type_fun` ty_res
 183                                                  :: Root_of_Type (Type_Root_of_Expr root)
 184                                                                  (Lambda lam h_arg h_res)) $
 185                                                 Forall_Repr_with_Context $
 186                                                  \c -> lam $ \arg -> res (arg `Context_Next` c)
 187                          _ -> Left $ Just $ error_lambda_lift $
 188                                 Error_Expr_Fun_Wrong_number_of_arguments 3 ast
 189                 error_lambda_lift
 190                  :: Error_Expr_Lambda (Error_of_Type AST (Type_Root_of_Expr root)) (Type_Root_of_Expr root) AST
 191                  -> Error_of_Expr AST root
 192                 error_lambda_lift = error_expr_lift
 193
 194 -- * Type 'Error_Expr_Lambda'
 195 data Error_Expr_Lambda err_ty ty ast
 196  =   Error_Expr_Lambda_Not_a_lambda ast
 197  |   Error_Expr_Lambda_Var_unbound Var_Name ast
 198  |   Error_Expr_Fun_Wrong_number_of_arguments Int ast
 199  |   Error_Expr_Fun_Argument_mismatch (Exists_Type ty) (Exists_Type ty) ast
 200  |   Error_Expr_Type err_ty ast
 201  deriving (Eq, Show)