Language/Symantic/Expr/Lambda.hs

   1 {-# LANGUAGE DefaultSignatures #-}
   2 {-# LANGUAGE FlexibleContexts #-}
   3 {-# LANGUAGE FlexibleInstances #-}
   4 {-# LANGUAGE MultiParamTypeClasses #-}
   5 {-# LANGUAGE Rank2Types #-}
   6 {-# LANGUAGE ScopedTypeVariables #-}
   7 {-# LANGUAGE TypeFamilies #-}
   8 -- | Expression for /lambda abstraction/s
   9 -- in /Higher-Order Abstract Syntax/ (HOAS).
  10 module Language.Symantic.Expr.Lambda where
  11
  12 import Data.Proxy (Proxy(..))
  13 import Data.Type.Equality ((:~:)(Refl))
  14 import Data.Text (Text)
  15
  16 import Language.Symantic.Type
  17 import Language.Symantic.Expr.Common
  18 import Language.Symantic.Trans.Common
  19
  20 -- * Class 'Sym_Lambda'
  21
  22 -- | Symantic.
  23 --
  24 -- NOTE: argument @arg@ and result @res@ of 'Lambda'
  25 -- wrapped inside 'lam': to control the calling
  26 -- in the 'Repr_Host' instance.
  27 --
  28 -- NOTE: the default definitions supplied for:
  29 -- 'app', 'inline', 'val' and 'lazy'
  30 -- are there to avoid boilerplate code
  31 -- when writting 'Trans' instances which
  32 -- do not need to alterate those methods.
  33 class (lam ~ Lambda_from_Repr repr) => Sym_Lambda lam repr where
  34         -- | This type constructor is used like
  35         -- the functional dependency: @repr -> lam@
  36         -- (ie. knowing @repr@ one can determine @lam@)
  37         -- in order to avoid to introduce a 'Proxy' @lam@
  38         -- in 'let_inline', 'let_val' and 'let_lazy'.
  39         --
  40         -- Distinguishing between @lam@ and @repr@ is used to maintain
  41         -- the universal polymorphism of @repr@ in 'Expr_from';
  42         -- a downside of this approach is
  43         -- that to be an instance of 'Sym_Lambda' for all @lam@,
  44         -- the @repr@ type of an interpreter
  45         -- has to be parameterized by @lam@,
  46         -- even when it does not actually need @lam@ to do its work
  47         -- (eg. 'Repr_Text').
  48         --
  49         -- Basically this means having sometimes to add a type annotation
  50         -- to the interpreter call to specify @lam@.
  51         type Lambda_from_Repr repr :: {-lam-}(* -> *)
  52
  53         -- | /Lambda application/.
  54         app :: repr (Lambda lam arg res) -> repr arg -> repr res
  55
  56         -- | /Call-by-name/ /lambda abstraction/.
  57         inline :: (repr arg -> repr res) -> repr (Lambda lam arg res)
  58         -- | /Call-by-value/ /lambda abstraction/.
  59         val    :: (repr arg -> repr res) -> repr (Lambda lam arg res)
  60         -- | /Call-by-need/ /lambda abstraction/ (aka. /lazyness/): lazy shares its argument, no matter what.
  61         lazy   :: (repr arg -> repr res) -> repr (Lambda lam arg res)
  62
  63         default app    :: Trans t repr => t repr (Lambda lam arg res) -> t repr arg -> t repr res
  64         default inline :: Trans t repr => (t repr arg -> t repr res) -> t repr (Lambda lam arg res)
  65         default val    :: Trans t repr => (t repr arg -> t repr res) -> t repr (Lambda lam arg res)
  66         default lazy   :: Trans t repr => (t repr arg -> t repr res) -> t repr (Lambda lam arg res)
  67         app  f x = trans_lift $ trans_apply f `app` trans_apply x
  68         inline f = trans_lift $ inline $ trans_apply . f . trans_lift
  69         val    f = trans_lift $ val    $ trans_apply . f . trans_lift
  70         lazy   f = trans_lift $ lazy   $ trans_apply . f . trans_lift
  71
  72         -- | Convenient 'inline' wrapper.
  73         let_inline
  74          :: Sym_Lambda lam repr
  75          => repr var -> (repr var -> repr res) -> repr res
  76         let_inline x y = inline y `app` x
  77         -- | Convenient 'val' wrapper.
  78         let_val
  79          :: Sym_Lambda lam repr
  80          => repr var -> (repr var -> repr res) -> repr res
  81         let_val x y = val y `app` x
  82         -- | Convenient 'lazy' wrapper.
  83         let_lazy
  84          :: Sym_Lambda lam repr
  85          => repr var -> (repr var -> repr res) -> repr res
  86         let_lazy x y = lazy y `app` x
  87 infixl 5 `app`
  88
  89 -- * Type 'Expr_Lambda'
  90 -- | Expression.
  91 data Expr_Lambda (lam:: * -> *) (root:: *)
  92 type instance Root_of_Expr      (Expr_Lambda lam root)      = root
  93 type instance Type_of_Expr      (Expr_Lambda lam root)      = Type_Fun lam
  94 type instance Sym_of_Expr       (Expr_Lambda lam root) repr = Sym_Lambda lam repr
  95 type instance Error_of_Expr ast (Expr_Lambda lam root)      = Error_Expr_Lambda ast
  96
  97 -- | Parsing utility to check that the given type is a 'Type_Fun'
  98 -- or raise 'Error_Expr_Type_mismatch'.
  99 check_type_fun
 100  :: forall ast ex root lam ty h ret.
 101  ( root ~ Root_of_Expr ex
 102  , ty ~ Type_Root_of_Expr ex
 103  , Lift_Type   (Type_Fun lam) (Type_of_Expr root)
 104  , Unlift_Type (Type_Fun lam) (Type_of_Expr root)
 105  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
 106                    (Error_of_Expr ast root)
 107  )
 108  => Proxy ex -> ast -> ty h
 109  -> (Type_Fun lam ty h -> Either (Error_of_Expr ast root) ret)
 110  -> Either (Error_of_Expr ast root) ret
 111 check_type_fun ex ast ty k =
 112         case unlift_type $ unType_Root ty of
 113          Just ty_f -> k ty_f
 114          Nothing -> Left $
 115                 error_expr ex $
 116                 Error_Expr_Type_mismatch ast
 117                  (Exists_Type (type_var SZero `type_fun` type_var (SSucc SZero)
 118                  :: Type_Root_of_Expr ex (Lambda lam Zero (Succ Zero))))
 119                  (Exists_Type ty)
 120
 121 -- | Parse a /lambda variable/.
 122 var_from
 123  :: forall ast lam root hs ret.
 124  ( Type_from ast (Type_Root_of_Expr root)
 125  , Lift_Error_Expr (Error_Expr_Lambda ast)
 126                    (Error_of_Expr ast root)
 127  , Root_of_Expr root ~ root
 128  ) => Text -> Expr_From ast (Expr_Lambda lam root) hs ret
 129 var_from name _ex ast = go
 130         where
 131         go :: forall ex hs'. (ex ~ (Expr_Lambda lam root))
 132          => Context (Lambda_Var (Type_Root_of_Expr ex)) hs'
 133          -> ( forall h. Type_Root_of_Expr ex h
 134             -> Forall_Repr_with_Context ex hs' h
 135             -> Either (Error_of_Expr ast (Root_of_Expr ex)) ret )
 136          ->    Either (Error_of_Expr ast (Root_of_Expr ex)) ret
 137         go c k' =
 138                 case c of
 139                  Context_Empty -> Left $ lift_error_expr $
 140                         Error_Expr_Lambda_Var_unbound name ast
 141                  Lambda_Var n ty `Context_Next` _ | n == name ->
 142                         k' ty $ Forall_Repr_with_Context $
 143                          \(repr `Context_Next` _) -> repr
 144                  _ `Context_Next` ctx' ->
 145                         go ctx' $ \ty (Forall_Repr_with_Context repr) ->
 146                                 k' ty $ Forall_Repr_with_Context $
 147                                  \(_ `Context_Next` c') -> repr c'
 148
 149 -- | Parse 'app'.
 150 app_from
 151  :: forall ty ast lam root hs ret.
 152  ( ty ~ Type_Root_of_Expr root
 153  , Type_from ast ty
 154  , Eq_Type ty
 155  , Expr_from ast root
 156  , Lift_Type_Root (Type_Fun lam) ty
 157  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
 158                    (Error_of_Expr ast root)
 159  , Unlift_Type (Type_Fun lam) (Type_of_Expr root)
 160  , Root_of_Expr root ~ root
 161  ) => ast -> ast
 162  -> Expr_From ast (Expr_Lambda lam root) hs ret
 163 app_from ast_lam ast_arg_actual ex ast ctx k =
 164         expr_from (Proxy::Proxy root) ast_lam ctx $
 165          \(ty_lam::Type_Root_of_Expr root h_lam) (Forall_Repr_with_Context lam) ->
 166         expr_from (Proxy::Proxy root) ast_arg_actual ctx $
 167          \(ty_arg_actual::Type_Root_of_Expr root h_arg_actual)
 168           (Forall_Repr_with_Context arg_actual) ->
 169                 case unlift_type $ unType_Root ty_lam of
 170                  Nothing -> Left $
 171                         error_expr ex $
 172                         Error_Expr_Type_mismatch ast
 173                          (Exists_Type (type_var SZero `type_fun` type_var (SSucc SZero)
 174                          :: Type_Root_of_Expr (Expr_Lambda lam root) (Lambda lam Zero (Succ Zero))))
 175                          (Exists_Type ty_lam)
 176                  Just (ty_arg_expected `Type_Fun` ty_res
 177                   :: Type_Fun lam (Type_Root_of_Expr root) h_lam) ->
 178                         check_eq_type ex ast
 179                          ty_arg_expected ty_arg_actual $ \Refl ->
 180                                 k ty_res $ Forall_Repr_with_Context $
 181                                  \c -> lam c `app` arg_actual c
 182
 183 -- | Parse given /lambda abstraction/.
 184 lam_from
 185  :: forall ty ast lam root hs ret.
 186  ( ty ~ Type_Root_of_Expr root
 187  , Type_from ast ty
 188  , Expr_from ast root
 189  , Lift_Type_Root (Type_Fun lam) ty
 190  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
 191                    (Error_of_Expr ast root)
 192  , Root_of_Expr root ~ root
 193  ) => (forall repr arg res
 194       . Sym_Lambda lam repr
 195       => (repr arg -> repr res)
 196       -> repr (Lambda lam arg res))
 197  -> Text -> ast -> ast
 198  -> Expr_From ast (Expr_Lambda lam root) hs ret
 199 lam_from lam name ast_ty_arg ast_body ex ast ctx k =
 200         case type_from
 201          (Proxy::Proxy (Type_Root_of_Expr root))
 202          ast_ty_arg (Right . Exists_Type) of
 203          Left err -> Left $ error_expr ex $ Error_Expr_Type err ast
 204          Right (Exists_Type (ty_arg::Type_Root_of_Expr root h_arg)) ->
 205                 expr_from (Proxy::Proxy root) ast_body
 206                  (Lambda_Var name ty_arg `Context_Next` ctx) $
 207                  \(ty_res::Type_Root_of_Expr root h_res) (Forall_Repr_with_Context res) ->
 208                         k (ty_arg `type_fun` ty_res
 209                          :: Root_of_Type (Type_Root_of_Expr root)
 210                                          (Lambda lam h_arg h_res)) $
 211                         Forall_Repr_with_Context $
 212                          \c -> lam $
 213                                  \arg -> res (arg `Context_Next` c)
 214
 215 -- | Parse given /let/.
 216 let_from
 217  :: forall ty ast lam root hs ret.
 218  ( ty ~ Type_Root_of_Expr root
 219  , Type_from ast ty
 220  , Expr_from ast root
 221  , Lift_Type_Root (Type_Fun lam) ty
 222  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
 223                    (Error_of_Expr ast root)
 224  , Root_of_Expr root ~ root
 225  ) => (forall repr var res. Sym_Lambda lam repr
 226       => repr var -> (repr var -> repr res) -> repr res)
 227  -> Text -> ast -> ast
 228  -> Expr_From ast (Expr_Lambda lam root) hs ret
 229 let_from let_ name ast_var ast_body _ex _ast ctx k =
 230         expr_from (Proxy::Proxy root) ast_var ctx $
 231          \(ty_var::Type_Root_of_Expr root h_var) (Forall_Repr_with_Context var) ->
 232                 expr_from (Proxy::Proxy root) ast_body
 233                  (Lambda_Var name ty_var `Context_Next` ctx) $
 234                  \(ty_res::Type_Root_of_Expr root h_res) (Forall_Repr_with_Context res) ->
 235                         k ty_res $ Forall_Repr_with_Context $
 236                          \c -> let_ (var c) $
 237                                  \arg -> res (arg `Context_Next` c)
 238
 239 -- * Type 'Error_Expr_Lambda'
 240 data Error_Expr_Lambda ast
 241  =   Error_Expr_Lambda_Var_unbound Lambda_Var_Name ast
 242  deriving (Eq, Show)