Language/Symantic/Type/Fun.hs

   1 {-# LANGUAGE FlexibleContexts #-}
   2 {-# LANGUAGE FlexibleInstances #-}
   3 {-# LANGUAGE GADTs #-}
   4 {-# LANGUAGE MultiParamTypeClasses #-}
   5 {-# LANGUAGE OverloadedStrings #-}
   6 {-# LANGUAGE PatternSynonyms #-}
   7 {-# LANGUAGE Rank2Types #-}
   8 {-# LANGUAGE ScopedTypeVariables #-}
   9 {-# LANGUAGE TypeFamilies #-}
  10 {-# OPTIONS_GHC -fno-warn-orphans #-}
  11 module Language.Symantic.Type.Fun where
  12
  13 import Data.Proxy
  14 import Data.Type.Equality ((:~:)(Refl))
  15 import Language.Symantic.Type.Root
  16 import Language.Symantic.Type.Error
  17 import Language.Symantic.Type.Type0
  18 import Language.Symantic.Type.Type1
  19 import Language.Symantic.Type.Type2
  20
  21 -- * Type 'Type_Fun'
  22 -- | The @->@ type.
  23 type Type_Fun lam
  24  = Type_Type2 (Proxy (Lambda lam))
  25
  26 type instance Constraint2_of (Proxy (Lambda lam))
  27  = Constraint2_Empty
  28 instance Unlift_Type1 (Type_Type2 (Proxy (Lambda lam))) where
  29         unlift_type1 (Type_Type2 px a b) k =
  30                 k ( Type_Type1 (Proxy::Proxy (Lambda lam a)) b
  31                   , Lift_Type1 (\(Type_Type1 _ b') -> Type_Type2 px a b')
  32                   )
  33 instance Eq_Type root => Eq_Type1 (Type_Type2 (Proxy (Lambda lam)) root) where
  34         eq_type1 (Type_Type2 _ a1 _b1) (Type_Type2 _ a2 _b2)
  35          | Just Refl <- eq_type a1 a2
  36          = Just Refl
  37         eq_type1 _ _ = Nothing
  38 instance Constraint_Type1 Functor     (Type_Fun lam root)
  39 instance Constraint_Type1 Applicative (Type_Fun lam root)
  40 instance Constraint_Type1 Traversable (Type_Fun lam root)
  41 instance Constraint_Type1 Monad       (Type_Fun lam root)
  42
  43 pattern Type_Fun
  44  :: root arg -> root res
  45  -> Type_Fun lam root ((Lambda lam) arg res)
  46 pattern Type_Fun arg res
  47  = Type_Type2 Proxy arg res
  48
  49 instance -- Eq_Type
  50  Eq_Type root =>
  51  Eq_Type (Type_Type2 (Proxy (Lambda lam)) root) where
  52         eq_type
  53          (Type_Type2 _ arg1 res1)
  54          (Type_Type2 _ arg2 res2)
  55          | Just Refl <- arg1 `eq_type` arg2
  56          , Just Refl <- res1 `eq_type` res2
  57          = Just Refl
  58         eq_type _ _ = Nothing
  59 instance -- String_from_Type
  60  String_from_Type root =>
  61  String_from_Type (Type_Fun lam root) where
  62         string_from_type (Type_Type2 _ arg res) =
  63                 "(" ++ string_from_type arg ++ " -> "
  64                     ++ string_from_type res ++ ")"
  65
  66 -- ** Type 'Lambda'
  67 -- | A newtype for the host-type function (->),
  68 -- wrapping argument and result within a type constructor @lam@,
  69 -- which is used in the 'Repr_Host' instance of 'Sym_Lambda'
  70 -- to control the calling (see 'val' and 'lazy').
  71 --
  72 -- NOTE: a newtype is used instead of a type synonym
  73 -- in order to be able to use it as a type constructor: @Lambda lam arg@,
  74 -- which for instance has instances: 'Functor', 'Applicative', and 'Monad'.
  75 newtype Lambda lam arg res
  76  =      Lambda { unLambda :: (->) (lam arg) (lam res) }
  77
  78 -- | Convenient alias to include a 'Type_Fun' within a type.
  79 type_fun
  80  :: forall lam root h_arg h_res.
  81  Lift_Type_Root (Type_Fun lam) root
  82  => root h_arg -> root h_res
  83  -> root (Lambda lam h_arg h_res)
  84 type_fun arg res = lift_type_root (Type_Fun arg res
  85          ::Type_Fun lam root (Lambda lam h_arg h_res))
  86
  87 -- | Parse 'Type_Fun'.
  88 type_fun_from
  89  :: forall (lam :: * -> *) (root :: * -> *) ast ret.
  90  ( Lift_Type_Root (Type_Fun lam) root
  91  , Type_from ast root
  92  , Root_of_Type root ~ root
  93  ) => Proxy (Type_Fun lam root)
  94  -> ast -> ast
  95  -> (forall h. root h -> Either (Error_of_Type ast root) ret)
  96  -> Either (Error_of_Type ast root) ret
  97 type_fun_from _ty ast_arg ast_res k =
  98         type_from (Proxy::Proxy root) ast_arg $ \(ty_arg::root h_arg) ->
  99         type_from (Proxy::Proxy root) ast_res $ \(ty_res::root h_res) ->
 100         k (ty_arg `type_fun` ty_res
 101          :: root (Lambda lam h_arg h_res))