Language/Symantic/Expr/Functor.hs

   1 {-# LANGUAGE ConstraintKinds #-}
   2 {-# LANGUAGE DefaultSignatures #-}
   3 {-# LANGUAGE GADTs #-}
   4 {-# LANGUAGE FlexibleContexts #-}
   5 {-# LANGUAGE FlexibleInstances #-}
   6 {-# LANGUAGE MultiParamTypeClasses #-}
   7 {-# LANGUAGE ScopedTypeVariables #-}
   8 {-# LANGUAGE TypeFamilies #-}
   9 {-# LANGUAGE TypeOperators #-}
  10 {-# LANGUAGE UndecidableInstances #-}
  11 {-# OPTIONS_GHC -fno-warn-orphans #-}
  12 -- | Expression for 'Functor'.
  13 module Language.Symantic.Expr.Functor where
  14
  15 import Data.Proxy (Proxy(..))
  16 import Data.Type.Equality ((:~:)(Refl))
  17 import Prelude hiding (fmap)
  18 import qualified Data.Function as Fun
  19
  20 import Language.Symantic.Type
  21 import Language.Symantic.Trans.Common
  22 import Language.Symantic.Expr.Root
  23 import Language.Symantic.Expr.Error
  24 import Language.Symantic.Expr.From
  25 import Language.Symantic.Expr.Lambda
  26
  27 -- * Class 'Sym_Functor'
  28 -- | Symantic.
  29 class Sym_Lambda repr => Sym_Functor repr where
  30         fmap :: Functor f => repr ((->) a b) -> repr (f a) -> repr (f b)
  31         default fmap
  32          :: (Trans t repr, Functor f)
  33          => t repr ((->) a b)
  34          -> t repr (f a)
  35          -> t repr (f b)
  36         fmap = trans_map2 fmap
  37
  38         (<$) :: Functor f => repr a -> repr (f b) -> repr (f a)
  39         (<$) a = fmap (lam (Fun.const a))
  40 infixl 4 <$
  41
  42 -- | 'fmap' alias.
  43 (<$>) :: (Sym_Functor repr, Functor f)
  44  => repr ((->) a b) -> repr (f a) -> repr (f b)
  45 (<$>) = fmap
  46 infixl 4 <$>
  47
  48 -- * Type 'Expr_Functor'
  49 -- | Expression.
  50 data Expr_Functor (root:: *)
  51 type instance Root_of_Expr      (Expr_Functor root)      = root
  52 type instance Type_of_Expr      (Expr_Functor root)      = No_Type
  53 type instance Sym_of_Expr       (Expr_Functor root) repr = (Sym_Functor repr)
  54 type instance Error_of_Expr ast (Expr_Functor root)      = No_Error_Expr
  55
  56 -- | Parse 'fmap'.
  57 fmap_from
  58  :: forall root ty ast hs ret.
  59  ( ty ~ Type_Root_of_Expr (Expr_Functor root)
  60  , Eq_Type ty
  61  , Expr_from ast root
  62  , Lift_Type   Type_Fun (Type_of_Expr root)
  63  , Unlift_Type Type_Fun (Type_of_Expr root)
  64  , Unlift_Type1 (Type_of_Expr root)
  65  , Lift_Error_Expr (Error_Expr (Error_of_Type ast ty) ty ast)
  66                    (Error_of_Expr ast root)
  67  , Root_of_Expr root ~ root
  68  , Constraint_Type1 Functor ty
  69  ) => ast -> ast
  70  -> Expr_From ast (Expr_Functor root) hs ret
  71 fmap_from ast_g ast_fa ex ast ctx k =
  72  -- NOTE: fmap :: Functor f => (a -> b) -> f a -> f b
  73         expr_from (Proxy::Proxy root) ast_g ctx $
  74          \(ty_g::ty h_g) (Forall_Repr_with_Context g) ->
  75         expr_from (Proxy::Proxy root) ast_fa ctx $
  76          \(ty_fa::ty h_fa) (Forall_Repr_with_Context fa) ->
  77         check_type_fun ex ast ty_g $ \(Type_Type2 Proxy ty_g_a ty_g_b
  78          :: Type_Fun ty h_g) ->
  79         check_type1 ex ast ty_fa $ \(Type_Type1 f ty_fa_a, Lift_Type1 f_lift) ->
  80         check_constraint_type1 ex (Proxy::Proxy Functor) ast ty_fa $ \Dict ->
  81         check_eq_type ex ast ty_g_a ty_fa_a $ \Refl ->
  82         k (Type_Root $ f_lift $ Type_Type1 f ty_g_b) $ Forall_Repr_with_Context $
  83          \c -> fmap (g c) (fa c)