Language/Symantic/Expr/Monad.hs

   1 {-# LANGUAGE DefaultSignatures #-}
   2 {-# LANGUAGE GADTs #-}
   3 {-# LANGUAGE FlexibleContexts #-}
   4 {-# LANGUAGE FlexibleInstances #-}
   5 {-# LANGUAGE MultiParamTypeClasses #-}
   6 {-# LANGUAGE OverloadedStrings #-}
   7 {-# LANGUAGE Rank2Types #-}
   8 {-# LANGUAGE ScopedTypeVariables #-}
   9 {-# LANGUAGE TypeFamilies #-}
  10 {-# LANGUAGE TypeOperators #-}
  11 {-# OPTIONS_GHC -fno-warn-orphans #-}
  12 -- | Expression for 'Monad'.
  13 module Language.Symantic.Expr.Monad where
  14
  15 import Control.Monad (Monad)
  16 import qualified Control.Monad as Monad
  17 import qualified Data.Function as Fun
  18 import Data.Proxy (Proxy(..))
  19 import Data.Type.Equality ((:~:)(Refl))
  20 import Prelude hiding ((<$>), Monad(..))
  21
  22 import Language.Symantic.Type
  23 import Language.Symantic.Repr
  24 import Language.Symantic.Expr.Root
  25 import Language.Symantic.Expr.Error
  26 import Language.Symantic.Expr.From
  27 import Language.Symantic.Expr.Lambda
  28 import Language.Symantic.Expr.Functor
  29 import Language.Symantic.Trans.Common
  30
  31 -- * Class 'Sym_Monad'
  32 -- | Symantic.
  33 class Sym_Functor repr => Sym_Monad repr where
  34         return :: Monad m => repr a -> repr (m a)
  35         (>>=)  :: Monad m => repr (m a) -> repr (a -> m b) -> repr (m b)
  36
  37         default return :: (Trans t repr, Monad m)
  38          => t repr a -> t repr (m a)
  39         default (>>=) :: (Trans t repr, Monad m)
  40          => t repr (m a) -> t repr (a -> m b) -> t repr (m b)
  41
  42         return = trans_map1 return
  43         (>>=)  = trans_map2 (>>=)
  44 infixl 1 >>=
  45 instance Sym_Monad Repr_Host where
  46         return = Monad.liftM Monad.return
  47         (>>=)  = Monad.liftM2 (Monad.>>=)
  48 instance Sym_Monad Repr_Text where
  49         return = repr_text_app1 "return"
  50         (>>=)  = repr_text_infix ">>=" (Precedence 1)
  51 instance (Sym_Monad r1, Sym_Monad r2) => Sym_Monad (Repr_Dup r1 r2) where
  52         return = repr_dup1 sym_Monad return
  53         (>>=)  = repr_dup2 sym_Monad (>>=)
  54
  55 sym_Monad :: Proxy Sym_Monad
  56 sym_Monad = Proxy
  57
  58 -- * Type 'Expr_Monad'
  59 -- | Expression.
  60 data Expr_Monad (root:: *)
  61 type instance Root_of_Expr      (Expr_Monad root)      = root
  62 type instance Type_of_Expr      (Expr_Monad root)      = No_Type
  63 type instance Sym_of_Expr       (Expr_Monad root) repr = Sym_Monad repr
  64 type instance Error_of_Expr ast (Expr_Monad root)      = No_Error_Expr
  65
  66 return_from
  67  :: forall root ty ast hs ret.
  68  ( ty ~ Type_Root_of_Expr (Expr_Monad root)
  69  , Type0_Eq ty
  70  , Type1_From ast ty
  71  , Type1_Constraint Monad ty
  72  , Expr_From ast root
  73  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
  74                    (Error_of_Expr ast root)
  75  , Root_of_Expr root ~ root
  76  ) => ast -> ast
  77  -> ExprFrom ast (Expr_Monad root) hs ret
  78 return_from ast_f ast_a ex ast ctx k =
  79  -- return :: Monad f => a -> f a
  80         either (\err -> Left $ error_expr ex $ Error_Expr_Type err ast) Fun.id $
  81         type1_from (Proxy::Proxy ty) ast_f $ \_f ty_f -> Right $
  82         expr_from (Proxy::Proxy root) ast_a ctx $
  83          \(ty_a::ty h_a) (Forall_Repr_with_Context a) ->
  84         let ty_fa = ty_f ty_a in
  85         check_type1_constraint ex (Proxy::Proxy Monad) ast ty_fa $ \Dict ->
  86         k ty_fa $ Forall_Repr_with_Context $
  87          \c -> return (a c)
  88
  89 bind_from
  90  :: forall root ty ast hs ret.
  91  ( ty ~ Type_Root_of_Expr (Expr_Monad root)
  92  , Type0_Eq ty
  93  , Type1_Eq ty
  94  , Expr_From ast root
  95  , Type0_Lift   Type_Fun (Type_of_Expr root)
  96  , Type0_Unlift Type_Fun (Type_of_Expr root)
  97  , Type1_Unlift (Type_of_Expr root)
  98  , Error_Expr_Lift (Error_Expr (Error_of_Type ast ty) ty ast)
  99                    (Error_of_Expr ast root)
 100  , Root_of_Expr root ~ root
 101  , Type1_Constraint Monad ty
 102  ) => ast -> ast
 103  -> ExprFrom ast (Expr_Monad root) hs ret
 104 bind_from ast_ma ast_f ex ast ctx k =
 105  -- (>>=) :: Monad m => m a -> (a -> m b) -> m b
 106         expr_from (Proxy::Proxy root) ast_ma ctx $
 107          \(ty_ma::ty h_ma) (Forall_Repr_with_Context ma) ->
 108         expr_from (Proxy::Proxy root) ast_f ctx $
 109          \(ty_f::ty h_f) (Forall_Repr_with_Context f) ->
 110         check_type1 ex ast ty_ma $ \(Type1 m ty_m_a, Type1_Lift ty_m) ->
 111         check_type_fun ex ast ty_f $ \(Type2 Proxy ty_f_a ty_f_mb) ->
 112         check_type0_eq ex ast ty_m_a ty_f_a $ \Refl ->
 113         check_type1 ex ast ty_f_mb $ \(Type1 _ ty_f_m_b, _) ->
 114         check_type1_eq ex ast ty_ma ty_f_mb $ \Refl ->
 115         check_type1_constraint ex (Proxy::Proxy Monad) ast ty_ma $ \Dict ->
 116         k (Type_Root $ ty_m $ Type1 m ty_f_m_b) $ Forall_Repr_with_Context $
 117          \c -> (>>=) (ma c) (f c)